Elementary Particles

Transcript

Elementary Particles A basic physics Contents 1 2 Fermion 1 1.1 Elementary fermions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Composite fermions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2.1 Skyrmions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.3 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.4 Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Quark 3 2.1 Classification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.2 History 4 2.3 Etymology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.4 Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.4.1 Electric charge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.4.2 Spin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.4.3 Weak interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.4.4 Strong interaction and color charge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.4.5 Mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.4.6 Table of properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Interacting quarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.5.1 Sea quarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.5.2 Other phases of quark matter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.6 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.7 Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.8 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.9 Further reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.10 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 Hadron 14 3.1 Etymology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 3.2 Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 3.3 Baryons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 3.4 Mesons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 3.5 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.5 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i ii CONTENTS 3.6 4 5 6 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 Boson 17 4.1 Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 4.2 Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 4.3 Elementary bosons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 4.4 Composite bosons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 4.5 To which states can bosons crowd? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 4.6 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 4.7 Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 4.8 References 19 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Lepton 20 5.1 Etymology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 5.2 History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 5.3 Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 5.3.1 Spin and chirality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 5.3.2 Electromagnetic interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 5.3.3 Weak Interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 5.3.4 Mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 5.3.5 Leptonic numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 5.4 Universality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 5.5 Table of leptons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 5.6 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 5.7 Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 5.8 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 5.9 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 Meson 26 6.1 History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 6.2 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 6.2.1 Spin, orbital angular momentum, and total angular momentum . . . . . . . . . . . . . . . 27 6.2.2 Parity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 6.2.3 C-parity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 6.2.4 G-parity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 6.2.5 Isospin and charge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 6.2.6 Flavour quantum numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 Classification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 6.3.1 Types of meson . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 6.3.2 Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 6.4 Exotic mesons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 6.5 List . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 6.3 CONTENTS iii 6.6 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 6.7 Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 6.8 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 6.9 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 6.9.1 32 7 8 Recent findings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Photon 33 7.1 Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 7.2 Physical properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 7.2.1 Experimental checks on photon mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 7.3 Historical development . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 7.4 Einstein’s light quantum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 7.5 Early objections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 7.6 Wave–particle duality and uncertainty principles . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 7.7 Bose–Einstein model of a photon gas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 7.8 Stimulated and spontaneous emission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 7.9 Second quantization and high energy photon interactions . . . . . . . . . . . . . . . . . . . . . . . 40 7.10 The hadronic properties of the photon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 7.11 The photon as a gauge boson . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 7.12 Contributions to the mass of a system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 7.13 Photons in matter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 7.14 Technological applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 7.15 Recent research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 7.16 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 7.17 Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 7.18 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 7.19 Additional references . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 7.20 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 Gluon 49 8.1 Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 8.2 Numerology of gluons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 8.2.1 Color charge and superposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 8.2.2 Color singlet states . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 8.2.3 Eight gluon colors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 8.2.4 Group theory details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 8.3 Confinement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 8.4 Experimental observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 8.5 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 8.6 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 8.7 Further reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 iv 9 CONTENTS Higgs boson 53 9.1 A non-technical summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 9.1.1 “Higgs” terminology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 9.1.2 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 Significance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 9.2.1 Scientific impact . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 9.2.2 “Real world” impact . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 Summary and impact of the PRL papers . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 Theoretical properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 9.4.1 Theoretical need for the Higgs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 9.4.2 Properties of the Higgs field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 9.4.3 Properties of the Higgs boson . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 9.4.4 Production . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 9.4.5 Decay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 9.4.6 Alternative models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 9.4.7 Further theoretical issues and hierarchy problem . . . . . . . . . . . . . . . . . . . . . . . 60 9.2 9.3 History 9.3.1 9.4 9.5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 9.5.1 Search prior to 4 July 2012 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 9.5.2 Discovery of candidate boson at CERN . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 9.5.3 The new particle tested as a possible Higgs boson . . . . . . . . . . . . . . . . . . . . . . 62 9.5.4 Preliminary confirmation of existence and current status . . . . . . . . . . . . . . . . . . . 63 Public discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 9.6.1 Naming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 9.6.2 Media explanations and analogies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 9.6.3 Recognition and awards . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 9.7 Technical aspects and mathematical formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 9.8 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 9.9 Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 9.6 Experimental search 9.10 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 9.11 Further reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 9.12 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 9.12.1 Popular science, mass media, and general coverage . . . . . . . . . . . . . . . . . . . . . 76 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 9.12.3 Introductions to the field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 9.13 Text and image sources, contributors, and licenses . . . . . . . . . . . . . . . . . . . . . . . . . . 78 9.13.1 Text . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 9.13.2 Images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 9.13.3 Content license . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 9.12.2 Significant papers and other Chapter 1 Fermion obey the Pauli exclusion principle. Fermions include all quarks and leptons, as well as any composite particle made of an odd number of these, such as all baryons and many atoms and nuclei. Fermions differ from bosons, which obey Bose–Einstein statistics. A fermion can be an elementary particle, such as the electron, or it can be a composite particle, such as the proton. According to the spin-statistics theorem in any reasonable relativistic quantum field theory, particles with integer spin are bosons, while particles with half-integer spin are fermions. Besides this spin characteristic, fermions have another specific property: they possess conserved baryon or lepton quantum numbers. Therefore what is usually referred as the spin statistics relation is in fact a spin statisticsquantum number relation.[2] As a consequence of the Pauli exclusion principle, only one fermion can occupy a particular quantum state at any given time. If multiple fermions have the same spatial probability distribution, then at least one property of each fermion, such as its spin, must be different. Fermions are usually associated with matter, whereas bosons are generally force carrier particles, although in the current state of particle physics the distinction between the two concepts is unclear. at low temperature fermions show superfluidity for uncharged particles and superconductivity for charged particles. Composite fermions, such as protons and neutrons, are the key building blocks of everyday matter. Weakly interacting fermions can also display bosonic behavior under extreme conditions, such as superconductivity. Enrico Fermi 1.1 Elementary fermions The Standard Model recognizes two types of elementary fermions, quarks and leptons. In all, the model distinAntisymmetric wavefunction for a (fermionic) 2-particle state in guishes 24 different fermions. There are six quarks (up, down, strange, charm, bottom and top quarks), and six an infinite square well potential. leptons (electron, electron neutrino, muon, muon neuIn particle physics, a fermion (a name coined by Paul trino, tau particle and tau neutrino), along with the correDirac[1] from the surname of Enrico Fermi) is any particle sponding antiparticle of each of these. characterized by Fermi–Dirac statistics. These particles Mathematically, fermions come in three types - Weyl 1 2 CHAPTER 1. FERMION fermions (massless), Dirac fermions (massive), and Majorana fermions (each its own antiparticle). Most Standard Model fermions are believed to be Dirac fermions, although it is unknown at this time whether the neutrinos are Dirac or a Majorana fermions. Dirac fermions can be treated as a combination of two Weyl fermions.[3]:106 1.2 Composite fermions and they can be fermionic even if all the constituent particles are bosons. This was discovered by Tony Skyrme in the early 1960s, so fermions made of bosons are named skyrmions after him. Skyrme’s original example involved fields which take values on a three-dimensional sphere, the original nonlinear sigma model which describes the large distance behavior of pions. In Skyrme’s model, reproduced in the large N or string approximation to quantum chromodynamics (QCD), the proton and neutron are fermionic topological solitons of the pion field. See also: List of particles § Composite particles Whereas Skyrme’s example involved pion physics, there is a much more familiar example in quantum electrodyComposite particles (such as hadrons, nuclei, and atoms) namics with a magnetic monopole. A bosonic monopole can be bosons or fermions depending on their con- with the smallest possible magnetic charge and a bosonic stituents. More precisely, because of the relation between version of the electron will form a fermionic dyon. spin and statistics, a particle containing an odd number of The analogy between the Skyrme field and the Higgs field fermions is itself a fermion. It will have half-integer spin. of the electroweak sector has been used[4] to postulate that all fermions are skyrmions. This could explain why all known fermions have baryon or lepton quantum num• A baryon, such as the proton or neutron, contains bers and provide a physical mechanism for the Pauli exthree fermionic quarks and thus it is a fermion. clusion principle. Examples include the following: • The nucleus of a carbon-13 atom contains six protons and seven neutrons and is therefore a fermion. • The atom helium-3 (3 He) is made of two protons, one neutron, and two electrons, and therefore it is a fermion. The number of bosons within a composite particle made up of simple particles bound with a potential has no effect on whether it is a boson or a fermion. Fermionic or bosonic behavior of a composite particle (or system) is only seen at large (compared to size of the system) distances. At proximity, where spatial structure begins to be important, a composite particle (or system) behaves according to its constituent makeup. Fermions can exhibit bosonic behavior when they become loosely bound in pairs. This is the origin of superconductivity and the superfluidity of helium-3: in superconducting materials, electrons interact through the exchange of phonons, forming Cooper pairs, while in helium-3, Cooper pairs are formed via spin fluctuations. The quasiparticles of the fractional quantum Hall effect are also known as composite fermions, which are electrons with an even number of quantized vortices attached to them. 1.2.1 Skyrmions Main article: Skyrmion In a quantum field theory, there can be field configurations of bosons which are topologically twisted. These are coherent states (or solitons) which behave like a particle, 1.3 See also 1.4 Notes [1] Notes on Dirac’s lecture Developments in Atomic Theory at Le Palais de la Découverte, 6 December 1945, UKNATARCHI Dirac Papers BW83/2/257889. See note 64 on page 331 in “The Strangest Man: The Hidden Life of Paul Dirac, Mystic of the Atom” by Graham Farmelo [2] Physical Review D volume 87, page 0550003, year 2013, author Weiner, Richard M., title “Spin-statistics-quantum number connection and supersymmetry” arxiv:1302.0969 [3] T. Morii; C. S. Lim; S. N. Mukherjee (1 January 2004). The Physics of the Standard Model and Beyond. World Scientific. ISBN 978-981-279-560-1. [4] Weiner, Richard M. (2010). “The Mysteries of Fermions”. International Journal of Theoretical Physics 49 (5): 1174–1180. arXiv:0901.3816. Bibcode:2010IJTP...49.1174W. doi:10.1007/s10773010-0292-7. Chapter 2 Quark This article is about the particle. For other uses, see Accelerator experiments have provided evidence for all Quark (disambiguation). six flavors. The top quark was the last to be discovered at Fermilab in 1995.[5] A quark (/ˈkwɔrk/ or /ˈkwɑrk/) is an elementary particle and a fundamental constituent of matter. Quarks combine to form composite particles called hadrons, the most 2.1 Classification stable of which are protons and neutrons, the components of atomic nuclei.[1] Due to a phenomenon known as color See also: Standard Model confinement, quarks are never directly observed or found The Standard Model is the theoretical framework dein isolation; they can be found only within hadrons, such as baryons (of which protons and neutrons are examples), and mesons.[2][3] For this reason, much of what is known about quarks has been drawn from observations of the hadrons themselves. Quarks have various intrinsic properties, including electric charge, mass, color charge and spin. Quarks are the only elementary particles in the Standard Model of particle physics to experience all four fundamental interactions, also known as fundamental forces (electromagnetism, gravitation, strong interaction, and weak interaction), as well as the only known particles whose electric charges are not integer multiples of the elementary charge. There are six types of quarks, known as flavors: up, down, strange, charm, top, and bottom.[4] Up and down quarks have the lowest masses of all quarks. The heavier quarks rapidly change into up and down quarks through a process of particle decay: the transformation from a higher mass state to a lower mass state. Because of this, up and down quarks are generally stable and the most common in the universe, whereas strange, charm, bottom, and top quarks can only be produced in high energy collisions (such as those involving cosmic rays and in particle accelerators). For every quark flavor there is a corresponding type of antiparticle, known as an antiquark, that differs from the quark only in that some of its properties have equal magnitude but opposite sign. Six of the particles in the Standard Model are quarks (shown in purple). Each of the first three columns forms a generation of matter. scribing all the currently known elementary particles. This model contains six flavors of quarks (q), named up (u), down (d), strange (s), charm (c), bottom (b), and top (t).[4] Antiparticles of quarks are called antiquarks, and are denoted by a bar over the symbol for the corresponding quark, such as u for an up antiquark. As with antimatter in general, antiquarks have the same mass, mean lifetime, and spin as their respective quarks, but the electric charge and other charges have the opposite sign.[8] The quark model was independently proposed by physicists Murray Gell-Mann and George Zweig in 1964.[5] Quarks were introduced as parts of an ordering scheme for hadrons, and there was little evidence for their physical existence until deep inelastic scattering experiments at the Stanford Linear Accelerator Center in 1968.[6][7] Quarks are spin-1 ⁄2 particles, implying that they are fermions according to the spin-statistics theorem. They are subject to the Pauli exclusion principle, which states that no two identical fermions can simultaneously occupy the same quantum state. This is in contrast to bosons (particles with integer spin), any number of which can be 3 4 in the same state.[9] Unlike leptons, quarks possess color charge, which causes them to engage in the strong interaction. The resulting attraction between different quarks causes the formation of composite particles known as hadrons (see "Strong interaction and color charge" below). CHAPTER 2. QUARK 2.2 History The quarks which determine the quantum numbers of hadrons are called valence quarks; apart from these, any hadron may contain an indefinite number of virtual (or sea) quarks, antiquarks, and gluons which do not influence its quantum numbers.[10] There are two families of hadrons: baryons, with three valence quarks, and mesons, with a valence quark and an antiquark.[11] The most common baryons are the proton and the neutron, the building blocks of the atomic nucleus.[12] A great number of hadrons are known (see list of baryons and list of mesons), most of them differentiated by their quark content and the properties these constituent quarks confer. The existence of “exotic” hadrons with more valence quarks, such as tetraquarks (qqqq) and pentaquarks (qqqqq), has been conjectured[13] but not proven.[nb 1][13][14] Elementary fermions are grouped into three generations, each comprising two leptons and two quarks. The first generation includes up and down quarks, the second strange and charm quarks, and the third bottom and top quarks. All searches for a fourth generation of quarks and other elementary fermions have failed,[15] and there is strong indirect evidence that no more than three generations exist.[nb 2][16] Particles in higher generations generally have greater mass and less stability, causing them to decay into lower-generation particles by means of weak interactions. Only first-generation (up and down) quarks occur commonly in nature. Heavier quarks can only be created in high-energy collisions (such as in those involving cosmic rays), and decay quickly; however, they are thought to have been present during the first fractions of a second after the Big Bang, when the universe was in an extremely hot and dense phase (the quark epoch). Studies of heavier quarks are conducted in artificially created conditions, such as in particle accelerators.[17] Having electric charge, mass, color charge, and flavor, quarks are the only known elementary particles that engage in all four fundamental interactions of contemporary physics: electromagnetism, gravitation, strong interaction, and weak interaction.[12] Gravitation is too weak to be relevant to individual particle interactions except at extremes of energy (Planck energy) and distance scales (Planck distance). However, since no successful quantum theory of gravity exists, gravitation is not described by the Standard Model. Murray Gell-Mann at TED in 2007. Gell-Mann and George Zweig proposed the quark model in 1964. The quark model was independently proposed by physicists Murray Gell-Mann[18] (pictured) and George Zweig[19][20] in 1964.[5] The proposal came shortly after Gell-Mann’s 1961 formulation of a particle classification system known as the Eightfold Way—or, in more technical terms, SU(3) flavor symmetry.[21] Physicist Yuval Ne'eman had independently developed a scheme similar to the Eightfold Way in the same year.[22][23] At the time of the quark theory’s inception, the "particle zoo" included, amongst other particles, a multitude of hadrons. Gell-Mann and Zweig posited that they were not elementary particles, but were instead composed of combinations of quarks and antiquarks. Their model involved three flavors of quarks, up, down, and strange, to which they ascribed properties such as spin and electric charge.[18][19][20] The initial reaction of the physics community to the proposal was mixed. There was particular contention about whether the quark was a physical entity or a mere abstraction used to explain concepts that were not fully understood at the time.[24] In less than a year, extensions to the Gell-Mann–Zweig model were proposed. Sheldon Lee Glashow and James Bjorken predicted the existence of a fourth flavor of quark, which they called charm. The addition was proSee the table of properties below for a more complete posed because it allowed for a better description of the weak interaction (the mechanism that allows quarks to overview of the six quark flavors’ properties. decay), equalized the number of known quarks with the number of known leptons, and implied a mass formula that correctly reproduced the masses of the known mesons.[25] 2.3. ETYMOLOGY 5 In 1968, deep inelastic scattering experiments at the Stanford Linear Accelerator Center (SLAC) showed that the proton contained much smaller, point-like objects and was therefore not an elementary particle.[6][7][26] Physicists were reluctant to firmly identify these objects with quarks at the time, instead calling them "partons"— a term coined by Richard Feynman.[27][28][29] The objects that were observed at SLAC would later be identified as up and down quarks as the other flavors were discovered.[30] Nevertheless, “parton” remains in use as a collective term for the constituents of hadrons (quarks, antiquarks, and gluons). indicator of the top quark’s existence: without the top quark, the bottom quark would have been without a partner. However, it was not until 1995 that the top quark was finally observed, also by the CDF[39] and DØ[40] teams at Fermilab.[5] It had a mass much larger than had been previously expected,[41] almost as large as that of a gold atom.[42] In the following years a number of suggestions appeared for extending the quark model to six quarks. Of these, the 1975 paper by Haim Harari[35] was the first to coin the terms top and bottom for the additional quarks.[36] Zweig preferred the name ace for the particle he had theorized, but Gell-Mann’s terminology came to prominence once the quark model had been commonly accepted.[45] 2.3 Etymology For some time, Gell-Mann was undecided on an actual The strange quark’s existence was indirectly validated by spelling for the term he intended to coin, until he found SLAC’s scattering experiments: not only was it a neces- the word quark in James Joyce's book Finnegans Wake: sary component of Gell-Mann and Zweig’s three-quark model, but it provided an explanation for the kaon (K) and Three quarks for Muster Mark! pion (π) hadrons discovered in cosmic rays in 1947.[31] Sure he has not got much of a bark And sure any he has it’s all beside the mark. In a 1970 paper, Glashow, John Iliopoulos and Luciano —James Joyce, Finnegans Wake[43] Maiani presented further reasoning for the existence of [32][33] the as-yet undiscovered charm quark. The number of supposed quark flavors grew to the current six in 1973, when Makoto Kobayashi and Toshihide Maskawa noted Gell-Mann went into further detail regarding the name of that the experimental observation of CP violation[nb 3][34] the quark in his book The Quark and the Jaguar:[44] could be explained if there were another pair of quarks. In 1963, when I assigned the name “quark” to the fundamental constituents of the nucleon, I had the sound first, without the spelling, which could have been “kwork”. Then, in one of my occasional perusals of Finnegans Wake, by James Joyce, I came across the word “quark” in the phrase “Three quarks for Muster Mark”. Since “quark” (meaning, for one thing, the cry of the gull) was clearly intended to rhyme with “Mark”, as well as “bark” and other such words, I had to find an excuse to pronounce it as “kwork”. But the book represents the dream of a publican named Humphrey Chimpden Earwicker. Words in the text are Photograph of the event that led to the discovery of the Σ++ typically drawn from several sources at once, c baryon, at the Brookhaven National Laboratory in 1974 like the "portmanteau" words in “Through the Looking-Glass”. From time to time, phrases Charm quarks were produced almost simultaneously by occur in the book that are partially determined two teams in November 1974 (see November Revoluby calls for drinks at the bar. I argued, theretion)—one at SLAC under Burton Richter, and one at fore, that perhaps one of the multiple sources Brookhaven National Laboratory under Samuel Ting. of the cry “Three quarks for Muster Mark” The charm quarks were observed bound with charm anmight be “Three quarts for Mister Mark”, in tiquarks in mesons. The two parties had assigned the diswhich case the pronunciation “kwork” would covered meson two different symbols, J and ψ; thus, it not be totally unjustified. In any case, the numbecame formally known as the J/ψ meson. The discovber three fitted perfectly the way quarks occur ery finally convinced the physics community of the quark in nature. model’s validity.[29] The quark flavors were given their names for a number In 1977, the bottom quark was observed by a team at of reasons. The up and down quarks are named after the Fermilab led by Leon Lederman.[37][38] This was a strong up and down components of isospin, which they carry.[46] 6 CHAPTER 2. QUARK Strange quarks were given their name because they were discovered to be components of the strange particles discovered in cosmic rays years before the quark model was proposed; these particles were deemed “strange” because they had unusually long lifetimes.[47] Glashow, who coproposed charm quark with Bjorken, is quoted as saying, “We called our construct the 'charmed quark', for we were fascinated and pleased by the symmetry it brought to the subnuclear world.”[48] The names “bottom” and “top”, coined by Harari, were chosen because they are “logical partners for up and down quarks”.[35][36][47] In the past, bottom and top quarks were sometimes referred to as “beauty” and “truth” respectively, but these names have somewhat fallen out of use.[49] While “truth” never did catch on, accelerator complexes devoted to massive production of bottom quarks are sometimes called "beauty factories".[50] nounced “h bar”). For quarks, a measurement of the spin vector component along any axis can only yield the values +ħ/2 or −ħ/2; for this reason quarks are classified as spin1 ⁄2 particles.[53] The component of spin along a given axis – by convention the z axis – is often denoted by an up arrow ↑ for the value +1 ⁄2 and down arrow ↓ for the value −1 ⁄2 , placed after the symbol for flavor. For example, an up quark with a spin of +1 ⁄2 along the z axis is denoted by u↑.[54] 2.4.3 Weak interaction Main article: Weak interaction A quark of one flavor can transform into a quark of 2.4 Properties 2.4.1 Electric charge See also: Electric charge Quarks have fractional electric charge values – either 1 ⁄3 or 2 ⁄3 times the elementary charge (e), depending on flavor. Up, charm, and top quarks (collectively referred to as up-type quarks) have a charge of +2 ⁄3 e, while down, strange, and bottom quarks (down-type quarks) have −1 ⁄3 e. Antiquarks have the opposite charge to their corresponding quarks; up-type antiquarks have charges of −2 ⁄3 e and down-type antiquarks have charges of +1 ⁄3 e. Since the electric charge of a hadron is the sum of the charges of the constituent quarks, all hadrons have integer charges: the combination of three quarks (baryons), three antiquarks (antibaryons), or a quark and an antiquark (mesons) always results in integer charges.[51] For example, the hadron constituents of atomic nuclei, neutrons and protons, have charges of 0 e and +1 e respectively; the neutron is composed of two down quarks and one up quark, and the proton of two up quarks and one down quark.[12] Feynman diagram of beta decay with time flowing upwards. The CKM matrix (discussed below) encodes the probability of this and other quark decays. another flavor only through the weak interaction, one of the four fundamental interactions in particle physics. By absorbing or emitting a W boson, any up-type quark (up, charm, and top quarks) can change into any downtype quark (down, strange, and bottom quarks) and vice versa. This flavor transformation mechanism causes the radioactive process of beta decay, in which a neutron (n) “splits” into a proton (p), an electron (e−) and an electron antineutrino (ν 2.4.2 Spin e) (see picture). This occurs when one of the down quarks See also: Spin (physics) in the neutron (udd) decays into an up quark by emitting a virtual W− boson, transforming the neutron into a proton decays into an electron and Spin is an intrinsic property of elementary particles, and (uud). The W− boson then [55] an electron antineutrino. its direction is an important degree of freedom. It is sometimes visualized as the rotation of an object around Both beta decay and the inverse process of inverse beta its own axis (hence the name "spin"), though this notion decay are routinely used in medical applications such as is somewhat misguided at subatomic scales because ele- positron emission tomography (PET) and in experiments involving neutrino detection. mentary particles are believed to be point-like.[52] Spin can be represented by a vector whose length is mea- While the process of flavor transformation is the same sured in units of the reduced Planck constant ħ (pro- for all quarks, each quark has a preference to trans- 2.4. PROPERTIES up-type: u 7 c t s b Strong Weak down-type: d The strengths of the weak interactions between the six quarks. The “intensities” of the lines are determined by the elements of the CKM matrix. form into the quark of its own generation. The relative tendencies of all flavor transformations are described by a mathematical table, called the Cabibbo–Kobayashi– Maskawa matrix (CKM matrix). Enforcing unitarity, the approximate magnitudes of the entries of the CKM matrix are:[56]     |Vud | |Vus | |Vub | 0.974 0.225 0.003 |Vcd | |Vcs | |Vcb | ≈ 0.225 0.973 0.041, |Vtd | |Vts | |Vtb | 0.009 0.040 0.999 where Vij represents the tendency of a quark of flavor i to change into a quark of flavor j (or vice versa).[nb 4] There exists an equivalent weak interaction matrix for leptons (right side of the W boson on the above beta decay diagram), called the Pontecorvo–Maki–Nakagawa– Sakata matrix (PMNS matrix).[57] Together, the CKM and PMNS matrices describe all flavor transformations, but the links between the two are not yet clear.[58] 2.4.4 Strong interaction and color charge See also: Color charge and Strong interaction According to quantum chromodynamics (QCD), quarks possess a property called color charge. There are three types of color charge, arbitrarily labeled blue, green, and red.[nb 5] Each of them is complemented by an anticolor – antiblue, antigreen, and antired. Every quark carries a color, while every antiquark carries an anticolor.[59] The system of attraction and repulsion between quarks charged with different combinations of the three colors is called strong interaction, which is mediated by force carrying particles known as gluons; this is discussed at length below. The theory that describes strong interactions is called quantum chromodynamics (QCD). A quark, which All types of hadrons have zero total color charge. will have a single color value, can form a bound system with an antiquark carrying the corresponding anticolor. The result of two attracting quarks will be color neutrality: a quark with color charge ξ plus an antiquark with color charge −ξ will result in a color charge of 0 (or “white” 8 CHAPTER 2. QUARK gg b u d gr b g 8 qb qg qr g gg r 3 g8 qr g3 gr g t s qg b qb gb r c gb g The pattern of strong charges for the three colors of quark, three antiquarks, and eight gluons (with two of zero charge overlapping). Current quark masses for all six flavors in comparison, as balls of proportional volumes. Proton and electron (red) are shown in bottom left corner for scale color) and the formation of a meson. This is analogous to the additive color model in basic optics. Similarly, the combination of three quarks, each with different color charges, or three antiquarks, each with anticolor charges, will result in the same “white” color charge and the formation of a baryon or antibaryon.[60] quark mass refers to the mass of a quark by itself, while constituent quark mass refers to the current quark mass plus the mass of the gluon particle field surrounding the quark.[65] These masses typically have very different values. Most of a hadron’s mass comes from the gluons that bind the constituent quarks together, rather than from the quarks themselves. While gluons are inherently massless, they possess energy – more specifically, quantum chromodynamics binding energy (QCBE) – and it is this that contributes so greatly to the overall mass of the hadron (see mass in special relativity). For example, a proton has a mass of approximately 938 MeV/c2 , of which the rest mass of its three valence quarks only contributes about 11 MeV/c2 ; much of the remainder can be attributed to the gluons’ QCBE.[66][67] In modern particle physics, gauge symmetries – a kind of symmetry group – relate interactions between particles (see gauge theories). Color SU(3) (commonly abbreviated to SU(3) ) is the gauge symmetry that relates the color charge in quarks and is the defining symmetry for quantum chromodynamics.[61] Just as the laws of physics are independent of which directions in space are designated x, y, and z, and remain unchanged if the coordinate axes are rotated to a new orientation, the physics of quantum chromodynamics is independent of which directions in three-dimensional color space are identified as blue, red, and green. SU(3) color transformations correspond to “rotations” in color space (which, mathematically speaking, is a complex space). Every quark flavor f, each with subtypes fB, fG, fR corresponding to the quark colors,[62] forms a triplet: a three-component quantum field which transforms under the fundamental representation of SU(3) .[63] The requirement that SU(3) should be local – that is, that its transformations be allowed to vary with space and time – determines the properties of the strong interaction, in particular the existence of eight gluon types to act as its force carriers.[61][64] The Standard Model posits that elementary particles derive their masses from the Higgs mechanism, which is related to the Higgs boson. Physicists hope that further research into the reasons for the top quark’s large mass of ~173 GeV/c2 , almost the mass of a gold atom,[66][68] might reveal more about the origin of the mass of quarks and other elementary particles.[69] 2.4.6 Table of properties See also: Flavor (particle physics) The following table summarizes the key properties of the six quarks. Flavor quantum numbers (isospin (I 3 ), charm 2.4.5 Mass (C), strangeness (S, not to be confused with spin), topness (T), and bottomness (B′)) are assigned to certain quark See also: Invariant mass flavors, and denote qualities of quark-based systems and hadrons. The baryon number (B) is +1 ⁄3 for all quarks, Two terms are used in referring to a quark’s mass: current as baryons are made of three quarks. For antiquarks, the 2.5. INTERACTING QUARKS J = total angular momentum, B = baryon number, Q = electric charge, I 3 = isospin, C = charm, S = strangeness, T = topness, B′ = bottomness. * Notation such as 4190+180 −60 denotes measurement uncertainty. In the case of the top quark, the first uncertainty is statistical in nature, and the second is systematic. 2.5 Interacting quarks See also: Color confinement and Gluon field splits; this process also works in reverse in that the annihilation of two sea quarks produces a gluon. The result is a constant flux of gluon splits and creations colloquially known as “the sea”.[76] Sea quarks are much less stable than their valence counterparts, and they typically annihilate each other within the interior of the hadron. Despite this, sea quarks can hadronize into baryonic or mesonic particles under certain circumstances.[77] 2.5.2 Other phases of quark matter Main article: QCD matter Under sufficiently extreme conditions, quarks may beTemperature electric charge (Q) and all flavor quantum numbers (B, I 3 , C, S, T, and B′) are of opposite sign. Mass and total angular momentum (J; equal to spin for point particles) do not change sign for the antiquarks. 9 Quark-gluon-plasma As described by quantum chromodynamics, the strong interaction between quarks is mediated by gluons, massless vector gauge bosons. Each gluon carries one color charge and one anticolor charge. In the standard framework of Hadronic phase Color superconductivity particle interactions (part of a more general formulation known as perturbation theory), gluons are constantly exNuclear matter changed between quarks through a virtual emission and Baryonic Density absorption process. When a gluon is transferred between quarks, a color change occurs in both; for example, if a red quark emits a red–antigreen gluon, it becomes green, A qualitative rendering of the phase diagram of quark matter. details of the diagram are the subject of ongoing and if a green quark absorbs a red–antigreen gluon, it be- The precise [78][79] comes red. Therefore, while each quark’s color constantly research. changes, their strong interaction is preserved.[70][71][72] come deconfined and exist as free particles. In the course Since gluons carry color charge, they themselves are of asymptotic freedom, the strong interaction becomes able to emit and absorb other gluons. This causes weaker at higher temperatures. Eventually, color conasymptotic freedom: as quarks come closer to each finement would be lost and an extremely hot plasma other, the chromodynamic binding force between them of freely moving quarks and gluons would be formed. weakens.[73] Conversely, as the distance between quarks This theoretical phase of matter is called quark–gluon increases, the binding force strengthens. The color field plasma.[80] The exact conditions needed to give rise to this becomes stressed, much as an elastic band is stressed state are unknown and have been the subject of a great when stretched, and more gluons of appropriate color are deal of speculation and experimentation. A recent estispontaneously created to strengthen the field. Above a mate puts the needed temperature at (1.90±0.02)×1012 certain energy threshold, pairs of quarks and antiquarks kelvin.[81] While a state of entirely free quarks and gluare created. These pairs bind with the quarks being sep- ons has never been achieved (despite numerous attempts arated, causing new hadrons to form. This phenomenon by CERN in the 1980s and 1990s),[82] recent experiments is known as color confinement: quarks never appear in at the Relativistic Heavy Ion Collider have yielded eviisolation.[71][74] This process of hadronization occurs be- dence for liquid-like quark matter exhibiting “nearly perfore quarks, formed in a high energy collision, are able to fect” fluid motion.[83] interact in any other way. The only exception is the top The quark–gluon plasma would be characterized by a quark, which may decay before it hadronizes.[75] great increase in the number of heavier quark pairs in relation to the number of up and down quark pairs. It is believed that in the period prior to 10−6 seconds after the 2.5.1 Sea quarks Big Bang (the quark epoch), the universe was filled with quark–gluon plasma, as the temperature was too high for Hadrons, along with the valence quarks (q [84] v) that contribute to their quantum numbers, contain hadrons to be stable. virtual quark–antiquark (qq) pairs known as sea quarks Given sufficiently high baryon densities and relatively low (q temperatures – possibly comparable to those found in s). Sea quarks form when a gluon of the hadron’s color neutron stars – quark matter is expected to degenerate 10 into a Fermi liquid of weakly interacting quarks. This liquid would be characterized by a condensation of colored quark Cooper pairs, thereby breaking the local SU(3) symmetry. Because quark Cooper pairs harbor color charge, such a phase of quark matter would be color superconductive; that is, color charge would be able to pass through it with no resistance.[85] 2.6 See also • Color–flavor locking • Neutron magnetic moment • Leptons • Preons – Hypothetical particles which were once postulated to be subcomponents of quarks and leptons • Quarkonium – Mesons made of a quark and antiquark of the same flavor • Quark star – A hypothetical degenerate neutron star with extreme density • Quark–lepton complementarity – Possible fundamental relation between quarks and leptons 2.7 Notes [1] Several research groups claimed to have proven the existence of tetraquarks and pentaquarks in the early 2000s. While the status of tetraquarks is still under debate, all known pentaquark candidates have since been established as non-existent. [2] The main evidence is based on the resonance width of the Z0 boson, which constrains the 4th generation neutrino to have a mass greater than ~45 GeV/c2 . This would be highly contrasting with the other three generations’ neutrinos, whose masses cannot exceed 2 MeV/c2 . [3] CP violation is a phenomenon which causes weak interactions to behave differently when left and right are swapped (P symmetry) and particles are replaced with their corresponding antiparticles (C symmetry). [4] The actual probability of decay of one quark to another is a complicated function of (amongst other variables) the decaying quark’s mass, the masses of the decay products, and the corresponding element of the CKM matrix. This probability is directly proportional (but not equal) to the magnitude squared (|Vij|2 ) of the corresponding CKM entry. [5] Despite its name, color charge is not related to the color spectrum of visible light. CHAPTER 2. QUARK 2.8 References [1] “Quark (subatomic particle)". Encyclopædia Britannica. Retrieved 2008-06-29. [2] R. Nave. “Confinement of Quarks”. HyperPhysics. Georgia State University, Department of Physics and Astronomy. Retrieved 2008-06-29. [3] R. Nave. “Bag Model of Quark Confinement”. HyperPhysics. Georgia State University, Department of Physics and Astronomy. Retrieved 2008-06-29. [4] R. Nave. “Quarks”. HyperPhysics. Georgia State University, Department of Physics and Astronomy. Retrieved 2008-06-29. [5] B. Carithers, P. Grannis (1995). “Discovery of the Top Quark” (PDF). Beam Line (SLAC) 25 (3): 4–16. Retrieved 2008-09-23. [6] E.D. Bloom et al. (1969). “High-Energy Inelastic e–p Scattering at 6° and 10°". Physical Review Letters 23 (16): 930–934. Bibcode:1969PhRvL..23..930B. doi:10.1103/PhysRevLett.23.930. [7] M. Breidenbach et al. (1969). “Observed Behavior of Highly Inelastic Electron–Proton Scattering”. Physical Review Letters 23 (16): 935–939. Bibcode:1969PhRvL..23..935B. doi:10.1103/PhysRevLett.23.935. [8] S.S.M. Wong (1998). Introductory Nuclear Physics (2nd ed.). Wiley Interscience. p. 30. ISBN 0-471-23973-9. [9] K.A. Peacock (2008). The Quantum Revolution. Greenwood Publishing Group. p. 125. ISBN 0-31333448-X. [10] B. Povh, C. Scholz, K. Rith, F. Zetsche (2008). Particles and Nuclei. Springer. p. 98. ISBN 3-540-79367-4. [11] Section 6.1. in P.C.W. Davies (1979). The Forces of Nature. Cambridge University Press. ISBN 0-521-22523-X. [12] M. Munowitz (2005). Knowing. Oxford University Press. p. 35. ISBN 0-19-516737-6. [13] W.-M. Yao (Particle Data Group) et al. (2006). “Review of Particle Physics: Pentaquark Update” (PDF). Journal of Physics G 33 (1): 1–1232. arXiv:astro-ph/0601168. Bibcode:2006JPhG...33....1Y. doi:10.1088/09543899/33/1/001. [14] C. Amsler (Particle Data Group) et al. (2008). “Review of Particle Physics: Pentaquarks” (PDF). Physics Letters B 667 (1): 1–1340. Bibcode:2008PhLB..667....1P. doi:10.1016/j.physletb.2008.07.018. C. Amsler (Particle Data Group) et al. (2008). “Review of Particle Physics: New CharmoniumLike States” (PDF). Physics Letters B 667 Bibcode:2008PhLB..667....1P. (1): 1–1340. doi:10.1016/j.physletb.2008.07.018. E.V. Shuryak (2004). The QCD Vacuum, Hadrons and Superdense Matter. World Scientific. p. 59. ISBN 981-238-574-6. 2.8. REFERENCES [15] C. Amsler (Particle Data Group) et al. (2008). “Review of Particle Physics: b′ (4th Generation) Quarks, Searches for” (PDF). Physics Letters B 667 (1): 1–1340. Bibcode:2008PhLB..667....1P. doi:10.1016/j.physletb.2008.07.018. C. Amsler (Particle Data Group) et al. (2008). “Review of Particle Physics: t′ (4th Generation) Quarks, Searches for” (PDF). Physics Letters B 667 (1): 1–1340. Bibcode:2008PhLB..667....1P. doi:10.1016/j.physletb.2008.07.018. [16] D. Decamp; Deschizeaux, B.; Lees, J.-P.; Minard, M.-N.; Crespo, J.M.; Delfino, M.; Fernandez, E.; Martinez, M. et al. (1989). “Determination of the number of light neutrino species”. Physics Letters B 231 (4): 519. Bibcode:1989PhLB..231..519D. doi:10.1016/0370-2693(89)90704-1. A. Fisher (1991). “Searching for the Beginning of Time: Cosmic Connection”. Popular Science 238 (4): 70. J.D. Barrow (1997) [1994]. “The Singularity and Other Problems”. The Origin of the Universe (Reprint ed.). Basic Books. ISBN 978-0-465-05314-8. [17] D.H. Perkins (2003). Particle Astrophysics. Oxford University Press. p. 4. ISBN 0-19-850952-9. [18] M. Gell-Mann (1964). “A Schematic Model of Baryons and Mesons”. Physics Letters 8 (3): 214– 215. Bibcode:1964PhL.....8..214G. doi:10.1016/S00319163(64)92001-3. [19] G. Zweig (1964). “An SU(3) Model for Strong Interaction Symmetry and its Breaking” (PDF). CERN Report No.8182/TH.401. [20] G. Zweig (1964). “An SU(3) Model for Strong Interaction Symmetry and its Breaking: II” (PDF). CERN Report No.8419/TH.412. 11 [26] J.I. Friedman. “The Road to the Nobel Prize”. Hue University. Retrieved 2008-09-29. [27] R.P. Feynman (1969). “Very High-Energy Collisions of Hadrons”. Physical Review Letters 23 (24): 1415–1417. Bibcode:1969PhRvL..23.1415F. doi:10.1103/PhysRevLett.23.1415. [28] S. Kretzer et al. (2004). “CTEQ6 Parton Distributions with Heavy Quark Mass Effects”. Physical Review D 69 (11): 114005. arXiv:hepBibcode:2004PhRvD..69k4005K. ph/0307022. doi:10.1103/PhysRevD.69.114005. [29] D.J. Griffiths (1987). Introduction to Elementary Particles. John Wiley & Sons. p. 42. ISBN 0-471-60386-4. [30] M.E. Peskin, D.V. Schroeder (1995). An introduction to quantum field theory. Addison–Wesley. p. 556. ISBN 0-201-50397-2. [31] V.V. Ezhela (1996). Particle physics. Springer. p. 2. ISBN 1-56396-642-5. [32] S.L. Glashow, J. Iliopoulos, L. Maiani; Iliopoulos; Maiani (1970). “Weak Interactions with Lepton–Hadron Symmetry”. Physical Review D 2 (7): 1285–1292. Bibcode:1970PhRvD...2.1285G. doi:10.1103/PhysRevD.2.1285. [33] D.J. Griffiths (1987). Introduction to Elementary Particles. John Wiley & Sons. p. 44. ISBN 0-471-60386-4. [34] M. Kobayashi, T. Maskawa; Maskawa (1973). “CPViolation in the Renormalizable Theory of Weak Interaction”. Progress of Theoretical Physics 49 (2): 652–657. Bibcode:1973PThPh..49..652K. doi:10.1143/PTP.49.652. [21] M. Gell-Mann (2000) [1964]. “The Eightfold Way: A theory of strong interaction symmetry”. In M. Gell-Mann, Y. Ne'eman. The Eightfold Way. Westview Press. p. 11. ISBN 0-7382-0299-1. Original: M. Gell-Mann (1961). “The Eightfold Way: A theory of strong interaction symmetry”. Synchrotron Laboratory Report CTSL-20 (California Institute of Technology). [35] H. Harari (1975). “A new quark model for hadrons”. Physics Letters B 57B (3): 265. Bibcode:1975PhLB...57..265H. doi:10.1016/03702693(75)90072-6. [22] Y. Ne'eman (2000) [1964]. “Derivation of strong interactions from gauge invariance”. In M. Gell-Mann, Y. Ne'eman. The Eightfold Way. Westview Press. ISBN 0-7382-0299-1. Original Y. Ne'eman (1961). “Derivation of strong interactions from gauge invariance”. Nuclear Physics 26 (2): 222. Bibcode:1961NucPh..26..222N. doi:10.1016/00295582(61)90134-1. [37] S.W. Herb et al. (1977). “Observation of a Dimuon Resonance at 9.5 GeV in 400-GeV Proton-Nucleus Collisions”. Physical Review Letters 39 (5): 252. Bibcode:1977PhRvL..39..252H. doi:10.1103/PhysRevLett.39.252. [23] R.C. Olby, G.N. Cantor (1996). Companion to the History of Modern Science. Taylor & Francis. p. 673. ISBN 0415-14578-3. [24] A. Pickering (1984). Constructing Quarks. University of Chicago Press. pp. 114–125. ISBN 0-226-66799-5. [25] B.J. Bjorken, S.L. Glashow; Glashow (1964). “Elementary Particles and SU(4)". Physics Letters 11 (3): 255– 257. Bibcode:1964PhL....11..255B. doi:10.1016/00319163(64)90433-0. [36] K.W. Staley (2004). The Evidence for the Top Quark. Cambridge University Press. pp. 31–33. ISBN 978-0521-82710-2. [38] M. Bartusiak (1994). A Positron named Priscilla. National Academies Press. p. 245. ISBN 0-309-04893-1. [39] F. Abe (CDF Collaboration) et al. (1995). “Observation of Top Quark Production in pp Collisions with the Collider Detector at Fermilab”. Physical Review Letters 74 (14): 2626–2631. Bibcode:1995PhRvL..74.2626A. doi:10.1103/PhysRevLett.74.2626. PMID 10057978. [40] S. Abachi (DØ Collaboration) et al. (1995). “Search for High Mass Top Quark Production in pp Collisions at √s = 1.8 TeV”. Physical Review Letters 74 (13): 2422–2426. Bibcode:1995PhRvL..74.2422A. doi:10.1103/PhysRevLett.74.2422. 12 CHAPTER 2. QUARK [41] K.W. Staley (2004). The Evidence for the Top Quark. Cambridge University Press. p. 144. ISBN 0-521-827108. [59] R. Nave. “The Color Force”. HyperPhysics. Georgia State University, Department of Physics and Astronomy. Retrieved 2009-04-26. [42] “New Precision Measurement of Top Quark Mass”. Brookhaven National Laboratory News. 2004. Retrieved 2013-11-03. [60] B.A. Schumm (2004). Deep Down Things. Johns Hopkins University Press. pp. 131–132. ISBN 0-8018-7971X. OCLC 55229065. [43] J. Joyce (1982) [1939]. Finnegans Wake. Penguin Books. p. 383. ISBN 0-14-006286-6. [44] M. Gell-Mann (1995). The Quark and the Jaguar: Adventures in the Simple and the Complex. Henry Holt and Co. p. 180. ISBN 978-0-8050-7253-2. [45] J. Gleick (1992). Genius: Richard Feynman and modern physics. Little Brown and Company. p. 390. ISBN 0316-90316-7. [61] Part III of M.E. Peskin, D.V. Schroeder (1995). An Introduction to Quantum Field Theory. Addison–Wesley. ISBN 0-201-50397-2. [62] V. Icke (1995). The force of symmetry. Cambridge University Press. p. 216. ISBN 0-521-45591-X. [63] M.Y. Han (2004). A story of light. World Scientific. p. 78. ISBN 981-256-034-3. [46] J.J. Sakurai (1994). S.F Tuan, ed. Modern Quantum Mechanics (Revised ed.). Addison–Wesley. p. 376. ISBN 0-201-53929-2. [64] C. Sutton. “Quantum chromodynamics (physics)". Encyclopædia Britannica Online. Retrieved 2009-05-12. [47] D.H. Perkins (2000). Introduction to high energy physics. Cambridge University Press. p. 8. ISBN 0-521-62196-8. [65] A. Watson (2004). The Quantum Quark. Cambridge University Press. pp. 285–286. ISBN 0-521-82907-0. [48] M. Riordan (1987). The Hunting of the Quark: A True Story of Modern Physics. Simon & Schuster. p. 210. ISBN 978-0-671-50466-3. [66] K. Nakamura et al. (Particle Data Group), JP G 37, 075021 (2010) and 2011 partial update for the 2012 edition (URL: http://pdg.lbl.gov) [49] F. Close (2006). The New Cosmic Onion. CRC Press. p. 133. ISBN 1-58488-798-2. [67] W. Weise, A.M. Green (1984). Quarks and Nuclei. World Scientific. pp. 65–66. ISBN 9971-966-61-1. [50] J.T. Volk et al. (1987). “Letter of Intent for a Tevatron Beauty Factory” (PDF). Fermilab Proposal #783. [51] G. Fraser (2006). The New Physics for the Twenty-First Century. Cambridge University Press. p. 91. ISBN 0521-81600-9. [52] “The Standard Model of Particle Physics”. BBC. 2002. Retrieved 2009-04-19. [53] F. Close (2006). The New Cosmic Onion. CRC Press. pp. 80–90. ISBN 1-58488-798-2. [54] D. Lincoln (2004). Understanding the Universe. World Scientific. p. 116. ISBN 981-238-705-6. [55] “Weak Interactions”. Virtual Visitor Center. Stanford Linear Accelerator Center. 2008. Retrieved 2008-09-28. [56] K. Nakamura et al. (2010). “Review of Particles Physics: The CKM Quark-Mixing Matrix” (PDF). J. Phys. G 37 (75021): 150. [57] Z. Maki, M. Nakagawa, S. Sakata (1962). “Remarks on the Unified Model of Elementary Particles”. Progress of Theoretical Physics 28 (5): 870. Bibcode:1962PThPh..28..870M. doi:10.1143/PTP.28.870. [58] B.C. Chauhan, M. Picariello, J. Pulido, E. Torrente-Lujan (2007). “Quark–lepton complementarity, neutrino and standard model data predict θPMNS 13 = 9°+1° −2° ". European Physical Journal C50 (3): 573–578. arXiv:hep-ph/0605032. Bibcode:2007EPJC...50..573C. doi:10.1140/epjc/s10052-007-0212-z. [68] D. McMahon (2008). Quantum Field Theory Demystified. McGraw–Hill. p. 17. ISBN 0-07-154382-1. [69] S.G. Roth (2007). Precision electroweak physics at electron–positron colliders. Springer. p. VI. ISBN 3-54035164-7. [70] R.P. Feynman (1985). QED: The Strange Theory of Light and Matter (1st ed.). Princeton University Press. pp. 136– 137. ISBN 0-691-08388-6. [71] M. Veltman (2003). Facts and Mysteries in Elementary Particle Physics. World Scientific. pp. 45–47. ISBN 981238-149-X. [72] F. Wilczek, B. Devine (2006). Fantastic Realities. World Scientific. p. 85. ISBN 981-256-649-X. [73] F. Wilczek, B. Devine (2006). Fantastic Realities. World Scientific. pp. 400ff. ISBN 981-256-649-X. [74] T. Yulsman (2002). Origin. CRC Press. p. 55. ISBN 0-7503-0765-X. [75] F. Garberson (2008). “Top Quark Mass and Cross Section Results from the Tevatron”. arXiv:0808.0273 [hep-ex]. [76] J. Steinberger (2005). Learning about Particles. Springer. p. 130. ISBN 3-540-21329-5. [77] C.-Y. Wong (1994). Introduction to High-energy Heavyion Collisions. World Scientific. p. 149. ISBN 981-020263-6. 2.10. EXTERNAL LINKS 13 [78] S.B. Rüester, V. Werth, M. Buballa, I.A. Shovkovy, D.H. Rischke; Werth; Buballa; Shovkovy; Rischke (2005). “The phase diagram of neutral quark matter: Self-consistent treatment of quark masses”. Physical Review D 72 (3): 034003. arXiv:hepph/0503184. Bibcode:2005PhRvD..72c4004R. doi:10.1103/PhysRevD.72.034004. • B. Povh (1995). Particles and Nuclei: An Introduction to the Physical Concepts. Springer–Verlag. ISBN 0-387-59439-6. [79] M.G. Alford, K. Rajagopal, T. Schaefer, A. Schmitt; Schmitt; Rajagopal; Schäfer (2008). “Color superconductivity in dense quark matter”. Reviews of Modern Physics 80 (4): 1455–1515. arXiv:0709.4635. Bibcode:2008RvMP...80.1455A. doi:10.1103/RevModPhys.80.1455. • B.A. Schumm (2004). Deep Down Things: The Breathtaking Beauty of Particle Physics. Johns Hopkins University Press. ISBN 0-8018-7971-X. [80] S. Mrowczynski (1998). “Quark–Gluon Plasma”. Acta Physica Polonica B 29: 3711. arXiv:nucl-th/9905005. Bibcode:1998AcPPB..29.3711M. [81] Z. Fodor, S.D. Katz; Katz (2004). “Critical point of QCD at finite T and μ, lattice results for physical quark masses”. Journal of High Energy Physics 2004 (4): 50. arXiv:hep-lat/0402006. Bibcode:2004JHEP...04..050F. doi:10.1088/1126-6708/2004/04/050. [82] U. Heinz, M. Jacob (2000). “Evidence for a New State of Matter: An Assessment of the Results from the CERN Lead Beam Programme”. arXiv:nucl-th/0002042. [83] “RHIC Scientists Serve Up “Perfect” Liquid”. Brookhaven National Laboratory News. 2005. Retrieved 2009-05-22. [84] T. Yulsman (2002). Origins: The Quest for Our Cosmic Roots. CRC Press. p. 75. ISBN 0-7503-0765-X. [85] A. Sedrakian, J.W. Clark, M.G. Alford (2007). Pairing in fermionic systems. World Scientific. pp. 2–3. ISBN 981-256-907-3. 2.9 Further reading • A. Ali, G. Kramer; Kramer (2011). “JETS and QCD: A historical review of the discovery of the quark and gluon jets and its impact on QCD”. European Physical Journal H 36 (2): 245. arXiv:1012.2288. Bibcode:2011EPJH...36..245A. doi:10.1140/epjh/e2011-10047-1. • D.J. Griffiths (2008). Introduction to Elementary Particles (2nd ed.). Wiley–VCH. ISBN 3-52740601-8. • I.S. Hughes (1985). Elementary particles (2nd ed.). Cambridge University Press. ISBN 0-521-26092-2. • R. Oerter (2005). The Theory of Almost Everything: The Standard Model, the Unsung Triumph of Modern Physics. Pi Press. ISBN 0-13-236678-9. • A. Pickering (1984). Constructing Quarks: A Sociological History of Particle Physics. The University of Chicago Press. ISBN 0-226-66799-5. • M. Riordan (1987). The Hunting of the Quark: A true story of modern physics. Simon & Schuster. ISBN 0-671-64884-5. 2.10 External links • 1969 Physics Nobel Prize lecture by Murray GellMann • 1976 Physics Nobel Prize lecture by Burton Richter • 1976 Physics Nobel Prize lecture by Samuel C.C. Ting • 2008 Physics Nobel Prize lecture by Makoto Kobayashi • 2008 Physics Nobel Prize lecture by Toshihide Maskawa • The Top Quark And The Higgs Particle by T.A. Heppenheimer – A description of CERN's experiment to count the families of quarks. • Bowley, Roger; Copeland, Ed. “Quarks”. Sixty Symbols. Brady Haran for the University of Nottingham. Chapter 3 Hadron In particle physics, a hadron i /ˈhædrɒn/ (Greek: ἁδρός, hadrós, “stout, thick”) is a composite particle made of quarks held together by the strong force (in a similar way as molecules are held together by the electromagnetic force). Hadrons are categorized into two families: baryons, made of three quarks, and mesons, made of one quark and one antiquark. Protons and neutrons are examples of baryons; pions are an example of a meson. A tetraquark state (an exotic meson), named the Z(4430)− was discovered in 2014 by the LHCb collaboration.[1] Other types of exotic hadrons may exist, such as pentaquarks (exotic baryons), but no current evidence conclusively suggests their existence.[2][3] Of the hadrons, protons are stable, and neutrons bound within atomic nuclei are stable. Other hadrons are unstable under ordinary conditions; free neutrons decay with a half-life of about 611 seconds. Experimentally, hadron physics is studied by colliding protons or nuclei of heavy elements such as lead, and detecting the debris in the produced particle showers. 3.1 Etymology “hadronic” (the Greek ἁδρός signifies “large”, “massive”, in contrast to λεπτός which means “small”, “light”). I hope that this terminology will prove to be convenient. — Lev B. Okun, 1962 3.2 Properties According to the quark model,[5] the properties of hadrons are primarily determined by their so-called valence quarks. For example, a proton is composed of two up quarks (each with electric charge +2 ⁄3 , for a total of +4 ⁄3 together) and one down quark (with electric charge −1 ⁄3 ). Adding these together yields the proton charge of +1. Although quarks also carry color charge, hadrons must have zero total color charge because of a phenomenon called color confinement. That is, hadrons must be “colorless” or “white”. These are the simplest of the two ways: three quarks of different colors, or a quark of one color and an antiquark carrying the corresponding anticolor. Hadrons with the first arrangement are called baryons, and those with the second arrangement are mesons. Hadrons, however, are not composed of just three or The term “hadron” was introduced by Lev B. Okun in a two quarks, because of the strength of the strong force. plenary talk at the 1962 International Conference on High More accurately, strong force gluons have enough energy (E) to have resonances composed of massive (m) quarks Energy Physics.[4] In this talk he said: (E > mc2 ) . Thus, virtual quarks and antiquarks, in a 1:1 ratio, form the majority of massive particles inside a Not withstanding the fact that this rehadron. The two or three quarks are the excess of quarks port deals with weak interactions, we shall vs. antiquarks in hadrons, and vice versa in anti-hadrons. frequently have to speak of strongly interBecause the virtual quarks are not stable wave packets acting particles. These particles pose not (quanta), but irregular and transient phenomena, it is not only numerous scientific problems, but also meaningful to ask which quark is real and which virtual; a terminological problem. The point is that only the excess is apparent from the outside. Massless “strongly interacting particles” is a very clumsy virtual gluons compose the numerical majority of partiterm which does not yield itself to the forcles inside hadrons. mation of an adjective. For this reason, to take but one instance, decays into strongly interacting particles are called non-leptonic. This definition is not exact because “nonleptonic” may also signify “photonic”. In this report I shall call strongly interacting particles “hadrons”, and the corresponding decays Like all subatomic particles, hadrons are assigned quantum numbers corresponding to the representations of the Poincaré group: JPC (m), where J is the spin quantum number, P the intrinsic parity (or P-parity), and C, the charge conjugation (or C-parity), and the particle’s mass, m. Note that the mass of a hadron has very little to do 14 3.3. BARYONS 15 with the mass of its valence quarks; rather, due to mass– energy equivalence, most of the mass comes from the large amount of energy associated with the strong interaction. Hadrons may also carry flavor quantum numbers such as isospin (or G parity), and strangeness. All quarks carry an additive, conserved quantum number called a baryon number (B), which is +1 ⁄3 for quarks and −1 ⁄3 for antiquarks. This means that baryons (groups of three quarks) have B = 1 whereas mesons have B = 0. Hadrons have excited states known as resonances. Each ground state hadron may have several excited states; several hundreds of resonances have been observed in particle physics experiments. Resonances decay extremely quickly (within about 10−24 seconds) via the strong nuclear force. In other phases of matter the hadrons may disappear. For example, at very high temperature and high pressure, unless there are sufficiently many flavors of quarks, the theory of quantum chromodynamics (QCD) predicts that quarks and gluons will no longer be confined within hadrons, “because the strength of the strong interaction diminishes with energy". This property, which is known as asymptotic freedom, has been experimentally confirmed in the energy range between 1 GeV (gigaelectronvolt) and 1 TeV (teraelectronvolt).[6] All free hadrons except the proton (and antiproton) are unstable. 3.3 Baryons Main article: Baryon All known baryons are made of three valence quarks, so they are fermions, i.e., they have odd half-integral spin, because they have an odd number of quarks. As quarks possess baryon number B = 1 ⁄3 , baryons have baryon number B = 1. The best-known baryons are the proton and the neutron. One can hypothesise baryons with further quarkantiquark pairs in addition to their three quarks. Hypothetical baryons with one extra quark-antiquark pair (5 quarks in all) are called pentaquarks.[7] Several pentaquark candidates were found in the early 2000s, but upon further review these states have now been established as nonexistent.[8] (This does not rule against pentaquarks in general, only the candidates put forward). All types of hadrons have zero total color charge. (three examples shown) Each type of baryon has a corresponding antiparticle (antibaryon) in which quarks are replaced by their corresponding antiquarks. For example, just as a proton is made of two up-quarks and one down-quark, its corresponding antiparticle, the antiproton, is made of two upantiquarks and one down-antiquark. 16 3.4 Mesons Main article: Meson Mesons are hadrons composed of a quark-antiquark pair. They are bosons, meaning they have integral spin, i.e., 0, 1, or −1, as they have an even number of quarks. They have baryon number B = 0. Examples of mesons commonly produced in particle physics experiments include pions and kaons. Pions also play a role in holding atomic nuclei together via the residual strong force. In principle, mesons with more than one quark-antiquark pair may exist; a hypothetical meson with two pairs is called a tetraquark. Several tetraquark candidates were found in the 2000s, but their status is under debate.[9] Several other hypothetical “exotic” mesons lie outside the quark model of classification. These include glueballs and hybrid mesons (mesons bound by excited gluons). 3.5 See also • Hadronization, the formation of hadrons out of quarks and gluons • Large Hadron Collider (LHC) • List of particles • Standard model • Subatomic particles • Hadron therapy, a.k.a. particle therapy • Exotic hadrons 3.6 References [1] LHCb collaboration (2014): Observation of the resonant character of the Z(4430)− state [2] W.-M. Yao et al. (2006): Particle listings – Θ+ [3] C. Amsler et al. (2008): Pentaquarks [4] Lev B. Okun (1962). “The Theory of Weak Interaction”. Proceedings of 1962 International Conference on High-Energy Physics at CERN. Geneva. p. 845. Bibcode:1962hep..conf..845O. [5] C. Amsler et al. (Particle Data Group) (2008). “Review of Particle Physics – Quark Model” (PDF). Physics Letters B 667: 1. Bibcode:2008PhLB..667....1P. doi:10.1016/j.physletb.2008.07.018. [6] S. Bethke (2007). “Experimental tests of asymptotic freedom”. Progress in Particle and Nuclear Physics 58 (2): 351. arXiv:hepBibcode:2007PrPNP..58..351B. ex/0606035. doi:10.1016/j.ppnp.2006.06.001. CHAPTER 3. HADRON [7] S. Kabana (2005). “Review of the experimental evidence on pentaquarks and critical discussion”. AIP Conference Proceedings 756: 195. arXiv:hep-ex/0503020. doi:10.1063/1.1920947. [8] C. Amsler et al. (Particle Data Group) (2008). “Review of Particle Physics – Pentaquarks” (PDF). Physics Letters B 667: 1. Bibcode:2008PhLB..667....1P. doi:10.1016/j.physletb.2008.07.018. [9] Mysterious Subatomic Particle May Represent Exotic New Form of Matter Chapter 4 Boson For other uses, see Boson (disambiguation). In quantum mechanics, a boson (/ˈboʊsɒn/,[1] An important characteristic of bosons is that their statistics do not restrict the number of them that occupy the same quantum state. This property is exemplified by helium-4 when it is cooled to become a superfluid.[9] Unlike bosons, two identical fermions cannot occupy the same quantum space. Whereas the elementary particles that make up matter (i.e. leptons and quarks) are fermions, the elementary bosons are force carriers that function as the 'glue' holding matter together.[10] This property holds for all particles with integer spin (s = 0, 1, 2 etc.) as a consequence of the spin–statistics theorem. when a gas of Bose particle is cooled up to absolute zero then the kinetic energy of the particle reduces to a negligible amount and it will be condensed into a lowest energy level. this phenomenon is called the Bose-Einstein condensation. It is believed that this phenomenon is the secret behind super fluidity of liquids. 4.1 Types Bosons may be either elementary, like photons, or composite, like mesons. While most bosons are composite particles, in the Standard Model there are five bosons which are elementary: Satyendra Nath Bose /ˈboʊzɒn/[2] ) is a particle that follows Bose–Einstein statistics. Bosons make up one of the two classes of particles, the other being fermions.[3] The name boson was coined by Paul Dirac[4] to commemorate the contribution of the Indian physicist Satyendra Nath Bose[5][6] in developing, with Einstein, Bose–Einstein statistics—which theorizes the characteristics of elementary particles.[7] Examples of bosons include fundamental particles such as photons, gluons, and W and Z bosons (the four force-carrying gauge bosons of the Standard Model), the Higgs boson, and the still-theoretical graviton of quantum gravity; composite particles (e.g. mesons and stable nuclei of even mass number such as deuterium (with one proton and one neutron, mass number = 2), helium-4, or lead-208[Note 1] ); and some quasiparticles (e.g. Cooper pairs, plasmons, and phonons).[8]:130 • the four gauge bosons (γ · g · Z · W±) • the only scalar boson (the Higgs boson (H0)) Additionally, the graviton (G) is a hypothetical elementary particle not incorporated in the Standard Model. If it exists, a graviton must be a boson, and could conceivably be a gauge boson. Composite bosons are important in superfluidity and other applications of Bose–Einstein condensates. when a gas of Bose particles is cooled to absolute zero its kinetic energy decreases up to a negligible amount then the particles would condense into the lowest energy state. this phenomenon is known as Bose-Einstein condensation and it is believed that this phenomenon is the secret behind super fluidity of liquids. 17 18 4.2 Properties CHAPTER 4. BOSON theorem shows that half-integer spin particles cannot be bosons and integer spin particles cannot be fermions.[12] In large systems, the difference between bosonic and fermionic statistics is only apparent at large densities— when their wave functions overlap. At low densities, both types of statistics are well approximated by Maxwell– Boltzmann statistics, which is described by classical mechanics. 4.3 Elementary bosons See also: List of particles: Bosons Symmetric wavefunction for a (bosonic) 2-particle state in an infinite square well potential. Bosons differ from fermions, which obey Fermi–Dirac statistics. Two or more identical fermions cannot occupy the same quantum state (see Pauli exclusion principle). Since bosons with the same energy can occupy the same place in space, bosons are often force carrier particles. Fermions are usually associated with matter (although in quantum physics the distinction between the two concepts is not clear cut). All observed elementary particles are either fermions or bosons. The observed elementary bosons are all gauge bosons: photons, W and Z bosons, gluons, and the Higgs boson. • Photons are the force carriers of the electromagnetic field. • W and Z bosons are the force carriers which mediate the weak force. • Gluons are the fundamental force carriers underlying the strong force. Bosons are particles which obey Bose–Einstein statistics: • Higgs Bosons give other particles mass via the Higgs when one swaps two bosons (of the same species), the mechanism. Their existence was confirmed by wavefunction of the system is unchanged.[11] Fermions, CERN on 14 March 2013. on the other hand, obey Fermi–Dirac statistics and the Pauli exclusion principle: two fermions cannot occupy the same quantum state, resulting in a “rigidity” or “stiff- Finally, many approaches to quantum gravity postulate a ness” of matter which includes fermions. Thus fermions force carrier for gravity, the graviton, which is a boson of are sometimes said to be the constituents of matter, while spin plus or minus two. bosons are said to be the particles that transmit interactions (force carriers), or the constituents of radiation. The quantum fields of bosons are bosonic fields, obeying 4.4 Composite bosons canonical commutation relations. The properties of lasers and masers, superfluid helium- See also: List of particles: Composite particles 4 and Bose–Einstein condensates are all consequences of statistics of bosons. Another result is that the spec- Composite particles (such as hadrons, nuclei, and atoms) trum of a photon gas in thermal equilibrium is a Planck can be bosons or fermions depending on their conspectrum, one example of which is black-body radia- stituents. More precisely, because of the relation between tion; another is the thermal radiation of the opaque early spin and statistics, a particle containing an even number Universe seen today as microwave background radia- of fermions is a boson, since it has integer spin. tion. Interactions between elementary particles are called fundamental interactions. The fundamental interactions Examples include the following: of virtual bosons with real particles result in all forces we • Any meson, since mesons contain one quark and one know. antiquark. All known elementary and composite particles are bosons or fermions, depending on their spin: particles with half• The nucleus of a carbon-12 atom, which contains 6 integer spin are fermions; particles with integer spin are protons and 6 neutrons. bosons. In the framework of nonrelativistic quantum me• The helium-4 atom, consisting of 2 protons, 2 neuchanics, this is a purely empirical observation. However, in relativistic quantum field theory, the spin–statistics trons and 2 electrons. 4.8. REFERENCES The number of bosons within a composite particle made up of simple particles bound with a potential has no effect on whether it is a boson or a fermion. 4.5 To which states can bosons crowd? Bose–Einstein statistics encourages identical bosons to crowd into one quantum state, but not any state is necessarily convenient for it. Aside of statistics, bosons can interact – for example, helium-4 atoms are repulsed by intermolecular force on a very close approach, and if one hypothesizes their condensation in a spatially-localized state, then gains from the statistics cannot overcome a prohibitive force potential. A spatially-delocalized state (i.e. with low |ψ(x)|) is preferable: if the number density of the condensate is about the same as in ordinary liquid or solid state, then the repulsive potential for the Nparticle condensate in such state can be not higher than for a liquid or a crystalline lattice of the same N particles described without quantum statistics. Thus, Bose– Einstein statistics for a material particle is not a mechanism to bypass physical restrictions on the density of the corresponding substance, and superfluid liquid helium has the density comparable to the density of ordinary liquid matter. Spatially-delocalized states also permit for a low momentum according to uncertainty principle, hence for low kinetic energy; that’s why superfluidity and superconductivity are usually observed in low temperatures. Photons do not interact with themselves and hence do not experience this difference in states where to crowd (see squeezed coherent state). 4.6 See also • Anyon • Bose gas • Identical particles • Parastatistics 19 (see even and odd atomic nuclei#Odd proton, odd neutron); these odd–odd bosons are: 2 1H, 6 3Li,10 5B, 14 7N and 180m 73Ta). All have nonzero integer spin. 4.8 References [1] Wells, John C. (1990). Longman pronunciation dictionary. Harlow, England: Longman. ISBN 0582053838. entry “Boson” [2] “boson”. Collins Dictionary. [3] Carroll, Sean (2007) Dark Matter, Dark Energy: The Dark Side of the Universe, Guidebook Part 2 p. 43, The Teaching Company, ISBN 1598033506 "...boson: A force-carrying particle, as opposed to a matter particle (fermion). Bosons can be piled on top of each other without limit. Examples include photons, gluons, gravitons, weak bosons, and the Higgs boson. The spin of a boson is always an integer, such as 0, 1, 2, and so on...” [4] Notes on Dirac’s lecture Developments in Atomic Theory at Le Palais de la Découverte, 6 December 1945, UKNATARCHI Dirac Papers BW83/2/257889. See note 64 to p. 331 in “The Strangest Man” by Graham Farmelo [5] Daigle, Katy (10 July 2012). “India: Enough about Higgs, let’s discuss the boson”. AP News. Retrieved 10 July 2012. [6] Bal, Hartosh Singh (19 September 2012). “The Bose in the Boson”. New York Times blog. Retrieved 21 September 2012. [7] “Higgs boson: The poetry of subatomic particles”. BBC News. 4 July 2012. Retrieved 6 July 2012. [8] Charles P. Poole, Jr. (11 March 2004). Encyclopedic Dictionary of Condensed Matter Physics. Academic Press. ISBN 978-0-08-054523-3. [9] “boson”. Merriam-Webster Online Dictionary. Retrieved 21 March 2010. [10] Carroll, Sean. “Explain it in 60 seconds: Bosons”. Symmetry Magazine. Fermilab/SLAC. Retrieved 15 February 2013. • Fermion [11] Srednicki, Mark (2007). Quantum Field Theory, Cambridge University Press, pp. 28–29, ISBN 978-0-52186449-7. 4.7 Notes [12] Sakurai, J.J. (1994). Modern Quantum Mechanics (Revised Edition), p. 362. Addison-Wesley, ISBN 0-20153929-2. [1] Even-mass-number nuclides, which comprise 152/255 = ~ 60% of all stable nuclides, are bosons, i.e. they have integer spin. Almost all (148 of the 152) are even-proton, even-neutron (EE) nuclides, which necessarily have spin 0 because of pairing. The remainder of the stable bosonic nuclides are 5 odd-proton, odd-neutron stable nuclides Chapter 5 Lepton For other uses, see Lepton (disambiguation). A lepton is an elementary, half-integer spin (spin 1 ⁄2 ) particle that does not undergo strong interactions, but is subject to the Pauli exclusion principle.[1] The best known of all leptons is the electron, which governs nearly all of chemistry as it is found in atoms and is directly tied to all chemical properties. Two main classes of leptons exist: charged leptons (also known as the electron-like leptons), and neutral leptons (better known as neutrinos). Charged leptons can combine with other particles to form various composite particles such as atoms and positronium, while neutrinos rarely interact with anything, and are consequently rarely observed. There are six types of leptons, known as flavours, forming three generations.[2] The first generation is the electronic leptons, comprising the electron (e−) and electron neutrino (ν e); the second is the muonic leptons, comprising the muon (μ−) and muon neutrino (ν μ); and the third is the tauonic leptons, comprising the tau (τ−) and the tau neutrino (ν τ). Electrons have the least mass of all the charged leptons. The heavier muons and taus will rapidly change into electrons through a process of particle decay: the transformation from a higher mass state to a lower mass state. Thus electrons are stable and the most common charged lepton in the universe, whereas muons and taus can only be produced in high energy collisions (such as those involving cosmic rays and those carried out in particle accelerators). Leptons have various intrinsic properties, including electric charge, spin, and mass. Unlike quarks however, leptons are not subject to the strong interaction, but they are subject to the other three fundamental interactions: gravitation, electromagnetism (excluding neutrinos, which are electrically neutral), and the weak interaction. For every lepton flavor there is a corresponding type of antiparticle, known as antilepton, that differs from the lepton only in that some of its properties have equal magnitude but opposite sign. However, according to certain theories, neutrinos may be their own antiparticle, but it is not currently known whether this is the case or not. The first charged lepton, the electron, was theorized in the mid-19th century by several scientists[3][4][5] and was discovered in 1897 by J. J. Thomson.[6] The next lepton to be observed was the muon, discovered by Carl D. Anderson in 1936, which was classified as a meson at the time.[7] After investigation, it was realized that the muon did not have the expected properties of a meson, but rather behaved like an electron, only with higher mass. It took until 1947 for the concept of “leptons” as a family of particle to be proposed.[8] The first neutrino, the electron neutrino, was proposed by Wolfgang Pauli in 1930 to explain certain characteristics of beta decay.[8] It was first observed in the Cowan–Reines neutrino experiment conducted by Clyde Cowan and Frederick Reines in 1956.[8][9] The muon neutrino was discovered in 1962 by Leon M. Lederman, Melvin Schwartz and Jack Steinberger,[10] and the tau discovered between 1974 and 1977 by Martin Lewis Perl and his colleagues from the Stanford Linear Accelerator Center and Lawrence Berkeley National Laboratory.[11] The tau neutrino remained elusive until July 2000, when the DONUT collaboration from Fermilab announced its discovery.[12][13] Leptons are an important part of the Standard Model. Electrons are one of the components of atoms, alongside protons and neutrons. Exotic atoms with muons and taus instead of electrons can also be synthesized, as well as lepton–antilepton particles such as positronium. 5.1 Etymology The name lepton comes from the Greek λεπτός leptós, “fine, small, thin” (neuter form: λεπτόν leptón);[14][15] the earliest attested form of the word is the Mycenaean Greek , re-po-to, written in Linear B syllabic script.[16] Lepton was first used by physicist Léon Rosenfeld in 1948:[17] Following a suggestion of Prof. C. Møller, I adopt — as a pendant to “nucleon” — the denomination “lepton” (from λεπτός, small, thin, delicate) to denote a particle of small mass. The etymology incorrectly implies that all the leptons are of small mass. When Rosenfeld named them, the 20 5.3. PROPERTIES only known leptons were electrons and muons, which are in fact of small mass — the mass of an electron (0.511 MeV/c2 )[18] and the mass of a muon (with a value of 105.7 MeV/c2 )[19] are fractions of the mass of the “heavy” proton (938.3 MeV/c2 ).[20] However, the mass of the tau (discovered in the mid 1970s) (1777 MeV/c2 )[21] is nearly twice that of the proton, and about 3,500 times that of the electron. 5.2 History 21 tween 1974 and 1977 by Martin Lewis Perl with his colleagues at the SLAC LBL group.[27] Like the electron and the muon, it too was expected to have an associated neutrino. The first evidence for tau neutrinos came from the observation of “missing” energy and momentum in tau decay, analogous to the “missing” energy and momentum in beta decay leading to the discovery of the electron neutrino. The first detection of tau neutrino interactions was announced in 2000 by the DONUT collaboration at Fermilab, making it the latest particle of the Standard Model to have been directly observed,[28] apart from the Higgs boson, which probably has been discovered in 2012. See also: Electron § Discovery, Muon § History and Tau Although all present data is consistent with three genera(particle) § History The first lepton identified was the electron, discovered tions of leptons, some particle physicists are searching for a fourth generation. The current lower limit on the mass of such a fourth charged lepton is 100.8 GeV/c2 ,[29] while its associated neutrino would have a mass of at least 45.0 GeV/c2 .[30] 5.3 Properties 5.3.1 Spin and chirality Right-handed: A muon transmutes into a muon neutrino by emitting a W− boson. The W− boson subsequently decays into an electron and an electron antineutrino. by J.J. Thomson and his team of British physicists in 1897.[22][23] Then in 1930 Wolfgang Pauli postulated the electron neutrino to preserve conservation of energy, conservation of momentum, and conservation of angular momentum in beta decay.[24] Pauli theorized that an undetected particle was carrying away the difference between the energy, momentum, and angular momentum of the initial and observed final particles. The electron neutrino was simply called the neutrino, as it was not yet known that neutrinos came in different flavours (or different “generations”). Nearly 40 years after the discovery of the electron, the muon was discovered by Carl D. Anderson in 1936. Due to its mass, it was initially categorized as a meson rather than a lepton.[25] It later became clear that the muon was much more similar to the electron than to mesons, as muons do not undergo the strong interaction, and thus the muon was reclassified: electrons, muons, and the (electron) neutrino were grouped into a new group of particles – the leptons. In 1962 Leon M. Lederman, Melvin Schwartz and Jack Steinberger showed that more than one type of neutrino exists by first detecting interactions of the muon neutrino, which earned them the 1988 Nobel Prize, although by then the different flavours of neutrino had already been theorized.[26] Left-handed: p S p S Left-handed and right-handed helicities Leptons are spin-1 ⁄2 particles. The spin-statistics theorem thus implies that they are fermions and thus that they are subject to the Pauli exclusion principle; no two leptons of the same species can be in exactly the same state at the same time. Furthermore, it means that a lepton can have only two possible spin states, namely up or down. A closely related property is chirality, which in turn is closely related to a more easily visualized property called helicity. The helicity of a particle is the direction of its spin relative to its momentum; particles with spin in the same direction as their momentum are called righthanded and otherwise they are called left-handed. When a particle is mass-less, the direction of its momentum relative to its spin is frame independent, while for massive particles it is possible to 'overtake' the particle by a Lorentz transformation flipping the helicity. Chirality is a technical property (defined through the transformation behaviour under the Poincaré group) that agrees with helicity for (approximately) massless particles and is still well defined for massive particles. In many quantum field theories—such as quantum elecThe tau was first detected in a series of experiments be- trodynamics and quantum chromodynamics—left and 22 CHAPTER 5. LEPTON right-handed fermions are identical. However in the Standard Model left-handed and right-handed fermions are treated asymmetrically. Only left-handed fermions participate in the weak interaction, while there are no righthanded neutrinos. This is an example of parity violation. In the literature left-handed fields are often denoted by a capital L subscript (e.g. e−L) and right-handed fields are denoted by a capital R subscript. 5.3.2 Electromagnetic interaction factor for the lepton. First order approximation quantum mechanics predicts that the g-factor is 2 for all leptons. However, higher order quantum effects caused by loops in Feynman diagrams introduce corrections to this value. These corrections, referred to as the anomalous magnetic dipole moment, are very sensitive to the details of a quantum field theory model and thus provide the opportunity for precision tests of the standard model. The theoretical and measured values for the electron anomalous magnetic dipole moment are within agreement within eight significant figures.[31] 5.3.3 Weak Interaction e− e− γ Lepton-photon interaction One of the most prominent properties of leptons is their electric charge, Q. The electric charge determines the strength of their electromagnetic interactions. It determines the strength of the electric field generated by the particle (see Coulomb’s law) and how strongly the particle reacts to an external electric or magnetic field (see Lorentz force). Each generation contains one lepton with Q = −e (conventionally the charge of a particle is expressed in units of the elementary charge) and one lepton with zero electric charge. The lepton with electric charge is commonly simply referred to as a 'charged lepton' while the neutral lepton is called a neutrino. For example the first generation consists of the electron e− with a negative electric charge and the electrically neutral electron neutrino ν e. In the language of quantum field theory the electromagnetic interaction of the charged leptons is expressed by the fact that the particles interact with the quantum of the electromagnetic field, the photon. The Feynman diagram of the electron-photon interaction is shown on the right. In the Standard Model the left-handed charged lepton and the left-handed neutrino are arranged in doublet (ν eL, e−L) that transforms in the spinor representation (T = 1 ⁄2 ) of the weak isospin SU(2) gauge symmetry. This means that these particles are eigenstates of the isospin projection T 3 with eigenvalues 1 ⁄2 and −1 ⁄2 respectively. In the meantime, the right-handed charged lepton transforms as a weak isospin scalar (T = 0) and thus does not participate in the weak interaction, while there is no righthanded neutrino at all. The Higgs mechanism recombines the gauge fields of the weak isospin SU(2) and the weak hypercharge U(1) symmetries to three massive vector bosons (W+, W−, Z0) mediating the weak interaction, and one massless vector boson, the photon, responsible for the electromagnetic interaction. The electric charge Q can be calculated from the isospin projection T 3 and weak hypercharge YW through the Gell-Mann–Nishijima formula, Q = T 3 + YW/2 To recover the observed electric charges for all particles the left-handed weak isospin doublet (ν eL, e−L) must thus have YW = −1, while the right-handed isospin scalar e− R must have YW = −2. The interaction of the leptons with the massive weak interaction vector bosons is shown in the figure on the left. 5.3.4 Mass In the Standard Model each lepton starts out with no intrinsic mass. The charged leptons (i.e. the electron, muon, and tau) obtain an effective mass through interacBecause leptons possess an intrinsic rotation in the form tion with the Higgs field, but the neutrinos remain massof their spin, charged leptons generate a magnetic field. less. For technical reasons the masslessness of the neuThe size of their magnetic dipole moment μ is given by, trinos implies that there is no mixing of the different generations of charged leptons as there is for quarks. This is in close agreement with current experimental Qℏ observations.[32] µ=g , 4m However, it is known from experiments – most promiwhere m is the mass of the lepton and g is the so-called g- nently from observed neutrino oscillations[33] – that neu- 5.4. UNIVERSALITY trinos do in fact have some very small mass, probably less than 2 eV/c2 .[34] This implies the existence of physics beyond the Standard Model. The currently most favoured extension is the so-called seesaw mechanism, which would explain both why the left-handed neutrinos are so light compared to the corresponding charged leptons, and why we have not yet seen any right-handed neutrinos. 5.3.5 Leptonic numbers 23 5.4 Universality The coupling of the leptons to gauge bosons are flavourindependent (i.e., the interactions between leptons and gauge bosons are the same for all leptons).[35] This property is called lepton universality and has been tested in measurements of the tau and muon lifetimes and of Z boson partial decay widths, particularly at the Stanford Linear Collider (SLC) and Large Electron-Positron Collider (LEP) experiments.[36]:241–243[37]:138 The decay rate (Γ) of muons through the process μ− → e− + ν Main article: Lepton number e+ν μ is approximately given by an expression of the form (see The members of each generation’s weak isospin doublet muon decay for more details)[35] are assigned leptonic numbers that are conserved under the Standard Model.[35] Electrons and electron neutrinos ( ) have an electronic number of Lₑ = 1, while muons and Γ µ− → e− + ν¯e + νµ = K1 G2 m5 , F µ muon neutrinos have a muonic number of Lμ = 1, while tau particles and tau neutrinos have a tauonic number of where K 1 is some constant, and GF is the Fermi coupling Lτ = 1. The antileptons have their respective generation’s constant. The decay rate of tau particles through the process τ− → e− + ν leptonic numbers of −1. e+ν Conservation of the leptonic numbers means that the τ is given by an expression of the same form[35] number of leptons of the same type remains the same, when particles interact. This implies that leptons and antileptons must be created in pairs of a single generation. Γ (τ − → e− + ν¯ + ν ) = K G2 m5 , e τ 2 F τ For example, the following processes are allowed under where K 2 is some constant. Muon–Tauon universality conservation of leptonic numbers: implies that K 1 = K 2 . On the other hand, electron–muon universality implies[35] ( ) ( ) Γ τ − → e− + ν¯e + ντ = Γ τ − → µ− + ν¯µ + ντ . Each generation forms a weak isospin doublet. e− + e+ → γ + γ, τ− + τ+ → Z0 + Z0, This explains why the branching ratios for the electronic mode (17.85%) and muonic (17.36%) mode of tau decay are equal (within error).[21] Universality also accounts for the ratio of muon and tau lifetimes. The lifetime of a lepton (τ ) is related to the decay rate by[35] but not these: τl = γ → e− + μ+, W− → e− + ν τ, B (l− → e− + ν¯e + νl ) , Γ (l− → e− + ν¯e + νl ) where B(x → y) and Γ(x → y) denotes the branching ratios and the resonance width of the process x → y. The ratio of tau and muon lifetime is thus given by[35] Z0 → μ− + τ+. However, neutrino oscillations are known to violate the conservation of the individual leptonic numbers. Such a violation is considered to be smoking gun evidence for physics beyond the Standard Model. A much stronger conservation law is the conservation of the total number of leptons (L), conserved even in the case of neutrino oscillations, but even it is still violated by a tiny amount by the chiral anomaly. ττ B (τ − → e− + ν¯e + ντ ) = τµ B (µ− → e− + ν¯e + νµ ) ( mµ mτ )5 . Using the values of the 2008 Review of Particle Physics for the branching ratios of muons[19] and tau[21] yields a lifetime ratio of ~1.29×10−7 , comparable to the measured lifetime ratio of ~1.32×10−7 . The difference is due to K 1 and K 2 not actually being constants; they depend on the mass of leptons. 24 CHAPTER 5. LEPTON 5.5 Table of leptons J.; Larsen, R.; Litke, A.; Lüke, D.; Lulu, B.; Lüth, V.; Lyon, D.; Morehouse, C.; Paterson, J.; Pierre, F.; Pun, T.; Rapidis, P.; Richter, B.; Sadoulet, B. et al. (1975). “Evidence for Anomalous Lepton Production in e+e− Annihilation”. Physical Review Letters 35 (22): 1489. Bibcode:1975PhRvL..35.1489P. doi:10.1103/PhysRevLett.35.1489. 5.6 See also • Koide formula • List of particles [12] “Physicists Find First Direct Evidence for Tau Neutrino at Fermilab” (Press release). Fermilab. 20 July 2000. • Preons – hypothetical particles which were once postulated to be subcomponents of quarks and lep- [13] K. Kodama et al. (DONUT Collaboration); Kodama; tons Ushida; Andreopoulos; Saoulidou; Tzanakos; Yager; 5.7 Notes [1] “Lepton (physics)". Encyclopædia Britannica. Retrieved 2010-09-29. [2] R. Nave. “Leptons”. HyperPhysics. Georgia State University, Department of Physics and Astronomy. Retrieved 2010-09-29. [3] W.V. Farrar (1969). “Richard Laming and the Coal-Gas Industry, with His Views on the Structure of Matter”. Annals of Science 25 (3): 243–254. doi:10.1080/00033796900200141. [4] T. Arabatzis (2006). Representing Electrons: A Biographical Approach to Theoretical Entities. University of Chicago Press. pp. 70–74. ISBN 0-226-02421-0. Baller; Boehnlein; Freeman; Lundberg; Morfin; Rameika; Yun; Song; Yoon; Chung; Berghaus; Kubantsev; Reay; Sidwell; Stanton; Yoshida; Aoki; Hara; Rhee; Ciampa; Erickson; Graham et al. (2001). “Observation of tau neutrino interactions”. Physics Letters B 504 (3): 218. arXiv:hep-ex/0012035. Bibcode:2001PhLB..504..218D. doi:10.1016/S0370-2693(01)00307-0. [14] “lepton”. Online Etymology Dictionary. [15] λεπτός. Liddell, Henry George; Scott, Robert; A Greek– English Lexicon at the Perseus Project. [16] Found on the KN L 693 and PY Un 1322 tablets. “The Linear B word re-po-to”. Palaeolexicon. Word study tool of ancient languages. Raymoure, K.A. “re-po-to”. Minoan Linear A & Mycenaean Linear B. Deaditerranean. “KN 693 L (103)". “PY 1322 Un + fr. (Cii)". DĀMOS: Database of Mycenaean at Oslo. University of Oslo. [17] L. Rosenfeld (1948) [5] J.Z. Buchwald, A. Warwick (2001). Histories of the Electron: The Birth of Microphysics. MIT Press. pp. 195–203. ISBN 0-262-52424-4. [6] J.J. Thomson (1897). “Cathode Philosophical Magazine 44 (269): doi:10.1080/14786449708621070. Rays”. 293. [18] C. Amsler et al. (2008): Particle listings – e− [19] C. Amsler et al. (2008): Particle listings – μ− [20] C. Amsler et al. (2008): Particle listings – p+ [21] C. Amsler et al. (2008): Particle listings – τ− [7] S.H. Neddermeyer, C.D. Anderson; Anderson (1937). “Note on the Nature of CosmicRay Particles”. Physical Review 51 (10): 884–886. Bibcode:1937PhRv...51..884N. doi:10.1103/PhysRev.51.884. [22] S. Weinberg (2003) [8] “The Reines-Cowan Experiments: Detecting the Poltergeist” (PDF). Los Alamos Science 25: 3. 1997. Retrieved 2010-02-10. [25] S.H. Neddermeyer, C.D. Anderson (1937) [9] F. Reines, C.L. Cowan, Jr.; Cowan (1956). “The Neutrino”. Nature 178 (4531): 446. Bibcode:1956Natur.178..446R. doi:10.1038/178446a0. [23] R. Wilson (1997) [24] K. Riesselmann (2007) [26] I.V. Anicin (2005) [27] M.L. Perl et al. (1975) [28] K. Kodama (2001) [29] C. Amsler et al. (2008) Heavy Charged Leptons Searches [10] G. Danby; Gaillard, J-M.; Goulianos, K.; Lederman, L.; Mistry, N.; Schwartz, M.; Steinberger, J. et al. (1962). “Observation of high-energy neutrino reactions and the existence of two kinds of neutrinos”. Physical Review Letters 9: 36. Bibcode:1962PhRvL...9...36D. doi:10.1103/PhysRevLett.9.36. [11] M.L. Perl; Abrams, G.; Boyarski, A.; Breidenbach, M.; Briggs, D.; Bulos, F.; Chinowsky, W.; Dakin, J.; Feldman, G.; Friedberg, C.; Fryberger, D.; Goldhaber, G.; Hanson, G.; Heile, F.; Jean-Marie, B.; Kadyk, [30] C. Amsler et al. (2008) Searches for Heavy Neutral Leptons [31] M.E. Peskin, D.V. Schroeder (1995), p. 197 [32] M.E. Peskin, D.V. Schroeder (1995), p. 27 [33] Y. Fukuda et al. (1998) [34] C.Amsler et al. (2008): Particle listings – Neutrino properties 5.9. EXTERNAL LINKS [35] B.R. Martin, G. Shaw (1992) [36] J. P. Cumalat (1993). Physics in Collision 12. Atlantica Séguier Frontières. ISBN 978-2-86332-129-4. [37] G Fraser (1 January 1998). The Particle Century. CRC Press. ISBN 978-1-4200-5033-2. [38] J. Peltoniemi, J. Sarkamo (2005) 5.8 References • C. Amsler et al. (Particle Data Group); Amsler; Doser; Antonelli; Asner; Babu; Baer; Band; Barnett; Bergren; Beringer; Bernardi; Bertl; Bichsel; Biebel; Bloch; Blucher; Blusk; Cahn; Carena; Caso; Ceccucci; Chakraborty; Chen; Chivukula; Cowan; Dahl; d'Ambrosio; Damour et al. (2008). “Review of Particle Physics”. Physics Letters B 667: 1. Bibcode:2008PhLB..667....1P. doi:10.1016/j.physletb.2008.07.018. • I.V. Anicin (2005). “The Neutrino – Its Past, Present and Future”. SFIN (Institute of Physics, Belgrade) year XV, Series A: Conferences, No. A2 (2002) 3–59: 3172. arXiv:physics/0503172. Bibcode:2005physics...3172A. • Y.Fukuda; Hayakawa, T.; Ichihara, E.; Inoue, K.; Ishihara, K.; Ishino, H.; Itow, Y.; Kajita, T. et al. (1998). “Evidence for Oscillation of Atmospheric Neutrinos”. Physical Review Letters 81 (8): 1562–1567. arXiv:hepex/9807003. Bibcode:1998PhRvL..81.1562F. doi:10.1103/PhysRevLett.81.1562. • K. Kodama; Ushida, N.; Andreopoulos, C.; Saoulidou, N.; Tzanakos, G.; Yager, P.; Baller, B.; Boehnlein, D.; Freeman, W.; Lundberg, B.; Morfin, J.; Rameika, R.; Yun, J.C.; Song, J.S.; Yoon, C.S.; Chung, S.H.; Berghaus, P.; Kubantsev, M.; Reay, N.W.; Sidwell, R.; Stanton, N.; Yoshida, S.; Aoki, S.; Hara, T.; Rhee, J.T.; Ciampa, D.; Erickson, C.; Graham, M.; Heller, K. et al. (2001). “Observation of tau neutrino interactions”. arXiv:hepPhysics Letters B 504 (3): 218. ex/0012035. Bibcode:2001PhLB..504..218D. doi:10.1016/S0370-2693(01)00307-0. • B.R. Martin, G. Shaw (1992). “Chapter 2 – Leptons, quarks and hadrons”. Particle Physics. John Wiley & Sons. pp. 23–47. ISBN 0-471-92358-3. • S.H. Neddermeyer, C.D. Anderson; Anderson (1937). “Note on the Nature of CosmicPhysical Review 51 (10): Ray Particles”. Bibcode:1937PhRv...51..884N. 884–886. doi:10.1103/PhysRev.51.884. 25 • J. Peltoniemi, J. Sarkamo (2005). “Laboratory measurements and limits for neutrino properties”. The Ultimate Neutrino Page. Retrieved 2008-11-07. • M.L. Perl; Abrams, G.; Boyarski, A.; Breidenbach, M.; Briggs, D.; Bulos, F.; Chinowsky, W.; Dakin, J. et al. (1975). “Evidence for Anomalous Lepton Production in e+ –e− Annihilation”. Physical Review Letters 35 (22): 1489–1492. Bibcode:1975PhRvL..35.1489P. doi:10.1103/PhysRevLett.35.1489. • M.E. Peskin, D.V. Schroeder (1995). Introduction to Quantum Field Theory. Westview Press. ISBN 0-201-50397-2. • K. Riesselmann (2007). “Logbook: Neutrino Invention”. Symmetry Magazine 4 (2). • L. Rosenfeld (1948). Nuclear Forces. Interscience Publishers. p. xvii. • R. Shankar (1994). “Chapter 2 – Rotational Invariance and Angular Momentum”. Principles of Quantum Mechanics (2nd ed.). Springer. pp. 305–352. ISBN 978-0-306-44790-7. • S. Weinberg (2003). The Discovery of Subatomic Particles. Cambridge University Press. ISBN 0521-82351-X. • R. Wilson (1997). Astronomy Through the Ages: The Story of the Human Attempt to Understand the Universe. CRC Press. p. 138. ISBN 0-7484-07480. 5.9 External links • Particle Data Group homepage. The PDG compiles authoritative information on particle properties. • Leptons, a summary of leptons from Hyperphysics. Chapter 6 Meson In particle physics, mesons (/ˈmiːzɒnz/ or /ˈmɛzɒnz/) are hadronic subatomic particles composed of one quark and one antiquark, bound together by the strong interaction. Because mesons are composed of sub-particles, they have a physical size, with a diameter of roughly one fermi, which is about 2 ⁄3 the size of a proton or neutron. All mesons are unstable, with the longest-lived lasting for only a few hundredths of a microsecond. Charged mesons decay (sometimes through intermediate particles) to form electrons and neutrinos. Uncharged mesons may decay to photons. Mesons are not produced by radioactive decay, but appear in nature only as short-lived products of very highenergy interactions in matter, between particles made of quarks. In cosmic ray interactions, for example, such particles are ordinary protons and neutrons. Mesons are also frequently produced artificially in high-energy particle accelerators that collide protons, anti-protons, or other particles. In nature, the importance of lighter mesons is that they are the associated quantum-field particles that transmit the nuclear force, in the same way that photons are the particles that transmit the electromagnetic force. The higher energy (more massive) mesons were created momentarily in the Big Bang, but are not thought to play a role in nature today. However, such particles are regularly created in experiments, in order to understand the nature of the heavier types of quark that compose the heavier mesons. Mesons are part of the hadron particle family, defined simply as particles composed of two quarks. The other members of the hadron family are the baryons: subatomic particles composed of three quarks rather than two. Some experiments show evidence of exotic mesons, which don't have the conventional valence quark content of one quark and one antiquark. antiquark; and its corresponding antiparticle, the negative pion (π−), is made of one up antiquark and one down quark. Because mesons are composed of quarks, they participate in both the weak and strong interactions. Mesons with net electric charge also participate in the electromagnetic interaction. They are classified according to their quark content, total angular momentum, parity and various other properties, such as C-parity and G-parity. Although no meson is stable, those of lower mass are nonetheless more stable than the most massive mesons, and are easier to observe and study in particle accelerators or in cosmic ray experiments. They are also typically less massive than baryons, meaning that they are more easily produced in experiments, and thus exhibit certain higher energy phenomena more readily than baryons composed of the same quarks would. For example, the charm quark was first seen in the J/Psi meson (J/ψ) in 1974,[1][2] and the bottom quark in the upsilon meson (ϒ) in 1977.[3] 6.1 History From theoretical considerations, in 1934 Hideki Yukawa[4][5] predicted the existence and the approximate mass of the “meson” as the carrier of the nuclear force that holds atomic nuclei together. If there were no nuclear force, all nuclei with two or more protons would fly apart because of the electromagnetic repulsion. Yukawa called his carrier particle the meson, from μέσος mesos, the Greek word for “intermediate,” because its predicted mass was between that of the electron and that of the proton, which has about 1,836 times the mass of the electron. Yukawa had originally named his particle the “mesotron”, but he was corrected by the physicist Werner Heisenberg (whose father was a professor of Greek at the University of Munich). Heisenberg pointed out that there is no “tr” in the Greek word “mesos”.[6] Because quarks have a spin of 1 ⁄2 , the difference in quarknumber between mesons and baryons results in conventional two-quark mesons being bosons, whereas baryons The first candidate for Yukawa’s meson, now known in are fermions. modern terminology as the muon, was discovered in 1936 Each type of meson has a corresponding antiparticle (anby Carl David Anderson and others in the decay products timeson) in which quarks are replaced by their correof cosmic ray interactions. The mu meson had about the sponding antiquarks and vice versa. For example, a posright mass to be Yukawa’s carrier of the strong nuclear itive pion (π+) is made of one up quark and one down force, but over the course of the next decade, it became 26 6.2. OVERVIEW 27 and S = −1 ⁄2 ). Two quarks can have their spins aligned, in which case the two spin vectors add to make a vector of length S = 1 and three spin projections (S = +1, S = 0, and S = −1), called the spin-1 triplet. If two quarks have unaligned spins, the spin vectors add up to make a vector of length S = 0 and only one spin projection (S = 0), called the spin-0 singlet. Because mesons are made of There were years of delays in the subatomic particle re- one quark and one antiquark, they can be found in triplet and singlet spin states. search during World War II in 1939–45, with most physicists working in applied projects for wartime necessi- There is another quantity of quantized angular momenties. When the war ended in August 1945, many physi- tum, called the orbital angular momentum (quantum cists gradually returned to peacetime research. The first number L), that comes in increments of 1 ħ, which repretrue meson to be discovered was what would later be sent the angular momentum due to quarks orbiting around called the "pi meson" (or pion). This discovery was made each other. The total angular momentum (quantum numin 1947, by Cecil Powell, César Lattes, and Giuseppe ber J) of a particle is therefore the combination of intrinOcchialini, who were investigating cosmic ray products sic angular momentum (spin) and orbital angular momenat the University of Bristol in England, based on pho- tum. It can take any value from J = |L − S| to J = |L + S|, tographic films placed in the Andes mountains. Some in increments of 1. mesons in these films had about the same mass as the already-known meson, yet seemed to decay into it, leading physicist Robert Marshak to hypothesize in 1947 that it was actually a new and different meson. Over the next Particle physicists are most interested in mesons with no few years, more experiments showed that the pion was orbital angular momentum (L = 0), therefore the two indeed involved in strong interactions. The pion (as a groups of mesons most studied are the S = 1; L = 0 and S virtual particle) is the primary force carrier for the nuclear = 0; L = 0, which corresponds to J = 1 and J = 0, although force in atomic nuclei. Other mesons, such as the rho they are not the only ones. It is also possible to obtain J mesons are involved in mediating this force as well, but = 1 particles from S = 0 and L = 1. How to distinguish to lesser extents. Following the discovery of the pion, between the S = 1, L = 0 and S = 0, L = 1 mesons is an Yukawa was awarded the 1949 Nobel Prize in Physics active area of research in meson spectroscopy. for his predictions. evident that it was not the right particle. It was eventually found that the “mu meson” did not participate in the strong nuclear interaction at all, but rather behaved like a heavy version of the electron, and was eventually classed as a lepton like the electron, rather than a meson. Physicists in making this choice decided that properties other than particle mass should control their classification. The word meson has at times been used to mean any force carrier, such as the "Z0 meson", which is involved in me- 6.2.2 Parity diating the weak interaction.[7] However, this spurious usage has fallen out of favor. Mesons are now defined as Main article: Parity (physics) particles composed of pairs of quarks and antiquarks. If the universe were reflected in a mirror, most of the laws of physics would be identical—things would behave the 6.2 Overview same way regardless of what we call “left” and what we call “right”. This concept of mirror reflection is called 6.2.1 Spin, orbital angular momentum, parity (P). Gravity, the electromagnetic force, and the strong interaction all behave in the same way regardless and total angular momentum of whether or not the universe is reflected in a mirror, and thus are said to conserve parity (P-symmetry). However, Main articles: Spin (physics), angular momentum opera- the weak interaction does distinguish “left” from “right”, tor, Total angular momentum and Quantum numbers a phenomenon called parity violation (P-violation). Based on this, one might think that, if the wavefunction for each particle (more precisely, the quantum field for each particle type) were simultaneously mirror-reversed, then the new set of wavefunctions would perfectly satisfy the laws of physics (apart from the weak interaction). It turns out that this is not quite true: In order for the equations to be satisfied, the wavefunctions of certain types of particles have to be multiplied by −1, in addition to beQuarks are fermions—specifically in this case, particles ing mirror-reversed. Such particle types are said to have having spin 1 ⁄2 (S = 1 ⁄2 ). Because spin projections vary in negative or odd parity (P = −1, or alternatively P = –), increments of 1 (that is 1 ħ), a single quark has a spin vec- whereas the other particles are said to have positive or tor of length 1 ⁄2 , and has two spin projections (S = +1 ⁄2 even parity (P = +1, or alternatively P = +). Spin (quantum number S) is a vector quantity that represents the “intrinsic” angular momentum of a particle. It comes in increments of 1 ⁄2 ħ. The ħ is often dropped because it is the “fundamental” unit of spin, and it is implied that “spin 1” means “spin 1 ħ". (In some systems of natural units, ħ is chosen to be 1, and therefore does not appear in equations). 28 CHAPTER 6. MESON For mesons, the parity is related to the orbital angular momentum by the relation:[8] L+1 P = (−1) |q1 q¯2 ⟩ = |q¯1 q2 ⟩ then, the meson is “G even” (G = +1). On the other hand, if where the L is a result of the parity of the corresponding spherical harmonic of the wavefunction. The '+1' in the exponent comes from the fact that, according to the Dirac |q1 q¯2 ⟩ = −|q¯1 q2 ⟩ equation, a quark and an antiquark have opposite intrinsic parities. Therefore, the intrinsic parity of a meson is then the meson is “G odd” (G = −1). the product of the intrinsic parities of the quark (+1) and antiquark (−1). As these are different, their product is 6.2.5 Isospin and charge −1, and so it contributes a +1 in the exponent. As a consequence, mesons with no orbital angular mo- Main article: Isospin The concept of isospin was first proposed by Werner mentum (L = 0) all have odd parity (P = −1). 6.2.3 C-parity Main article: C-parity C-parity is only defined for mesons that are their own antiparticle (i.e. neutral mesons). It represents whether or not the wavefunction of the meson remains the same under the interchange of their quark with their antiquark.[9] If |q q¯⟩ = |¯ q q⟩ Combinations of one u, d or s quarks and one u, d, or s antiquark then, the meson is “C even” (C = +1). On the other hand, in JP = 0− configuration form a nonet. if |q q¯⟩ = −|¯ q q⟩ then the meson is “C odd” (C = −1). C-parity rarely is studied on its own, but more commonly in combination with P-parity into CP-parity. CP-parity was thought to be conserved, but was later found to be violated in weak interactions.[10][11][12] 6.2.4 G-parity Main article: G-parity G parity is a generalization of the C-parity. Instead of simply comparing the wavefunction after exchanging quarks and antiquarks, it compares the wavefunction after exchanging the meson for the corresponding antimeson, regardless of quark content.[13] In the case of neutral meson, G-parity is equivalent to C-parity because neutral mesons are their own antiparticles. If Combinations of one u, d or s quarks and one u, d, or s antiquark in JP = 1− configuration also form a nonet. Heisenberg in 1932 to explain the similarities between protons and neutrons under the strong interaction.[14] Although they had different electric charges, their masses were so similar that physicists believed that they were actually the same particle. The different electric charges were explained as being the result of some unknown excitation similar to spin. This unknown excitation was later 6.3. CLASSIFICATION dubbed isospin by Eugene Wigner in 1937.[15] When the first mesons were discovered, they too were seen through the eyes of isospin and so the three pions were believed to be the same particle, but in different isospin states. 29 cle mass. The higher the mass, the lower the strangeness (the more s quarks). Particles could be described with isospin projections (related to charge) and strangeness (mass) (see the uds nonet figures). As other quarks were discovered, new quantum numbers were made to have similar description of udc and udb nonets. Because only the u and d mass are similar, this description of particle mass and charge in terms of isospin and flavour quantum numbers only works well for the nonets made of one u, one d and one other quark and breaks down for the other nonets (for example ucb nonet). If the quarks all had the same mass, their behaviour would be called symmetric, because they would all behave in exactly the same way with respect to the strong interaction. However, as quarks do not have the same mass, they do not interact in the same way (exactly like an electron placed in an electric field will accelerate more than a proton placed in the same field because of its lighter mass), and the symmetry is said to be broken. This belief lasted until Murray Gell-Mann proposed the quark model in 1964 (containing originally only the u, d, and s quarks).[16] The success of the isospin model is now understood to be the result of the similar masses of the u and d quarks. Because the u and d quarks have similar masses, particles made of the same number of them also have similar masses. The exact specific u and d quark composition determines the charge, because u quarks carry charge +2 ⁄3 whereas d quarks carry charge −1 ⁄3 . For example the three pions all have different charges (π+ (ud), π0 (a quantum superposition of uu and dd states), π− (du)), but have similar masses (~140 MeV/c2 ) as they are each made of a same number of total of up and down quarks and antiquarks. Under the isospin model, they were considered to be a single particle in different charged states. It was noted that charge (Q) was related to the isospin The mathematics of isospin was modeled after that of projection (I 3 ), the baryon number (B) and flavour quan(S, C, B′, T) by the Gell-Mann–Nishijima spin. Isospin projections varied in increments of 1 just tum numbers [17] formula: like those of spin, and to each projection was associated a "charged state". Because the “pion particle” had three “charged states”, it was said to be of isospin I = 1. Its “charged states” π+, π0, and π−, corresponded to the isospin projections I 3 = +1, I 3 = 0, and I 3 = −1 respectively. Another example is the "rho particle", also with three charged states. Its “charged states” ρ+, ρ0, and ρ−, corresponded to the isospin projections I 3 = +1, I 3 = 0, and I 3 = −1 respectively. It was later noted that the isospin projections were related to the up and down quark content of particles by the relation I3 = 1 [(nu − nu¯ ) − (nd − nd¯)], 2 1 Q = I3 + (B + S + C + B ′ + T ), 2 where S, C, B′, and T represent the strangeness, charm, bottomness and topness flavour quantum numbers respectively. They are related to the number of strange, charm, bottom, and top quarks and antiquark according to the relations: S = −(ns − ns¯) C = +(nc − nc¯) where the n's are the number of up and down quarks and B ′ = −(nb − n¯b ) antiquarks. In the “isospin picture”, the three pions and three rhos T = +(nt − nt¯), were thought to be the different states of two particles. However, in the quark model, the rhos are excited states of pions. Isospin, although conveying an inaccurate picture of things, is still used to classify hadrons, leading to unnatural and often confusing nomenclature. Because mesons are hadrons, the isospin classification is also used, with I 3 = +1 ⁄2 for up quarks and down antiquarks, and I 3 = −1 ⁄2 for up antiquarks and down quarks. 6.2.6 Flavour quantum numbers meaning that the Gell-Mann–Nishijima formula is equivalent to the expression of charge in terms of quark content: Q= 2 1 [(nu −nu¯ )+(nc −nc¯)+(nt −nt¯)]− [(nd −nd¯)+(ns −ns¯)+(nb −n¯b 3 3 6.3 Classification Mesons are classified into groups according to their Main article: Flavour (particle physics) § Flavour isospin (I), total angular momentum (J), parity (P), Gquantum numbers parity (G) or C-parity (C) when applicable, and quark (q) content. The rules for classification are defined by the The strangeness quantum number S (not to be confused Particle Data Group, and are rather convoluted.[18] The with spin) was noticed to go up and down along with parti- rules are presented below, in table form for simplicity. 30 CHAPTER 6. MESON 6.3.1 6.4 Exotic mesons Types of meson Mesons are classified into types according to their spin Main article: Exotic meson configurations. Some specific configurations are given special names based on the mathematical properties of There is experimental evidence for particles that are their spin configuration. hadrons (i.e., are composed of quarks) and are colorneutral with zero baryon number, and thus by conventional definition are mesons. Yet, these particles do not consist of a single quark-antiquark pair, as all the other conventional mesons discussed above do. A tentative cat6.3.2 Nomenclature egory for these particles is exotic mesons. Flavourless mesons There are at least five exotic meson resonances that have Flavourless mesons are mesons made of pair of quark and antiquarks of the same flavour (all their flavour quantum numbers are zero: S = 0, C = 0, B′ = 0, T = 0).[20] The rules for flavourless mesons are:[18] † ^ The C parity is only relevant to neutral mesons. †† ^ For J PC =1−− , the ψ is called the J/ψ been experimentally confirmed to exist by two or more independent experiments. The most statistically significant of these is the Z(4430), discovered by the Belle experiment in 2007 and confirmed by LHCb in 2014. It is a candidate for being a tetraquark: a particle composed of two quarks and two antiquarks.[21] See the main article above for other particle resonances that are candidates for being exotic mesons. In addition: • When the spectroscopic state of the meson is known, it is added in parentheses. 6.5 List Main article: List of mesons • When the spectroscopic state is unknown, mass (in MeV/c2 ) is added in parentheses. • When the meson is in its ground state, nothing is added in parentheses. 6.6 See also • Standard Model Flavoured mesons Flavoured mesons are mesons made of pair of quark and antiquarks of different flavours. The rules are simpler in this case: the main symbol depends on the heavier quark, the superscript depends on the charge, and the subscript (if any) depends on the lighter quark. In table form, they are:[18] 6.7 Notes [1] J.J. Aubert et al. (1974) [2] J.E. Augustin et al. (1974) [3] S.W. Herb et al. (1977) [4] The Noble Foundation (1949) Nobel Prize in Physics 1949 – Presentation Speech In addition: [5] H. Yukawa (1935) • If J is in the “normal series” (i.e., J = 0 , 1 , 2 , 3− , ...), a superscript ∗ is added. P P + − + • If the meson is not pseudoscalar (J P = 0− ) or vector (J P = 1− ), J is added as a subscript. • When the spectroscopic state of the meson is known, it is added in parentheses. • When the spectroscopic state is unknown, mass (in MeV/c2 ) is added in parentheses. • When the meson is in its ground state, nothing is added in parentheses. [6] G. Gamow (1961) [7] J. Steinberger (1998) [8] C. Amsler et al. (2008): Quark Model [9] M.S. Sozzi (2008b) [10] J.W. Cronin (1980) [11] V.L. Fitch (1980) [12] M.S. Sozzi (2008c) [13] K. Gottfried, V.F. Weisskopf (1986) 6.8. REFERENCES [14] W. Heisenberg (1932) [15] E. Wigner (1937) [16] M. Gell-Mann (1964) [17] S.S.M Wong (1998) [18] C. Amsler et al. (2008): Naming scheme for hadrons [19] W.E. Burcham, M. Jobes (1995) [20] For the purpose of nomenclature, the isospin projection I 3 isn't considered a flavour quantum number. This means that the charged pion-like mesons (π± , a± , b± , and ρ± mesons) follow the rules of flavourless mesons, even if they aren't truly “flavourless”. [21] LHCb collaborators (2014): Observation of the resonant character of the Z(4430)− state 6.8 References • M.S. Sozzi (2008a). “Parity”. Discrete Symmetries and CP Violation: From Experiment to Theory. Oxford University Press. pp. 15–87. ISBN 0-19929666-9. • M.S. Sozzi (2008b). “Charge Conjugation”. Discrete Symmetries and CP Violation: From Experiment to Theory. Oxford University Press. pp. 88– 120. ISBN 0-19-929666-9. • M.S. Sozzi (2008c). “CP-Symmetry”. Discrete Symmetries and CP Violation: From Experiment to Theory. Oxford University Press. pp. 231–275. ISBN 0-19-929666-9. • C. Amsler et al. (Particle Data Group) (2008). “Review of Particle Physics”. Physics Letters B 667 (1): 1–1340. Bibcode:2008PhLB..667....1P. doi:10.1016/j.physletb.2008.07.018. • S.S.M. Wong (1998). “Nucleon Structure”. Introductory Nuclear Physics (2nd ed.). New York (NY): John Wiley & Sons. pp. 21–56. ISBN 0-47123973-9. • W.E. Burcham, M. Jobes (1995). Nuclear and Particle Physics (2nd ed.). Longman Publishing. ISBN 0-582-45088-8. • R. Shankar (1994). Principles of Quantum Mechanics (2nd ed.). New York (NY): Plenum Press. ISBN 0-306-44790-8. • J. Steinberger (1989). “Experiments with highenergy neutrino beams”. Reviews of Modern Physics 61 (3): 533–545. Bibcode:1989RvMP...61..533S. doi:10.1103/RevModPhys.61.533. 31 • K. Gottfried, V.F. Weisskopf (1986). “Hadronic Spectroscopy: G-parity”. Concepts of Particle Physics 2. Oxford University Press. pp. 303–311. ISBN 0-19-503393-0. • J.W. Cronin (1980). “CP Symmetry Violation— The Search for its origin” (PDF). The Nobel Foundation. • V.L. Fitch (1980). “The Discovery of Charge— Conjugation Parity Asymmetry” (PDF). The Nobel Foundation. • S.W. Herb; Hom, D.; Lederman, L.; Sens, J.; Snyder, H.; Yoh, J.; Appel, J.; Brown, B. et al. (1977). “Observation of a Dimuon Resonance at 9.5 Gev in 400-GeV Proton-Nucleus Collisions”. Physical Review Letters 39 (5): 252–255. Bibcode:1977PhRvL..39..252H. doi:10.1103/PhysRevLett.39.252. • J.J. Aubert; Becker, U.; Biggs, P.; Burger, J.; Chen, M.; Everhart, G.; Goldhagen, P.; Leong, J. et al. (1974). “Experimental Observation of a Heavy Particle J". Physical Review Letters 33 (23): 1404–1406. Bibcode:1974PhRvL..33.1404A. doi:10.1103/PhysRevLett.33.1404. • J.E. Augustin; Boyarski, A.; Breidenbach, M.; Bulos, F.; Dakin, J.; Feldman, G.; Fischer, G.; Fryberger, D. et al. (1974). “Discovery of a Narrow Resonance in e+ e− Annihilation”. Physical Review Letters 33 (23): 1406–1408. Bibcode:1974PhRvL..33.1406A. doi:10.1103/PhysRevLett.33.1406. • M. Gell-Mann (1964). “A Schematic of Baryons and Mesons”. Physics Letters 8 (3): 214–215. Bibcode:1964PhL.....8..214G. doi:10.1016/S00319163(64)92001-3. • Ishfaq Ahmad (1965). “the Interactions of 200 MeV π± -Mesons with Complex Nuclei Proposal to Study the Interactions of 200 MeV π± -Mesons with Complex Nuclei” (PDF). CERN documents 3 (5). • G. Gamow (1988) [1961]. The Great Physicists from Galileo to Einstein (Reprint ed.). Dover Publications. p. 315. ISBN 978-0-486-25767-9. • E. Wigner (1937). “On the Consequences of the Symmetry of the Nuclear Hamiltonian on the Spectroscopy of Nuclei”. Physical Review 51 (2): 106–119. Bibcode:1937PhRv...51..106W. doi:10.1103/PhysRev.51.106. • H. Yukawa (1935). “On the Interaction of Elementary Particles” (PDF). Proc. Phys. Math. Soc. Jap. 17 (48). 32 CHAPTER 6. MESON • W. Heisenberg (1932). "Über den Bau der Atomkerne I”. Zeitschrift für Physik (in German) 77: 1–11. Bibcode:1932ZPhy...77....1H. doi:10.1007/BF01342433. • W. Heisenberg (1932). "Über den Bau der Atomkerne II”. Zeitschrift für Physik (in German) 78 (3–4): 156–164. Bibcode:1932ZPhy...78..156H. doi:10.1007/BF01337585. • W. Heisenberg (1932). "Über den Bau der Atomkerne III”. Zeitschrift für Physik (in German) 80 (9–10): 587–596. Bibcode:1933ZPhy...80..587H. doi:10.1007/BF01335696. 6.9 External links • A table of some mesons and their properties • Particle Data Group—Compiles authoritative information on particle properties • hep-ph/0211411: The light scalar mesons within quark models • Naming scheme for hadrons (a PDF file) • Mesons made thinkable, an interactive visualisation allowing physical properties to be compared 6.9.1 Recent findings • What Happened to the Antimatter? Fermilab’s DZero Experiment Finds Clues in Quick-Change Meson • CDF experiment’s definitive observation of matterantimatter oscillations in the Bs meson Chapter 7 Photon This article is about the elementary particle of light. For consequence of physical laws having a certain symmetry other uses, see Photon (disambiguation). at every point in spacetime. The intrinsic properties of particles, such as charge, mass and spin, are determined A photon is an elementary particle, the quantum of light by the properties of this gauge symmetry. The photon and all other forms of electromagnetic radiation. It is concept has led to momentous advances in experimenthe force carrier for the electromagnetic force, even when tal and theoretical physics, such as lasers, Bose–Einstein static via virtual photons. The effects of this force are eas- condensation, quantum field theory, and the probabilistic ily observable at the microscopic and at the macroscopic interpretation of quantum mechanics. It has been aplevel, because the photon has zero rest mass; this allows plied to photochemistry, high-resolution microscopy, and long distance interactions. Like all elementary particles, measurements of molecular distances. Recently, photons photons are currently best explained by quantum mechan- have been studied as elements of quantum computers and ics and exhibit wave–particle duality, exhibiting proper- for applications in optical imaging and optical communities of waves and of particles. For example, a single pho- cation such as quantum cryptography. ton may be refracted by a lens or exhibit wave interference with itself, but also act as a particle giving a definite result when its position is measured. The modern photon concept was developed gradually by Albert Einstein in the first years of the 20th century to explain experimental observations that did not fit the classical wave model of light. In particular, the photon model accounted for the frequency dependence of light’s energy, and explained the ability of matter and radiation to be in thermal equilibrium. It also accounted for anomalous observations, including the properties of black-body radiation, that other physicists, most notably Max Planck, had sought to explain using semiclassical models, in which light is still described by Maxwell’s equations, but the material objects that emit and absorb light do so in amounts of energy that are quantized (i.e., they change energy only by certain particular discrete amounts and cannot change energy in any arbitrary way). Although these semiclassical models contributed to the development of quantum mechanics, many further experiments[2][3] starting with Compton scattering of single photons by electrons, first observed in 1923, validated Einstein’s hypothesis that light itself is quantized. In 1926 the optical physicist Frithiof Wolfers and the chemist Gilbert N. Lewis coined the name photon for these particles, and after 1927, when Arthur H. Compton won the Nobel Prize for his scattering studies, most scientists accepted the validity that quanta of light have an independent existence, and the term photon for light quanta was accepted. 7.1 Nomenclature In 1900, the German physicist Max Planck was working on black-body radiation and suggested that the energy in electromagnetic waves could only be released in “packets” of energy. In his 1901 article [4] in Annalen der Physik he called these packets “energy elements”. The word quanta (singular quantum) was used even before 1900 to mean particles or amounts of different quantities, including electricity. Later, in 1905, Albert Einstein went further by suggesting that electromagnetic waves could only exist in these discrete wave-packets.[5] He called such a wave-packet the light quantum (German: das Lichtquant).[Note 1] The name photon derives from the Greek word for light, φῶς (transliterated phôs). Arthur Compton used photon in 1928, referring to Gilbert N. Lewis.[6] The same name was used earlier, by the American physicist and psychologist Leonard T. Troland, who coined the word in 1916, in 1921 by the Irish physicist John Joly, in 1924 by the French physiologist René Wurmser (1890-1993) and in 1926 by the French physicist Frithiof Wolfers (1891-1971).[7] The name was suggested initially as a unit related to the illumination of the eye and the resulting sensation of light and was used later on in a physiological context. Although Wolfers’s and Lewis’s theories were never accepted, as they were contradicted by many experiments, the new name was In the Standard Model of particle physics, photons and adopted very soon by most physicists after Compton used other elementary particles are described as a necessary it.[7][Note 2] 33 34 CHAPTER 7. PHOTON In physics, a photon is usually denoted by the symbol γ (the Greek letter gamma). This symbol for the photon probably derives from gamma rays, which were discovered in 1900 by Paul Villard,[8][9] named by Ernest Rutherford in 1903, and shown to be a form of electromagnetic radiation in 1914 by Rutherford and Edward Andrade.[10] In chemistry and optical engineering, photons are usually symbolized by hν, the energy of a photon, where h is Planck’s constant and the Greek letter ν (nu) is the photon’s frequency. Much less commonly, the photon can be symbolized by hf, where its frequency is denoted by f. 7.2 Physical properties See also: Special relativity and Photonic molecule A photon is massless,[Note 3] has no electric charge,[11] Time vector or as a (relativistic) four-vector; in the latter case it belongs to the light cone (pictured). Different signs of the four-vector denote different circular polarizations, but in the 3-vector representation one should account for the polarization state separately; it actually is a spin quantum number. In both cases the space of possible wave vectors is three-dimensional. The photon is the gauge boson for electromagnetism,[12]:29-30 and therefore all other quantum numbers of the photon (such as lepton number, baryon number, and flavour quantum numbers) are zero.[13] Also, the photon does not obey the Pauli exclusion principle.[14]:1221 Photons are emitted in many natural processes. For example, when a charge is accelerated it emits synchrotron radiation. During a molecular, atomic or nuclear transition to a lower energy level, photons of various energy will be emitted, from radio waves to gamma rays. A photon can also be emitted when a particle and its corresponding antiparticle are annihilated (for example, electron– positron annihilation).[14]:572, 1114, 1172 In empty space, the photon moves at c (the speed of light) and its energy and momentum are related by E = pc, where p is the magnitude of the momentum vector p. This derives from the following relativistic relation, with m = 0:[15] E 2 = p2 c2 + m2 c4 . The energy and momentum of a photon depend only on its frequency (ν) or inversely, its wavelength (λ): Space E = ℏω = hν = hc λ p = ℏk, where k is the wave vector (where the wave number k = |k| = 2π/λ), ω = 2πν is the angular frequency, and ħ = h/2π is the reduced Planck constant.[16] Since p points in the direction of the photon’s propagation, the magnitude of the momentum is The cone shows possible values of wave 4-vector of a photon. The “time” axis gives the angular frequency (rad s−1 ) and the “space” axes represent the angular wavenumber (rad m−1 ). Green and indigo represent left and right polarization p = ℏk = h hν = . c λ The photon also carries spin angular momentum that does not depend on its frequency.[17] The magnitude of its spin √ is 2ℏ and the component measured along its direction of motion, its helicity, must be ±ħ. These two possible helicities, called right-handed and left-handed, correspond to the two possible circular polarization states of the photon.[18] and is stable. A photon has two possible polarization states. In the momentum representation, which is preferred in quantum field theory, a photon is described by its wave vector, which determines its wavelength λ and its direction of propagation. A photon’s wave vector may To illustrate the significance of these formulae, the annot be zero and can be represented either as a spatial 3- nihilation of a particle with its antiparticle in free space 7.3. HISTORICAL DEVELOPMENT must result in the creation of at least two photons for the following reason. In the center of momentum frame, the colliding antiparticles have no net momentum, whereas a single photon always has momentum (since it is determined, as we have seen, only by the photon’s frequency or wavelength—which cannot be zero). Hence, conservation of momentum (or equivalently, translational invariance) requires that at least two photons are created, with zero net momentum. (However, it is possible if the system interacts with another particle or field for annihilation to produce one photon, as when a positron annihilates with a bound atomic electron, it is possible for only one photon to be emitted, as the nuclear Coulomb field breaks translational symmetry.)[19]:64-65 The energy of the two photons, or, equivalently, their frequency, may be determined from conservation of four-momentum. Seen another way, the photon can be considered as its own antiparticle. The reverse process, pair production, is the dominant mechanism by which high-energy photons such as gamma rays lose energy while passing through matter.[20] That process is the reverse of “annihilation to one photon” allowed in the electric field of an atomic nucleus. 35 Sharper upper limits have been obtained in experiments designed to detect effects caused by the galactic vector potential. Although the galactic vector potential is very large because the galactic magnetic field exists on very long length scales, only the magnetic field is observable if the photon is massless. In case of a massive photon, the mass term 12 m2 Aµ Aµ would affect the galactic plasma. The fact that no such effects are seen implies an upper bound on the photon mass of m < 3×10−27 eV/c2 .[25] The galactic vector potential can also be probed directly by measuring the torque exerted on a magnetized ring.[26] Such methods were used to obtain the sharper upper limit of 10−18 eV/c2 (the equivalent of 1.07×10−27 atomic mass units) given by the Particle Data Group.[27] These sharp limits from the non-observation of the effects caused by the galactic vector potential have been shown to be model dependent.[28] If the photon mass is generated via the Higgs mechanism then the upper limit of m≲10−14 eV/c2 from the test of Coulomb’s law is valid. Photons inside superconductors do develop a nonzero effective rest mass; as a result, electromagnetic forces become short-range inside superconductors.[29] The classical formulae for the energy and momentum of See also: Supernova/Acceleration Probe electromagnetic radiation can be re-expressed in terms of photon events. For example, the pressure of electromagnetic radiation on an object derives from the transfer of photon momentum per unit time and unit area to that ob- 7.3 Historical development ject, since pressure is force per unit area and force is the change in momentum per unit time.[21] Main article: Light In most theories up to the eighteenth century, light 7.2.1 Experimental checks on photon mass Current commonly accepted physical theories imply or assume the photon to be strictly massless, but this should be also checked experimentally. If the photon is not a strictly massless particle, it would not move at the exact speed of light in vacuum, c. Its speed would be lower and depend on its frequency. Relativity would be unaffected by this; the so-called speed of light, c, would then not be the actual speed at which light moves, but a constant of nature which is the maximum speed that any object could Thomas Young's double-slit experiment in 1801 showed that light theoretically attain in space-time.[22] Thus, it would still can act as a wave, helping to invalidate early particle theories of be the speed of space-time ripples (gravitational waves light.[14]:964 and gravitons), but it would not be the speed of photons. If a photon did have non-zero mass, there would be other effects as well. Coulomb’s law would be modified and the electromagnetic field would have an extra physical degree of freedom. These effects yield more sensitive experimental probes of the photon mass than the frequency dependence of the speed of light. If Coulomb’s law is not exactly valid, then that would cause the presence of an electric field inside a hollow conductor when it is subjected to an external electric field. This thus allows one to test Coulomb’s law to very high precision.[23] A null result of such an experiment has set a limit of m ≲ 10−14 eV/c2 .[24] was pictured as being made up of particles. Since particle models cannot easily account for the refraction, diffraction and birefringence of light, wave theories of light were proposed by René Descartes (1637),[30] Robert Hooke (1665),[31] and Christiaan Huygens (1678);[32] however, particle models remained dominant, chiefly due to the influence of Isaac Newton.[33] In the early nineteenth century, Thomas Young and August Fresnel clearly demonstrated the interference and diffraction of light and by 1850 wave models were generally accepted.[34] In 1865, James Clerk Maxwell's prediction[35] that light was an electromagnetic wave— 36 CHAPTER 7. PHOTON which was confirmed experimentally in 1888 by Heinrich validity of Maxwell’s theory, Einstein pointed out that Hertz's detection of radio waves[36] —seemed to be the fi- many anomalous experiments could be explained if the nal blow to particle models of light. energy of a Maxwellian light wave were localized into point-like quanta that move independently of one another, even if the wave itself is spread continuously over Light wave λ = wave length space.[5] In 1909[40] and 1916,[42] Einstein showed that, λ if Planck’s law of black-body radiation is accepted, the E = amplitude of electric field energy quanta must also carry momentum p = h/λ, makE M M = amplitude of ing them full-fledged particles. This photon momentum magnetic field was observed experimentally[43] by Arthur Compton, for which he received the Nobel Prize in 1927. The pivotal question was then: how to unify Maxwell’s wave theory distance of light with its experimentally observed particle nature? The answer to this question occupied Albert Einstein for the rest of his life,[44] and was solved in quantum elecIn 1900, Maxwell’s theoretical model of light as oscillating electric and magnetic fields seemed complete. However, sev- trodynamics and its successor, the Standard Model (see eral observations could not be explained by any wave model of Second quantization and The photon as a gauge boson, electromagnetic radiation, leading to the idea that light-energy below). was packaged into quanta described by E=hν. Later experiments showed that these light-quanta also carry momentum and, thus, can be considered particles: the photon concept was born, leading to a deeper understanding of the electric and magnetic fields themselves. The Maxwell wave theory, however, does not account for all properties of light. The Maxwell theory predicts that the energy of a light wave depends only on its intensity, not on its frequency; nevertheless, several independent types of experiments show that the energy imparted by light to atoms depends only on the light’s frequency, not on its intensity. For example, some chemical reactions are provoked only by light of frequency higher than a certain threshold; light of frequency lower than the threshold, no matter how intense, does not initiate the reaction. Similarly, electrons can be ejected from a metal plate by shining light of sufficiently high frequency on it (the photoelectric effect); the energy of the ejected electron is related only to the light’s frequency, not to its intensity.[37][Note 4] At the same time, investigations of blackbody radiation carried out over four decades (1860–1900) by various researchers[38] culminated in Max Planck's hypothesis[4][39] that the energy of any system that absorbs or emits electromagnetic radiation of frequency ν is an integer multiple of an energy quantum E = hν. As shown by Albert Einstein,[5][40] some form of energy quantization must be assumed to account for the thermal equilibrium observed between matter and electromagnetic radiation; for this explanation of the photoelectric effect, Einstein received the 1921 Nobel Prize in physics.[41] Since the Maxwell theory of light allows for all possible energies of electromagnetic radiation, most physicists assumed initially that the energy quantization resulted from some unknown constraint on the matter that absorbs or emits the radiation. In 1905, Einstein was the first to propose that energy quantization was a property of electromagnetic radiation itself.[5] Although he accepted the 7.4 Einstein’s light quantum Unlike Planck, Einstein entertained the possibility that there might be actual physical quanta of light—what we now call photons. He noticed that a light quantum with energy proportional to its frequency would explain a number of troubling puzzles and paradoxes, including an unpublished law by Stokes, the ultraviolet catastrophe, and of course the photoelectric effect. Stokes’s law said simply that the frequency of fluorescent light cannot be greater than the frequency of the light (usually ultraviolet) inducing it. Einstein eliminated the ultraviolet catastrophe by imagining a gas of photons behaving like a gas of electrons that he had previously considered. He was advised by a colleague to be careful how he wrote up this paper, in order to not challenge Planck too directly, as he was a powerful figure, and indeed the warning was justified, as Planck never forgave him for writing it.[45] 7.5 Early objections Einstein’s 1905 predictions were verified experimentally in several ways in the first two decades of the 20th century, as recounted in Robert Millikan's Nobel lecture.[46] However, before Compton’s experiment[43] showing that photons carried momentum proportional to their wave number (or frequency) (1922), most physicists were reluctant to believe that electromagnetic radiation itself might be particulate. (See, for example, the Nobel lectures of Wien,[38] Planck[39] and Millikan.[46] ) Instead, there was a widespread belief that energy quantization resulted from some unknown constraint on the matter that absorbs or emits radiation. Attitudes changed over time. In part, the change can be traced to experiments such as Compton scattering, where it was much more difficult not to ascribe quantization to light itself to explain the ob- 7.6. WAVE–PARTICLE DUALITY AND UNCERTAINTY PRINCIPLES 37 by the 1970s, this evidence could not be considered as absolutely definitive; since it relied on the interaction of light with matter, a sufficiently complicated theory of matter could in principle account for the evidence. Nevertheless, all semiclassical theories were refuted definitively in the 1970s and 1980s by photoncorrelation experiments.[Note 5] Hence, Einstein’s hypothesis that quantization is a property of light itself is considered to be proven. 7.6 Wave–particle duality and uncertainty principles Up to 1923, most physicists were reluctant to accept that light itself was quantized. Instead, they tried to explain photon behavior by quantizing only matter, as in the Bohr model of the hydrogen atom (shown here). Even though these semiclassical models were only a first approximation, they were accurate for simple systems and they led to quantum mechanics. served results.[47] Even after Compton’s experiment, Niels Bohr, Hendrik Kramers and John Slater made one last attempt to preserve the Maxwellian continuous electromagnetic field model of light, the so-called BKS model.[48] To account for the data then available, two drastic hypotheses had to be made: 1. Energy and momentum are conserved only on the average in interactions between matter and radiation, not in elementary processes such as absorption and emission. This allows one to reconcile the discontinuously changing energy of the atom (jump between energy states) with the continuous release of energy into radiation. 2. Causality is abandoned. For example, spontaneous emissions are merely emissions induced by a “virtual” electromagnetic field. However, refined Compton experiments showed that energy–momentum is conserved extraordinarily well in elementary processes; and also that the jolting of the electron and the generation of a new photon in Compton scattering obey causality to within 10 ps. Accordingly, Bohr and his co-workers gave their model “as honorable a funeral as possible”.[44] Nevertheless, the failures of the BKS model inspired Werner Heisenberg in his development of matrix mechanics.[49] A few physicists persisted[50] in developing semiclassical models in which electromagnetic radiation is not quantized, but matter appears to obey the laws of quantum mechanics. Although the evidence for photons from chemical and physical experiments was overwhelming See also: Wave–particle duality, Squeezed coherent state, Uncertainty principle and De Broglie–Bohm theory Photons, like all quantum objects, exhibit wave-like and particle-like properties. Their dual wave–particle nature can be difficult to visualize. The photon displays clearly wave-like phenomena such as diffraction and interference on the length scale of its wavelength. For example, a single photon passing through a double-slit experiment lands on the screen exhibiting interference phenomena but only if no measure was made on the actual slit being run across. To account for the particle interpretation that phenomenon is called probability distribution but behaves according to Maxwell’s equations.[51] However, experiments confirm that the photon is not a short pulse of electromagnetic radiation; it does not spread out as it propagates, nor does it divide when it encounters a beam splitter.[52] Rather, the photon seems to be a point-like particle since it is absorbed or emitted as a whole by arbitrarily small systems, systems much smaller than its wavelength, such as an atomic nucleus (≈10−15 m across) or even the point-like electron. Nevertheless, the photon is not a point-like particle whose trajectory is shaped probabilistically by the electromagnetic field, as conceived by Einstein and others; that hypothesis was also refuted by the photon-correlation experiments cited above. According to our present understanding, the electromagnetic field itself is produced by photons, which in turn result from a local gauge symmetry and the laws of quantum field theory (see the Second quantization and Gauge boson sections below). A key element of quantum mechanics is Heisenberg’s uncertainty principle, which forbids the simultaneous measurement of the position and momentum of a particle along the same direction. Remarkably, the uncertainty principle for charged, material particles requires the quantization of light into photons, and even the frequency dependence of the photon’s energy and momentum. An elegant illustration is Heisenberg’s thought experiment for locating an electron with an ideal microscope.[53] The position of the electron can be determined to within the resolving power of the microscope, which is given by a 38 CHAPTER 7. PHOTON both matter and fields must obey a consistent set of quantum laws, if either one is to be quantized.[54] The analogous uncertainty principle for photons forbids the simultaneous measurement of the number n of photons (see Fock state and the Second quantization section below) in an electromagnetic wave and the phase ϕ of that wave ∆n∆ϕ > 1 See coherent state and squeezed coherent state for more details. Both (photons and material) particles such as electrons create analogous interference patterns when passing through a double-slit experiment. For photons, this corresponds to the interference of a Maxwell light wave whereas, for material particles, this corresponds to the interference of the Schrödinger wave equation. Although this similarity might suggest that Maxwell’s equations are simply Schrödinger’s equation for photons, most physicists do not agree.[55][56] For one thing, they are mathematically different; most obviously, Schrödinger’s one equation solves for a complex field, whereas Maxwell’s Heisenberg’s thought experiment for locating an electron (shown four equations solve for real fields. More generally, the in blue) with a high-resolution gamma-ray microscope. The innormal concept of a Schrödinger probability wave funccoming gamma ray (shown in green) is scattered by the electron [57] Being massless, up into the microscope’s aperture angle θ. The scattered gamma tion cannot be applied to photons. they cannot be localized without being destroyed; techray is shown in red. Classical optics shows that the electron position can be resolved only up to an uncertainty Δx that depends nically, photons cannot have a position eigenstate |r⟩ , and, thus, the normal Heisenberg uncertainty principle on θ and the wavelength λ of the incoming light. ∆x∆p > h/2 does not pertain to photons. A few substitute wave functions have been suggested for the formula from classical optics photon,[58][59][60][61] but they have not come into general use. Instead, physicists generally accept the secondquantized theory of photons described below, quantum λ ∆x ∼ electrodynamics, in which photons are quantized excitasin θ tions of electromagnetic modes. where θ is the aperture angle of the microscope. Thus, the position uncertainty ∆x can be made arbitrarily small Another interpretation, that avoids duality, is the De by reducing the wavelength λ. The momentum of the Broglie–Bohm theory: knowned also as the pilot-wave the photon in this theory is both, wave and electron is uncertain, since it received a “kick” ∆p from model, [62] particle. “This idea seems to me so natural and simthe light scattering from it into the microscope. If light ple, to resolve the wave-particle dilemma in such a clear were not quantized into photons, the uncertainty ∆p and ordinary way, that it is a great mystery to me that it could be made arbitrarily small by reducing the light’s [63] J.S.Bell. was so generally ignored”, intensity. In that case, since the wavelength and intensity of light can be varied independently, one could simultaneously determine the position and momentum to arbitrarily high accuracy, violating the uncertainty prin- 7.7 Bose–Einstein model of a phociple. By contrast, Einstein’s formula for photon momenton gas tum preserves the uncertainty principle; since the photon is scattered anywhere within the aperture, the uncertainty Main articles: Bose gas, Bose–Einstein statistics, Spinof momentum transferred equals statistics theorem and Gas in a box h sin θ λ In 1924, Satyendra Nath Bose derived Planck’s law of black-body radiation without using any electromaggiving the product ∆x∆p ∼ h , which is Heisenberg’s netism, but rather a modification of coarse-grained countuncertainty principle. Thus, the entire world is quantized; ing of phase space.[64] Einstein showed that this modifi- ∆p ∼ pphoton sin θ = 7.8. STIMULATED AND SPONTANEOUS EMISSION cation is equivalent to assuming that photons are rigorously identical and that it implied a “mysterious non-local interaction”,[65][66] now understood as the requirement for a symmetric quantum mechanical state. This work led to the concept of coherent states and the development of the laser. In the same papers, Einstein extended Bose’s formalism to material particles (bosons) and predicted that they would condense into their lowest quantum state at low enough temperatures; this Bose–Einstein condensation was observed experimentally in 1995.[67] It was later used by Lene Hau to slow, and then completely stop, light in 1999[68] and 2001.[69] The modern view on this is that photons are, by virtue of their integer spin, bosons (as opposed to fermions with half-integer spin). By the spin-statistics theorem, all bosons obey Bose–Einstein statistics (whereas all fermions obey Fermi–Dirac statistics).[70] 39 frequency ν and transition from a lower energy Ej to a higher energy Ei is proportional to the number Nj of atoms with energy Ej and to the energy density ρ(ν) of ambient photons with that frequency, Rji = Nj Bji ρ(ν) where Bji is the rate constant for absorption. For the reverse process, there are two possibilities: spontaneous emission of a photon, and a return to the lower-energy state that is initiated by the interaction with a passing photon. Following Einstein’s approach, the corresponding rate Rij for the emission of photons of frequency ν and transition from a higher energy Ei to a lower energy Ej is Rij = Ni Aij + Ni Bij ρ(ν) 7.8 Stimulated and spontaneous emission where Aij is the rate constant for emitting a photon spontaneously, and Bij is the rate constant for emitting it in response to ambient photons (induced or stimulated emission). In thermodynamic equilibrium, the Main articles: Stimulated emission and Laser number of atoms in state i and that of atoms in state In 1916, Einstein showed that Planck’s radiation law j must, on average, be constant; hence, the rates Rji and Rij must be equal. Also, by arguments analogous to the derivation of Boltzmann statistics, the ratio of Ni and Nj is gi /gj exp (Ej − Ei )/kT ), where gi,j are the degeneracy of the state i and that of j, respectively, Ei,j their energies, k the Boltzmann constant and T the system’s temperature. From this, it is readily derived that gi Bij = gj Bji and Stimulated emission (in which photons “clone” themselves) was predicted by Einstein in his kinetic analysis, and led to the development of the laser. Einstein’s derivation inspired further developments in the quantum treatment of light, which led to the statistical interpretation of quantum mechanics. could be derived from a semi-classical, statistical treatment of photons and atoms, which implies a relation between the rates at which atoms emit and absorb photons. The condition follows from the assumption that light is emitted and absorbed by atoms independently, and that the thermal equilibrium is preserved by interaction with atoms. Consider a cavity in thermal equilibrium and filled with electromagnetic radiation and atoms that can emit and absorb that radiation. Thermal equilibrium requires that the energy density ρ(ν) of photons with frequency ν (which is proportional to their number density) is, on average, constant in time; hence, the rate at which photons of any particular frequency are emitted must equal the rate of absorbing them.[71] Aij = 8πhν 3 Bij . c3 The A and Bs are collectively known as the Einstein coefficients.[72] Einstein could not fully justify his rate equations, but claimed that it should be possible to calculate the coefficients Aij , Bji and Bij once physicists had obtained “mechanics and electrodynamics modified to accommodate the quantum hypothesis”.[73] In fact, in 1926, Paul Dirac derived the Bij rate constants in using a semiclassical approach,[74] and, in 1927, succeeded in deriving all the rate constants from first principles within the framework of quantum theory.[75][76] Dirac’s work was the foundation of quantum electrodynamics, i.e., the quantization of the electromagnetic field itself. Dirac’s approach is also called second quantization or quantum field theory;[77][78][79] earlier quantum mechanical treatments only treat material particles as quantum mechanical, not the electromagnetic field. Einstein began by postulating simple proportionality re- Einstein was troubled by the fact that his theory seemed lations for the different reaction rates involved. In his incomplete, since it did not determine the direction of a model, the rate Rji for a system to absorb a photon of spontaneously emitted photon. A probabilistic nature of 40 light-particle motion was first considered by Newton in his treatment of birefringence and, more generally, of the splitting of light beams at interfaces into a transmitted beam and a reflected beam. Newton hypothesized that hidden variables in the light particle determined which path it would follow.[33] Similarly, Einstein hoped for a more complete theory that would leave nothing to chance, beginning his separation[44] from quantum mechanics. Ironically, Max Born's probabilistic interpretation of the wave function[80][81] was inspired by Einstein’s later work searching for a more complete theory.[82] CHAPTER 7. PHOTON oscillators are known to be E = nhν , where ν is the oscillator frequency. The key new step was to identify an electromagnetic mode with energy E = nhν as a state with n photons, each of energy hν . This approach gives the correct energy fluctuation formula. 7.9 Second quantization and high energy photon interactions Main article: Quantum field theory In 1910, Peter Debye derived Planck’s law of black-body In quantum field theory, the probability of an event is computed by summing the probability amplitude (a complex number) for all possible ways in which the event can occur, as in the Feynman diagram shown here; the probability equals the square of the modulus of the total amplitude. Dirac took this one step further.[75][76] He treated the interaction between a charge and an electromagnetic field as a small perturbation that induces transitions in the photon states, changing the numbers of photons in the modes, 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 while conserving energy and momentum overall. Dirac Distance (microns) was able to derive Einstein’s Aij and Bij coefficients Different electromagnetic modes (such as those depicted here) from first principles, and showed that the Bose–Einstein can be treated as independent simple harmonic oscillators. A statistics of photons is a natural consequence of quantizphoton corresponds to a unit of energy E=hν in its electromag- ing the electromagnetic field correctly (Bose’s reasoning went in the opposite direction; he derived Planck’s law netic mode. of black-body radiation by assuming B–E statistics). In radiation from a relatively simple assumption.[83] He cor- Dirac’s time, it was not yet known that all bosons, includrectly decomposed the electromagnetic field in a cavity ing photons, must obey Bose–Einstein statistics. into its Fourier modes, and assumed that the energy in Dirac’s second-order perturbation theory can involve any mode was an integer multiple of hν , where ν is the virtual photons, transient intermediate states of the elecfrequency of the electromagnetic mode. Planck’s law of tromagnetic field; the static electric and magnetic interblack-body radiation follows immediately as a geomet- actions are mediated by such virtual photons. In such ric sum. However, Debye’s approach failed to give the quantum field theories, the probability amplitude of obcorrect formula for the energy fluctuations of blackbody servable events is calculated by summing over all possible radiation, which were derived by Einstein in 1909.[40] intermediate steps, even ones that are unphysical; hence, In 1925, Born, Heisenberg and Jordan reinterpreted Debye’s concept in a key way.[84] As may be shown classically, the Fourier modes of the electromagnetic field—a complete set of electromagnetic plane waves indexed by their wave vector k and polarization state—are equivalent to a set of uncoupled simple harmonic oscillators. Treated quantum mechanically, the energy levels of such virtual photons are not constrained to satisfy E = pc , and may have extra polarization states; depending on the gauge used, virtual photons may have three or four polarization states, instead of the two states of real photons. Although these transient virtual photons can never be observed, they contribute measurably to the probabilities of observable events. Indeed, such second-order 7.12. CONTRIBUTIONS TO THE MASS OF A SYSTEM 41 and higher-order perturbation calculations can give apparently infinite contributions to the sum. Such unphysical results are corrected for using the technique of renormalization. The electromagnetic field can be understood as a gauge field, i.e., as a field that results from requiring that a gauge symmetry holds independently at every position in spacetime.[92] For the electromagnetic field, this gauge Other virtual particles may contribute to the summation symmetry is the Abelian U(1) symmetry of a complex as well; for example, two photons may interact indirectly number, which reflects the ability to vary the phase of through virtual electron–positron pairs.[85] In fact, such a complex number without affecting observables or real photon-photon scattering (see two-photon physics), as valued functions made from it, such as the energy or the Lagrangian. well as electron-photon scattering, is meant to be one of the modes of operations of the planned particle acceler- The quanta of an Abelian gauge field must be massless, ator, the International Linear Collider.[86] uncharged bosons, as long as the symmetry is not broIn modern physics notation, the quantum state of the elec- ken; hence, the photon is predicted to be massless, and to tromagnetic field is written as a Fock state, a tensor prod- have zero electric charge and integer spin. The particular form of the electromagnetic interaction specifies that uct of the states for each electromagnetic mode the photon must have spin ±1; thus, its helicity must be ±ℏ . These two spin components correspond to the classical concepts of right-handed and left-handed circularly |nk0 ⟩ ⊗ |nk1 ⟩ ⊗ · · · ⊗ |nkn ⟩ . . . polarized light. However, the transient virtual photons of quantum electrodynamics may also adopt unphysical powhere |nki ⟩ represents the state in which nki photons are larization states.[92] in the mode ki . In this notation, the creation of a new photon in mode ki (e.g., emitted from an atomic transi- In the prevailing Standard Model of physics, the photion) is written as |nki ⟩ → |nki + 1⟩ . This notation ton is one of four gauge bosons in the electroweak in+ − merely expresses the concept of Born, Heisenberg and teraction; the other three are denoted W , W and 0 Z and are responsible for the weak interaction. UnJordan described above, and does not add any physics. like the photon, these gauge bosons have mass, owing to a mechanism that breaks their SU(2) gauge symThe unification of the photon with W and Z 7.10 The hadronic properties of the metry. gauge bosons in the electroweak interaction was accomphoton plished by Sheldon Glashow, Abdus Salam and Steven Weinberg, for which they were awarded the 1979 Nobel Prize in physics.[93][94][95] Physicists continue to hypothMeasurements of the interaction between energetic photons and hadrons show that the interaction is much more esize grand unified theories that connect these four gauge intense than expected by the interaction of merely pho- bosons with the eight gluon gauge bosons of quantum tons with the hadron’s electric charge. Furthermore, the chromodynamics; however, key predictions of these theinteraction of energetic photons with protons is similar ories, such as proton decay, have not been observed [96] to the interaction of photons with neutrons[87] in spite of experimentally. the fact that the electric charge structures of protons and neutrons are substantially different. A theory called Vector Meson Dominance (VMD) was 7.12 Contributions to the mass of a developed to explain this effect. According to VMD, system the photon is a superposition of the pure electromagnetic photon (which interacts only with electric charges) and vector meson.[88] See also: Mass in special relativity and General relativity However, if experimentally probed at very short distances, the intrinsic structure of the photon is recognized The energy of a system that emits a photon is decreased by as a flux of quark and gluon components, quasi-free ac- the energy E of the photon as measured in the rest frame cording to asymptotic freedom in QCD and described of the emitting system, which may result in a reduction in by the photon structure function.[89][90] A comprehensive mass in the amount E/c2 . Similarly, the mass of a syscomparison of data with theoretical predictions is pre- tem that absorbs a photon is increased by a corresponding sented in a recent review.[91] amount. As an application, the energy balance of nuclear reactions involving photons is commonly written in terms of the masses of the nuclei involved, and terms of the 7.11 The photon as a gauge boson form E/c2 for the gamma photons (and for other[97]relevant energies, such as the recoil energy of nuclei). Main article: Gauge theory This concept is applied in key predictions of quantum electrodynamics (QED, see above). In that theory, the 42 mass of electrons (or, more generally, leptons) is modified by including the mass contributions of virtual photons, in a technique known as renormalization. Such “radiative corrections” contribute to a number of predictions of QED, such as the magnetic dipole moment of leptons, the Lamb shift, and the hyperfine structure of bound lepton pairs, such as muonium and positronium.[98] Since photons contribute to the stress–energy tensor, they exert a gravitational attraction on other objects, according to the theory of general relativity. Conversely, photons are themselves affected by gravity; their normally straight trajectories may be bent by warped spacetime, as in gravitational lensing, and their frequencies may be lowered by moving to a higher gravitational potential, as in the Pound–Rebka experiment. However, these effects are not specific to photons; exactly the same effects would be predicted for classical electromagnetic waves.[99] 7.13 Photons in matter See also: Group velocity and Photochemistry Any 'explanation' of how photons travel through matter has to explain why different arrangements of matter are transparent or opaque at different wavelengths (light through carbon as diamond or not, as graphite) and why individual photons behave in the same way as large groups. Explanations that invoke 'absorption' and 'reemission' have to provide an explanation for the directionality of the photons (diffraction, reflection) and further explain how entangled photon pairs can travel through matter without their quantum state collapsing. The simplest explanation is that light that travels through transparent matter does so at a lower speed than c, the speed of light in a vacuum. In addition, light can also undergo scattering and absorption. There are circumstances in which heat transfer through a material is mostly radiative, involving emission and absorption of photons within it. An example would be in the core of the Sun. Energy can take about a million years to reach the surface.[100] However, this phenomenon is distinct from scattered radiation passing diffusely through matter, as it involves local equilibrium between the radiation and the temperature. Thus, the time is how long it takes the energy to be transferred, not the photons themselves. Once in open space, a photon from the Sun takes only 8.3 minutes to reach Earth. The factor by which the speed of light is decreased in a material is called the refractive index of the material. In a classical wave picture, the slowing can be explained by the light inducing electric polarization in the matter, the polarized matter radiating new light, and the new light interfering with the original light wave to form a delayed wave. In a particle picture, the slowing can instead be described as a blending of the photon with quantum excitation of the matter (quasi-particles such as CHAPTER 7. PHOTON phonons and excitons) to form a polariton; this polariton has a nonzero effective mass, which means that it cannot travel at c. Alternatively, photons may be viewed as always traveling at c, even in matter, but they have their phase shifted (delayed or advanced) upon interaction with atomic scatters: this modifies their wavelength and momentum, but not speed.[101] A light wave made up of these photons does travel slower than the speed of light. In this view the photons are “bare”, and are scattered and phase shifted, while in the view of the preceding paragraph the photons are “dressed” by their interaction with matter, and move without scattering or phase shifting, but at a lower speed. Light of different frequencies may travel through matter at different speeds; this is called dispersion. In some cases, it can result in extremely slow speeds of light in matter. The effects of photon interactions with other quasi-particles may be observed directly in Raman scattering and Brillouin scattering.[102] Photons can also be absorbed by nuclei, atoms or molecules, provoking transitions between their energy levels. A classic example is the molecular transition of retinal C20 H28 O, which is responsible for vision, as discovered in 1958 by Nobel laureate biochemist George Wald and co-workers. The absorption provokes a cistrans isomerization that, in combination with other such transitions, is transduced into nerve impulses. The absorption of photons can even break chemical bonds, as in the photodissociation of chlorine; this is the subject of photochemistry.[103][104] Analogously, gamma rays can in some circumstances dissociate atomic nuclei in a process called photodisintegration. 7.14 Technological applications Photons have many applications in technology. These examples are chosen to illustrate applications of photons per se, rather than general optical devices such as lenses, etc. that could operate under a classical theory of light. The laser is an extremely important application and is discussed above under stimulated emission. Individual photons can be detected by several methods. The classic photomultiplier tube exploits the photoelectric effect: a photon landing on a metal plate ejects an electron, initiating an ever-amplifying avalanche of electrons. Charge-coupled device chips use a similar effect in semiconductors: an incident photon generates a charge on a microscopic capacitor that can be detected. Other detectors such as Geiger counters use the ability of photons to ionize gas molecules, causing a detectable change in conductivity.[105] Planck’s energy formula E = hν is often used by engineers and chemists in design, both to compute the change in energy resulting from a photon absorption and to predict the frequency of the light emitted for a given en- 7.17. NOTES ergy transition. For example, the emission spectrum of a fluorescent light bulb can be designed using gas molecules with different electronic energy levels and adjusting the typical energy with which an electron hits the gas molecules within the bulb.[Note 6] Under some conditions, an energy transition can be excited by “two” photons that individually would be insufficient. This allows for higher resolution microscopy, because the sample absorbs energy only in the region where two beams of different colors overlap significantly, which can be made much smaller than the excitation volume of a single beam (see two-photon excitation microscopy). Moreover, these photons cause less damage to the sample, since they are of lower energy.[106] 43 • Doppler shift • Electromagnetic radiation • HEXITEC • Laser • Light • Luminiferous aether • Medipix • Phonons • Photon counting In some cases, two energy transitions can be coupled so that, as one system absorbs a photon, another nearby system “steals” its energy and re-emits a photon of a different frequency. This is the basis of fluorescence resonance energy transfer, a technique that is used in molecular biology to study the interaction of suitable proteins.[107] • Photon energy Several different kinds of hardware random number generator involve the detection of single photons. In one example, for each bit in the random sequence that is to be produced, a photon is sent to a beam-splitter. In such a situation, there are two possible outcomes of equal probability. The actual outcome is used to determine whether the next bit in the sequence is “0” or “1”.[108][109] • Photonics • Photon polarization • Photonic molecule • Photography • Quantum optics • Single photon sources • Static forces and virtual-particle exchange • Two-photon physics • EPR paradox 7.15 Recent research • Dirac equation See also: Quantum optics 7.17 Notes Much research has been devoted to applications of photons in the field of quantum optics. Photons seem wellsuited to be elements of an extremely fast quantum computer, and the quantum entanglement of photons is a focus of research. Nonlinear optical processes are another active research area, with topics such as two-photon absorption, self-phase modulation, modulational instability and optical parametric oscillators. However, such processes generally do not require the assumption of photons per se; they may often be modeled by treating atoms as nonlinear oscillators. The nonlinear process of spontaneous parametric down conversion is often used to produce single-photon states. Finally, photons are essential in some aspects of optical communication, especially for quantum cryptography.[Note 7] 7.16 See also • Advanced Photon Source at Argonne National Laboratory • Ballistic photon [1] Although the 1967 Elsevier translation of Planck’s Nobel Lecture interprets Planck’s Lichtquant as “photon”, the more literal 1922 translation by Hans Thacher Clarke and Ludwik Silberstein The origin and development of the quantum theory, The Clarendon Press, 1922 (here ) uses “light-quantum”. No evidence is known that Planck himself used the term “photon” by 1926 (see also this note). [2] Isaac Asimov credits Arthur Compton with defining quanta of energy as photons in 1923. Asimov, I. (1966). The Neutrino, Ghost Particle of the Atom. Garden City (NY): Doubleday. ISBN 0-380-00483-6. LCCN 66017073. and Asimov, I. (1966). The Universe From Flat Earth To Quasar. New York (NY): Walker. ISBN 0-8027-0316-X. LCCN 66022515. [3] The mass of the photon is believed to be exactly zero, based on experiment and theoretical considerations described in the article. Some sources also refer to the relativistic mass concept, which is just the energy scaled to units of mass. For a photon with wavelength λ or energy E, this is h/λc or E/c2 . This usage for the term “mass” is no longer common in scientific literature. Further info: What is the mass of a photon? http://math.ucr.edu/home/ baez/physics/ParticleAndNuclear/photon_mass.html 44 [4] The phrase “no matter how intense” refers to intensities below approximately 1013 W/cm2 at which point perturbation theory begins to break down. In contrast, in the intense regime, which for visible light is above approximately 1014 W/cm2 , the classical wave description correctly predicts the energy acquired by electrons, called ponderomotive energy. (See also: Boreham et al. (1996). "Photon density and the correspondence principle of electromagnetic interaction".) By comparison, sunlight is only about 0.1 W/cm2 . [5] These experiments produce results that cannot be explained by any classical theory of light, since they involve anticorrelations that result from the quantum measurement process. In 1974, the first such experiment was carried out by Clauser, who reported a violation of a classical Cauchy–Schwarz inequality. In 1977, Kimble et al. demonstrated an analogous anti-bunching effect of photons interacting with a beam splitter; this approach was simplified and sources of error eliminated in the photon-anticorrelation experiment of Grangier et al. (1986). This work is reviewed and simplified further in Thorn et al. (2004). (These references are listed below under #Additional references.) [6] An example is US Patent Nr. 5212709. [7] Introductory-level material on the various sub-fields of quantum optics can be found in Fox, M. (2006). Quantum Optics: An Introduction. Oxford University Press. ISBN 0-19-856673-5. 7.18 References [1] Amsler, C. (Particle Data Group); Amsler; Doser; Antonelli; Asner; Babu; Baer; Band; Barnett; Bergren; Beringer; Bernardi; Bertl; Bichsel; Biebel; Bloch; Blucher; Blusk; Cahn; Carena; Caso; Ceccucci; Chakraborty; Chen; Chivukula; Cowan; Dahl; d'Ambrosio; Damour et al. (2008). “Review of Particle Physics: Gauge and Higgs bosons” (PDF). Physics Letters B 667: 1. Bibcode:2008PhLB..667....1P. doi:10.1016/j.physletb.2008.07.018. [2] Kimble, H.J.; Dagenais, M.; Mandel, L.; Dagenais; Mandel (1977). “Photon Anti-bunching in Resonance Fluorescence”. Physical Review Letters 39 (11): 691–695. Bibcode:1977PhRvL..39..691K. doi:10.1103/PhysRevLett.39.691. [3] Grangier, P.; Roger, G.; Aspect, A.; Roger; Aspect (1986). “Experimental Evidence for a Photon Anticorrelation Effect on a Beam Splitter: A New Light on SinglePhoton Interferences”. Europhysics Letters 1 (4): 173– 179. Bibcode:1986EL......1..173G. doi:10.1209/02955075/1/4/004. [4] Planck, M. (1901). “On the Law of Distribution of Energy in the Normal Spectrum”. Annalen der Physik 4 (3): 553–563. Bibcode:1901AnP...309..553P. doi:10.1002/andp.19013090310. Archived from the original on 2008-04-18. CHAPTER 7. PHOTON [5] Einstein, A. (1905). "Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt” (PDF). Annalen der Physik (in German) 17 (6): 132–148. Bibcode:1905AnP...322..132E. doi:10.1002/andp.19053220607.. An English translation is available from Wikisource. [6] “Discordances entre l'expérience et la théorie électromagnétique du rayonnement.” In Électrons et Photons. Rapports et Discussions de Cinquième Conseil de Physique, edited by Institut International de Physique Solvay. Paris: Gauthier-Villars, pp. 55-85. [7] Helge Kragh: Photon: New light on an old name. Arxiv, 2014-2-28 [8] Villard, P. (1900). “Sur la réflexion et la réfraction des rayons cathodiques et des rayons déviables du radium”. Comptes Rendus des Séances de l'Académie des Sciences (in French) 130: 1010–1012. [9] Villard, P. (1900). “Sur le rayonnement du radium”. Comptes Rendus des Séances de l'Académie des Sciences (in French) 130: 1178–1179. [10] Rutherford, E.; Andrade, E.N.C. (1914). “The Wavelength of the Soft Gamma Rays from Radium B”. Philosophical Magazine 27 (161): 854–868. doi:10.1080/14786440508635156. [11] Kobychev, V.V.; Popov, S.B. (2005). “Constraints on the photon charge from observations of extragalactic sources”. Astronomy Letters 31 (3): 147–151. arXiv:hep-ph/0411398. Bibcode:2005AstL...31..147K. doi:10.1134/1.1883345. [12] Role as gauge boson and polarization section 5.1 inAitchison, I.J.R.; Hey, A.J.G. (1993). Gauge Theories in Particle Physics. IOP Publishing. ISBN 0-85274-328-9. [13] See p.31 inAmsler, C. et al. (2008). “Review of Particle Physics”. Physics Letters B 667: 1–1340. Bibcode:2008PhLB..667....1P. doi:10.1016/j.physletb.2008.07.018. [14] Halliday, David; Resnick, Robert; Walker, Jerl (2005), Fundamental of Physics (7th ed.), USA: John Wiley and Sons, Inc., ISBN 0-471-23231-9 [15] See section 1.6 in Alonso, M.; Finn, E.J. (1968). Fundamental University Physics Volume III: Quantum and Statistical Physics. Addison-Wesley. ISBN 0-201-00262-0. [16] Davison E. Soper, Electromagnetic radiation is made of photons, Institute of Theoretical Science, University of Oregon [17] This property was experimentally verified by Raman and Bhagavantam in 1931: Raman, C.V.; Bhagavantam, S. (1931). “Experimental proof of the spin of the photon” (PDF). Indian Journal of Physics 6: 353. [18] Burgess, C.; Moore, G. (2007). “1.3.3.2”. The Standard Model. A Primer. Cambridge University Press. ISBN 0521-86036-9. 7.18. REFERENCES 45 [19] Griffiths, David J. (2008), Introduction to Elementary Particles (2nd revised ed.), WILEY-VCH, ISBN 978-3-52740601-2 [33] Newton, I. (1952) [1730]. Opticks (4th ed.). Dover (NY): Dover Publications. Book II, Part III, Propositions XII– XX; Queries 25–29. ISBN 0-486-60205-2. [20] E.g., section 9.3 in Alonso, M.; Finn, E.J. (1968). Fundamental University Physics Volume III: Quantum and Statistical Physics. Addison-Wesley. [34] Buchwald, J.Z. (1989). The Rise of the Wave Theory of Light: Optical Theory and Experiment in the Early Nineteenth Century. University of Chicago Press. ISBN 0-22607886-8. OCLC 18069573. [21] E.g., Appendix XXXII in Born, M. (1962). Physics. Blackie & Son. ISBN 0-486-65984-4. Atomic [22] Mermin, David (February 1984). “Relativity without light”. American Journal of Physics 52 (2): 119–124. Bibcode:1984AmJPh..52..119M. doi:10.1119/1.13917. [23] Plimpton, S.; Lawton, W. (1936). “A Very Accurate Test of Coulomb’s Law of Force Between Charges”. Physical Review 50 (11): 1066. Bibcode:1936PhRv...50.1066P. doi:10.1103/PhysRev.50.1066. [24] Williams, E.; Faller, J.; Hill, H. (1971). “New Experimental Test of Coulomb’s Law: A Laboratory Upper Limit on the Photon Rest Mass”. Physical Review Letters 26 (12): 721. Bibcode:1971PhRvL..26..721W. doi:10.1103/PhysRevLett.26.721. [25] Chibisov, G V (1976). “Astrophysical upper limits on the photon rest mass”. Soviet Physics Uspekhi 19 (7): 624. Bibcode:1976SvPhU..19..624C. doi:10.1070/PU1976v019n07ABEH005277. [26] Lakes, Roderic (1998). “Experimental Limits on the Photon Mass and Cosmic Magnetic Vector Potential”. Physical Review Letters 80 (9): 1826. Bibcode:1998PhRvL..80.1826L. doi:10.1103/PhysRevLett.80.1826. [27] Amsler, C; Doser, M; Antonelli, M; Asner, D; Babu, K; Baer, H; Band, H; Barnett, R et al. (2008). “Review of Particle Physics⁎". Physics Letters B 667: 1. Bibcode:2008PhLB..667....1P. doi:10.1016/j.physletb.2008.07.018. Summary Table [28] Adelberger, Eric; Dvali, Gia; Gruzinov, Andrei (2007). “Photon-Mass Bound Destroyed by Vortices”. Physical Review Letters 98 (1): 010402. arXiv:hepph/0306245. Bibcode:2007PhRvL..98a0402A. doi:10.1103/PhysRevLett.98.010402. PMID 17358459. preprint [29] Wilczek, Frank (2010). The Lightness of Being: Mass, Ether, and the Unification of Forces. Basic Books. p. 212. ISBN 978-0-465-01895-6. [30] Descartes, R. (1637). Discours de la méthode (Discourse on Method) (in French). Imprimerie de Ian Maire. ISBN 0-268-00870-1. [31] Hooke, R. (1667). Micrographia: or some physiological descriptions of minute bodies made by magnifying glasses with observations and inquiries thereupon ... London (UK): Royal Society of London. ISBN 0-486-495647. [32] Huygens, C. (1678). Traité de la lumière (in French).. An English translation is available from Project Gutenberg [35] Maxwell, J.C. (1865). "A Dynamical Theory of the Electromagnetic Field". Philosophical Transactions of the Royal Society 155: 459–512. Bibcode:1865RSPT..155..459C. doi:10.1098/rstl.1865.0008. This article followed a presentation by Maxwell on 8 December 1864 to the Royal Society. [36] Hertz, H. (1888). "Über Strahlen elektrischer Kraft”. Sitzungsberichte der Preussischen Akademie der Wissenschaften (Berlin) (in German) 1888: 1297–1307. [37] Frequency-dependence of luminiscence p. 276f., photoelectric effect section 1.4 in Alonso, M.; Finn, E.J. (1968). Fundamental University Physics Volume III: Quantum and Statistical Physics. Addison-Wesley. ISBN 0-201-002620. [38] Wien, W. (1911). “Wilhelm Wien Nobel Lecture”. [39] Planck, M. (1920). “Max Planck’s Nobel Lecture”. [40] Einstein, A. (1909). "Über die Entwicklung unserer Anschauungen über das Wesen und die Konstitution der Strahlung” (PDF). Physikalische Zeitschrift (in German) 10: 817–825.. An English translation is available from Wikisource. [41] Presentation speech by Svante Arrhenius for the 1921 Nobel Prize in Physics, December 10, 1922. Online text from [nobelprize.org], The Nobel Foundation 2008. Access date 2008-12-05. [42] Einstein, A. (1916). “Zur Quantentheorie der Strahlung”. Mitteilungen der Physikalischen Gesellschaft zu Zürich 16: 47. Also Physikalische Zeitschrift, 18, 121–128 (1917). (German) [43] Compton, A. (1923). “A Quantum Theory of the Scattering of X-rays by Light Elements”. Physical Review 21 (5): 483–502. Bibcode:1923PhRv...21..483C. doi:10.1103/PhysRev.21.483. [44] Pais, A. (1982). Subtle is the Lord: The Science and the Life of Albert Einstein. Oxford University Press. ISBN 0-19-853907-X. [45] Einstein and the Quantum: The Quest of the Valiant Swabian, A. Douglas Stone, Princeton University Press, 2013. [46] Millikan, R.A (1924). “Robert A. Millikan’s Nobel Lecture”. [47] Hendry, J. (1980). “The development of attitudes to the wave-particle duality of light and quantum theory, 1900–1920”. Annals of Science 37 (1): 59–79. doi:10.1080/00033798000200121. 46 CHAPTER 7. PHOTON [48] Bohr, N.; Kramers, H.A.; Slater, J.C. (1924). “The Quantum Theory of Radiation”. Philosophical Magazine 47: 785–802. doi:10.1080/14786442408565262. Also Zeitschrift für Physik, 24, 69 (1924). [64] Bose, S.N. (1924). “Plancks Gesetz und Lichtquantenhypothese”. Zeitschrift für Physik (in German) 26: 178–181. Bibcode:1924ZPhy...26..178B. doi:10.1007/BF01327326. [49] Heisenberg, W. (1933). “Heisenberg Nobel lecture”. [65] Einstein, A. (1924). “Quantentheorie des einatomigen idealen Gases”. Sitzungsberichte der Preussischen Akademie der Wissenschaften (Berlin), Physikalischmathematische Klasse (in German) 1924: 261–267. [50] Mandel, L. (1976). E. Wolf, ed. “The case for and against semiclassical radiation theory”. Progress in Optics. Progress in Optics (North-Holland) 13: 27–69. doi:10.1016/S0079-6638(08)70018-0. ISBN 978-0-44410806-7. [51] Taylor, G.I. (1909). Interference fringes with feeble light. Proceedings of the Cambridge Philosophical Society 15: 114–115. [52] Saleh, B. E. A. and Teich, M. C. (2007). Fundamentals of Photonics. Wiley. ISBN 0-471-35832-0. [53] Heisenberg, W. (1927). "Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik”. Zeitschrift für Physik (in German) 43 (3–4): 172–198. Bibcode:1927ZPhy...43..172H. doi:10.1007/BF01397280. [54] E.g., p. 10f. in Schiff, L.I. (1968). Quantum Mechanics (3rd ed.). McGraw-Hill. ASIN B001B3MINM. ISBN 007-055287-8. [55] Kramers, H.A. (1958). Quantum Mechanics. Amsterdam: North-Holland. ASIN B0006AUW5C. ISBN 0486-49533-7. [56] Bohm, D. (1989) [1954]. Quantum Theory. Dover Publications. ISBN 0-486-65969-0. [57] Newton, T.D.; Wigner, E.P. (1949). “Localized states for elementary particles”. Reviews of Modern Physics 21 (3): 400–406. Bibcode:1949RvMP...21..400N. doi:10.1103/RevModPhys.21.400. [58] Bialynicki-Birula, I. (1994). “On the wave function of the photon” (PDF). Acta Physica Polonica A 86: 97–116. [59] Sipe, J.E. (1995). “Photon wave functions”. Physical Review A 52 (3): 1875– 1883. Bibcode:1995PhRvA..52.1875S. doi:10.1103/PhysRevA.52.1875. [60] Bialynicki-Birula, I. (1996). “Photon wave function”. Progress in Optics. Progress in Optics 36: 245–294. doi:10.1016/S0079-6638(08)70316-0. ISBN 978-0-44482530-8. [61] Scully, M.O.; Zubairy, M.S. (1997). Quantum Optics. Cambridge (UK): Cambridge University Press. ISBN 0521-43595-1. [62] The best illustration is the Couder experiment, demonstrating the behaviour of a mechanical analog, see https: //www.youtube.com/watch?v=W9yWv5dqSKk [63] Bell, J. S., “Speakable and Unspeakable in Quantum Mechanics”, Cambridge: Cambridge University Press, 1987. [66] Einstein, A. (1925). “Quantentheorie des einatomigen idealen Gases, Zweite Abhandlung”. Sitzungsberichte der Preussischen Akademie der Wissenschaften (Berlin), Physikalisch-mathematische Klasse (in German) 1925: 3– 14. doi:10.1002/3527608958.ch28. ISBN 978-3-52760895-9. [67] Anderson, M.H.; Ensher, J.R.; Matthews, M.R.; Wieman, C.E.; Cornell, E.A. (1995). “Observation of Bose– Einstein Condensation in a Dilute Atomic Vapor”. Science 269 (5221): 198–201. Bibcode:1995Sci...269..198A. doi:10.1126/science.269.5221.198. JSTOR 2888436. PMID 17789847. [68] “Physicists Slow Speed of Light”. News.harvard.edu (1999-02-18). Retrieved on 2015-05-11. [69] “Light Changed to Matter, Then Stopped and Moved”. photonics.com (February 2007). Retrieved on 2015-0511. [70] Streater, R.F.; Wightman, A.S. (1989). PCT, Spin and Statistics, and All That. Addison-Wesley. ISBN 0-20109410-X. [71] Einstein, A. (1916). “Strahlungs-emission und absorption nach der Quantentheorie”. Verhandlungen der Deutschen Physikalischen Gesellschaft (in German) 18: 318–323. Bibcode:1916DPhyG..18..318E. [72] Section 1.4 in Wilson, J.; Hawkes, F.J.B. (1987). Lasers: Principles and Applications. New York: Prentice Hall. ISBN 0-13-523705-X. [73] P. 322 in Einstein, A. (1916). “Strahlungs-emission und -absorption nach der Quantentheorie”. Verhandlungen der Deutschen Physikalischen Gesellschaft (in German) 18: 318–323. Bibcode:1916DPhyG..18..318E.: n Die Konstanten An m and Bm würden sich direkt berechnen lassen, wenn wir im Besitz einer im Sinne der Quantenhypothese modifizierten Elektrodynamik und Mechanik wären.” [74] Dirac, P.A.M. (1926). “On the Theory of Quantum Mechanics”. Proceedings of the Royal Society A 112 (762): 661–677. Bibcode:1926RSPSA.112..661D. doi:10.1098/rspa.1926.0133. [75] Dirac, P.A.M. (1927). “The Quantum Theory of the Emission and Absorption of Radiation” (PDF). Proceedings of the Royal Society A 114 Bibcode:1927RSPSA.114..243D. (767): 243–265. doi:10.1098/rspa.1927.0039. 7.18. REFERENCES [76] Dirac, P.A.M. (1927b). The Quantum Theory of Dispersion. Proceedings of the Royal Society A 114: 710–728. doi:10.1098/rspa.1927.0071. [77] Heisenberg, W.; Pauli, W. (1929). “Zur Quantentheorie der Wellenfelder”. Zeitschrift für Physik (in German) 56: 1. Bibcode:1929ZPhy...56....1H. doi:10.1007/BF01340129. [78] Heisenberg, W.; Pauli, W. (1930). “Zur Quantentheorie der Wellenfelder”. Zeitschrift für Physik (in German) 59 (3–4): 139. Bibcode:1930ZPhy...59..168H. doi:10.1007/BF01341423. [79] Fermi, E. (1932). “Quantum Theory of Radiation” (PDF). Reviews of Modern Physics 4: 87. Bibcode:1932RvMP....4...87F. doi:10.1103/RevModPhys.4.87. [80] Born, M. (1926). “Zur Quantenmechanik der Stossvorgänge” (PDF). Zeitschrift für Physik (in German) 37 (12): 863–867. Bibcode:1926ZPhy...37..863B. doi:10.1007/BF01397477. [81] Born, M. (1926). “Quantenmechanik der Stossvorgänge”. Zeitschrift für Physik (in German) 38 (11–12): 803. Bibcode:1926ZPhy...38..803B. doi:10.1007/BF01397184. [82] Pais, A. (1986). Inward Bound: Of Matter and Forces in the Physical World. Oxford University Press. p. 260. ISBN 0-19-851997-4. Specifically, Born claimed to have been inspired by Einstein’s never-published attempts to develop a “ghost-field” theory, in which point-like photons are guided probabilistically by ghost fields that follow Maxwell’s equations. [83] Debye, P. (1910). “Der Wahrscheinlichkeitsbegriff in der Theorie der Strahlung”. Annalen der Physik (in German) 33 (16): 1427–1434. Bibcode:1910AnP...338.1427D. doi:10.1002/andp.19103381617. [84] Born, M.; Heisenberg, W.; Jordan, P. (1925). “Quantenmechanik II”. Zeitschrift für Physik (in German) 35 (8–9): 557–615. Bibcode:1926ZPhy...35..557B. doi:10.1007/BF01379806. [85] Photon-photon-scattering section 7-3-1, renormalization chapter 8-2 in Itzykson, C.; Zuber, J.-B. (1980). Quantum Field Theory. McGraw-Hill. ISBN 0-07-032071-3. 47 [89] Walsh, T. F.; Zerwas, P. (1973). “Two-photon processes in the parton model”. Physics Letters B 44 (2): 195. Bibcode:1973PhLB...44..195W. doi:10.1016/03702693(73)90520-0. [90] Witten, E. (1977). “Anomalous cross section for photonphoton scattering in gauge theories”. Nuclear Physics B 120 (2): 189. Bibcode:1977NuPhB.120..189W. doi:10.1016/0550-3213(77)90038-4. [91] Nisius, R. (2000). “The photon structure from deep inelastic electron–photon scattering”. Physics Reports 332 (4–6): 165. Bibcode:2000PhR...332..165N. doi:10.1016/S0370-1573(99)00115-5. [92] Ryder, L.H. (1996). Quantum field theory (2nd ed.). Cambridge University Press. ISBN 0-521-47814-6. [93] Sheldon Glashow Nobel lecture, delivered 8 December 1979. [94] Abdus Salam Nobel lecture, delivered 8 December 1979. [95] Steven Weinberg Nobel lecture, delivered 8 December 1979. [96] E.g., chapter 14 in Hughes, I. S. (1985). Elementary particles (2nd ed.). Cambridge University Press. ISBN 0-52126092-2. [97] E.g., section 10.1 in Dunlap, R.A. (2004). An Introduction to the Physics of Nuclei and Particles. Brooks/Cole. ISBN 0-534-39294-6. [98] Radiative correction to electron mass section 7-1-2, anomalous magnetic moments section 7-2-1, Lamb shift section 7-3-2 and hyperfine splitting in positronium section 10-3 in Itzykson, C.; Zuber, J.-B. (1980). Quantum Field Theory. McGraw-Hill. ISBN 0-07-032071-3. [99] E. g. sections 9.1 (gravitational contribution of photons) and 10.5 (influence of gravity on light) in Stephani, H.; Stewart, J. (1990). General Relativity: An Introduction to the Theory of Gravitational Field. Cambridge University Press. pp. 86 ff, 108 ff. ISBN 0-521-37941-5. [100] Naeye, R. (1998). Through the Eyes of Hubble: Birth, Life and Violent Death of Stars. CRC Press. ISBN 0-75030484-7. OCLC 40180195. [101] Ch 4 in Hecht, Eugene (2001). Optics. Addison Wesley. [86] Weiglein, G. (2008). “Electroweak Physics at the ILC”. ISBN 978-0-8053-8566-3. Journal of Physics: Conference Series 110 (4): 042033. arXiv:0711.3003. Bibcode:2008JPhCS.110d2033W. [102] Polaritons section 10.10.1, Raman and Brillouin scattering section 10.11.3 in Patterson, J.D.; Bailey, B.C. (2007). doi:10.1088/1742-6596/110/4/042033. Solid-State Physics: Introduction to the Theory. Springer. [87] Bauer, T. H.; Spital, R. D.; Yennie, D. R.; Pipkin, pp. 569 ff, 580 ff. ISBN 3-540-24115-9. F. M. (1978). “The hadronic properties of the photon in high-energy interactions”. Reviews of Modern [103] E.g., section 11-5 C in Pine, S.H.; Hendrickson, J.B.; Cram, D.J.; Hammond, G.S. (1980). Organic Chemistry Physics 50 (2): 261. Bibcode:1978RvMP...50..261B. (4th ed.). McGraw-Hill. ISBN 0-07-050115-7. doi:10.1103/RevModPhys.50.261. [88] Sakurai, J. J. (1960). “Theory of strong interactions”. [104] Nobel lecture given by G. Wald on December 12, 1967, Annals of Physics 11: 1. Bibcode:1960AnPhy..11....1S. online at nobelprize.org: The Molecular Basis of Visual doi:10.1016/0003-4916(60)90126-3. Excitation. 48 [105] Photomultiplier section 1.1.10, CCDs section 1.1.8, Geiger counters section 1.3.2.1 in Kitchin, C.R. (2008). Astrophysical Techniques. Boca Raton (FL): CRC Press. ISBN 1-4200-8243-4. [106] Denk, W.; Svoboda, K. (1997). “Photon upmanship: Why multiphoton imaging is more than a gimmick”. Neuron 18 (3): 351–357. doi:10.1016/S08966273(00)81237-4. PMID 9115730. CHAPTER 7. PHOTON • Roychoudhuri, C.; Rajarshi, R. (2003). “The nature of light: what is a photon?". Optics and Photonics News 14: S1 (Supplement). • Zajonc, A. “Light reconsidered”. Optics and Photonics News 14: S2–S5 (Supplement). • Loudon, R. “What is a photon?". Optics and Photonics News 14: S6–S11 (Supplement). [107] Lakowicz, J.R. (2006). Principles of Fluorescence Spectroscopy. Springer. pp. 529 ff. ISBN 0-387-31278-1. • Finkelstein, D. “What is a photon?". Optics and Photonics News 14: S12–S17 (Supplement). [108] Jennewein, T.; Achleitner, U.; Weihs, G.; Weinfurter, H.; Zeilinger, A. (2000). “A fast and compact quantum random number generator”. Review of Scientific Instruments 71 (4): 1675–1680. arXiv:quant-ph/9912118. Bibcode:2000RScI...71.1675J. doi:10.1063/1.1150518. • Muthukrishnan, A.; Scully, M.O.; Zubairy, M.S. “The concept of the photon—revisited”. Optics and Photonics News 14: S18–S27 (Supplement). [109] Stefanov, A.; Gisin, N.; Guinnard, O.; Guinnard, L.; Zbiden, H. (2000). “Optical quantum random number generator”. Journal of Modern Optics 47 (4): 595–598. doi:10.1080/095003400147908. 7.19 Additional references By date of publication: • Clauser, J.F. (1974). “Experimental distinction between the quantum and classical field-theoretic predictions for the photoelectric effect”. Physical Review D 9 (4): 853–860. Bibcode:1974PhRvD...9..853C. doi:10.1103/PhysRevD.9.853. • Kimble, H.J.; Dagenais, M.; Mandel, L. (1977). “Photon Anti-bunching in Resonance Fluorescence”. Physical Review Letters 39 (11): 691–695. Bibcode:1977PhRvL..39..691K. doi:10.1103/PhysRevLett.39.691. • Pais, A. (1982). Subtle is the Lord: The Science and the Life of Albert Einstein. Oxford University Press. • Feynman, Richard (1985). QED: The Strange Theory of Light and Matter. Princeton University Press. ISBN 978-0-691-12575-6. • Grangier, P.; Roger, G.; Aspect, A. (1986). “Experimental Evidence for a Photon Anticorrelation Effect on a Beam Splitter: A New Light on Single-Photon Interferences”. Europhysics Letters 1 (4): 173–179. Bibcode:1986EL......1..173G. doi:10.1209/0295-5075/1/4/004. • Lamb, W.E. (1995). “Anti-photon”. Applied Physics B 60 (2–3): 77– 84. Bibcode:1995ApPhB..60...77L. doi:10.1007/BF01135846. • Special supplemental issue of Optics and Photonics News (vol. 14, October 2003) article web link • Mack, H.; Schleich, W.P.. “A photon viewed from Wigner phase space”. Optics and Photonics News 14: S28–S35 (Supplement). • Glauber, R. (2005). “One Hundred Years of Light Quanta” (PDF). 2005 Physics Nobel Prize Lecture. • Hentschel, K. (2007). “Light quanta: The maturing of a concept by the stepwise accretion of meaning”. Physics and Philosophy 1 (2): 1–20. Education with single photons: • Thorn, J.J.; Neel, M.S.; Donato, V.W.; Bergreen, G.S.; Davies, R.E.; Beck, M. (2004). “Observing the quantum behavior of light in an undergraduate laboratory” (PDF). American Journal of Physics 72 (9): 1210–1219. Bibcode:2004AmJPh..72.1210T. doi:10.1119/1.1737397. • Bronner, P.; Strunz, Andreas; Silberhorn, Christine; Meyn, Jan-Peter (2009). “Interactive screen experiments with single photons”. European Journal of Physics 30 (2): 345–353. Bibcode:2009EJPh...30..345B. doi:10.1088/01430807/30/2/014. 7.20 External links • The dictionary definition of photon at Wiktionary • Media related to Photon at Wikimedia Commons Chapter 8 Gluon Gluons /ˈɡluːɒnz/ are elementary particles that act as the 8.2 Numerology of gluons exchange particles (or gauge bosons) for the strong force between quarks, analogous to the exchange of photons Unlike the single photon of QED or the three W and Z in the electromagnetic force between two charged parti- bosons of the weak interaction, there are eight indepencles.[6] dent types of gluon in QCD. In technical terms, gluons are vector gauge bosons that This may be difficult to understand intuitively. Quarks mediate strong interactions of quarks in quantum chro- carry three types of color charge; antiquarks carry three modynamics (QCD). Gluons themselves carry the color types of anticolor. Gluons may be thought of as carrying charge of the strong interaction. This is unlike the photon, both color and anticolor, but to correctly understand how which mediates the electromagnetic interaction but lacks they are combined, it is necessary to consider the mathean electric charge. Gluons therefore participate in the matics of color charge in more detail. strong interaction in addition to mediating it, making QCD significantly harder to analyze than QED (quantum electrodynamics). 8.2.1 Color charge and superposition In quantum mechanics, the states of particles may be added according to the principle of superposition; that is, they may be in a “combined state” with a probability, if some particular quantity is measured, of giving several different outcomes. A relevant illustration in the case at hand would be a gluon with a color state described by: 8.1 Properties √ (r¯b + b¯ r)/ 2. This is read as “red–antiblue plus blue–antired”. (The factor of the square root of two is required for normalization, a detail that is not crucial to understand in this discussion.) If one were somehow able to make a direct measurement of the color of a gluon in this state, there would be a 50% chance of it having red-antiblue color charge and a 50% chance of blue-antired color charge. Diagram 2: e+ e− → Υ(9.46) → 3g 8.2.2 Color singlet states The gluon is a vector boson; like the photon, it has a spin of 1. While massive spin-1 particles have three polarization states, massless gauge bosons like the gluon have only two polarization states because gauge invariance requires the polarization to be transverse. In quantum field theory, unbroken gauge invariance requires that gauge bosons have zero mass (experiment limits the gluon’s rest mass to less than a few meV/c2 ). The gluon has negative intrinsic parity. It is often said that the stable strongly interacting particles (such as the proton and the neutron, i.e. hadrons) observed in nature are “colorless”, but more precisely they are in a “color singlet” state, which is mathematically analogous to a spin singlet state.[7] Such states allow interaction with other color singlets, but not with other color states; because long-range gluon interactions do not exist, this illustrates that gluons in the singlet state do not exist either.[7] 49 50 CHAPTER 8. GLUON The color singlet state is:[7] Since gluons themselves carry color charge, they participate in strong interactions. These gluon-gluon interactions constrain color fields to string-like objects called √ "flux tubes", which exert constant force when stretched. (r¯ r + b¯b + g¯ g )/ 3. Due to this force, quarks are confined within composite limits the range In words, if one could measure the color of the state, there particles called hadrons. This effectively −15 of the strong interaction to 1×10 meters, roughly the would be equal probabilities of it being red-antired, blueatomic nucleus. Beyond a certain distance, the size of an antiblue, or green-antigreen. energy of the flux tube binding two quarks increases linearly. At a large enough distance, it becomes energetically more favorable to pull a quark-antiquark pair out 8.2.3 Eight gluon colors of the vacuum rather than increase the length of the flux tube. There are eight remaining independent color states, which correspond to the “eight types” or “eight colors” of gluons. Gluons also share this property of being confined within Because states can be mixed together as discussed above, hadrons. One consequence is that gluons are not directly there are many ways of presenting these states, which are involved in the nuclear forces between hadrons. The force known as the “color octet”. One commonly used list is:[7] mediators for these are other hadrons called mesons. These are equivalent to the Gell-Mann matrices; the Although in the normal phase of QCD single gluons may translation between the two is that red-antired is the not travel freely, it is predicted that there exist hadrons upper-left matrix entry, red-antiblue is the upper mid- that are formed entirely of gluons — called glueballs. dle entry, blue-antigreen is the middle right entry, and so There are also conjectures about other exotic hadrons in on. The critical feature of these particular eight states is which real gluons (as opposed to virtual ones found in orthat they are linearly independent, and also independent dinary hadrons) would be primary constituents. Beyond of the singlet state; there is no way to add any combina- the normal phase of QCD (at extreme temperatures and tion of states to produce any other. (It is also impossible pressures), quark–gluon plasma forms. In such a plasma to add them to make rr, gg, or bb[8] otherwise the for- there are no hadrons; quarks and gluons become free parbidden singlet state could also be made.) There are many ticles. other possible choices, but all are mathematically equivalent, at least equally complex, and give the same physical results. 8.4 Experimental observations 8.2.4 Group theory details Technically, QCD is a gauge theory with SU(3) gauge symmetry. Quarks are introduced as spinor fields in N flavors, each in the fundamental representation (triplet, denoted 3) of the color gauge group, SU(3). The gluons are vector fields in the adjoint representation (octets, denoted 8) of color SU(3). For a general gauge group, the number of force-carriers (like photons or gluons) is always equal to the dimension of the adjoint representation. For the simple case of SU(N), the dimension of this representation is N 2 − 1. In terms of group theory, the assertion that there are no color singlet gluons is simply the statement that quantum chromodynamics has an SU(3) rather than a U(3) symmetry. There is no known a priori reason for one group to be preferred over the other, but as discussed above, the experimental evidence supports SU(3).[7] 8.3 Confinement Main article: Color confinement Quarks and gluons (colored) manifest themselves by fragmenting into more quarks and gluons, which in turn hadronize into normal (colorless) particles, correlated in jets. As shown in 1978 summer conferences[2] the PLUTO detector at the electron-positron collider DORIS (DESY) produced the first evidence that the hadronic decays of the very narrow resonance Υ(9.46) could be interpreted as three-jet event topologies produced by three gluons. Later published analyses by the same experiment confirmed this interpretation and also the spin 1 nature of the gluon[9][10] (see also the recollection[2] and PLUTO experiments). In summer 1979 at higher energies at the electronpositron collider PETRA (DESY) again three-jet topologies were observed, now interpreted as qq gluon bremsstrahlung, now clearly visible, by TASSO,[11] MARK-J[12] and PLUTO experiments[13] (later in 1980 also by JADE[14] ). The spin 1 of the gluon was confirmed in 1980 by TASSO[15] and PLUTO experiments[16] (see also the review[3] ). In 1991 a subsequent experiment at the LEP storage ring at CERN again confirmed this result.[17] The gluons play an important role in the elementary strong interactions between quarks and gluons, described by QCD and studied particularly at the electron-proton 8.6. REFERENCES collider HERA at DESY. The number and momentum distribution of the gluons in the proton (gluon density) have been measured by two experiments, H1 and ZEUS,[18] in the years 1996 till today (2012). The gluon contribution to the proton spin has been studied by the HERMES experiment at HERA.[19] The gluon density in the photon (when behaving hadronically) also has been measured.[20] Color confinement is verified by the failure of free quark searches (searches of fractional charges). Quarks are normally produced in pairs (quark + antiquark) to compensate the quantum color and flavor numbers; however at Fermilab single production of top quarks has been shown (technically this still involves a pair production, but quark and antiquark are of different flavor).[21] No glueball has been demonstrated. Deconfinement was claimed in 2000 at CERN SPS[22] in heavy-ion collisions, and it implies a new state of matter: quark–gluon plasma, less interacting than in the nucleus, almost as in a liquid. It was found at the Relativistic Heavy Ion Collider (RHIC) at Brookhaven in the years 2004–2010 by four contemporaneous experiments.[23] A quark–gluon plasma state has been confirmed at the CERN Large Hadron Collider (LHC) by the three experiments ALICE, ATLAS and CMS in 2010.[24] 8.5 See also • Quark • Hadron • Meson • Gauge boson • Quark model • Quantum chromodynamics • Quark–gluon plasma • Color confinement • Glueball • Gluon field • Gluon field strength tensor • Exotic hadrons • Standard Model • Three-jet events • Deep inelastic scattering 51 8.6 References [1] M. Gell-Mann (1962). “Symmetries of Baryons and Mesons”. Physical Review 125 (3): 1067–1084. Bibcode:1962PhRv..125.1067G. doi:10.1103/PhysRev.125.1067. [2] B.R. Stella and H.-J. Meyer (2011). "Υ(9.46 GeV) and the gluon discovery (a critical recollection of PLUTO results)". European Physical Journal H 36 (2): 203–243. arXiv:1008.1869v3. Bibcode:2011EPJH...36..203S. doi:10.1140/epjh/e2011-10029-3. [3] P. Söding (2010). “On the discovery of the gluon”. European Physical Journal H 35 (1): 3–28. Bibcode:2010EPJH...35....3S. doi:10.1140/epjh/e201000002-5. [4] W.-M. Yao et al. (2006). “Review of Particle Physics” (PDF). Journal of Physics G 33: 1. arXiv:astro-ph/0601168. Bibcode:2006JPhG...33....1Y. doi:10.1088/0954-3899/33/1/001. [5] F. Yndurain (1995). “Limits on the mass of the gluon”. Physics Letters B 345 (4): 524. Bibcode:1995PhLB..345..524Y. doi:10.1016/03702693(94)01677-5. [6] C.R. Nave. “The Color Force”. HyperPhysics. Georgia State University, Department of Physics. Retrieved 201204-02. [7] David Griffiths (1987). Introduction to Elementary Particles. John Wiley & Sons. pp. 280–281. ISBN 0-47160386-4. [8] J. Baez. “Why are there eight gluons and not nine?". Retrieved 2009-09-13. [9] Ch. Berger et al. (PLUTO Collaboration) (1979). “Jet analysis of the Υ(9.46) decay into charged hadrons”. Physics Letters B 82 (3–4): 449. Bibcode:1979PhLB...82..449B. doi:10.1016/03702693(79)90265-X. [10] Ch. Berger et al. (PLUTO Collaboration) (1981). “Topology of the Υ decay”. Zeitschrift für Physik C 8 (2): 101. Bibcode:1981ZPhyC...8..101B. doi:10.1007/BF01547873. [11] R. Brandelik et al. (TASSO collaboration) (1979). “Evidence for Planar Events in e+ e− Annihilation at Physics Letters B 86 (2): 243– High Energies”. 249. Bibcode:1979PhLB...86..243B. doi:10.1016/03702693(79)90830-X. [12] D.P. Barber et al. (MARK-J collaboration) (1979). “Discovery of Three-Jet Events and a Test of Quantum Chromodynamics at PETRA”. Physical Review Letters 43 (12): 830. Bibcode:1979PhRvL..43..830B. doi:10.1103/PhysRevLett.43.830. [13] Ch. Berger et al. (PLUTO Collaboration) (1979). “Evidence for Gluon Bremsstrahlung in e+ e− Annihilations at High Energies”. Physics Letters B 86 (3–4): 418. Bibcode:1979PhLB...86..418B. doi:10.1016/03702693(79)90869-4. 52 [14] W. Bartel et al. (JADE Collaboration) (1980). “Observation of planar three-jet events in e+ e− annihilation and evidence for gluon bremsstrahlung”. Physics Letters B 91: 142. Bibcode:1980PhLB...91..142B. doi:10.1016/03702693(80)90680-2. [15] R. Brandelik et al. (TASSO Collaboration) (1980). “Evidence for a spin-1 gluon in three-jet events”. Physics Letters B 97 (3–4): 453. Bibcode:1980PhLB...97..453B. doi:10.1016/0370-2693(80)90639-5. [16] Ch. Berger et al. (PLUTO Collaboration) (1980). “A study of multi-jet events in e+ e− annihilation”. Physics Letters B 97 (3–4): 459. Bibcode:1980PhLB...97..459B. doi:10.1016/0370-2693(80)90640-1. [17] G. Alexander et al. (OPAL Collaboration) (1991). “Measurement of Three-Jet Distributions Sensitive to the Gluon Spin in e+ e− Annihilations at √s = 91 GeV”. Zeitschrift für Physik C 52 (4): 543. Bibcode:1991ZPhyC..52..543A. doi:10.1007/BF01562326. [18] L. Lindeman (H1 and ZEUS collaborations) (1997). “Proton structure functions and gluon density at HERA”. Nuclear Physics B Proceedings Supplements 64: 179–183. Bibcode:1998NuPhS..64..179L. doi:10.1016/S09205632(97)01057-8. [19] http://www-hermes.desy.de [20] C. Adloff et al. (H1 collaboration) (1999). “Charged particle cross sections in the photoproduction and extraction of the gluon density in the photon”. European Physical Journal C 10: 363–372. arXiv:hep-ex/9810020. Bibcode:1999EPJC...10..363H. doi:10.1007/s100520050761. [21] M. Chalmers (6 March 2009). “Top result for Tevatron”. Physics World. Retrieved 2012-04-02. [22] M.C. Abreu et al. (2000). “Evidence for deconfinement of quark and antiquark from the J/Ψ suppression pattern measured in Pb-Pb collisions at the CERN SpS”. Physics Letters B 477: 28–36. Bibcode:2000PhLB..477...28A. doi:10.1016/S0370-2693(00)00237-9. [23] D. Overbye (15 February 2010). “In Brookhaven Collider, Scientists Briefly Break a Law of Nature”. New York Times. Retrieved 2012-04-02. [24] “LHC experiments bring new insight into primordial universe” (Press release). CERN. 26 November 2010. Retrieved 2012-04-02. 8.7 Further reading • A. Ali and G. Kramer (2011). “JETS and QCD: A historical review of the discovery of the quark and gluon jets and its impact on QCD”. European Physical Journal H 36 (2): 245–326. arXiv:1012.2288. Bibcode:2011EPJH...36..245A. doi:10.1140/epjh/e2011-10047-1. CHAPTER 8. GLUON Chapter 9 Higgs boson The Higgs boson or Higgs particle is an elementary particle in the Standard Model of particle physics. Observation of the particle allows scientists to explore the Higgs field[6][7] —a fundamental field of crucial importance to particle physics theory,[7] first suspected to exist in the 1960s, that unlike other known fields such as the electromagnetic field, takes a non-zero constant value almost everywhere. For several decades the question of the Higgs Field’s existence was the last unverified part of the Standard Model of particle physics and “the central problem in particle physics”.[8][9] The presence of this field, now believed to be confirmed, explains why some fundamental particles have mass when, based on the symmetries controlling their interactions, they should be massless. It also solves several other long-standing puzzles, such as the reason for the weak force’s extremely short range. Despite being present everywhere, the existence of the Higgs field is very hard to confirm. It can be detected through its excitations (i.e. Higgs particles), but these are extremely hard to produce and detect. The importance of this fundamental question led to a 40 year search, and the construction of one of the world’s most expensive and complex experimental facilities to date, CERN's Large Hadron Collider,[10] able to create Higgs bosons and other particles for observation and study. On 4 July 2012, the discovery of a new particle with a mass between 125 and 127 GeV/c2 was announced; physicists suspected that it was the Higgs boson.[11][12][13] By March 2013, the particle had been proven to behave, interact and decay in many of the ways predicted by the Standard Model, and was also tentatively confirmed to have even parity and zero spin,[1] two fundamental attributes of a Higgs boson. This appears to be the first elementary scalar particle discovered in nature.[14] More data is needed to know if the discovered particle exactly matches the predictions of the Standard Model, or whether, as predicted by some theories, multiple Higgs bosons exist.[3] died in 2011 and the Nobel Prize is not ordinarily given posthumously).[15] Although Higgs’s name has come to be associated with this theory, several researchers between about 1960 and 1972 each independently developed different parts of it. In mainstream media the Higgs boson has often been called the “God particle”, from a 1993 book on the topic; the nickname is strongly disliked by many physicists, including Higgs, who regard it as inappropriate sensationalism.[16][17][18] In the Standard Model, the Higgs particle is a boson with no spin, electric charge, or colour charge. It is also very unstable, decaying into other particles almost immediately. It is a quantum excitation of one of the four components of the Higgs field. The latter constitutes a scalar field, with two neutral and two electrically charged components, and forms a complex doublet of the weak isospin SU(2) symmetry. The Higgs field is tachyonic (this does not refer to faster-than-light speeds, it means that symmetry-breaking through condensation of a particle must occur under certain conditions), and has a "Mexican hat" shaped potential with nonzero strength everywhere (including otherwise empty space), which in its vacuum state breaks the weak isospin symmetry of the electroweak interaction. When this happens, three components of the Higgs field are “absorbed” by the SU(2) and U(1) gauge bosons (the "Higgs mechanism") to become the longitudinal components of the now-massive W and Z bosons of the weak force. The remaining electrically neutral component separately couples to other particles known as fermions (via Yukawa couplings), causing these to acquire mass as well. Some versions of the theory predict more than one kind of Higgs fields and bosons. Alternative “Higgsless” models would have been considered if the Higgs boson was not discovered. The Higgs boson is named after Peter Higgs, one of six 9.1 physicists who, in 1964, proposed the mechanism that suggested the existence of such a particle. On December 9.1.1 10, 2013 two of these, Peter Higgs and François Englert, were awarded the Nobel Prize in Physics for their work and prediction (Englert’s co-researcher Robert Brout had 53 A non-technical summary “Higgs” terminology 54 9.1.2 CHAPTER 9. HIGGS BOSON Overview In particle physics, elementary particles and forces give rise to the world around us. Nowadays, physicists explain the behaviour of these particles and how they interact using the Standard Model—a widely accepted and “remarkably” accurate[21] framework based on gauge invariance and symmetries, believed to explain almost everything in the world we see, other than gravity.[22] But by around 1960 all attempts to create a gauge invariant theory for two of the four fundamental forces had consistently failed at one crucial point: although gauge invariance seemed extremely important, it seemed to make any theory of electromagnetism and the weak force go haywire, by demanding that either many particles with mass were massless or that non-existent forces and massless particles had to exist. Scientists had no idea how to get past this point. In 1962 physicist Philip Anderson wrote a paper that built upon work by Yoichiro Nambu concerning “broken symmetries” in superconductivity and particle physics. He suggested that “broken symmetries” might also be the missing piece needed to solve the problems of gauge invariance. In 1964 a theory was created almost simultaneously by 3 different groups of researchers, that showed Anderson’s suggestion was possible - the gauge theory and “mass problems” could indeed be resolved if an unusual kind of field existed throughout the universe; if this kind of field did exist, it would apparently cause existing particles to acquire mass instead of new massless particles being formed. Although these ideas did not gain much initial support or attention, by 1972 it had been developed into a comprehensive theory and proved capable of giving “sensible” results that were extremely accurate, including very accurate predictions of several other particles discovered during the following years.[Note 7] During the 1970s these theories rapidly became the "standard model" favoured by physicists and used to describe particle physics and particle interactions in nature. There was not yet any direct evidence that this field actually existed, but even without proof of the field, the accuracy of its predictions led scientists to believe the theory might be true. By the 1980s the question whether or not such a field existed and whether this was the correct explanation, was considered to be one of the most important unanswered questions in particle physics, and by the 1990s two of the largest experimental installations ever created were being designed and constructed to find the answer. If this new kind of field did exist in nature, it would be a monumental discovery for science and human knowledge, and would open doorways to new knowledge in many disciplines. If not, then other more complicated theories would need to be explored. The simplest solution to whether the field existed was by searching for a new kind of particle it would have to give off, known as “Higgs bosons” or the “Higgs particle”. These would be extremely difficult to find, so it was only many years later that experimental technology became sophisticated enough to answer the question. While several symmetries in nature are spontaneously broken through a form of the Higgs mechanism, in the context of the Standard Model the term "Higgs mechanism" almost always means symmetry breaking of the electroweak field. It is considered confirmed, but revealing the exact cause has been difficult. Various analogies have also been invented to describe the Higgs field and boson, including analogies with wellknown symmetry breaking effects such as the rainbow and prism, electric fields, ripples, and resistance of macro objects moving through media, like people moving through crowds or some objects moving through syrup or molasses. However, analogies based on simple resistance to motion are inaccurate as the Higgs field does not work by resisting motion. 9.2 Significance 9.2.1 Scientific impact Evidence of the Higgs field and its properties has been extremely significant scientifically, for many reasons. The Higgs boson’s importance is largely that it is able to be examined using existing knowledge and experimental technology, as a way to confirm and study the entire Higgs field theory.[6][7] Conversely, proof that the Higgs field and boson do not exist would also have been significant. In discussion form, the relevance includes: 9.2.2 “Real world” impact As yet, there are no known immediate technological benefits of finding the Higgs particle. However, observers in both media and science point out that when fundamental discoveries are made about our world, their practical uses can take decades to emerge, but are often worldchanging when they do. A common pattern for fundamental discoveries is for practical applications to follow later, once the discovery has been explored further, at which point they become the basis for social change and new technologies.[44][45][46] Other observers highlight technological spin-offs from this and related particle physics activities, which have already brought major developments to society. For example, the World Wide Web as used today was created by physicists working in global collaborations on particle experiments at CERN to share their results. The results of massive amounts of data produced by the Large Hadron Collider have led to significant advances in distributed and cloud computing, now well established within mainstream services.[45] 9.3. HISTORY 9.3 History See also: 1964 PRL symmetry breaking papers, Higgs mechanism and History of quantum field theory Particle physicists study matter made from fundamental Nobel Prize Laureate Peter Higgs in Stockholm, December 2013 particles whose interactions are mediated by exchange particles - gauge bosons - acting as force carriers. At the beginning of the 1960s a number of these particles had been discovered or proposed, along with theories suggesting how they relate to each other, some of which had already been reformulated as field theories in which the objects of study are not particles and forces, but quantum fields and their symmetries.[47]:150 However, attempts to unify known fundamental forces such as the electromagnetic force and the weak nuclear force were known to be incomplete. One known omission was that gauge invariant approaches, including non-abelian models such as Yang–Mills theory (1954), which held great promise for unified theories, also seemed to predict known massive particles as massless.[48] Goldstone’s theorem, relating to continuous symmetries within some theories, also appeared to rule out many obvious solutions,[49] since it appeared to show that zero-mass particles would have to also exist that were “simply not seen”.[50] According to Guralnik, physicists had “no understanding” how these problems could be overcome.[50] 55 realized in QCD, where the strong interactions get rid of the massless “gluon” states at long distances. By the very early sixties, people had begun to understand another source of massless particles: spontaneous symmetry breaking of a continuous symmetry. What Philip Anderson realized and worked out in the summer of 1962 was that, when you have both gauge symmetry and spontaneous symmetry breaking, the Nambu–Goldstone massless mode can combine with the massless gauge field modes to produce a physical massive vector field. This is what happens in superconductivity, a subject about which Anderson was (and is) one of the leading experts.” [text condensed] [48] The Higgs mechanism is a process by which vector bosons can get rest mass without explicitly breaking gauge invariance, as a byproduct of spontaneous symmetry breaking.[51][52] The mathematical theory behind spontaneous symmetry breaking was initially conceived and published within particle physics by Yoichiro Nambu in 1960,[53] the concept that such a mechanism could offer a possible solution for the “mass problem” was originally suggested in 1962 by Philip Anderson (who had previously written papers on broken symmetry and its outcomes in superconductivity[54] and concluded in his 1963 paper on Yang-Mills theory that “considering the superconducting analog... [t]hese two types of bosons seem capable of canceling each other out... leaving finite mass bosons”),[55]:4–5[56] and Abraham Klein and Benjamin Lee showed in March 1964 that Goldstone’s theorem could be avoided this way in at least some non-relativistic cases and speculated it might be possible in truly relativistic cases.[57] These approaches were quickly developed into a full relativistic model, independently and almost simultaneously, by three groups of physicists: by François Englert and Robert Brout in August 1964;[58] by Peter Higgs in October 1964;[59] and by Gerald Guralnik, Carl Hagen, and Tom Kibble (GHK) in November 1964.[60] Higgs also wrote a short but important[51] response published in September 1964 to an objection by Gilbert,[61] which showed that if calculating within the radiation gauge, Goldstone’s theorem and Gilbert’s objection would become inapplicable.[Note 11] (Higgs later described Gilbert’s objection as prompting his own paper.[62] ) Properties of the model were further considered by Guralnik in 1965,[63] by Higgs in 1966,[64] by Particle physicist and mathematician Peter Woit sum- Kibble in 1967,[65] and further by GHK in 1967.[66] The marised the state of research at the time: original three 1964 papers showed that when a gauge theory is combined with an additional field that sponta“Yang and Mills work on non-abelian gauge neously breaks the symmetry, the gauge bosons can contheory had one huge problem: in perturbation sistently acquire a finite mass.[51][52][67] In 1967, Steven theory it has massless particles which don’t Weinberg[68] and Abdus Salam[69] independently showed correspond to anything we see. One way of how a Higgs mechanism could be used to break the elecgetting rid of this problem is now fairly welltroweak symmetry of Sheldon Glashow's unified model for the weak and electromagnetic interactions[70] (itself understood, the phenomenon of confinement 56 an extension of work by Schwinger), forming what became the Standard Model of particle physics. Weinberg was the first to observe that this would also provide mass terms for the fermions.[71] [Note 12] However, the seminal papers on spontaneous breaking of gauge symmetries were at first largely ignored, because it was widely believed that the (non-Abelian gauge) theories in question were a dead-end, and in particular that they could not be renormalised. In 1971–72, Martinus Veltman and Gerard 't Hooft proved renormalisation of Yang–Mills was possible in two papers covering massless, and then massive, fields.[71] Their contribution, and others’ work on the renormalization group including “substantial” theoretical work by Russian physicists Ludvig Faddeev, Andrei Slavnov, Efim Fradkin and Igor Tyutin[72] - was eventually “enormously profound and influential”,[73] but even with all key elements of the eventual theory published there was still almost no wider interest. For example, Coleman found in a study that “essentially no-one paid any attention” to Weinberg’s paper prior to 1971[74] and discussed by David Politzer in his 2004 Nobel speech.[73] – now the most cited in particle physics[75] – and even in 1970 according to Politzer, Glashow’s teaching of the weak interaction contained no mention of Weinberg’s, Salam’s, or Glashow’s own work.[73] In practice, Politzer states, almost everyone learned of the theory due to physicist Benjamin Lee, who combined the work of Veltman and 't Hooft with insights by others, and popularised the completed theory.[73] In this way, from 1971, interest and acceptance “exploded” [73] and the ideas were quickly absorbed in the mainstream.[71][73] CHAPTER 9. HIGGS BOSON anniversary celebration.[67] Their six authors were also awarded the 2010 J. J. Sakurai Prize for Theoretical Particle Physics for this work.[77] (A controversy also arose the same year, because in the event of a Nobel Prize only up to three scientists could be recognised, with six being credited for the papers.[78] ) Two of the three PRL papers (by Higgs and by GHK) contained equations for the hypothetical field that eventually would become known as the Higgs field and its hypothetical quantum, the Higgs boson.[59][60] Higgs’ subsequent 1966 paper showed the decay mechanism of the boson; only a massive boson can decay and the decays can prove the mechanism. In the paper by Higgs the boson is massive, and in a closing sentence Higgs writes that “an essential feature” of the theory “is the prediction of incomplete multiplets of scalar and vector bosons".[59] (Frank Close comments that 1960s gauge theorists were focused on the problem of massless vector bosons, and the implied existence of a massive scalar boson was not seen as important; only Higgs directly addressed it.[79]:154, 166, 175 ) In the paper by GHK the boson is massless and decoupled from the massive states.[60] In reviews dated 2009 and 2011, Guralnik states that in the GHK model the boson is massless only in a lowest-order approximation, but it is not subject to any constraint and acquires mass at higher orders, and adds that the GHK paper was the only one to show that there are no massless Goldstone bosons in the model and to give a complete analysis of the general Higgs mechanism.[50][80] All three reached similar conclusions, despite their very different approaches: Higgs’ paper essentially used classical techniques, Englert and Brout’s involved calculating vacuum polarization in perThe resulting electroweak theory and Standard Model turbation theory around an assumed symmetry-breaking vacuum state, and GHK used operator formalism and have correctly predicted (among other discoveries) weak in which neutral currents, three bosons, the top and charm quarks, conservation laws to explore in depth the ways Goldstone’s theorem may be worked around.[51] and with great precision, the mass and other properties of some of these.[Note 7] Many of those involved eventually won Nobel Prizes or other renowned awards. A 1974 paper and comprehensive review in Reviews of Mod- 9.4 Theoretical properties ern Physics commented that “while no one doubted the [mathematical] correctness of these arguments, no one Main article: Higgs mechanism quite believed that nature was diabolically clever enough [76]:9 to take advantage of them”, adding that the theory had so far produced meaningful answers that accorded with experiment, but it was unknown whether the theory was actually correct.[76]:9,36(footnote),43–44,47 By 1986 9.4.1 Theoretical need for the Higgs and again in the 1990s it became possible to write that understanding and proving the Higgs sector of the Stan- Gauge invariance is an important property of modern pardard Model was “the central problem today in particle ticle theories such as the Standard Model, partly due to its success in other areas of fundamental physics such physics”.[8][9] as electromagnetism and the strong interaction (quantum chromodynamics). However, there were great difficulties in developing gauge theories for the weak nuclear force or 9.3.1 Summary and impact of the PRL pa- a possible unified electroweak interaction. Fermions with pers a mass term would violate gauge symmetry and therefore cannot be gauge invariant. (This can be seen by exThe three papers written in 1964 were each recognised as amining the Dirac Lagrangian for a fermion in terms of milestone papers during Physical Review Letters 's 50th left and right handed components; we find none of the 9.4. THEORETICAL PROPERTIES 57 Higgs field (and with other particles capable of interacting with the Higgs field) instead of becoming new massless particles, the intractable problems of both underlying theories “neutralise” each other, and the residual outcome is that elementary particles acquire a consistent mass based on how strongly they interact with the Higgs field. It is the simplest known process capable of giving mass to the "Symmetry breaking illustrated": – At high energy levels (left) the gauge bosons while remaining compatible with gauge theball settles in the center, and the result is symmetrical. At lower [81] Its quantum would be a scalar boson, known as energy levels (right), the overall “rules” remain symmetrical, but ories. the Higgs boson.[82] the “Mexican hat” potential comes into effect: “local” symmetry inevitably becomes broken since eventually the ball must at random roll one way or another. spin-half particles could ever flip helicity as required for mass, so they must be massless.[Note 13] ) W and Z bosons are observed to have mass, but a boson mass term contains terms, which clearly depend on the choice of gauge and therefore these masses too cannot be gauge invariant. Therefore it seems that none of the standard model fermions or bosons could “begin” with mass as an inbuilt property except by abandoning gauge invariance. If gauge invariance were to be retained, then these particles had to be acquiring their mass by some other mechanism or interaction. Additionally, whatever was giving these particles their mass, had to not “break” gauge invariance as the basis for other parts of the theories where it worked well, and had to not require or predict unexpected massless particles and long-range forces (seemingly an inevitable consequence of Goldstone’s theorem) which did not actually seem to exist in nature. Leptons e µ τ γ νe νµ τν W q Z Weak Bosons Photon H Quarks g Gluons Higgs Boson Summary of interactions between certain particles described by the Standard Model. 9.4.2 Properties of the Higgs field In the Standard Model, the Higgs field is a scalar tachyonic field – 'scalar' meaning it does not transform under Lorentz transformations, and 'tachyonic' meaning the field (but not the particle) has imaginary mass and in certain configurations must undergo symmetry breaking. It consists of four components, two neutral ones and two charged component fields. Both of the charged components and one of the neutral fields are Goldstone bosons, which act as the longitudinal third-polarization components of the massive W+ , W− , and Z bosons. The quanThe Standard Model hypothesizes a field which is respon- tum of the remaining neutral component corresponds sible for this effect, called the Higgs field (symbol: ϕ to (and[83]is theoretically realised as) the massive Higgs ), which has the unusual property of a non-zero ampli- boson, this component can interact with fermions viua tude in its ground state; i.e., a non-zero vacuum expecta- Yukawa coupling to give them mass, as well. tion value. It can have this effect because of its unusual Mathematically, the Higgs field has imaginary mass and is “Mexican hat” shaped potential whose lowest “point” is therefore a tachyonic field.[84] While tachyons (particles not at its “centre”. Below a certain extremely high energy that move faster than light) are a purely hypothetical conlevel the existence of this non-zero vacuum expectation cept, fields with imaginary mass have come to play an imspontaneously breaks electroweak gauge symmetry which portant role in modern physics.[85][86] Under no circumin turn gives rise to the Higgs mechanism and triggers the stances do any excitations ever propagate faster than light acquisition of mass by those particles interacting with the in such theories — the presence or absence of a tachyonic field. This effect occurs because scalar field components mass has no effect whatsoever on the maximum velocity of the Higgs field are “absorbed” by the massive bosons of signals (there is no violation of causality).[87] Instead of as degrees of freedom, and couple to the fermions via faster-than-light particles, the imaginary mass creates an Yukawa coupling, thereby producing the expected mass instability:- any configuration in which one or more field terms. In effect when symmetry breaks under these con- excitations are tachyonic must spontaneously decay, and ditions, the Goldstone bosons that arise interact with the the resulting configuration contains no physical tachyons. A solution to all of these overlapping problems came from the discovery of a previously unnoticed borderline case hidden in the mathematics of Goldstone’s theorem,[Note 11] that under certain conditions it might theoretically be possible for a symmetry to be broken without disrupting gauge invariance and without any new massless particles or forces, and having “sensible” (renormalisable) results mathematically: this became known as the Higgs mechanism. 58 CHAPTER 9. HIGGS BOSON This process is known as tachyon condensation, and is 9.4.4 Production now believed to be the explanation for how the Higgs mechanism itself arises in nature, and therefore the rea- If Higgs particle theories are correct, then a Higgs particle can be produced much like other particles that are son behind electroweak symmetry breaking. studied, in a particle collider. This involves accelerating Although the notion of imaginary mass might seem troua large number of particles to extremely high energies bling, it is only the field, and not the mass itself, that and extremely close to the speed of light, then allowing is quantized. Therefore the field operators at spacelike them to smash together. Protons and lead ions (the bare separated points still commute (or anticommute), and innuclei of lead atoms) are used at the LHC. In the extreme formation and particles still do not propagate faster than energies of these collisions, the desired esoteric particles [88] light. Tachyon condensation drives a physical system will occasionally be produced and this can be detected that has reached a local limit and might naively be exand studied; any absence or difference from theoretipected to produce physical tachyons, to an alternate stable cal expectations can also be used to improve the theory. state where no physical tachyons exist. Once a tachyonic The relevant particle theory (in this case the Standard field such as the Higgs field reaches the minimum of the Model) will determine the necessary kinds of collisions potential, its quanta are not tachyons any more but rather and detectors. The Standard Model predicts that Higgs [89] are ordinary particles such as the Higgs boson. bosons could be formed in a number of ways,[97][98][99] although the probability of producing a Higgs boson in any collision is always expected to be very small—for example, only 1 Higgs boson per 10 billion collisions in the Large Hadron Collider.[Note 14] The most common expected processes for Higgs boson production are: 9.4.3 Properties of the Higgs boson Since the Higgs field is scalar, the Higgs boson has no spin. The Higgs boson is also its own antiparticle and is CP-even, and has zero electric and colour charge.[90] The Minimal Standard Model does not predict the mass of the Higgs boson.[91] If that mass is between 115 and 180 GeV/c2 , then the Standard Model can be valid at energy scales all the way up to the Planck scale (1019 GeV).[92] Many theorists expect new physics beyond the Standard Model to emerge at the TeV-scale, based on unsatisfactory properties of the Standard Model.[93] The highest possible mass scale allowed for the Higgs boson (or some other electroweak symmetry breaking mechanism) is 1.4 TeV; beyond this point, the Standard Model becomes inconsistent without such a mechanism, because unitarity is violated in certain scattering processes.[94] It is also possible, although experimentally difficult, to estimate the mass of the Higgs boson indirectly. In the Standard Model, the Higgs boson has a number of indirect effects; most notably, Higgs loops result in tiny corrections to masses of W and Z bosons. Precision measurements of electroweak parameters, such as the Fermi constant and masses of W/Z bosons, can be used to calculate constraints on the mass of the Higgs. As of July 2011, the precision electroweak measurements tell us that the mass of the Higgs boson is likely to be less than about 161 GeV/c2 at 95% confidence level (this upper limit would increase to 185 GeV/c2 if the lower bound of 114.4 GeV/c2 from the LEP-2 direct search is allowed for[95] ). These indirect constraints rely on the assumption that the Standard Model is correct. It may still be possible to discover a Higgs boson above these masses if it is accompanied by other particles beyond those predicted by the Standard Model.[96] • Gluon fusion. If the collided particles are hadrons such as the proton or antiproton—as is the case in the LHC and Tevatron—then it is most likely that two of the gluons binding the hadron together collide. The easiest way to produce a Higgs particle is if the two gluons combine to form a loop of virtual quarks. Since the coupling of particles to the Higgs boson is proportional to their mass, this process is more likely for heavy particles. In practice it is enough to consider the contributions of virtual top and bottom quarks (the heaviest quarks). This process is the dominant contribution at the LHC and Tevatron being about ten times more likely than any of the other processes.[97][98] • Higgs Strahlung. If an elementary fermion collides with an anti-fermion—e.g., a quark with an antiquark or an electron with a positron—the two can merge to form a virtual W or Z boson which, if it carries sufficient energy, can then emit a Higgs boson. This process was the dominant production mode at the LEP, where an electron and a positron collided to form a virtual Z boson, and it was the second largest contribution for Higgs production at the Tevatron. At the LHC this process is only the third largest, because the LHC collides protons with protons, making a quark-antiquark collision less likely than at the Tevatron. Higgs Strahlung is also known as associated production.[97][98][99] • Weak boson fusion. Another possibility when two (anti-)fermions collide is that the two exchange a virtual W or Z boson, which emits a Higgs boson. The colliding fermions do not need to be the same type. So, for example, an up quark may exchange a Z boson with an anti-down quark. This process 9.4. THEORETICAL PROPERTIES 59 is the second most important for the production of ratio; the fraction of the total number decays that follows Higgs particle at the LHC and LEP.[97][99] that process. The SM predicts these branching ratios as a function of the Higgs mass (see plot). • Top fusion. The final process that is commonly considered is by far the least likely (by two orders of One way that the Higgs can decay is by splitting into magnitude). This process involves two colliding glu- a fermion–antifermion pair. As general rule, the Higgs ons, which each decay into a heavy quark–antiquark is more likely to decay into heavy fermions than light pair. A quark and antiquark from each pair can then fermions, because the mass of a fermion is proportional to the strength of its interaction with the Higgs.[102] By combine to form a Higgs particle.[97][98] this logic the most common decay should be into a top– antitop quark pair. However, such a decay is only possible if the Higgs is heavier than ~346 GeV/c2 , twice the 9.4.5 Decay mass of the top quark. For a Higgs mass of 126 GeV/c2 the SM predicts that the most common decay is into a bottom–antibottom quark pair, which happens 56.1% of the time.[5] The second most common fermion decay at that mass is a tau–antitau pair, which happens only about 6% of the time.[5] The Standard Model prediction for the decay width of the Higgs particle depends on the value of its mass. Quantum mechanics predicts that if it is possible for a particle to decay into a set of lighter particles, then it will eventually do so.[101] This is also true for the Higgs boson. The likelihood with which this happens depends on a variety of factors including: the difference in mass, the strength of the interactions, etc. Most of these factors are fixed by the Standard Model, except for the mass of the Higgs boson itself. For a Higgs boson with a mass of 126 GeV/c2 the SM predicts a mean life time of about 1.6×10−22 s.[Note 2] The Standard Model prediction for the branching ratios of the different decay modes of the Higgs particle depends on the value of its mass. Another possibility is for the Higgs to split into a pair of massive gauge bosons. The most likely possibility is for the Higgs to decay into a pair of W bosons (the light blue line in the plot), which happens about 23.1% of the time for a Higgs boson with a mass of 126 GeV/c2 .[5] The W bosons can subsequently decay either into a quark and an antiquark or into a charged lepton and a neutrino. However, the decays of W bosons into quarks are difficult to distinguish from the background, and the decays into leptons cannot be fully reconstructed (because neutrinos are impossible to detect in particle collision experiments). A cleaner signal is given by decay into a pair of Z-bosons (which happens about 2.9% of the time for a Higgs with a mass of 126 GeV/c2 ),[5] if each of the bosons subsequently decays into a pair of easy-to-detect charged leptons (electrons or muons). Decay into massless gauge bosons (i.e., gluons or photons) is also possible, but requires intermediate loop of virtual heavy quarks (top or bottom) or massive gauge bosons.[102] The most common such process is the decay into a pair of gluons through a loop of virtual heavy quarks. This process, which is the reverse of the gluon fusion process mentioned above, happens approximately 8.5% of the time for a Higgs boson with a mass of 126 GeV/c2 .[5] Much rarer is the decay into a pair of photons mediated by a loop of W bosons or heavy quarks, which happens only twice for every thousand decays.[5] However, this process is very relevant for experimental searches for the Higgs boson, because the energy and momentum of the photons can be measured very precisely, giving an accurate reconstruction of the mass of the decaying particle.[102] 9.4.6 Alternative models Since it interacts with all the massive elementary particles Main article: Alternatives to the Standard Model Higgs of the SM, the Higgs boson has many different processes through which it can decay. Each of these possible pro- The Minimal Standard Model as described above is the cesses has its own probability, expressed as the branching simplest known model for the Higgs mechanism with just 60 CHAPTER 9. HIGGS BOSON one Higgs field. However, an extended Higgs sector with additional Higgs particle doublets or triplets is also possible, and many extensions of the Standard Model have this feature. The non-minimal Higgs sector favoured by theory are the two-Higgs-doublet models (2HDM), which predict the existence of a quintet of scalar particles: two CP-even neutral Higgs bosons h0 and H0 , a CPodd neutral Higgs boson A0 , and two charged Higgs particles H± . Supersymmetry (“SUSY”) also predicts relations between the Higgs-boson masses and the masses of the gauge bosons, and could accommodate a 125 GeV/c2 neutral Higgs boson. The key method to distinguish between these different models involves study of the particles’ interactions (“coupling”) and exact decay processes (“branching ratios”), which can be measured and tested experimentally in particle collisions. In the Type-I 2HDM model one Higgs doublet couples to up and down quarks, while the second doublet does not couple to quarks. This model has two interesting limits, in which the lightest Higgs couples to just fermions (“gauge-phobic") or just gauge bosons (“fermiophobic”), but not both. In the Type-II 2HDM model, one Higgs doublet only couples to up-type quarks, the other only couples to down-type quarks.[103] The heavily researched Minimal Supersymmetric Standard Model (MSSM) includes a Type-II 2HDM Higgs sector, so it could be disproven by evidence of a Type-I 2HDM Higgs. as a parameter to be measured, rather than a value to be calculated. This is seen as theoretically unsatisfactory, particularly as quantum corrections (related to interactions with virtual particles) should apparently cause the Higgs particle to have a mass immensely higher than that observed, but at the same time the Standard Model requires a mass of the order of 100 to 1000 GeV to ensure unitarity (in this case, to unitarise longitudinal vector boson scattering).[106] Reconciling these points appears to require explaining why there is an almost-perfect cancellation resulting in the visible mass of ~ 125 GeV, and it is not clear how to do this. Because the weak force is about 1032 times stronger than gravity, and (linked to this) the Higgs boson’s mass is so much less than the Planck mass or the grand unification energy, it appears that either there is some underlying connection or reason for these observations which is unknown and not described by the Standard Model, or some unexplained and extremely precise fine-tuning of parameters – however at present neither of these explanations is proven. This is known as a hierarchy problem.[107] More broadly, the hierarchy problem amounts to the worry that a future theory of fundamental particles and interactions should not have excessive fine-tunings or unduly delicate cancellations, and should allow masses of particles such as the Higgs boson to be calculable. The problem is in some ways unique to spin-0 particles (such as the Higgs boson), which can give rise to issues related to quantum corrections that do not affect particles with spin.[106] A number of solutions have been proposed, including supersymmetry, conformal solutions and solutions via extra dimensions such as braneworld models. In other models the Higgs scalar is a composite particle. For example, in technicolor the role of the Higgs field is played by strongly bound pairs of fermions called techniquarks. Other models, feature pairs of top quarks (see top quark condensate). In yet other models, there is no Higgs field at all and the electroweak symmetry is There are also issues of quantum triviality, which suggests that it may not be possible to create a consistent quantum broken using extra dimensions.[104][105] field theory involving elementary scalar particles. 9.5 Experimental search Main article: Search for the Higgs boson A one-loop Feynman diagram of the first-order correction to the Higgs mass. In the Standard Model the effects of these corrections are potentially enormous, giving rise to the so-called hierarchy problem. 9.4.7 Further theoretical issues and hierarchy problem Main articles: Hierarchy problem and Hierarchy problem § The Higgs mass The Standard Model leaves the mass of the Higgs boson To produce Higgs bosons, two beams of particles are accelerated to very high energies and allowed to collide within a particle detector. Occasionally, although rarely, a Higgs boson will be created fleetingly as part of the collision byproducts. Because the Higgs boson decays very quickly, particle detectors cannot detect it directly. Instead the detectors register all the decay products (the decay signature) and from the data the decay process is reconstructed. If the observed decay products match a possible decay process (known as a decay channel) of a Higgs boson, this indicates that a Higgs boson may have been created. In practice, many processes may produce similar decay signatures. Fortunately, the Standard Model precisely predicts the likelihood of each of these, and each known process, occurring. So, if the detector detects more decay signatures consistently matching a Higgs 9.5. EXPERIMENTAL SEARCH 61 boson than would otherwise be expected if Higgs bosons ther ranges for the Higgs mass, and was shut down on did not exist, then this would be strong evidence that the 30 September 2011 because it no longer could keep up Higgs boson exists. with the LHC. The final analysis of the data excluded of a Higgs boson with a mass between 147 Because Higgs boson production in a particle collision is the possibility 2 GeV/c and 180 GeV/c2 . In addition, there was a small [Note 14] likely to be very rare (1 in 10 billion at the LHC), and many other possible collision events can have similar (but not significant) excess of events possibly indicating with a mass between 115 GeV/c2 and 140 decay signatures, the data of hundreds of trillions of col- a Higgs2 boson [113] lisions needs to be analysed and must “show the same pic- GeV/c . ture” before a conclusion about the existence of the Higgs boson can be reached. To conclude that a new particle has been found, particle physicists require that the statistical analysis of two independent particle detectors each indicate that there is lesser than a one-in-a-million chance that the observed decay signatures are due to just background random Standard Model events—i.e., that the observed number of events is more than 5 standard deviations (sigma) different from that expected if there was no new particle. More collision data allows better confirmation of the physical properties of any new particle observed, and allows physicists to decide whether it is indeed a Higgs boson as described by the Standard Model or some other hypothetical new particle. The Large Hadron Collider at CERN in Switzerland, was designed specifically to be able to either confirm or exclude the existence of the Higgs boson. Built in a 27 km tunnel under the ground near Geneva originally inhabited by LEP, it was designed to collide two beams of protons, initially at energies of 3.5 TeV per beam (7 TeV total), or almost 3.6 times that of the Tevatron, and upgradeable to 2 × 7 TeV (14 TeV total) in future. Theory suggested if the Higgs boson existed, collisions at these energy levels should be able to reveal it. As one of the most complicated scientific instruments ever built, its operational readiness was delayed for 14 months by a magnet quench event nine days after its inaugural tests, caused by a faulty electrical connection that damaged over 50 magnets and contaminated the vacuum To find the Higgs boson, a powerful particle accelerator superconducting [114][115][116] system. was needed, because Higgs bosons might not be seen in lower-energy experiments. The collider needed to have a Data collection at the LHC finally commenced in March high luminosity in order to ensure enough collisions were 2010.[117] By December 2011 the two main particle seen for conclusions to be drawn. Finally, advanced com- detectors at the LHC, ATLAS and CMS, had narputing facilities were needed to process the vast amount rowed down the mass range where the Higgs could exof data (25 petabytes per year as at 2012) produced ist to around 116-130 GeV (ATLAS) and 115-127 GeV by the collisions.[109] For the announcement of 4 July (CMS).[118][119] There had also already been a number 2012, a new collider known as the Large Hadron Collider of promising event excesses that had “evaporated” and was constructed at CERN with a planned eventual colli- proven to be nothing but random fluctuations. However sion energy of 14 TeV—over seven times any previous from around May 2011,[120] both experiments had seen collider—and over 300 trillion (3×1014 ) LHC proton– among their results, the slow emergence of a small yet proton collisions were analysed by the LHC Computing consistent excess of gamma and 4-lepton decay signatures Grid, the world’s largest computing grid (as of 2012), and several other particle decays, all hinting at a new parcomprising over 170 computing facilities in a worldwide ticle at a mass around 125 GeV.[120] By around Novemnetwork across 36 countries.[109][110][111] ber 2011, the anomalous data at 125 GeV was becoming “too large to ignore” (although still far from conclusive), and the team leaders at both ATLAS and CMS each privately suspected they might have found the Higgs.[120] On 9.5.1 Search prior to 4 July 2012 November 28, 2011, at an internal meeting of the two The first extensive search for the Higgs boson was con- team leaders and the director general of CERN, the latducted at the Large Electron–Positron Collider (LEP) est analyses were discussed outside their teams for the at CERN in the 1990s. At the end of its service in first time, suggesting both ATLAS and CMS might be 2000, LEP had found no conclusive evidence for the converging on a possible shared result at 125 GeV, and commenced in case of a successful Higgs.[Note 15] This implied that if the Higgs boson were to initial preparations [120] 2 [112] While this information was not known pubfinding. exist it would have to be heavier than 114.4 GeV/c . licly at the time, the narrowing of the possible Higgs range The search continued at Fermilab in the United States, to around 115–130 GeV and the repeated observation of where the Tevatron—the collider that discovered the top small but consistent event excesses across multiple chanquark in 1995—had been upgraded for this purpose. nels at both ATLAS and CMS in the 124-126 GeV region There was no guarantee that the Tevatron would be able (described as “tantalising hints” of around 2-3 sigma) to find the Higgs, but it was the only supercollider that was were public knowledge with “a lot of interest”.[121] It was operational since the Large Hadron Collider (LHC) was therefore widely anticipated around the end of 2011, that still under construction and the planned Superconducting the LHC would provide sufficient data to either exclude Super Collider had been cancelled in 1993 and never or confirm the finding of a Higgs boson by the end of completed. The Tevatron was only able to exclude fur- 62 CHAPTER 9. HIGGS BOSON 2012, when their 2012 collision data (with slightly higher 9.5.3 8 TeV collision energy) had been examined.[121][122] 9.5.2 Discovery of candidate boson at CERN On 22 June 2012 CERN announced an upcoming seminar covering tentative findings for 2012,[126][127] and shortly afterwards (from around 1 July 2012 according to an analysis of the spreading rumour in social media[128] ) rumours began to spread in the media that this would include a major announcement, but it was unclear whether this would be a stronger signal or a formal discovery.[129][130] Speculation escalated to a “fevered” pitch when reports emerged that Peter Higgs, who proposed the particle, was to be attending the seminar,[131][132] and that “five leading physicists” had been invited – generally believed to signify the five living 1964 authors – with Higgs, Englert, Guralnik, Hagen attending and Kibble confirming his invitation (Brout having died in 2011).[133][134] The new particle tested as a possible Higgs boson Following the 2012 discovery, it was still unconfirmed whether or not the 125 GeV/c2 particle was a Higgs boson. On one hand, observations remained consistent with the observed particle being the Standard Model Higgs boson, and the particle decayed into at least some of the predicted channels. Moreover, the production rates and branching ratios for the observed channels broadly matched the predictions by the Standard Model within the experimental uncertainties. However, the experimental uncertainties currently still left room for alternative explanations, meaning an announcement of the discovery of a Higgs boson would have been premature.[102] To allow more opportunity for data collection, the LHC’s proposed 2012 shutdown and 2013–14 upgrade were postponed by 7 weeks into 2013.[140] In November 2012, in a conference in Kyoto researchers said evidence gathered since July was falling into line with the basic Standard Model more than its alternatives, with a range of results for several interactions matching that theory’s predictions.[141] Physicist Matt Strassler highlighted “considerable” evidence that the new particle is not a pseudoscalar negative parity particle (consistent with this required finding for a Higgs boson), “evaporation” or lack of increased significance for previous hints of non-Standard Model findings, expected Standard Model interactions with W and Z bosons, absence of “significant new implications” for or against supersymmetry, and in general no significant deviations to date from the results expected of a Standard Model Higgs boson.[142] However some kinds of extensions to the Standard Model would also show very similar results;[143] so commentators noted that based on other particles that are still being understood long after their discovery, it may take years to be sure, and decades to fully understand the particle that has been found.[141][142] On 4 July 2012 both of the CERN experiments announced they had independently made the same discovery:[135] CMS of a previously unknown boson with mass 125.3 ± 0.6 GeV/c2[136][137] and ATLAS of a boson with mass 126.0 ± 0.6 GeV/c2 .[138][139] Using the combined analysis of two interaction types (known as 'channels’), both experiments independently reached a local significance of 5 sigma — implying that the probability of getting at least as strong a result by chance alone is less than 1 in 3 million. When additional channels were taken into account, the CMS significance was reduced to 4.9 These findings meant that as of January 2013, scientists sigma.[137] were very sure they had found an unknown particle of The two teams had been working 'blinded' from each mass ~ 125 GeV/c2 , and had not been misled by experiother from around late 2011 or early 2012,[120] meaning mental error or a chance result. They were also sure, from they did not discuss their results with each other, provid- initial observations, that the new particle was some kind ing additional certainty that any common finding was gen- of boson. The behaviours and properties of the particle, uine validation of a particle.[109] This level of evidence, so far as examined since July 2012, also seemed quite confirmed independently by two separate teams and ex- close to the behaviours expected of a Higgs boson. Even periments, meets the formal level of proof required to so, it could still have been a Higgs boson or some other announce a confirmed discovery. unknown boson, since future tests could show behaviours On 31 July 2012, the ATLAS collaboration presented ad- that do not match a Higgs boson, so as of December 2012 new particle was “consisditional data analysis on the “observation of a new par- CERN still only stated that the [11][13] and scientists did not tent with” the Higgs boson, ticle”, including data from a third channel, which im[144] Despite this, yet positively say it was the Higgs boson. proved the significance to 5.9 sigma (1 in 588 million in late 2012, widespread media reports announced (incorchance of obtaining at least as strong evidence by random rectly) that a Higgs boson had been confirmed during the background effects alone) and mass 126.0 ± 0.4 (stat) ± [Note 16] year. 2 [139] and CMS improved the signifi0.4 (sys) GeV/c , cance to 5-sigma and mass 125.3 ± 0.4 (stat) ± 0.5 (sys) In January 2013, CERN director-general Rolf-Dieter Heuer stated that based on data analysis to date, an anGeV/c2 .[136] 9.6. PUBLIC DISCUSSION swer could be possible 'towards’ mid-2013,[150] and the deputy chair of physics at Brookhaven National Laboratory stated in February 2013 that a “definitive” answer might require “another few years” after the collider’s 2015 restart.[151] In early March 2013, CERN Research Director Sergio Bertolucci stated that confirming spin0 was the major remaining requirement to determine whether the particle is at least some kind of Higgs boson.[152] 63 Nickname The Higgs boson is often referred to as the “God particle” in popular media outside the scientific community.[170][171][172][173][174] The nickname comes from the title of the 1993 book on the Higgs boson and particle physics - The God Particle: If the Universe Is the Answer, What Is the Question? by Nobel Physics prizewinner and Fermilab director Leon Lederman.[21] Lederman wrote it in the context of failing US government support for the Superconducting 9.5.4 Preliminary confirmation of exis- Super Collider,[175] a part-constructed titanic[176][177] tence and current status competitor to the Large Hadron Collider with planned collision energies of 2 × 20 TeV that was championed On 14 March 2013 CERN confirmed that: by Lederman since its 1983 inception[175][178][179] and shut down in 1993. The book sought in part to promote “CMS and ATLAS have compared a number awareness of the significance and need for such a project of options for the spin-parity of this particle, in the face of its possible loss of funding.[180] and these all prefer no spin and even parity [two While media use of this term may have contributed to fundamental criteria of a Higgs boson consiswider awareness and interest,[181] many scientists feel tent with the Standard Model]. This, coupled the name is inappropriate[16][17][182] since it is sensawith the measured interactions of the new partional hyperbole and misleads readers;[183] the particle ticle with other particles, strongly indicates that also has nothing to do with God,[183] leaves open numerit is a Higgs boson.” [1] ous questions in fundamental physics, and does not explain the ultimate origin of the universe. Higgs, an atheist, This also makes the particle the first elementary scalar was reported to be displeased and stated in a 2008 inparticle to be discovered in nature.[14] terview that he found it “embarrassing” because it was Examples of tests used to validate whether the 125 GeV “the kind of misuse... which I think might offend some particle is a Higgs boson:[142][153] people”.[183][184][185] Science writer Ian Sample stated in his 2010 book on the search that the nickname is “universally hate[d]" by physicists and perhaps the “worst derided” in the history of physics, but that (according to Lederman) the publisher rejected all titles mentioning “Higgs” as unimaginative and too unknown.[186] 9.6 Public discussion 9.6.1 Naming Names used by physicists The name most strongly associated with the particle and field is the Higgs boson[79]:168 and Higgs field. For some time the particle was known by a combination of its PRL author names (including at times Anderson), for example the Brout–Englert–Higgs particle, the AndersonHiggs particle, or the Englert–Brout–Higgs–Guralnik– Hagen–Kibble mechanism,[Note 17] and these are still used at times.[51][160] Fueled in part by the issue of recognition and a potential shared Nobel Prize,[160][161] the most appropriate name is still occasionally a topic of debate as at 2012.[160] (Higgs himself prefers to call the particle either by an acronym of all those involved, or “the scalar boson”, or “the so-called Higgs particle”.[161] ) A considerable amount has been written on how Higgs’ name came to be exclusively used. Two main explanations are offered. Lederman begins with a review of the long human search for knowledge, and explains that his tongue-in-cheek title draws an analogy between the impact of the Higgs field on the fundamental symmetries at the Big Bang, and the apparent chaos of structures, particles, forces and interactions that resulted and shaped our present universe, with the biblical story of Babel in which the primordial single language of early Genesis was fragmented into many disparate languages and cultures.[187] Today ... we have the standard model, which reduces all of reality to a dozen or so particles and four forces. ... It’s a hard-won simplicity [...and...] remarkably accurate. But it is also incomplete and, in fact, internally inconsistent... This boson is so central to the state of physics today, so crucial to our final understanding of the structure of matter, yet so elusive, that I have given it a nickname: the God Particle. Why God Particle? Two reasons. One, the publisher wouldn't let us call it the Goddamn Particle, though that might be a more appropriate title, given its villainous 64 CHAPTER 9. HIGGS BOSON nature and the expense it is causing. And two, there is a connection, of sorts, to another book, a much older one... —Leon M. Lederman and Dick Teresi, The God Particle: If the Universe is the Answer, What is the Question[21] p. 22 Lederman asks whether the Higgs boson was added just to perplex and confound those seeking knowledge of the universe, and whether physicists will be confounded by it as recounted in that story, or ultimately surmount the challenge and understand “how beautiful is the universe [God has] made”.[188] Other proposals A renaming competition by British newspaper The Guardian in 2009 resulted in their science correspondent choosing the name “the champagne bottle boson” as the best submission: “The bottom of a champagne bottle is in the shape of the Higgs potential and is often used as an illustration in physics lectures. So it’s not an embarrassingly grandiose name, it is memorable, and [it] has some physics connection too.”[189] The name Higgson was suggested as well, in an opinion piece in the Institute of Physics' online publication physicsworld.com.[190] 9.6.2 Media explanations and analogies Photograph of light passing through a dispersive prism: the rainbow effect arises because photons are not all affected to the same degree by the dispersive material of the prism. A similar explanation was offered by The Guardian:[196] The Higgs boson is essentially a ripple in a field said to have emerged at the birth of the universe and to span the cosmos to this day ... The particle is crucial however: it is the smoking gun, the evidence required to show the theory is right. There has been considerable public discussion of analogies and explanations for the Higgs particle and how the field creates mass,[191][192] including coverage of explanatory attempts in their own right and a competition in 1993 for the best popular explanation by then-UK Minister for Science Sir William Waldegrave[193] and articles in news- The Higgs field’s effect on particles was famously described by physicist David Miller as akin to a room full of papers worldwide. political party workers spread evenly throughout a room: An educational collaboration involving an LHC physicist the crowd gravitates to and slows down famous people but and a High School Teachers at CERN educator suggests does not slow down others.[Note 18] He also drew attention that dispersion of light – responsible for the rainbow and to well-known effects in solid state physics where an elecdispersive prism – is a useful analogy for the Higgs field’s tron’s effective mass can be much greater than usual in the symmetry breaking and mass-causing effect.[194] presence of a crystal lattice.[197] Matt Strassler uses electric fields as an analogy:[195] Some particles interact with the Higgs field while others don’t. Those particles that feel the Higgs field act as if they have mass. Something similar happens in an electric field – charged objects are pulled around and neutral objects can sail through unaffected. So you can think of the Higgs search as an attempt to make waves in the Higgs field [create Higgs bosons] to prove it’s really there. Analogies based on drag effects, including analogies of "syrup" or "molasses" are also well known, but can be somewhat misleading since they may be understood (incorrectly) as saying that the Higgs field simply resists some particles’ motion but not others’ – a simple resistive effect could also conflict with Newton’s third law.[199] 9.6.3 Recognition and awards There has been considerable discussion of how to allocate the credit if the Higgs boson is proven, made more pointed as a Nobel prize had been expected, and the very wide basis of people entitled to consideration. These in- 9.7. TECHNICAL ASPECTS AND MATHEMATICAL FORMULATION clude a range of theoreticians who made the Higgs mechanism theory possible, the theoreticians of the 1964 PRL papers (including Higgs himself), the theoreticians who derived from these, a working electroweak theory and the Standard Model itself, and also the experimentalists at CERN and other institutions who made possible the proof of the Higgs field and boson in reality. The Nobel prize has a limit of 3 persons to share an award, and some possible winners are already prize holders for other work, or are deceased (the prize is only awarded to persons in their lifetime). Existing prizes for works relating to the Higgs field, boson, or mechanism include: 65 9.7 Technical aspects and mathematical formulation See also: Standard Model (mathematical formulation) In the Standard Model, the Higgs field is a fourcomponent scalar field that forms a complex doublet of the weak isospin SU(2) symmetry: while the field has charge +1/2 under the weak hyper• Nobel Prize in Physics (1979) – Glashow, Salam, charge U(1) symmetry (in the convention where the elecand Weinberg, for contributions to the theory of tric charge, Q, the weak isospin, I3 , and the weak hyperthe unified weak and electromagnetic interaction be- charge, Y, are related by Q = I3 + Y).[206] tween elementary particles [200] • Nobel Prize in Physics (1999) – 't Hooft and Veltman, for elucidating the quantum structure of electroweak interactions in physics [201] • Nobel Prize in Physics (2008) – Nambu (shared), for the discovery of the mechanism of spontaneous broken symmetry in subatomic physics [53] • J. J. Sakurai Prize for Theoretical Particle Physics (2010) – Hagen, Englert, Guralnik, Higgs, Brout, and Kibble, for elucidation of the properties of spontaneous symmetry breaking in four-dimensional relativistic gauge theory and of the mechanism for the consistent generation of vector boson masses [77] (for the 1964 papers described above) • Wolf Prize (2004) – Englert, Brout, and Higgs The potential for the Higgs field, plotted as function of ϕ0 and • Nobel Prize in Physics (2013) - Peter Higgs and ϕ3 . It has a Mexican-hat or champagne-bottle profile at the François Englert, for the theoretical discovery of a ground. mechanism that contributes to our understanding of the origin of mass of subatomic particles, and which The Higgs part of the Lagrangian is[206] recently was confirmed through the discovery of the predicted fundamental particle, by the ATLAS and CMS experiments at CERN’s Large Hadron Collider [202] Additionally Physical Review Letters' 50-year review (2008) recognized the 1964 PRL symmetry breaking papers and Weinberg’s 1967 paper A model of Leptons (the most cited paper in particle physics, as of 2012) “milestone Letters”.[75] Following reported observation of the Higgs-like particle in July 2012, several Indian media outlets reported on the supposed neglect of credit to Indian physicist Satyendra Nath Bose after whose work in the 1920s the class of particles "bosons" is named[203][204] (although physicists have described Bose’s connection to the discovery as tenuous).[205] where Wµa and Bµ are the gauge bosons of the SU(2) and U(1) symmetries, g and g ′ their respective coupling constants, τ a = σ a /2 (where σ a are the Pauli matrices) a complete set generators of the SU(2) symmetry, and λ > 0 and µ2 > 0 , so that the ground state breaks the SU(2) symmetry (see figure). The ground state of the Higgs field (the bottom of the potential) is degenerate with different ground states related to each other by a SU(2) gauge transformation. It is always possible to pick a gauge such that in the ground state ϕ1 = ϕ2 = ϕ3 = 0 . The expectation value of ϕ0 in the ground state (the vacuum expectation value or vev) is then ⟨ϕ0 ⟩ = v , |µ| where v = √ . The measured value of this parameλ ter is ~246 GeV/c2 .[102] It has units of mass, and is the 66 CHAPTER 9. HIGGS BOSON only free parameter of the Standard Model that is not a dimensionless number. Quadratic terms in Wµ and Bµ arise, which give masses to the W and Z bosons:[206] • Quantum triviality • ZZ diboson • Scalar boson • Stueckelberg action • Tachyonic field with their ratio determining the Weinberg angle, W √ |g| cos θW = M , and leave a massless U(1) MZ = 2 ′2 9.9 Notes g +g photon, γ . The quarks and the leptons interact with the Higgs field through Yukawa interaction terms: where (d, u, e, ν)iL,R are left-handed and right-handed quarks and leptons of the ith generation, λij u,d,e are matrices of Yukawa couplings where h.c. denotes the hermitian conjugate terms. In the symmetry breaking ground state, only the terms containing ϕ0 remain, giving rise to mass terms for the fermions. Rotating the quark and lepton fields to the basis where the matrices of Yukawa couplings are diagonal, one gets where the masses of the fermions are miu,d,e = √ λiu,d,e v/ 2 , and λiu,d,e denote the eigenvalues of the Yukawa matrices.[206] 9.8 See also • Quantum gauge theory • History of quantum field theory • Introduction to quantum mechanics and • Standard Model (mathematical formulation) (and especially Standard Model fields overview and mass terms and the Higgs mechanism) Other • Bose–Einstein statistics • Dalitz plot • Higgs boson in fiction [2] In the Standard Model, the total decay width of a Higgs boson with a mass of 126 GeV/c2 is predicted to be 4.21×10−3 GeV.[5] The mean lifetime is given by τ = ℏ/Γ . [3] The range of a force is inversely proportional to the mass of the particles transmitting it.[19] In the Standard Model, forces are carried by virtual particles. These particles’ movement and interactions with each other are limited by the energy–time uncertainty principle. As a result, the more massive a single virtual particle is, the greater its energy, and therefore the shorter the distance it can travel. A particle’s mass therefore determines the maximum distance at which it can interact with other particles and on any force it mediates. By the same token, the reverse is also true: massless and near-massless particles can carry long distance forces. (See also: Compton wavelength and Static forces and virtual-particle exchange) Since experiments have shown that the weak force acts over only a very short range, this implies that there must exist massive gauge bosons. And indeed, their masses have since been confirmed by measurement. [4] It is quite common for a law of physics to hold true only if certain assumptions held true or only under certain conditions. For example, Newton’s laws of motion apply only at speeds where relativistic effects are negligible; and laws related to conductivity, gases, and classical physics (as opposed to quantum mechanics) may apply only within certain ranges of size, temperature, pressure, or other conditions. Standard Model • Noncommutative standard model noncommutative geometry generally [1] Note that such events also occur due to other processes. Detection involves a statistically significant excess of such events at specific energies. [5] Electroweak symmetry is broken by the Higgs field in its lowest energy state, called its "ground state". At high energy levels this does not happen, and the gauge bosons of the weak force would therefore be expected to be massless. [6] By the 1960s, many had already started to see gauge theories as failing to explain particle physics because theorists had been unable to solve the mass problem or even explain how gauge theory could provide a solution. So the idea that the Standard Model – which relied on a “Higgs field” not yet proved to exist – could be fundamentally incorrect was far from fanciful. Against this, once the entire model was developed around 1972, no better theory existed, and its predictions and solutions were so accurate, that it became the preferred theory anyway. It then became crucial to science, to know whether it was correct. 9.10. REFERENCES [7] The success of the Higgs based electroweak theory and Standard Model is illustrated by their predictions of the mass of two particles later detected: the W boson (predicted mass: 80.390 ± 0.018 GeV, experimental measurement: 80.387 ± 0.019 GeV), and the Z boson (predicted mass: 91.1874 ± 0.0021, experimental measurement: 91.1876 ± 0.0021 GeV). The existence of the Z boson was itself another prediction. Other correct predictions included the weak neutral current, the gluon, and the top and charm quarks, all later proven to exist as the theory said. [8] For example, Huffington Post/Reuters[35] and others[36][37] [9] The bubble’s effects would be expected to propagate across the universe at the speed of light from wherever it occurred. However space is vast – with even the nearest galaxy being over 2 million lightyears from us, and others being many billions of lightyears distant, so the effect of such an event would be unlikely to arise here for billions of years after first occurring.[39][40] [10] If the Standard Model is correct, then the particles and forces we observe in our universe exist as they do, because of underlying quantum fields. Quantum fields can have states of differing stability, including 'stable', 'unstable' and 'metastable' states (the latter remain stable unless sufficiently perturbed). If a more stable vacuum state were able to arise, then existing particles and forces would no longer arise as they presently do. Different particles or forces would arise from (and be shaped by) whatever new quantum states arose. The world we know depends upon these particles and forces, so if this happened, everything around us, from subatomic particles to galaxies, and all fundamental forces, would be reconstituted into new fundamental particles and forces and structures. The universe would potentially lose all of its present structures and become inhabited by new ones (depending upon the exact states involved) based upon the same quantum fields. [11] Goldstone’s theorem only applies to gauges having manifest Lorentz covariance, a condition that took time to become questioned. But the process of quantisation requires a gauge to be fixed and at this point it becomes possible to choose a gauge such as the 'radiation' gauge which is not invariant over time, so that these problems can be avoided. According to Bernstein (1974, p.8): “the “radiation gauge” condition ∇⋅A(x) = 0 is clearly noncovariant, which means that if we wish to maintain transversality of the photon in all Lorentz frames, the photon field Aμ(x) cannot transform like a four-vector. This is no catastrophe, since the photon field is not an observable, and one can readily show that the S-matrix elements, which are observable have covariant structures .... in gauge theories one might arrange things so that one had a symmetry breakdown because of the noninvariance of the vacuum; but, because the Goldstone et al. proof breaks down, the zero mass Goldstone mesons need not appear.” [Emphasis in original] Bernstein (1974) contains an accessible and comprehensive background and review of this area, see external links 67 [12] A field with the “Mexican hat” potential V (ϕ) = µ2 ϕ2 + λϕ4 and µ2 < 0 has a minimum not at zero but at some non-zero value ϕ0 . By expressing the action in terms of the field ϕ˜ = ϕ − ϕ0 (where ϕ0 is a constant independent of position), we find the Yukawa term has a component ¯ . Since both g and ϕ0 are constants, this looks gϕ0 ψψ exactly like the mass term for a fermion of mass gϕ0 . The field ϕ˜ is then the Higgs field. [13] In the Standard Model, the mass term arising from the ¯ . This Dirac Lagrangian for any fermion ψ is −mψψ is not invariant under the electroweak symmetry, as can be seen by writing ψ in terms of left and right handed components: ¯ = −m(ψ¯L ψR + ψ¯R ψL ) −mψψ i.e., contributions from ψ¯L ψL and ψ¯R ψR terms do not appear. We see that the mass-generating interaction is achieved by constant flipping of particle chirality. Since the spin-half particles have no right/left helicity pair with the same SU(2) and SU(3) representation and the same weak hypercharge, then assuming these gauge charges are conserved in the vacuum, none of the spin-half particles could ever swap helicity. Therefore in the absence of some other cause, all fermions must be massless. [14] The example is based on the production rate at the LHC operating at 7 TeV. The total cross-section for producing a Higgs boson at the LHC is about 10 picobarn,[97] while the total cross-section for a proton–proton collision is 110 millibarn.[100] [15] Just before LEP’s shut down, some events that hinted at a Higgs were observed, but it was not judged significant enough to extend its run and delay construction of the LHC. [16] Announced in articles in Time,[145] Forbes,[146] Slate,[147] NPR,[148] and others.[149] [17] Other names have included: the “Anderson–Higgs” mechanism,[159] “Higgs–Kibble” mechanism (by Abdus Salam)[79] and “ABEGHHK'tH” mechanism [for Anderson, Brout, Englert, Guralnik, Hagen, Higgs, Kibble and 't Hooft] (by Peter Higgs).[79] [18] In Miller’s analogy, the Higgs field is compared to political party workers spread evenly throughout a room. There will be some people (in Miller’s example an anonymous person) who pass through the crowd with ease, paralleling the interaction between the field and particles that do not interact with it, such as massless photons. There will be other people (in Miller’s example the British prime minister) who would find their progress being continually slowed by the swarm of admirers crowding around, paralleling the interaction for particles that do interact with the field and by doing so, acquire a finite mass.[197][198] 9.10 References [1] O'Luanaigh, C. (14 March 2013). “New results indicate that new particle is a Higgs boson”. CERN. Retrieved 2013-10-09. 68 [2] Bryner, J. (14 March 2013). “Particle confirmed as Higgs boson”. NBC News. Retrieved 2013-03-14. [3] Heilprin, J. (14 March 2013). “Higgs Boson Discovery Confirmed After Physicists Review Large Hadron Collider Data at CERN”. The Huffington Post. Retrieved 2013-03-14. CHAPTER 9. HIGGS BOSON [12] Siegfried, T. (20 July 2012). “Higgs Hysteria”. Science News. Retrieved 2012-12-09. In terms usually reserved for athletic achievements, news reports described the finding as a monumental milestone in the history of science. [4] ATLAS; CMS (26 March 2015). “Combined Measurement of the Higgs Boson Mass in pp Collisions at √s=7 and 8 TeV with the ATLAS and CMS Experiments”. arXiv:1503.07589. [13] Del Rosso, A. (19 November 2012). “Higgs: The beginning of the exploration”. CERN Bulletin (47–48). Retrieved 2013-01-09. Even in the most specialized circles, the new particle discovered in July is not yet being called the “Higgs boson”. Physicists still hesitate to call it that before they have determined that its properties fit with those the Higgs theory predicts the Higgs boson has. [5] LHC Higgs Cross Section Working Group; Dittmaier; Mariotti; Passarino; Tanaka; Alekhin; Alwall; Bagnaschi; Banfi (2012). “Handbook of LHC Higgs Cross Sections: 2. Differential Distributions”. CERN Report 2 (Tables A.1 – A.20) 1201: 3084. arXiv:1201.3084. Bibcode:2012arXiv1201.3084L. [14] Naik, G. (14 March 2013). “New Data Boosts Case for Higgs Boson Find”. The Wall Street Journal. Retrieved 2013-03-15. 'We've never seen an elementary particle with spin zero,' said Tony Weidberg, a particle physicist at the University of Oxford who is also involved in the CERN experiments. [6] Onyisi, P. (23 October 2012). “Higgs boson FAQ”. University of Texas ATLAS group. Retrieved 2013-0108. [15] Overbye, D. (8 October 2013). “For Nobel, They Can Thank the 'God Particle'". The New York Times. Retrieved 2013-11-03. [7] Strassler, M. (12 October 2012). “The Higgs FAQ 2.0”. ProfMattStrassler.com. Retrieved 2013-01-08. [Q] Why do particle physicists care so much about the Higgs particle? [A] Well, actually, they don’t. What they really care about is the Higgs field, because it is so important. [emphasis in original] [16] Sample, I. (29 May 2009). “Anything but the God particle”. The Guardian. Retrieved 2009-06-24. [8] José Luis Lucio and Arnulfo Zepeda (1987). Proceedings of the II Mexican School of Particles and Fields, Cuernavaca-Morelos, 1986. World Scientific. p. 29. ISBN 9971504340. [9] Gunion, Dawson, Kane, and Haber (199). The Higgs Hunter’s Guide (1st ed.). pp. 11 (?). ISBN 9780786743186. – quoted as being in the first (1990) edition of the book by Peter Higgs in his talk “My Life as a Boson”, 2001, ref#25. [10] Strassler, M. (8 October 2011). “The Known Particles – If The Higgs Field Were Zero”. ProfMattStrassler.com. Retrieved 13 November 2012. The Higgs field: so important it merited an entire experimental facility, the Large Hadron Collider, dedicated to understanding it. [11] Biever, C. (6 July 2012). “It’s a boson! But we need to know if it’s the Higgs”. New Scientist. Retrieved 201301-09. 'As a layman, I would say, I think we have it,' said Rolf-Dieter Heuer, director general of CERN at Wednesday’s seminar announcing the results of the search for the Higgs boson. But when pressed by journalists afterwards on what exactly 'it' was, things got more complicated. 'We have discovered a boson – now we have to find out what boson it is’ Q: 'If we don't know the new particle is a Higgs, what do we know about it?' We know it is some kind of boson, says Vivek Sharma of CMS [...] Q: 'are the CERN scientists just being too cautious? What would be enough evidence to call it a Higgs boson?' As there could be many different kinds of Higgs bosons, there’s no straight answer. [emphasis in original] [17] Evans, R. (14 December 2011). “The Higgs boson: Why scientists hate that you call it the 'God particle'". National Post. Retrieved 2013-11-03. [18] The nickname occasionally has been satirised in mainstream media as well. Borowitz, Andy (July 13, 2012). “5 questions for the Higgs boson”. The New Yorker. [19] Shu, F. H. (1982). The Physical Universe: An Introduction to Astronomy. University Science Books. pp. 107–108. ISBN 978-0-935702-05-7. [20] Shu, F. H. (1982). The Physical Universe: An Introduction to Astronomy. University Science Books. pp. 107–108. ISBN 978-0-935702-05-7. [21] Leon M. Lederman and Dick Teresi (1993). The God Particle: If the Universe is the Answer, What is the Question. Houghton Mifflin Company. [22] Heath, Nick, The Cern tech that helped track down the God particle, TechRepublic, 4 July 2012 [23] Rao, Achintya (2 July 2012). “Why would I care about the Higgs boson?". CMS Public Website. CERN. Retrieved 18 July 2012. [24] Max Jammer, Concepts of Mass in Contemporary Physics and Philosophy (Princeton, NJ: Princeton University Press, 2000) pp.162–163, who provides many references in support of this statement. [25] The Large Hadron Collider: Shedding Light on the Early Universe – lecture by R.-D. Heuer, CERN, Chios, Greece, 28 September 2011 [26] Alekhin, Djouadi and Moch, S.; Djouadi, A.; Moch, S. (2012-08-13). “The top quark and Higgs boson masses and the stability of the elecPhysics Letters B 716: 214. troweak vacuum”. arXiv:1207.0980. Bibcode:2012PhLB..716..214A. 9.10. REFERENCES doi:10.1016/j.physletb.2012.08.024. February 2013. 69 Retrieved 20 arXiv:1501.03781. Bibcode:2015PhLB..743..428S. doi:10.1016/j.physletb.2015.03.015. [27] M.S. Turner, F. Wilczek (1982). “Is our vacuum metastable?". Nature 298 (5875): 633–634. Bibcode:1982Natur.298..633T. doi:10.1038/298633a0. [39] Boyle, Alan (2013-02-19). “Will our universe end in a 'big slurp'? Higgs-like particle suggests it might”. NBC News’ Cosmic log. Retrieved 21 February 2013. [T]he bad news is that its mass suggests the universe will end in a fastspreading bubble of doom. The good news? It'll probably be tens of billions of years. The article quotes Fermilab's Joseph Lykken: "[T]he parameters for our universe, including the Higgs [and top quark’s masses] suggest that we're just at the edge of stability, in a “metastable” state. Physicists have been contemplating such a possibility for more than 30 years. Back in 1982, physicists Michael Turner and Frank Wilczek wrote in Nature that “without warning, a bubble of true vacuum could nucleate somewhere in the universe and move outwards...” [28] S. Coleman and F. De Luccia (1980). “Gravitational effects on and of vacuum decay”. Physical Review D21 (12): 3305. Bibcode:1980PhRvD..21.3305C. doi:10.1103/PhysRevD.21.3305. [29] M. Stone (1976). “Lifetime and decay of excited vacuum states”. Phys. Rev. D 14 (12): 3568–3573. Bibcode:1976PhRvD..14.3568S. doi:10.1103/PhysRevD.14.3568. [30] P.H. Frampton (1976). “Vacuum Instability and Higgs Scalar Mass”. Phys. Rev. Lett. 37 (21): 1378–1380. Bibcode:1976PhRvL..37.1378F. doi:10.1103/PhysRevLett.37.1378. [31] P.H. Frampton (1977). “Consequences of Vacuum Instability in Quantum Field Theory”. Phys. Rev. D15 (10): 2922–28. Bibcode:1977PhRvD..15.2922F. doi:10.1103/PhysRevD.15.2922. [32] Ellis, Espinosa, Giudice, Hoecker, & Riotto, J.; Espinosa, J.R.; Giudice, G.F.; Hoecker, A.; Riotto, A. (2009). “The Probable Fate of the Standard Model”. Phys. Lett. B 679 (4): 369– 375. arXiv:0906.0954. Bibcode:2009PhLB..679..369E. doi:10.1016/j.physletb.2009.07.054. [33] Masina, Isabella (2013-02-12). “Higgs boson and top quark masses as tests of electroweak vacuum stability”. Phys. Rev. D 87 (5): 53001. arXiv:1209.0393. Bibcode:2013PhRvD..87e3001M. doi:10.1103/PhysRevD.87.053001. [34] Buttazzo, Degrassi, Giardino, Giudice, Sala, Salvio, Strumia (2013-07-12). “Investigating the nearcriticality of the Higgs boson”. JHEP 1312 (2013) 089. arXiv:1307.3536. Bibcode:2013JHEP...12..089B. doi:10.1007/JHEP12(2013)089. [35] Irene Klotz (editing by David Adams and Todd Eastham) (2013-02-18). “Universe Has Finite Lifespan, Higgs Boson Calculations Suggest”. Huffington Post. Reuters. Retrieved 21 February 2013. Earth will likely be long gone before any Higgs boson particles set off an apocalyptic assault on the universe [36] Hoffman, Mark (2013-02-19). “Higgs Boson Will Destroy The Universe Eventually”. ScienceWorldReport. Retrieved 21 February 2013. [37] “Higgs boson will aid in creation of the universe – and how it will end”. Catholic Online/NEWS CONSORTIUM. 2013-02-20. Retrieved 21 February 2013. [T]he Earth will likely be long gone before any Higgs boson particles set off an apocalyptic assault on the universe [38] Salvio, tivated below Handed Alberto (2015-04-09). “A Simple MoCompletion of the Standard Model the Planck Scale: Axions and RightPhysics Letters B 743: 428. Neutrinos”. [40] Peralta, Eyder (2013-02-19). “If Higgs Boson Calculations Are Right, A Catastrophic 'Bubble' Could End Universe”. npr – two way. Retrieved 21 February 2013. Article cites Fermilab's Joseph Lykken: “The bubble forms through an unlikely quantum fluctuation, at a random time and place,” Lykken tells us. “So in principle it could happen tomorrow, but then most likely in a very distant galaxy, so we are still safe for billions of years before it gets to us.” [41] Bezrukov; Shaposhnikov (2007-10-19). “The Standard Model Higgs boson as the inflaton”. Phys.Lett. B659 (2008) 703-706. arXiv:0710.3755. Bibcode:2008PhLB..659..703B. doi:10.1016/j.physletb.2007.11.072. [42] Salvio, Alberto (2013-08-09). “Higgs Inflation at NNLO after the Boson Discovery”. Phys.Lett. B727 (2013) 234239. arXiv:1308.2244. Bibcode:2013PhLB..727..234S. doi:10.1016/j.physletb.2013.10.042. [43] Cole, K. (2000-12-14). “One Thing Is Perfectly Clear: Nothingness Is Perfect”. Los Angeles Times. p. 'Science File'. Retrieved 17 January 2013. [T]he Higgs’ influence (or the influence of something like it) could reach much further. For example, something like the Higgs—if not exactly the Higgs itself—may be behind many other unexplained “broken symmetries” in the universe as well ... In fact, something very much like the Higgs may have been behind the collapse of the symmetry that led to the Big Bang, which created the universe. When the forces first began to separate from their primordial sameness—taking on the distinct characters they have today—they released energy in the same way as water releases energy when it turns to ice. Except in this case, the freezing packed enough energy to blow up the universe. ... However it happened, the moral is clear: Only when the perfection shatters can everything else be born. [44] Higgs Matters – Kathy Sykes, 30 Nove 2012 [45] Why the public should care about the Higgs Boson – Jodi Lieberman, American Physical Society (APS) [46] Matt Strassler’s blog – Why the Higgs particle matters 2 July 2012 70 [47] Sean Carroll (13 November 2012). The Particle at the End of the Universe: How the Hunt for the Higgs Boson Leads Us to the Edge of a New World. Penguin Group US. ISBN 978-1-101-60970-5. [48] Woit, Peter (13 November 2010). “The Anderson–Higgs Mechanism”. Dr. Peter Woit (Senior Lecturer in Mathematics Columbia University and Ph.D. particle physics). Retrieved 12 November 2012. [49] Goldstone, J; Salam, Abdus; Weinberg, Steven (1962). “Broken Symmetries”. Physical Review 127 (3): 965–970. Bibcode:1962PhRv..127..965G. doi:10.1103/PhysRev.127.965. [50] Guralnik, G. S. (2011). “The Beginnings of Spontaneous Symmetry Breaking in Particle Physics”. arXiv:1110.2253 [physics.hist-ph]. [51] Kibble, T. W. B. (2009). “Englert–Brout–Higgs– Guralnik–Hagen–Kibble Mechanism”. Scholarpedia 4 (1): 6441. Bibcode:2009SchpJ...4.6441K. doi:10.4249/scholarpedia.6441. Retrieved 2012-11-23. [52] Kibble, T. W. B. “History of Englert– Brout–Higgs–Guralnik–Hagen–Kibble Mechanism (history)". Scholarpedia 4 (1): 8741. Bibcode:2009SchpJ...4.8741K. doi:10.4249/scholarpedia.8741. Retrieved 2012-11-23. [53] The Nobel Prize in Physics 2008 – official Nobel Prize website. [54] List of Anderson 1958–1959 papers referencing 'symmetry', at APS Journals [55] Higgs, Peter (2010-11-24). “My Life as a Boson” (PDF). Talk given by Peter Higgs at Kings College, London, Nov 24 2010, expanding on a paper originally presented in 2001. Retrieved 17 January 2013. – the original 2001 paper can be found at: Duff and Liu, ed. (2003) [year of publication]. 2001 A Spacetime Odyssey: Proceedings of the Inaugural Conference of the Michigan Center for Theoretical Physics, Michigan, USA, 21–25 May 2001. World Scientific. pp. 86–88. ISBN 9812382313. Retrieved 17 January 2013. CHAPTER 9. HIGGS BOSON [60] Guralnik, Gerald; Hagen, C. R.; Kibble, T. W. B. (1964). “Global Conservation Laws and Massless Particles”. Physical Review Letters 13 (20): 585–587. Bibcode:1964PhRvL..13..585G. doi:10.1103/PhysRevLett.13.585. [61] Higgs, Peter (1964). “Broken symmetries, massless particles and gauge fields”. Physics Letters 12 (2): 132– 133. Bibcode:1964PhL....12..132H. doi:10.1016/00319163(64)91136-9. [62] Higgs, Peter (2010-11-24). “My Life as a Boson” (PDF). Talk given by Peter Higgs at Kings College, London, Nov 24 2010. Retrieved 17 January 2013. Gilbert ... wrote a response to [Klein and Lee’s paper] saying 'No, you cannot do that in a relativistic theory. You cannot have a preferred unit time-like vector like that.' This is where I came in, because the next month was when I responded to Gilbert’s paper by saying 'Yes, you can have such a thing' but only in a gauge theory with a gauge field coupled to the current. [63] G.S. Guralnik (2011). “Gauge invariance and the Goldstone theorem – 1965 Feldafing talk”. Modern Physics Letters A 26 (19): 1381–1392. arXiv:1107.4592. Bibcode:2011MPLA...26.1381G. doi:10.1142/S0217732311036188. [64] Higgs, Peter (1966). “Spontaneous Symmetry Breakdown without Massless Bosons”. Physical Review 145 (4): 1156–1163. Bibcode:1966PhRv..145.1156H. doi:10.1103/PhysRev.145.1156. [65] Kibble, Tom (1967). “Symmetry Breaking in NonAbelian Gauge Theories”. Physical Review 155 (5): 1554–1561. Bibcode:1967PhRv..155.1554K. doi:10.1103/PhysRev.155.1554. [66] “Guralnik, G S; Hagen, C R and Kibble, T W B (1967). Broken Symmetries and the Goldstone Theorem. Advances in Physics, vol. 2” (PDF). [67] “Physical Review Letters – 50th Anniversary Milestone Papers”. Physical Review Letters. [56] Anderson, P. (1963). “Plasmons, gauge invariance and mass”. Physical Review 130: 439. Bibcode:1963PhRv..130..439A. doi:10.1103/PhysRev.130.439. [68] S. Weinberg (1967). “A Model of Leptons”. Physical Review Letters 19 (21): 1264–1266. Bibcode:1967PhRvL..19.1264W. doi:10.1103/PhysRevLett.19.1264. [57] Klein, A.; Lee, B. (1964). “Does Spontaneous Breakdown of Symmetry Imply ZeroMass Particles?". Physical Review Letters 12 Bibcode:1964PhRvL..12..266K. (10): 266. doi:10.1103/PhysRevLett.12.266. [69] A. Salam (1968). N. Svartholm, ed. Elementary Particle Physics: Relativistic Groups and Analyticity. Eighth Nobel Symposium. Stockholm: Almquvist and Wiksell. p. 367. [58] Englert, François; Brout, Robert (1964). “Broken Symmetry and the Mass of Gauge VecPhysical Review Letters 13 tor Mesons”. (9): 321–23. Bibcode:1964PhRvL..13..321E. doi:10.1103/PhysRevLett.13.321. [59] Higgs, Peter (1964). “Broken Symmetries and the Masses of Gauge Bosons”. Physical Review Letters 13 (16): 508–509. Bibcode:1964PhRvL..13..508H. doi:10.1103/PhysRevLett.13.508. [70] S.L. Glashow (1961). “Partial-symmetries of weak interactions”. Nuclear Physics 22 (4): 579–588. Bibcode:1961NucPh..22..579G. doi:10.1016/00295582(61)90469-2. [71] Ellis, John; Gaillard, Mary K.; Nanopoulos, Dimitri V. (2012). “A Historical Profile of the Higgs Boson”. arXiv:1201.6045 [hep-ph]. [72] “Martin Veltman Nobel Lecture, December 12, 1999, p.391” (PDF). Retrieved 2013-10-09. 9.10. REFERENCES [73] Politzer, David. “The Dilemma of Attribution”. Nobel Prize lecture, 2004. Nobel Prize. Retrieved 22 January 2013. Sidney Coleman published in Science magazine in 1979 a citation search he did documenting that essentially no one paid any attention to Weinberg’s Nobel Prize winning paper until the work of ’t Hooft (as explicated by Ben Lee). In 1971 interest in Weinberg’s paper exploded. I had a parallel personal experience: I took a one-year course on weak interactions from Shelly Glashow in 1970, and he never even mentioned the Weinberg–Salam model or his own contributions. [74] Coleman, Sidney (1979-12-14). “The 1979 Nobel Prize in Physics”. Science 206 (4424): 1290–1292. Bibcode:1979Sci...206.1290C. doi:10.1126/science.206.4424.1290. [75] Letters from the Past – A PRL Retrospective (50 year celebration, 2008) [76] Jeremy Bernstein (January 1974). “Spontaneous symmetry breaking, gauge theories, the Higgs mechanism and all that” (PDF). Reviews of Modern Bibcode:1974RvMP...46....7B. Physics 46 (1): 7. doi:10.1103/RevModPhys.46.7. Retrieved 2012-12-10. [77] American Physical Society – “J. J. Sakurai Prize for Theoretical Particle Physics”. [78] Merali, Zeeya (4 August 2010). “Physicists get political over Higgs”. Nature Magazine. Retrieved 28 December 2011. [79] Close, Frank (2011). The Infinity Puzzle: Quantum Field Theory and the Hunt for an Orderly Universe. Oxford: Oxford University Press. ISBN 978-0-19-959350-7. [80] G.S. Guralnik (2009). “The History of the Guralnik, Hagen and Kibble development of the Theory of Spontaneous Symmetry Breaking and Gauge Particles”. International Journal of Modern Physics A 24 (14): 2601–2627. arXiv:0907.3466. Bibcode:2009IJMPA..24.2601G. doi:10.1142/S0217751X09045431. 71 [86] Kutasov, David; Marino, Marcos & Moore, Gregory W. (2000). “Some exact results on tachyon condensation in string field theory”. JHEP 0010: 045. [87] Aharonov, Y.; Komar, A.; Susskind, L. (1969). “Superluminal Behavior, Causality, and Instability”. Phys. Rev. (American Physical Society) 182 (5): 1400–1403. Bibcode:1969PhRv..182.1400A. doi:10.1103/PhysRev.182.1400. [88] Feinberg, Gerald (1967). “Possibility of FasterThan-Light Particles”. Physical Review 159 (5): 1089–1105. Bibcode:1967PhRv..159.1089F. doi:10.1103/PhysRev.159.1089. [89] Michael E. Peskin and Daniel V. Schroeder (1995). An Introduction to Quantum Field Theory, Perseus books publishing. [90] Flatow, Ira (6 July 2012). “At Long Last, The Higgs Particle... Maybe”. NPR. Retrieved 10 July 2012. [91] “Explanatory Figures for the Higgs Boson Exclusion Plots”. ATLAS News. CERN. Retrieved 6 July 2012. [92] Bernardi, G.; Carena, M.; Junk, T. (2012). Bosons: Theory and Searches” (PDF). p. 7. “Higgs [93] Lykken, Joseph D. (2009). “Beyond the Standard Model”. Proceedings of the 2009 European School of High-Energy Physics, Bautzen, Germany, 14 – 27 June 2009. arXiv:1005.1676. [94] Plehn, Tilman (2012). Lectures on LHC Physics. Lecture Notes is Physics 844. Springer. Sec. 1.2.2. arXiv:0910.4122. ISBN 3642240399. [95] “LEP Electroweak Working Group”. [96] Peskin, Michael E.; Wells, James D. (2001). “How Can a Heavy Higgs Boson be Consistent with the Precision Electroweak Measurements?". Physical Review D 64 (9): 093003. arXiv:hepph/0101342. Bibcode:2001PhRvD..64i3003P. doi:10.1103/PhysRevD.64.093003. [81] Peskin, Michael E.; Schroeder, Daniel V. (1995). Introduction to Quantum Field Theory. Reading, MA: Addison-Wesley Publishing Company. pp. 717–719 and 787–791. ISBN 0-201-50397-2. [97] Baglio, Julien; Djouadi, Abdelhak (2011). “Higgs production at the lHC”. Journal of High Energy Physics 1103 (3): 055. arXiv:1012.0530. Bibcode:2011JHEP...03..055B. doi:10.1007/JHEP03(2011)055. [82] Peskin & Schroeder 1995, pp. 715–716 [98] Baglio, Julien; Djouadi, Abdelhak (2010). “Predictions for Higgs production at the Tevatron and the associated uncertainties”. Journal of High Energy Physics 1010 (10): 063. arXiv:1003.4266. Bibcode:2010JHEP...10..064B. doi:10.1007/JHEP10(2010)064. [83] Gunion, John (2000). The Higgs Hunter’s Guide (illustrated, reprint ed.). Westview Press. pp. 1–3. ISBN 9780738203058. [84] Lisa Randall, Warped Passages: Unraveling the Myster- [99] ies of the Universe’s Hidden Dimensions, p.286: “People initially thought of tachyons as particles travelling faster than the speed of light...But we now know that a tachyon indicates an instability in a theory that contains it. Regrettably for science fiction fans, tachyons are not real physical [100] particles that appear in nature.” Teixeira-Dias (LEP Higgs working group), P. (2008). “Higgs boson searches at LEP”. Journal of.Physics: Conference Series 110 (4): 042030. arXiv:0804.4146. Bibcode:2008JPhCS.110d2030T. doi:10.1088/17426596/110/4/042030. “Collisions”. LHC Machine Outreach. CERN. Retrieved 26 July 2012. [85] Sen, Ashoke (April 2002). “Rolling Tachyon”. J. High Energy Phys. 2002 (0204): 048. arXiv:hep-th/0203211. [101] Asquith, Lily (22 June 2012). “Why does the Higgs deBibcode:2002JHEP...04..048S. doi:10.1088/1126cay?". Life and Physics (London: The Guardian). Re6708/2002/04/048. trieved 14 August 2012. 72 CHAPTER 9. HIGGS BOSON [102] “Higgs bosons: theory and searches” (PDF). PDGLive. [116] “LHC to restart in 2009” (Press release). CERN Press Particle Data Group. 12 July 2012. Retrieved 15 August Office. 5 December 2008. Retrieved 8 December 2008. 2012. [117] “LHC progress report”. The Bulletin. CERN. 3 May [103] Branco, G. C.; Ferreira, P.M.; Lavoura, L.; Re2010. Retrieved 7 December 2011. belo, M.N.; Sher, Marc; Silva, João P. (July 2012). “Theory and phenomenology of two-Higgs-doublet [118] “ATLAS experiment presents latest Higgs search status”. ATLAS homepage. CERN. 13 December 2011. Retrieved models”. Physics Reports (Elsevier) 516 (1): 1–102. 13 December 2011. arXiv:1106.0034. Bibcode:2012PhR...516....1B. doi:10.1016/j.physrep.2012.02.002. [119] Taylor, Lucas (13 December 2011). “CMS search for the Standard Model Higgs Boson in LHC data from 2010 and [104] Csaki, C.; Grojean, C.; Pilo, L.; Terning, J. 2011”. CMS public website. CERN. Retrieved 13 Decem(2004). “Towards a realistic model of Higgsber 2011. less electroweak symmetry breaking”. Physical 101802. arXiv:hepReview Letters 92 (10): [120] Overbye, D. (5 March 2013). “Chasing The Higgs Boph/0308038. Bibcode:2004PhRvL..92j1802C. son”. The New York Times. Retrieved 2013-03-05. doi:10.1103/PhysRevLett.92.101802. PMID 15089195. [121] “ATLAS and CMS experiments present Higgs search sta[105] Csaki, C.; Grojean, C.; Pilo, L.; Terning, J.; Terning, John tus” (Press release). CERN Press Office. 13 December (2004). “Gauge theories on an interval: Unitarity without 2011. Retrieved 14 September 2012. the statistical siga Higgs”. Physical Review D 69 (5): 055006. arXiv:hepnificance is not large enough to say anything conclusive. Bibcode:2004PhRvD..69e5006C. ph/0305237. As of today what we see is consistent either with a backdoi:10.1103/PhysRevD.69.055006. ground fluctuation or with the presence of the boson. Refined analyses and additional data delivered in 2012 by [106] “The Hierarchy Problem: why the Higgs has a snowball’s this magnificent machine will definitely give an answer chance in hell”. Quantum Diaries. 2012-07-01. Retrieved 19 March 2013. [122] “WLCG Public Website”. CERN. Retrieved 29 October 2012. [107] “The Hierarchy Problem | Of Particular Significance”. Profmattstrassler.com. Retrieved 2013-10-09. [123] CMS collaboration (2014). “Precise determination of the mass of the Higgs boson and tests of compatibility of its [108] “Collisions”. LHC Machine Outreach. CERN. Retrieved couplings with the standard model predictions using pro26 July 2012. ton collisions at 7 and 8 TeV”. arXiv:1412.8662. [109] “Hunt for Higgs boson hits key decision point”. MSNBC. [124] ATLAS collaboration (2014). “Measurements of Higgs 2012-12-06. Retrieved 2013-01-19. boson production and couplings in the four-lepton channel [110] Worldwide LHC Computing Grid main page 14 Novemin pp collisions at center-of-mass energies of 7 and 8 TeV ber 2012: "[A] global collaboration of more than 170 comwith the ATLAS detector”. arXiv:1408.5191. puting centres in 36 countries ... to store, distribute and analyse the ~25 Petabytes (25 million Gigabytes) of data [125] ATLAS collaboration (2014). “Measurement of Higgs boson production in the diphoton decay channel in pp colannually generated by the Large Hadron Collider” lisions at center-of-mass energies of 7 and 8 TeV with the [111] What is the Worldwide LHC Computing Grid? (PubATLAS detector”. arXiv:1408.7084. lic 'About' page) 14 November 2012: “Currently WLCG is made up of more than 170 computing centers in 36 [126] “Press Conference: Update on the search for the Higgs boson at CERN on 4 July 2012”. Indico.cern.ch. 22 June countries...The WLCG is now the world’s largest comput2012. Retrieved 4 July 2012. ing grid” [112] W.-M. Yao et al. (2006). “Review of Parti- [127] “CERN to give update on Higgs search”. CERN. 22 June 2012. Retrieved 2 July 2011. cle Physics” (PDF). Journal of Physics G 33: 1. arXiv:astro-ph/0601168. Bibcode:2006JPhG...33....1Y. [128] “Scientists analyse global Twitter gossip around Higgs bodoi:10.1088/0954-3899/33/1/001. son discovery”. phys.org (from arXiv). 2013-01-23. Retrieved 6 February 2013. – stated to be " the first time [113] The CDF Collaboration, the D0 Collaboration, the Tevascientists have been able to analyse the dynamics of social tron New Physics, Higgs Working Group (2012). “Upmedia on a global scale before, during and after the andated Combination of CDF and D0 Searches for Standard nouncement of a major scientific discovery.” For the paModel Higgs Boson Production with up to 10.0 fb−1 of per itself see: De Domenico, M.; Lima, A.; Mougel, P.; Data”. arXiv:1207.0449 [hep-ex]. Musolesi, M. (2013). “The Anatomy of a Scientific Gos[114] “Interim Summary Report on the Analysis of the 19 sip”. arXiv:1301.2952. Bibcode:2013NatSR...3E2980D. September 2008 Incident at the LHC” (PDF). CERN. 15 doi:10.1038/srep02980. October 2008. EDMS 973073. Retrieved 28 September [129] “Higgs boson particle results could be a quantum leap”. 2009. Times LIVE. 28 June 2012. Retrieved 4 July 2012. [115] “CERN releases analysis of LHC incident” (Press release). CERN Press Office. 16 October 2008. Retrieved [130] CERN prepares to deliver Higgs particle findings, Australian Broadcasting Corporation. Retrieved 4 July 2012. 28 September 2009. 9.10. REFERENCES [131] “God Particle Finally Discovered? Higgs Boson News At Cern Will Even Feature Scientist It’s Named After”. Huffingtonpost.co.uk. Retrieved 2013-01-19. 73 still be learning important things about the Higgs during the coming few decades. We’ve no choice but to be patient. [132] Our Bureau (2012-07-04). “Higgs on way, theories [143] Sample, Ian (14 November 2012). “Higgs particle looks like a bog Standard Model boson, say scientists”. The thicken”. Calcutta, India: Telegraphindia.com. Retrieved Guardian (London). Retrieved 15 November 2012. 2013-01-19. [133] Thornhill, Ted (2013-07-03). “God Particle Finally Dis- [144] “CERN experiments observe particle consistent with long-sought Higgs boson”. CERN press release. 4 July covered? Higgs Boson News At Cern Will Even Feature 2012. Retrieved 4 July 2012. Scientist It’s Named After”. Huffington Post. Retrieved 23 July 2013. [145] “Person Of The Year 2012”. Time. 19 December 2012. [134] Cooper, Rob (2013-07-01) [updated subsequently]. “God [146] “Higgs Boson Discovery Has Been Confirmed”. Forbes. particle is 'found': Scientists at Cern expected to announce Retrieved 2013-10-09. on Wednesday Higgs boson particle has been discovered”. Daily Mail (London). Retrieved 23 July 2013. - States that [147] Slate Video Staff (2012-09-11). “Higgs Boson Con"“Five leading theoretical physicists have been invited to the firmed; CERN Discovery Passes Test”. Slate.com. Reevent on Wednesday - sparking speculation that the particle trieved 2013-10-09. has been discovered.”, including Higgs and Englert, and that Kibble - who was invited but unable to attend - “told [148] “The Year Of The Higgs, And Other Tiny Advances In Science”. NPR. 2013-01-01. Retrieved 2013-10-09. the Sunday Times: 'My guess is that is must be a pretty positive result for them to be asking us out there'.” [149] “Confirmed: the Higgs boson does exist”. The Sydney Morning Herald. 4 July 2012. [135] Adrian Cho (13 July 2012). “Higgs Boson Makes Its Debut After Decades-Long Search”. Science 337 (6091): [150] “AP CERN chief: Higgs boson quest could wrap up 141–143. doi:10.1126/science.337.6091.141. PMID by midyear”. MSNBC. Associated Press. 2013-01-27. 22798574. Retrieved 20 February 2013. Rolf Heuer, director of [CERN], said he is confident that “towards the middle of [136] CMS collaboration (2012). “Observation of a new the year, we will be there.” – Interview by AP, at the World boson at a mass of 125 GeV with the CMS experiEconomic Forum, 26 Jan 2013. ment at the LHC”. Physics Letters B 716 (1): 30– [137] [138] [139] [140] [141] 61. arXiv:1207.7235. Bibcode:2012PhLB..716...30C. [151] Boyle, Alan (2013-02-16). “Will our universe end in a doi:10.1016/j.physletb.2012.08.021. 'big slurp'? Higgs-like particle suggests it might”. NBCNews.com – cosmic log. Retrieved 20 February 2013. Taylor, Lucas (4 July 2012). “Observation of a New Par'it’s going to take another few years’ after the collider is ticle with a Mass of 125 GeV”. CMS Public Website. restarted to confirm definitively that the newfound partiCERN. Retrieved 4 July 2012. cle is the Higgs boson. “Latest Results from ATLAS Higgs Search”. ATLAS [152] Gillies, James (2013-03-06). “A question of spin for the News. CERN. 4 July 2012. Retrieved 4 July 2012. new boson”. CERN. Retrieved 7 March 2013. ATLAS collaboration (2012). “Observation of [153] Adam Falkowski (writing as 'Jester') (2013-02-27). a New Particle in the Search for the Standard “When shall we call it Higgs?". Résonaances particle Model Higgs Boson with the ATLAS Detector physics blog. Retrieved 7 March 2013. at the LHC”. Physics Letters B 716 (1): 1–29. arXiv:1207.7214. Bibcode:2012PhLB..716....1A. [154] CMS Collaboration (February 2013). “Study of the doi:10.1016/j.physletb.2012.08.020. Mass and Spin-Parity of the Higgs Boson Candidate via Its Decays to Z Boson Pairs”. Phys. Rev. Gillies, James (23 July 2012). “LHC 2012 proton run exLett. (American Physical Society) 110 (8): 081803. tended by seven weeks”. CERN bulletin. Retrieved 29 AuarXiv:1212.6639. Bibcode:2013PhRvL.110h1803C. gust 2012. doi:10.1103/PhysRevLett.110.081803. Retrieved 15 September 2014. “Higgs boson behaving as expected”. 3 News NZ. 15 November 2012. [155] ATLAS Collaboration (7 October 2013). “Evidence for the spin-0 nature of the Higgs boson using ATLAS data”. Phys. Lett. B (American Physical Society) 726 (1-3): 120–144. Bibcode:2013PhLB..726..120A. doi:10.1016/j.physletb.2013.08.026. Retrieved 15 September 2014. [142] Strassler, Matt (2012-11-14). “Higgs Results at Kyoto”. Of Particular Significance: Conversations About Science with Theoretical Physicist Matt Strassler. Prof. Matt Strassler’s personal particle physics website. Retrieved 10 January 2013. ATLAS and CMS only just co-discovered this particle in July ... We will not know after today [156] “Higgs-like Particle in a Mirror”. American Physical Sowhether it is a Higgs at all, whether it is a Standard ciety. Retrieved 26 February 2013. Model Higgs or not, or whether any particular speculative idea...is now excluded. [...] Knowledge about nature does [157] The CMS Collaboration (2014-06-22). “Evidence for the direct decay of the 125 GeV Higgs boson to fermions”. not come easy. We discovered the top quark in 1995, and Nature Publishing Group doi= 10.1038/nphys3005. we are still learning about its properties today... we will 74 CHAPTER 9. HIGGS BOSON [158] Adam Falkowski (writing as 'Jester') (2012-12-13). [173] Scientific American Editors (2012). The Higgs Boson: “Twin Peaks in ATLAS”. Résonaances particle physics Searching for the God Particle. Macmillan. ISBN 978blog. Retrieved 24 February 2013. 1-4668-2413-3. [159] Liu, G. Z.; Cheng, G. (2002). “Extension [174] Ted Jaeckel (2007). The God Particle: The Discovery and Modeling of the Ultimate Prime Particle. Universalof the Anderson-Higgs mechanism”. PhysiPublishers. ISBN 978-1-58112-959-5. cal Review B 65 (13): 132513. arXiv:condBibcode:2002PhRvB..65m2513L. mat/0106070. [175] Aschenbach, Joy (1993-12-05). “No Resurrection in doi:10.1103/PhysRevB.65.132513. Sight for Moribund Super Collider : Science: Global financial partnerships could be the only way to salvage such [160] Editorial (2012-03-21). “Mass appeal: As physicists a project. Some feel that Congress delivered a fatal blow”. close in on the Higgs boson, they should resist calls to Los Angeles Times. Retrieved 16 January 2013. 'We have change its name”. Nature. 483, 374 (7390): 374. to keep the momentum and optimism and start thinking Bibcode:2012Natur.483..374.. doi:10.1038/483374a. about international collaboration,' said Leon M. LederRetrieved 21 January 2013. man, the Nobel Prize-winning physicist who was the architect of the super collider plan [161] Becker, Kate (2012-03-29). “A Higgs by Any Other Name”. “NOVA” (PBS) physics. Retrieved 21 January [176] “A Supercompetition For Illinois”. Chicago Tribune. 2013. 1986-10-31. Retrieved 16 January 2013. The SSC, proposed by the U.S. Department of Energy in 1983, is a [162] “Frequently Asked Questions: The Higgs!". The Bulletin. mind-bending project ... this gigantic laboratory ... this CERN. Retrieved 18 July 2012. titanic project [163] Woit’s physics blog “Not Even Wrong”: Anderson on [177] Diaz, Jesus (2012-12-15). “This Is [The] World’s Largest Anderson-Higgs 2013-04-13 Super Collider That Never Was”. Gizmodo. Retrieved 16 January 2013. ...this titanic complex... [164] Sample, Ian (2012-07-04). “Higgs boson’s many great minds cause a Nobel prize headache”. The Guardian [178] Abbott, Charles (June 1987). “Illinois Issues journal, June (London). Retrieved 23 July 2013. 1987”. p. 18. Lederman, who considers himself an unofficial propagandist for the super collider, said the SSC [165] “Rochester’s Hagen Sakurai Prize Announcement” (Press could reverse the physics brain drain in which bright young release). University of Rochester. 2010. physicists have left America to work in Europe and else[166] C.R. Hagen Sakurai Prize Talk (YouTube). 2010. where. [167] Cho, A (2012-09-14). “Particle physics. Why [179] Kevles, Dan. “Good-bye to the SSC: On the Life and Death of the Superconducting Super Collider” (PDF). the 'Higgs’?" (PDF). Science 337 (6100): 1287. California Institute of Technology: “Engineering & Scidoi:10.1126/science.337.6100.1287. PMID 22984044. ence”. 58 no. 2 (Winter 1995): 16–25. Retrieved 16 JanLee ... apparently used the term 'Higgs Boson' as uary 2013. Lederman, one of the principal spokesmen for early as 1966... but what may have made the term the SSC, was an accomplished high-energy experimentalstick is a seminal paper Steven Weinberg...published in ist who had made Nobel Prize-winning contributions to 1967...Weinberg acknowledged the mix-up in an essay in the development of the Standard Model during the 1960s the New York Review of Books in May 2012. (See also (although the prize itself did not come until 1988). He the original article in New York Review of Books[168] and was a fixture at congressional hearings on the collider, an Frank Close’s 2011 book The Infinity Puzzle[79]:372 ) unbridled advocate of its merits. [168] Weinberg, Steven (2012-05-10). “The Crisis of Big Science”. The New York Review of Books (footnote 1). Re- [180] Calder, Nigel (2005). Magic Universe:A Grand Tour of Modern Science. pp. 369–370. ISBN 9780191622359. trieved 12 February 2013. The possibility that the next big machine would create [169] Examples of early papers using the term “Higgs boson” the Higgs became a carrot to dangle in front of funding include 'A phenomenological profile of the Higgs boson' agencies and politicians. A prominent American physi(Ellis, Gaillard and Nanopoulos, 1976), 'Weak interaction cist, Leon lederman [sic], advertised the Higgs as The God theory and neutral currents’ (Bjorken, 1977), and 'Mass of Particle in the title of a book published in 1993 ...Lederthe Higgs boson' (Wienberg, received 1975) man was involved in a campaign to persuade the US government to continue funding the Superconducting Super [170] Leon Lederman; Dick Teresi (2006). The God PartiCollider... the ink was not dry on Lederman’s book becle: If the Universe Is the Answer, What Is the Question?. fore the US Congress decided to write off the billions of Houghton Mifflin Harcourt. ISBN 0-547-52462-5. dollars already spent [171] Kelly Dickerson (September 8, 2014). “Stephen Hawk- [181] Alister McGrath, Higgs boson: the particle of faith, The ing Says 'God Particle' Could Wipe Out the Universe”. Daily Telegraph, Published 15 December 2011. Retrieved livescience.com. 15 December 2011. [172] Jim Baggott (2012). Higgs: The invention and discovery [182] Sample, Ian (3 March 2009). “Father of the God particle: of the 'God Particle'. Oxford University Press. ISBN 978Portrait of Peter Higgs unveiled”. London: The Guardian. 0-19-165003-1. Retrieved 24 June 2009. 9.11. FURTHER READING 75 [183] Chivers, Tom (2011-12-13). “How the 'God particle' got [194] “The Higgs particle: an analogy for Physics classroom its name”. The Telegraph (London). Retrieved 2012-12(section)". www.lhc-closer.es (a collaboration website of 03. LHCb physicist Xabier Vidal and High School Teachers at CERN educator Ramon Manzano). Retrieved 2013[184] Key scientist sure “God particle” will be found soon 01-09. Reuters news story. 7 April 2008. [195] Flam, Faye (2012-07-12). “Finally – A Higgs Boson [185] "Interview: the man behind the 'God particle'", New SciStory Anyone Can Understand”. The Philadelphia Inentist 13 September 2008, pp. 44–5 (original interview in quirer (philly.com). Retrieved 21 January 2013. the Guardian: Father of the 'God Particle', June 30, 2008) [186] Sample, Ian (2010). Massive: The Hunt for the God Particle. pp. 148–149 and 278–279. ISBN 9781905264957. [187] Cole, K. (2000-12-14). “One Thing Is Perfectly Clear: Nothingness Is Perfect”. Los Angeles Times. p. 'Science File'. Retrieved 17 January 2013. Consider the early universe–a state of pure, perfect nothingness; a formless fog of undifferentiated stuff ... 'perfect symmetry' ... What shattered this primordial perfection? One likely culprit is the so-called Higgs field ... Physicist Leon Lederman compares the way the Higgs operates to the biblical story of Babel [whose citizens] all spoke the same language ... Like God, says Lederman, the Higgs differentiated the perfect sameness, confusing everyone (physicists included) ... [Nobel Prizewinner Richard] Feynman wondered why the universe we live in was so obviously askew ... Perhaps, he speculated, total perfection would have been unacceptable to God. And so, just as God shattered the perfection of Babel, 'God made the laws only nearly symmetrical' [188] Lederman, p. 22 et seq: “Something we cannot yet detect and which, one might say, has been put there to test and confuse us ... The issue is whether physicists will be confounded by this puzzle or whether, in contrast to the unhappy Babylonians, we will continue to build the tower and, as Einstein put it, 'know the mind of God'.” “And the Lord said, Behold the people are un-confounding my confounding. And the Lord sighed and said, Go to, let us go down, and there give them the God Particle so that they may see how beautiful is the universe I have made”. [189] Sample, Ian (12 June 2009). “Higgs competition: Crack open the bubbly, the God particle is dead”. The Guardian (London). Retrieved 4 May 2010. [190] Gordon, Fraser (5 July 2012). “Introducing the higgson”. physicsworld.com. Retrieved 25 August 2012. [191] Wolchover, Natalie (2012-07-03). “Higgs Boson Explained: How 'God Particle' Gives Things Mass”. Huffington Post. Retrieved 21 January 2013. [192] Oliver, Laura (2012-07-04). “Higgs boson: how would you explain it to a seven-year-old?". The Guardian (London). Retrieved 21 January 2013. [193] Zimmer, Ben (2012-07-15). “Higgs boson metaphors as clear as molasses”. The Boston Globe. Retrieved 21 January 2013. [196] Sample, Ian (2011-04-28). “How will we know when the Higgs particle has been detected?". The Guardian (London). Retrieved 21 January 2013. [197] Miller, David. “A quasi-political Explanation of the Higgs Boson; for Mr Waldegrave, UK Science Minister 1993”. Retrieved 10 July 2012. [198] Kathryn Grim. “Ten things you may not know about the Higgs boson”. Symmetry Magazine. Retrieved 10 July 2012. [199] David Goldberg, Associate Professor of Physics, Drexel University (2010-10-17). “What’s the Matter with the Higgs Boson?". io9.com “Ask a physicist”. Retrieved 21 January 2013. [200] The Nobel Prize in Physics 1979 – official Nobel Prize website. [201] The Nobel Prize in Physics 1999 – official Nobel Prize website. [202] – official Nobel Prize website. [203] Daigle, Katy (10 July 2012). “India: Enough about Higgs, let’s discuss the boson”. AP News. Retrieved 10 July 2012. [204] Bal, Hartosh Singh (19 September 2012). “The Bose in the Boson”. New York Times. Retrieved 21 September 2012. [205] Alikhan, Anvar (16 July 2012). “The Spark In A Crowded Field”. Outlook India. Retrieved 10 July 2012. [206] Peskin & Schroeder 1995, Chapter 20 9.11 Further reading • Nambu, Yoichiro; Jona-Lasinio, Giovanni (1961). “Dynamical Model of Elementary Particles Based on an Analogy with Physical Review 122: Superconductivity”. Bibcode:1961PhRv..122..345N. 345–358. doi:10.1103/PhysRev.122.345. • Klein, Abraham; Lee, Benjamin W. (1964). “Does Spontaneous Breakdown of Symmetry Imply Zero-Mass Particles?". Physical Review Letters 12 (10): 266. Bibcode:1964PhRvL..12..266K. doi:10.1103/PhysRevLett.12.266. 76 CHAPTER 9. HIGGS BOSON • Anderson, Philip W. (1963). “Plasmons, Gauge Invariance, and Mass”. Physical Review 130: 439. Bibcode:1963PhRv..130..439A. doi:10.1103/PhysRev.130.439. • Higgs, Peter (2010). “My Life as a Boson” (PDF). Talk given at Kings College, London, Nov 24 2010. Retrieved 17 January 2013. (also: ) • Gilbert, Walter (1964). “Broken Symmetries and Massless Particles”. Physical Review Letters 12 (25): 713. Bibcode:1964PhRvL..12..713G. doi:10.1103/PhysRevLett.12.713. • Kibble, Tom (2009). “Englert–Brout– Higgs–Guralnik–Hagen–Kibble mechanism (history)". Scholarpedia. Retrieved 17 January 2013. (also: ) • Higgs, Peter (1964). “Broken Symmetries, Massless Particles and Gauge Fields”. Physics Letters 12 (2): 132–133. Bibcode:1964PhL....12..132H. doi:10.1016/0031-9163(64)91136-9. • Guralnik, Gerald (2009). “The History of the Guralnik, Hagen and Kibble development of the Theory of Spontaneous Symmetry Breaking and Gauge Particles”. International Journal of Modern Physics A 24 (14): 2601–2627. arXiv:0907.3466. Bibcode:2009IJMPA..24.2601G. doi:10.1142/S0217751X09045431., Guralnik, Gerald (2011). “The Beginnings of Spontaneous Symmetry Breaking in Particle Physics. Proceedings of the DPF-2011 Conference, Providence, RI, 8–13 August 2011”. arXiv:1110.2253v1 [physics.hist-ph]., and Guralnik, Gerald (2013). “Heretical Ideas that Provided the Cornerstone for the Standard Model of Particle Physics”. SPG MITTEILUNGEN March 2013, No. 39, (p. 14), and Talk at Brown University about the 1964 PRL papers • Guralnik, Gerald S.; Hagen, C.R.; Kibble, Tom W.B. (1968). “Broken Symmetries and the Goldstone Theorem”. In R.L. Cool and R.E. Marshak. Advances in Physics, Vol. 2. Interscience Publishers. pp. 567–708. ISBN 978-0470170571. 9.12 External links 9.12.1 Popular science, mass media, and general coverage • Hunting the Higgs Boson at C.M.S. Experiment, at CERN • Philip Anderson (not one of the PRL authors) on symmetry breaking in superconductivity and its migration into particle physics and the PRL papers • The Higgs Boson" by the CERN exploratorium. • “Particle Fever”, documentary film about the search for the Higgs Boson. • “The Atom Smashers”, documentary film about the search for the Higgs Boson at Fermilab. • Collected Articles at the Guardian • Cartoon about the search • Cham, Jorge (2014-02-19). “True Tales from the Road: The Higgs Boson Re-Explained”. Piled Higher and Deeper. Retrieved 2014-02-25. • Video (04:38) – CERN Announcement on 4 July 2012, of the discovery of a particle which is suspected will be a Higgs Boson. 9.12.2 • Video1 (07:44) + Video2 (07:44) – Higgs Boson Explained by CERN Physicist, Dr. Daniel Whiteson (16 June 2011). • HowStuffWorks: What exactly is the Higgs Boson? • Carroll, Sean. “Higgs Boson with Sean Carroll”. Sixty Symbols. University of Nottingham. • Overbye, Dennis (2013-03-05). “Chasing the Higgs Boson: How 2 teams of rivals at CERN searched for physics’ most elusive particle”. New York Times Science pages. Retrieved 22 July 2013. - New York Times “behind the scenes” style article on the Higgs’ search at ATLAS and CMS • The story of the Higgs theory by the authors of the PRL papers and others closely associated: Significant papers and other • Observation of a new particle in the search for the Standard Model Higgs Boson with the ATLAS detector at the LHC • Observation of a new Boson at a mass of 125 GeV with the CMS experiment at the LHC • Particle Data Group: Review of searches for Higgs Bosons. • 2001, a spacetime odyssey: proceedings of the Inaugural Conference of the Michigan Center for Theoretical Physics : Michigan, USA, 21–25 May 2001, (p.86 – 88), ed. Michael J. Duff, James T. Liu, ISBN 978-981-238-231-3, containing Higgs’ story of the Higgs Boson. 9.12. EXTERNAL LINKS • A.A. Migdal & A.M. Polyakov, Spontaneous Breakdown of Strong Interaction Symmetry and the Absence of Massless Particles, Sov.J.-JETP 24,91 (1966) - example of a 1966 Russian paper on the subject. 9.12.3 Introductions to the field • Spontaneous symmetry breaking, gauge theories, the Higgs mechanism and all that (Bernstein, Reviews of Modern Physics Jan 1974) - an introduction of 47 pages covering the development, history and mathematics of Higgs theories from around 1950 to 1974. 77 78 CHAPTER 9. HIGGS BOSON 9.13 Text and image sources, contributors, and licenses 9.13.1 Text • Fermion Source: https://en.wikipedia.org/wiki/Fermion?oldid=668594409 Contributors: AxelBoldt, Chenyu, CYD, Mav, Bryan Derksen, The Anome, Ben-Zin~enwiki, Alan Peakall, Dominus, Dcljr, Looxix~enwiki, Glenn, Nikai, Andres, Wikiborg, David Latapie, Phys, Bevo, Stormie, Olathe, Donarreiskoffer, Robbot, Merovingian, Rorro, Wikibot, HaeB, Giftlite, Fropuff, Xerxes314, Vivektewary, JoJan, Karol Langner, Tothebarricades.tk, Icairns, Hidaspal, Vsmith, Laurascudder, Lysdexia, Ashlux, Graham87, Magister Mathematicae, Kbdank71, Syndicate, Strait, Protez, Drrngrvy, FlaBot, Srleffler, Chobot, YurikBot, RobotE, Jimp, Bhny, Captaindan, SpuriousQ, Salsb, Lomn, Enormousdude, CharlesHBennett, Federalist51, Tom Lougheed, Unyoyega, Jrockley, MK8, BabuBhatt, Complexica, Zachorious, Shalom Yechiel, QFT, Garry Denke, Daniel.Cardenas, SashatoBot, Flipperinu, Dan Gluck, LearningKnight, Happy-melon, Paulfriedman7, Cydebot, Meno25, Zalgo, Thijs!bot, Mbell, Headbomb, Nick Number, Orionus, Shlomi Hillel, CosineKitty, NE2, Mwarren us, ZPM, Vanished user ty12kl89jq10, Joshua Davis, R'n'B, Tensegrity, Rod57, Dgiraffes, Alpvax, VolkovBot, TXiKiBoT, Red Act, Anonymous Dissident, Abdullais4u, ‫כל יכול‬, Tanhueiming, Antixt, Haiviet~enwiki, EmxBot, Kbrose, SieBot, Likebox, Jojalozzo, Dhatfield, Oxymoron83, TubularWorld, ClueBot, Seervoitek, Rodhullandemu, Jorisverbiest, Feebas factor, ChandlerMapBot, Nilradical, Wikeepedian, Stephen Poppitt, Addbot, Vectorboson, Luckas-bot, Yobot, Planlips, Dickdock, AnomieBOT, Icalanise, Materialscientist, Xqbot, Br77rino, Balaonair, , Paine Ellsworth, Blackoutjack, Kikeku, Rameshngbot, Tom.Reding, RedBot, Alarichus, Michael9422, Silicon-28, TjBot, EmausBot, WikitanvirBot, Quazar121, Solomonfromfinland, JSquish, Fimin, Quondum, AManWithNoPlan, EdoBot, ClueBot NG, PBot1, EthanChant, Bibcode Bot, Petermahlzahn, KingKhan85, ChrisGualtieri, BoethiusUK, DerekWinters, Tentinator, JNrgbKLM, Mohit rajpal, KasparBot, Jiswin1992 and Anonymous: 116 • Quark Source: https://en.wikipedia.org/wiki/Quark?oldid=668012339 Contributors: AxelBoldt, Derek Ross, Vicki Rosenzweig, Mav, Bryan Derksen, The Anome, Gareth Owen, Andre Engels, PierreAbbat, Peterlin~enwiki, Ben-Zin~enwiki, Zoe, Heron, Montrealais, Hfastedge, Edward, Dante Alighieri, Ixfd64, CesarB, Card~enwiki, NuclearWinner, Looxix~enwiki, Ahoerstemeier, Elliot100, Docu, J-Wiki, Nanobug, Aarchiba, Julesd, Glenn, Schneelocke, Jengod, A5, Timwi, Dysprosia, DJ Clayworth, Phys, Ed g2s, Bevo, Olathe, MD87, Jni, Phil Boswell, Sjorford, Donarreiskoffer, Robbot, Sanders muc, Moncrief, Merovingian, PxT, Texture, Bkell, UtherSRG, Widsith, Ancheta Wis, Giftlite, ShaunMacPherson, Harp, Nunh-huh, Lupin, Herbee, Leflyman, Monedula, 0x6D667061, Xerxes314, Anville, Hoho~enwiki, Alison, Beardo, Moogle10000, Wronkiew, Jackol, Bobblewik, Bodhitha, Piotrus, Kaldari, Elroch, Icairns, Zfr, TonyW, Ukexpat, BrianWilloughby, Grunt, O'Dea, Jiy, Discospinster, Rich Farmbrough, Guanabot, T Long, Vsmith, Saintswithin, SocratesJedi, Mani1, Bender235, Lancer, RJHall, Mr. Billion, El C, Kwamikagami, Laurascudder, Susvolans, Triona, Axezz, Bobo192, Army1987, C S, Ziggurat, Rangelov, Matt McIrvin, Jojit fb, Nk, Pentalis, Obradovic Goran, Fwb22, Lysdexia, Benjonson, Alansohn, Gary, Gintautasm, Guy Harris, Keenan Pepper, MonkeyFoo, Lectonar, Mac Davis, Wdfarmer, Snowolf, Schapel, Knowledge Seeker, Evil Monkey, VivaEmilyDavies, CloudNine, Kusma, Kazvorpal, Kay Dekker, Crosbiesmith, Mogigoma, Linas, Mindmatrix, JarlaxleArtemis, ScottDavis, LOL, Wdyoung, Before My Ken, Tylerni7, Jwanders, Dataphiliac, AndriyK, Noetica, Wayward, Wisq, Palica, Marudubshinki, Calréfa Wéná, GSlicer, Graham87, Deltabeignet, Kbdank71, Yurik, Crzrussian, Rjwilmsi, Bremen, Marasama, SpNeo, Mike Peel, Bubba73, DoubleBlue, Matt Deres, Yamamoto Ichiro, Algebra, Dsnow75, RobertG, Nihiltres, Jeff02, RexNL, TeaDrinker, Chobot, DVdm, Jpacold, Gwernol, Elfguy, Roboto de Ajvol, YurikBot, Wavelength, Bambaiah, Sceptre, Hairy Dude, Jimp, Phantomsteve, TheDoober, Dobromila, JabberWok, CambridgeBayWeather, Chaos, Salsb, Wimt, Ugur Basak, NawlinWiki, Spike Wilbury, Bossrat, SCZenz, Randolf Richardson, Danlaycock, Tony1, DRosenbach, Robertbyrne, Dna-webmaster, WAS 4.250, Closedmouth, Pietdesomere, Heathhunnicutt, Kevin, Banus, RG2, Kamickalo, That Guy, From That Show!, Veinor, MacsBug, SmackBot, Aigarius, BBandHB, Incnis Mrsi, InverseHypercube, C.Fred, Bazza 7, Ikip, Anastrophe, Jrockley, Eskimbot, AnOddName, Jonathan Karlsson, Edgar181, Gilliam, Dauto, NickGarvey, Vvarkey, Bluebot, KaragouniS, Keegan, Dahn, Bigfun, Miquonranger03, OrangeDog, Silly rabbit, Metacomet, Tripledot, Nbarth, DHN-bot~enwiki, Sbharris, Colonies Chris, Hallenrm, Scwlong, Gsp8181, Can't sleep, clown will eat me, Mallorn, Jeff DLB, TKD, Addshore, Mqjjb30e, Cybercobra, Khukri, B jonas, Jdlambert, Lpgeffen, Nrcprm2026, Akriasas, Zadignose, Jóna Þórunn, Bdushaw, Beyazid, TriTertButoxy, SashatoBot, SciBrad, Doug Bell, Soap, Richard L. Peterson, Mgiganteus1, SpyMagician, Edconrad, Loadmaster, 2T, Waggers, SandyGeorgia, Ravi12346, Dbzfrk15146, Peyre, Newone, GDallimore, Happy-melon, Majora4, Chovain, Tawkerbot2, Cryptic C62, JForget, Vaughan Pratt, Hello789, ZICO, SUPRATIM DEY, Ruslik0, CuriousEric, Paulfriedman7, Logical2u, Myasuda, RoddyYoung, Typewritten, Cydebot, Abeg92, Mike Christie, Grahamec, Gogo Dodo, Jayen466, 879(CoDe), Michael C Price, Tawkerbot4, Ameliorate!, Akcarver, Gimmetrow, SallyScot, Casliber, Thijs!bot, Epbr123, NeoPhyteRep, LeBofSportif, Markus Pössel, Anupam, Sopranosmob781, Headbomb, Marek69, John254, KJBurns, MichaelMaggs, Escarbot, Eleuther, Ice Ardor, Aadal, AntiVandalBot, SmokeyTheCat, Tyco.skinner, Exteray, RobJ1981, Rsocol, Ke garne, Deflective, Husond, MER-C, CosineKitty, Andonic, East718, Pkoppenb, DanPMK, Magioladitis, WolfmanSF, Thasaidon, Bongwarrior, VoABot II, ‫باسم‬, Inertiatic076, Kevinmon, Christoph Scholz~enwiki, Aka042, Giggy, Tanvirzaman, Johnbibby, Cyktsui, ArchStanton69, Ace42, Allstarecho, Shijualex, DerHexer, Elandra, Denis tarasov, MartinBot, Poeloq, Dorvaq, CommonsDelinker, HEL, J.delanoy, Nev1, Ops101ex, DrKiernan, Hgpot, Ferdyshenko, Jigesh, DJ1AM, Tarotcards, Coppertwig, TomasBat, Nikbuz, SJP, FJPB, Vainamainien, Tiggydong, Robprain, Sheliak, Cuzkatzimhut, Lights, X!, VolkovBot, CWii, ABF, John Darrow, Holme053, Nousernamesleft, Ryan032, GimmeBot, Davehi1, A4bot, Captain Courageous, Guillaume2303, Anonymous Dissident, Drestros power, Qxz, Anna Lincoln, Eldaran~enwiki, Leafyplant, Don4of4, PaulTanenbaum, Abdullais4u, Jbryancoop, Mbalelo, Gilisa, Eubulides, Chronitis, Seresin, Dustybunny, Insanity Incarnate, Upquark, Edge1212, Ollieho, AOEU Warrior, SieBot, Graham Beards, WereSpielChequers, Csmart287, Guguma5, Winchelsea, Jbmurray, Caltas, Vanished User 8a9b4725f8376, Keilana, Bentogoa, Aillema, RadicalOne, Arbor to SJ, Elcobbola, Physics one, Dhatfield, RSStockdale, Son of the right hand, Ngexpert5, Ngexpert6, Ngexpert7, Psycherevolt, Sean.hoyland, Mygerardromance, Dabomb87, Nergaal, Muhends, Romit3, SallyForth123, Atif.t2, ClueBot, The Thing That Should Not Be, Wwheaton, Xeno malleus, Harland1, Piledhigheranddeeper, Maxtitan, DragonBot, Glopso, Choonkiat.lee, Himynameisdumb, Worth my salt, Arthur Quark, Estirabot, Brews ohare, Jotterbot, PhySusie, Brianboulton, Dekisugi, ANOMALY-117, Sallicio, Yomangan, Jtle515, Katanada, DumZiBoT, TimothyRias, XLinkBot, Vayalir, Oldnoah, Saintlucifer2008, Nathanwesley3, Dragonfiremage, Devilist666, Mancune2001, Jbeans, WikiDao, SkyLined, Truthnlove, Airplaneman, Eklipse, Addbot, Eric Drexler, AVand, Some jerk on the Internet, Captain-tucker, Giants2008, Iceblock, Ronhjones, Quarksci, Mseanbrown, Looie496, LaaknorBot, Peti610botH, AgadaUrbanit, Tide rolls, Vicki breazeale, Gail, Extruder~enwiki, Abduallah mohammed, Dealer77, Luckas-bot, Yobot, Fraggle81, Cflm001, Legobot II, Amble, Mmxx, Superpenguin1984, Worm That Turned, The Vector Kid, Planlips, Fangfyre, TestEditBot, Azcolvin429, Vroo, Synchronism, Bility, Orion11M87, AnomieBOT, Xi rho, Rubinbot, Jim1138, Bookaneer, Yotcmdr, Crystal whacker, Sonic h, Materialscientist, Citation bot, Pitke, Vuerqex, Bci2, ArthurBot, LilHelpa, Xqbot, Jeffrey Mall, AbigailAbernathy, Srich32977, Alex2510, Almabot, Uscbino, Pmlineditor, RibotBOT, Shmomuffin, Gunjan verma81, Chotarocket, Ernsts, Renverse, A. di M., Weekendpartier, FrescoBot, Paine Ellsworth, DelphinidaeZeta, Steve Quinn, Citation bot 1, AstaBOTh15, Pinethicket, Jonesey95, Calmer Waters, Skyerise, Pmokeefe, Jschnur, Searsshoesales, Jrobbinz123, Lissajous, Turian, Lando Calrissian, Wotnow, Ansumang, Reaper Eternal, 564dude, Jackvancs, Bobotast, MINTOPOINT, TjBot, DexDor, 9.13. TEXT AND IMAGE SOURCES, CONTRIBUTORS, AND LICENSES 79 Антон Гліністы, Daggersteel10, Chiechiecheist, EmausBot, John of Reading, WikitanvirBot, Duskbrood, FergalG, Slightsmile, Barak90, Wikipelli, TheLemon1234, Manofgrass, Brazmyth, H3llBot, Stoneymufc29, GeorgeBarnick, Brandmeister, Ego White Tray, TYelliot, ClueBot NG, Gilderien, A520, Cheeseequalsyum, Timothy jordan, 123Hedgehog456, Maplelanefarm, 336, Helpful Pixie Bot, Jeffreyts11, 123456789malm, Bibcode Bot, BG19bot, Hurricanefan25, MusikAnimal, Davidiad, MosquitoBird11, Mydogpwnsall, MrBill3, Njavallil, Glacialfox, Walterpfeifer, Thebannana, CE9958, Marioedesouza, Mediran, Dexbot, Rishab021, Cjean42, Sriharsh1234, Sam boron100, Wankybanky, Wikitroll12345, RojoEsLardo, Jwratner1, NottNott, Saebre, JNrgbKLM, KheltonHeadley, AspaasBekkelund, HectorCabreraJr, Hazinho93, Quadrupedi, QuantumMatt101, Philipphilip0001, Monkbot, RiderDB, Egfraley, Tetra quark, Weed305, KasparBot and Anonymous: 698 • Hadron Source: https://en.wikipedia.org/wiki/Hadron?oldid=666478986 Contributors: Bryan Derksen, Manning Bartlett, Peterlin~enwiki, Edward, Erik Zachte, ESnyder2, Fruge~enwiki, TakuyaMurata, Darkwind, Glenn, Nikai, Ehn, Olya, Phys, Bevo, Topbanana, BenRG, Twang, Donarreiskoffer, Korath, Wjhonson, Merovingian, Ojigiri~enwiki, Sunray, JesseW, Xanzzibar, Giftlite, Xerxes314, Dratman, Physicist, Mikro2nd, LiDaobing, Pthompson, Icairns, Jimaginator, Mike Rosoft, Vsmith, Goochelaar, Sunborn, Livajo, El C, Kwamikagami, Shanes, Fwb22, Jumbuck, Cookiemobsta, Velella, Rebroad, Vuo, Kusma, DV8 2XL, Linas, GrouchyDan, Palica, Marudubshinki, Kbdank71, Mana Excalibur, Kinu, Strait, FlaBot, RexNL, Goudzovski, FrankTobia, YurikBot, Radishes, Bambaiah, Hydrargyrum, Salsb, NawlinWiki, Wiki alf, SCZenz, Davemck, Bota47, Scriber~enwiki, Modify, Katieh5584, Eog1916, SmackBot, McGeddon, Gilliam, Benjaminevans82, Dingar, Persian Poet Gal, Telempe, DHN-bot~enwiki, Audriusa, Acepectif, Kokot.kokotisko, JorisvS, JarahE, BranStark, SJCrew, Eratticus, Chrumps, Jtuggle, Q43, Epbr123, Wikid77, Headbomb, Escarbot, Deflective, Gcm, NE2, Trapezoidal, Naval Scene, ΚΕΚΡΩΨ, NeverWorker, Wwmbes, Alexllew, Lvwarren, Jebus0, DariusU, Khalid Mahmood, Adriaan, Rustyfence, Ron2, Leyo, J.delanoy, Maurice Carbonaro, JVersteeg, Rod57, Way2Smart22, Hugh Hudson, Y2H, Ansans, Bobxii, Chris Longley, Useight, Dylan bossart, VolkovBot, TXiKiBoT, Kinkydarkbird, Anonymous Dissident, Don4of4, Wordsmith, LeaveSleaves, Antixt, Enviroboy, Insanity Incarnate, Nibios, AlleborgoBot, SieBot, Yintan, LeadSongDog, RadicalOne, Paolo.dL, OKBot, JohnSawyer, Lazarus1907, Pinkadelica, Danthewhale, Martarius, ClueBot, Amaamaddq, Authoritative Physicist, Wwheaton, Rotational, DragonBot, Sciencedude9998, Tuchomator, El planeto, Kaiba, Thingg, Koshoid, Aitias, Apparition11, Rishi.bedi, TimothyRias, InternetMeme, Jbeans, MystBot, Sgpsaros, Tayste, Addbot, Pkkphysicist, Ehrenkater, Lightbot, Luckas-bot, Yobot, Nallimbot, Dagus2000, Fangfyre, LOLx9000, Thisaccountwillbebanned, Citation bot, Xqbot, Drilnoth, Br77rino, Wikiedit33, Ajahnjohn, Omnipaedista, RibotBOT, Mashmeister, Tjbright2, My cat’s breath smells like catfood, Haeinous, Citation bot 1, Javert, Gil987, I dream of horses, Jonesey95, Rameshngbot, Thinking of England, Alarichus, SkyMachine, FoxBot, Johnshnappay, Антон Гліністы, Teravolt, Racerx11, Naznin farhah, Tommy2010, Wikipelli, ZéroBot, StringTheory11, Hadron12, Donner60, Petrb, ClueBot NG, Gareth Griffith-Jones, Bibcode Bot, Dwightboone, Njavallil, Walterpfeifer, Pfeiferwalter, ChrisGualtieri, Ugog Nizdast, Lithelimbs, RoKo89, Michikohundred, KasparBot, Wwilliam726 and Anonymous: 163 • Boson Source: https://en.wikipedia.org/wiki/Boson?oldid=668714319 Contributors: CYD, The Anome, Xaonon, Aldie, Enchanter, Roadrunner, Ben-Zin~enwiki, Lisiate, Michael Hardy, Tim Starling, Kroose, Looxix~enwiki, Andrewa, Glenn, Andres, Kaihsu, Samw, Panoramix, Schneelocke, CAkira, Wikiborg, The Anomebot, Saltine, Phys, Drxenocide, Robbot, Altenmann, Bkalafut, Merovingian, Rorro, Hadal, Robinh, VanishedUser kfljdfjsg33k, Giftlite, Fropuff, Pharotic, Isidore, Alexf, Beland, Jossi, Icairns, Zfr, Cructacean, Ornil, Mormegil, DanielCD, Noisy, Discospinster, Rich Farmbrough, Guanabot, Hidaspal, Sunborn, Kbh3rd, Jensbn, Alxndr, La goutte de pluie, Anthony Appleyard, Jlandahl, Leoadec, H2g2bob, Rocastelo, Benbest, Mpatel, Nakos2208~enwiki, GregorB, SDC, Palica, Ashmoo, Graham87, Kbdank71, Zzedar, Drbogdan, Strait, Master Justin, Wragge, FlaBot, Srleffler, Chobot, YurikBot, Bhny, The1physicist, Salsb, NawlinWiki, Welsh, Pyg, Dna-webmaster, Enormousdude, NeilN, Finell, Hal peridol, SmackBot, Incnis Mrsi, Ashley thomas80, Melchoir, Gilliam, MK8, MalafayaBot, Complexica, Epastore, DHN-bot~enwiki, Scienz Guy, Sbharris, QFT, Voyajer, Grover cleveland, Philvarner, Bradenripple, SashatoBot, Lambiam, Turbothy, T-dot, MagnaMopus, Candamir, WhiteHatLurker, Dicklyon, Treyp, Focomoso, Dan Gluck, UltraHighVacuum, Iridescent, Mathninja, Buckyboy314, Ianji, Cydebot, Stebbins, W.F.Galway, VashiDonsk, Tenbergen, Ward3001, Abtvctkto61, Thijs!bot, Barticus88, Mbell, Frozenport, Headbomb, MichaelMaggs, Escarbot, Orionus, Shan23, Alomas, JAnDbot, Deflective, CosineKitty, Pkoppenb, TheEditrix2, Magioladitis, VoABot II, Inertiatic076, Vanished user ty12kl89jq10, CodeCat, MartinBot, STBot, R'n'B, Tarotcards, Uberdude85, RuneSylvester, The Wild Falcon, Asnr 6, TXiKiBoT, Hqb, Anonymous Dissident, Abdullais4u, Bertrem, Moutane, Dirkbb, Antixt, Jeraaldo, BriEnBest, SieBot, Jim E. Black, Gerakibot, RadicalOne, Flyer22, Radon210, Sunayanaa, Jojalozzo, Tpvibes, Nsajjansajja, Owhanow~enwiki, Mike2vil, Mgurgan, Startswithj, Danthewhale, PipepBot, Rodhullandemu, ChandlerMapBot, Excirial, PixelBot, Nilradical, Cenarium, Wikeepedian, Ouchitburns, Addbot, Bwr6, Minami Kana, Aboctok, Numbo3bot, OlEnglish, David0811, WikiDreamer Bot, Jack who built the house, Luckas-bot, Yobot, Ptbotgourou, Senator Palpatine, AnomieBOT, Jim1138, JackieBot, Kingpin13, Materialscientist, Xqbot, Gravitivistically, Daners, Tomwsulcer, GrouchoBot, MeDrewNotYou, , Ace of Spades, Alarics, Paul Laroque, Rameshngbot, RedBot, FoxBot, DixonDBot, Michael9422, Weedwhacker128, Tbhotch, TjBot, Ripchip Bot, EmausBot, JSquish, Kkm010, HiW-Bot, ZéroBot, StringTheory11, Lagomen, Robhenry9, Tls60, ClueBot NG, Raghavankl, GioGziro95, HBook, Helpful Pixie Bot, Bibcode Bot, 2001:db8, AvocatoBot, Nickni28, Minsbot, Blogger 20, Protomaestro, Abitoby, Darryl from Mars, NoRwEgIaNbAcTeRiUm, Jason7898, Valluvan888, Ov.kulkarni, Crpandya, Enamex, Lugia2453, Graphium, Federicoaolivieri, 77Mike77, Rltb, 314Username, Dllaughingwang, Codeusirae, Sometree, DR ROBERT HALT, KasparBot, Jiswin1992 and Anonymous: 218 • Lepton Source: https://en.wikipedia.org/wiki/Lepton?oldid=668095924 Contributors: Bryan Derksen, Andre Engels, PierreAbbat, BenZin~enwiki, Heron, Xavic69, Fruge~enwiki, Fwappler, Ahoerstemeier, Julesd, Glenn, Mxn, A5, Wikiborg, Dysprosia, Radiojon, Imc, Morwen, Fibonacci, Bcorr, Phil Boswell, Donarreiskoffer, Robbot, Merovingian, Wikibot, Giftlite, Smjg, DocWatson42, Harp, Herbee, Xerxes314, Sysin, Knutux, LiDaobing, LucasVB, ClockworkLunch, RetiredUser2, Icairns, Mike Rosoft, Chris j wood, Martinl~enwiki, Smalljim, Giraffedata, Jumbuck, RobPlatt, Neonumbers, Ahruman, Computerjoe, Simon M, Woohookitty, Mindmatrix, Rjwilmsi, Strait, Erkcan, FlaBot, DannyWilde, Mastorrent, Celebere, Peterl, YurikBot, Bambaiah, Jimp, Salsb, Spike Wilbury, Jaxl, SCZenz, DeadEyeArrow, Tetracube, Smoggyrob, Dmuth, Jaysbro, Sbyrnes321, That Guy, From That Show!, SmackBot, Bazza 7, KocjoBot~enwiki, Jrockley, Mom2jandk, Cool3, Hmains, Complexica, DHN-bot~enwiki, Mesons, Yevgeny Kats, TriTertButoxy, SashatoBot, Ouzo~enwiki, Happy-melon, Kurtan~enwiki, Myasuda, Cydebot, Meno25, Photocopier, Michael C Price, Casliber, Thijs!bot, Headbomb, Newton2, Mentifisto, Autotheist, Steveprutz, NeverWorker, NicoSan, MartinBot, Arjun01, HEL, J.delanoy, Numbo3, Gombang, Num1dgen, Ceoyoyo, VolkovBot, Macedonian, Mocirne, TXiKiBoT, Anonymous Dissident, Abdullais4u, Antixt, Jhb110, Thanatos666, AlleborgoBot, SieBot, ToePeu.bot, RadicalOne, Ngexpert7, Jacob.jose, Hamiltondaniel, TubularWorld, Muhends, ClueBot, ICAPTCHA, UniQue tree, Snigbrook, Fyyer, IceUnshattered, Cmj91uk, LieAfterLie, Manu-ve Pro Ski, TimothyRias, Addbot, Betterusername, AgadaUrbanit, Ehrenkater, OlEnglish, Zorrobot, Andy2308, Legobot, Luckas-bot, Ptbotgourou, Maxim Sabalyauskas, Planlips, JackieBot, Icalanise, Citation bot, .‫غامدي‬.‫أحمد‬24, ArthurBot, Almabot, Omnipaedista, Alexeymorgunov, , Tormine, MathFacts, Citation bot 1, MastiBot, Earthandmoon, EmausBot, John of Reading, Az29, Galaktiker, StringTheory11, Quondum, Surajt88, I hate whitespace, ClueBot NG, Scimath Genius, Braincricket, Widr, Helpful Pixie Bot, Bibcode Bot, Tyler6360534, Katagun5, Melenc, DerekWinters, Prasanna4s, Machosquirrel, Devinhorn, KasparBot and Anonymous: 146 80 CHAPTER 9. HIGGS BOSON • Meson Source: https://en.wikipedia.org/wiki/Meson?oldid=669138065 Contributors: AxelBoldt, Bryan Derksen, Josh Grosse, PierreAbbat, Ben-Zin~enwiki, Xavic69, TakuyaMurata, Fwappler, Ahoerstemeier, Ping, Phys, Bcorr, Jeffq, Donarreiskoffer, Robbot, Fredrik, Sanders muc, Merovingian, Rursus, Ojigiri~enwiki, Davidl9999, DocWatson42, Harp, Marcika, Xerxes314, Niteowlneils, Eequor, Physicist, Eroica, Icairns, Sam Hocevar, Lehi, Rich Farmbrough, Pjacobi, Tjic, Robotje, Nicke Lilltroll~enwiki, Pearle, Jumbuck, Jérôme, Bucephalus, Falcorian, Palica, Tevatron~enwiki, Mandarax, Kbdank71, Strait, Titoxd, FlaBot, Jeremygbyrne, Chobot, YurikBot, Wavelength, Bambaiah, Phmer, Jimp, Ozabluda, JabberWok, Salsb, Leutha, Długosz, SCZenz, Ravedave, Gadget850, Antiduh, Tetracube, SmackBot, Melchoir, Eskimbot, Chris the speller, DHN-bot~enwiki, Sbharris, Kevinpurcell, Mesons, DMacks, Jashank, JorisvS, Mgiganteus1, Geologyguy, Ryulong, JarahE, Myasuda, ChrisKennedy, Michael C Price, Thijs!bot, Headbomb, Escarbot, Orionus, Spartaz, Gökhan, Deflective, Magioladitis, Swpb, Khalid Mahmood, Tercer, Kostisl, Hans Dunkelberg, Tarotcards, Xiahou, JeffreyRMiles, VolkovBot, Prizrak, TXiKiBoT, Muro de Aguas, Martin451, LeaveSleaves, Antixt, SieBot, Majeston, Gerakibot, Graf Von Crayola, Humanityisthedisease, Mimihitam, Fratrep, OKBot, ClueBot, Terrorist96, Diagramma Della Verita, Brews ohare, Neville35, RMFan1, WikHead, Stephen Poppitt, Addbot, Gtakanis, Chzz, Debresser, CosmiCarl, AgadaUrbanit, Dickdock, Magog the Ogre, AnomieBOT, StratoWiki, Altruism2010, Citation bot, ArthurBot, Xqbot, Omnipaedista, WaysToEscape, FrescoBot, Paine Ellsworth, Ironboy11, Steve Quinn, 000ojjo000, Yehoshua2, Citation bot 1, Wdcf, Thinking of England, Puzl bustr, Ale And Quail, Discovery4, Mean as custard, Dkzico007, John of Reading, WikitanvirBot, GoingBatty, Hanretty, ZéroBot, StringTheory11, Markinvancouver, ClueBot NG, Christian.kolen, Wallace Kneeland, Helpful Pixie Bot, Bibcode Bot, Glevum, DerekWinters, Mark viking, Justin567Hicks, Prokaryotes, Monkbot, KasparBot and Anonymous: 86 • Photon Source: https://en.wikipedia.org/wiki/Photon?oldid=669468957 Contributors: AxelBoldt, WojPob, Mav, Bryan Derksen, The Anome, Tarquin, Koyaanis Qatsi, Ap, Josh Grosse, Ben-Zin~enwiki, Heron, Youandme, Spiff~enwiki, Bdesham, Michael Hardy, Ixfd64, TakuyaMurata, NuclearWinner, Looxix~enwiki, Snarfies, Ahoerstemeier, Stevenj, Julesd, Glenn, AugPi, Mxn, Smack, Pizza Puzzle, Wikiborg, Reddi, Lfh, Jitse Niesen, Kbk, Laussy, Bevo, Shizhao, Raul654, Jusjih, Donarreiskoffer, Robbot, Hankwang, Fredrik, Eman, Sanders muc, Altenmann, Bkalafut, Merovingian, Gnomon Kelemen, Hadal, Wereon, Anthony, Wjbeaty, Giftlite, Art Carlson, Herbee, Xerxes314, Everyking, Dratman, Michael Devore, Bensaccount, Foobar, Jaan513, DÅ‚ugosz, Zeimusu, LucasVB, Beland, Setokaiba, Kaldari, Vina, RetiredUser2, Icairns, Lumidek, Zondor, Randwicked, Eep², Chris Howard, Zowie, Naryathegreat, Discospinster, Rich Farmbrough, Yuval madar, Pjacobi, Vsmith, Ivan Bajlo, Dbachmann, Mani1, SpookyMulder, Kbh3rd, RJHall, Ben Webber, El C, Edwinstearns, Laurascudder, RoyBoy, Spoon!, Dalf, Drhex, Bobo192, Foobaz, I9Q79oL78KiL0QTFHgyc, La goutte de pluie, Zr40, Apostrophe, Minghong, Rport, Alansohn, Gary, Sade, Corwin8, PAR, UnHoly, Hu, Caesura, Wtmitchell, Bucephalus, Max rspct, BanyanTree, Cal 1234, Count Iblis, Egg, Dominic, Gene Nygaard, Ghirlandajo, Kazvorpal, UTSRelativity, Falcorian, Drag09, Richard Arthur Norton (1958- ), Woohookitty, Linas, Gerd Breitenbach, StradivariusTV, Oliphaunt, Cleonis, Pol098, Ruud Koot, Mpatel, Nakos2208~enwiki, Dbl2010, Ch'marr, SDC, CharlesC, Alan Canon, Reddwarf2956, Mandarax, BD2412, Kbdank71, Zalasur, Sjakkalle, Rjwilmsi, Саша Стефановић, Strait, MarSch, Dennis Estenson II, Trlovejoy, Mike Peel, HappyCamper, Bubba73, Brighterorange, Cantorman, Egopaint, Noon, Godzatswing, FlaBot, RobertG, Arnero, Mathbot, Nihiltres, Fresheneesz, TeaDrinker, Srleffler, BradBeattie, Chobot, Jaraalbe, DVdm, Elfguy, EamonnPKeane, YurikBot, Bambaiah, Splintercellguy, Jimp, RussBot, Supasheep, JabberWok, Wavesmikey, KevinCuddeback, Stephenb, Gaius Cornelius, Salsb, Trovatore, Długosz, Tailpig, Joelr31, SCZenz, Randolf Richardson, Ravedave, Tony1, Roy Brumback, Gadget850, Dna-webmaster, Enormousdude, Lt-wiki-bot, Oysteinp, JoanneB, Ligart, John Broughton, GrinBot~enwiki, Sbyrnes321, Itub, SmackBot, Moeron, Incnis Mrsi, KnowledgeOfSelf, CelticJobber, Melchoir, Rokfaith, WilyD, Jagged 85, Jab843, Cessator, AnOddName, Skizzik, Dauto, JSpudeman, Robin Whittle, Ati3414, Persian Poet Gal, MK8, Jprg1966, Complexica, Sbharris, Colonies Chris, Ebertek, WordLife565, V1adis1av, RWincek, Aces lead, Stangbat, Cybercobra, Valenciano, EVula, A.R., Mini-Geek, AEM, DMacks, N Shar, Sadi Carnot, FlyHigh, The Fwanksta, Drunken Pirate, Yevgeny Kats, Lambiam, Harryboyles, IronGargoyle, Ben Moore, A. Parrot, Mr Stephen, Fbartolom, Dicklyon, SandyGeorgia, Mets501, Ceeded, Ambuj.Saxena, Ryulong, Vincecate, Astrobayes, Newone, J Di, Lifeverywhere, Tawkerbot2, JRSpriggs, Chetvorno, Luis A. Veguilla-Berdecia, CalebNoble, Xod, Gregory9, CmdrObot, Wafulz, Van helsing, John Riemann Soong, Rwflammang, Wquester, Outriggr, Logical2u, Myasuda, Howardsr, Cydebot, Krauss, Kanags, A876, WillowW, Bvcrist, Hyperdeath, Hkyriazi, Rracecarr, Difluoroethene, Edgerck, Michael C Price, Tawkerbot4, Christian75, Ldussan, RelHistBuff, Waxigloo, Kozuch, Thijs!bot, Epbr123, Opabinia regalis, Markus Pössel, Mglg, 24fan24, Headbomb, Newton2, John254, J.christianson, Escarbot, Stannered, AntiVandalBot, Luna Santin, Jtrain4469, Normanmargolus, Tyco.skinner, TimVickers, NSH001, Dodecahedron~enwiki, Tim Shuba, Gdo01, Sluzzelin, Abyssoft, CosineKitty, AndyBloch, Bryanv, ScottStearns, Hroðulf, Bongwarrior, VoABot II, B&W Anime Fan, SHCarter, Lgoger, I JethroBT, Dirac66, Hveziris, Maliz, Lord GaleVII, TRWBW, Shijualex, Glen, DerHexer, Patstuart, Gwern, Taborgate, MartinBot, MNAdam, Jay Litman, HEL, Ralf 58, J.delanoy, DrKiernan, Trusilver, C. Trifle, AstroHurricane001, Numbo3, Pursey, CMDadabo, Kevin aylward, UchihaFury, Pirate452, H4xx0r, Iamthewalrus35, Iamthewalrus36, Gee Eff, Chimpy07, Dirkdiggler69, Lk69, Hallamfm, Annoying editter, Yehoodig, Acalamari, Foreigner1, McSly, Samtheboy, Tarotcards, Rominandreu, ARTE, Tanaats, Potatoswatter, Y2H, Divad89, Scott Illini, Stack27, THEblindwarrior, VolkovBot, AlnoktaBOT, Hyperlinker, DoorsAjar, TXiKiBoT, Cosmic Latte, The Original Wildbear, Davehi1, Chiefwaterfall, Vipinhari, Hqb, Anonymous Dissident, HansMair, Predator24, BotKung, Luuva, Calvin4986, Improve~enwiki, Kmhkmh, Richwil, Antixt, Gorank4, Falcon8765, GlassFET, Cryptophile, MattiasAndersson, AlleborgoBot, Carlodn6, NHRHS2010, Relilles~enwiki, Tpb, SieBot, Timb66, Graham Beards, WereSpielChequers, ToePeu.bot, JerrySteal, Android Mouse, Likebox, RadicalOne, Paolo.dL, Lightmouse, PbBot, Spartan-James, Duae Quartunciae, Hamiltondaniel, StewartMH, Dstebbins, ClueBot, Bobathon71, The Thing That Should Not Be, Mwengler, EoGuy, Jagun, RODERICKMOLASAR, Wwheaton, Dmlcyal8er, Razimantv, Mild Bill Hiccup, Feebas factor, J8079s, Rotational, MaxwellsLight, Awickert, Excirial, PixelBot, Sun Creator, NuclearWarfare, PhySusie, El bot de la dieta, DerBorg, Shamanchill, PoofyPeter99, J1.grammar natz, Laserheinz, TimothyRias, XLinkBot, Jovianeye, Petedskier, Hess88, Addbot, Mathieu Perrin, DOI bot, DougsTech, Download, James thirteen, AndersBot, LinkFA-Bot, Barak Sh, AgadaUrbanit, Тиверополник, Dayewalker, Quantumobserver, Kein Einstein, Legobot, Luckas-bot, Yobot, Kilom691, Allowgolf~enwiki, AnomieBOT, Ratul2000, Kingpin13, Materialscientist, Citation bot, Xqbot, Ambujarind69, Mananay, Emezei, Sharhalakis, Shirik, RibotBOT, Rickproser, SongRenKai, Max derner, Merrrr, A. di M., , CES1596, Paine Ellsworth, Gsthae with tempo!, Nageh, TimonyCrickets, WurzelT, Steve Quinn, Spacekid99, Radeksonic, Citation bot 1, Pinethicket, I dream of horses, HRoestBot, Tanweer Morshed, Eno crux, Tom.Reding, Jschnur, RedBot, IVAN3MAN, Gamewizard71, FoxBot, TobeBot, Earthandmoon, PleaseStand, Marie Poise, RjwilmsiBot, Антон Гліністы, Ripchip Bot, Ofercomay, Chemyanda, EmausBot, Bookalign, WikitanvirBot, Roxbreak, Word2need, Gcastellanos, Tommy2010, Dcirovic, K6ka, Hhhippo, Cogiati, 1howardsr1, StringTheory11, Waperkins, Jojojlj, Access Denied, Quondum, AManWithNoPlan, Raynor42, L Kensington, HCPotter, Haiti333, RockMagnetist, Rocketrod1960, ClueBot NG, JASMEET SINGH HAFIST, Schicagos, Snotbot, Vinícius Machado Vogt, Helpful Pixie Bot, SzMithrandir, Bibcode Bot, BG19bot, Roberticus, Paolo Lipparini, Wzrd1, Rifath119, Davidiad, Mark Arsten, Peter.sujak, Wikarchitect, Hamish59, Caypartisbot, Penguinstorm300, KSI ROX, Bhargavuk1997, Chromastone1998, TheJJJunk, Nimmo1859, EagerToddler39, Dexbot, EZas3pt14, Webclient101, Chrisanion, Vanquisher.UA, Tony Mach, PREMDASKANNAN, Meghas, Reatlas, Profb39, Zerberos, Thesuperseo, The User 111, Eyesnore, Ybidzian, Tentinator, Illusterati, Celso ad, Quenhitran, Manul, DrMattV, Anrnusna, Wyn.junior, K0RTD, Monkbot, Vieque, BethNaught, Markmizzi, Garfield Garfield, Smokey2022, Zargol Rejerfree, Shahriar Kabir Pavel, Sdjncskdjnfskje, Anshul1908, Professor Flornoy, Thatguytestw, Tetra quark, Harshit100, KasparBot, Chinta 01 and Anonymous: 491 9.13. TEXT AND IMAGE SOURCES, CONTRIBUTORS, AND LICENSES 81 • Gluon Source: https://en.wikipedia.org/wiki/Gluon?oldid=668044002 Contributors: AxelBoldt, CYD, Bryan Derksen, Gdarin, TakuyaMurata, Card~enwiki, Looxix~enwiki, Ellywa, Ahoerstemeier, Med, Schneelocke, Phys, Phil Boswell, Donarreiskoffer, Fredrik, Merovingian, Hadal, Giftlite, Herbee, Xerxes314, Eequor, Darrien, Keith Edkins, RetiredUser2, Icairns, Mike Rosoft, AlexChurchill, HedgeHog, Kenny TM~~enwiki, David Schaich, Ioliver, Mashford, El C, Kwamikagami, Ardric47, Obradovic Goran, Alansohn, Guy Harris, Dachannien, Ricky81682, Batmanand, Velella, Kazvorpal, April Arcus, Forteblast, Mpatel, Palica, BD2412, Kbdank71, Rjwilmsi, Macumba, Strait, Mike Peel, Bubba73, Klortho, FlaBot, Srleffler, Chobot, YurikBot, Wavelength, Bambaiah, Hairy Dude, Jimp, JabberWok, Zelmerszoetrop, Salsb, SCZenz, Randolf Richardson, Ravedave, Danlaycock, Bota47, LeonardoRob0t, Anclation~enwiki, Physicsdavid, Erudy, GrinBot~enwiki, Kgf0, SmackBot, Melchoir, Cessator, Benjaminevans82, Abtal, MK8, Colonies Chris, Can't sleep, clown will eat me, Decltype, Qcdmaestro, Edconrad, Darkpoison99, FredrickS, Omsharan, Pegasusbot, Gregbard, ProfessorPaul, Thijs!bot, Headbomb, Rriegs, Oreo Priest, AntiVandalBot, Shambolic Entity, Deflective, Mujokan, Yill577, Happycool, Mother.earth, Martynas Patasius, WiiWillieWiki, HEL, Hans Dunkelberg, Gombang, Inwind, Sheliak, Jonthaler, VolkovBot, TXiKiBoT, Davehi1, Kriak, Anonymous Dissident, Imasleepviking, AlleborgoBot, EJF, SieBot, Steven Zhang, OKBot, ClueBot, Wwheaton, Qsaw, Nucularphysicist, Ottava Rima, Gordon Ecker, Rhododendrites, Brews ohare, Cacadril, RexxS, JKeck, Against the current, SkyLined, Addbot, DOI bot, Lightbot, Skippy le Grand Gourou, Luckas-bot, Planlips, AnomieBOT, Jim1138, JackieBot, Citation bot, Bci2, ArthurBot, Xqbot, Neil95, Triclops200, Omnipaedista, TorKr, , Paine Ellsworth, Ivoras, Citation bot 1, Pekayer11, Rameshngbot, PNG, RjwilmsiBot, TjBot, Lilcal89012, EmausBot, Socob, JSquish, StringTheory11, Quondum, TyA, Maschen, RolteVolte, ClueBot NG, Timothy jordan, Maplelanefarm, Bibcode Bot, Gravitoweak, Cadiomals, Tropcho, Fraulein451, DrHjmHam, Rhlozier, D.shinkaruk, Yaara dildaara, BronzeRatio, KasparBot and Anonymous: 137 • Higgs boson Source: https://en.wikipedia.org/wiki/Higgs_boson?oldid=670152187 Contributors: AxelBoldt, CYD, ClaudeMuncey, Bryan Derksen, Manning Bartlett, Roadrunner, David spector, Heron, Ewen, Stevertigo, Edward, Boud, TeunSpaans, Dante Alighieri, Ixfd64, Gaurav, TakuyaMurata, CesarB, Anders Feder, Mgimpel~enwiki, Bueller 007, Mark Foskey, Kaihsu, Samw, Cherkash, Lee M, Mxn, Ehn, Timwi, Dcoetzee, Wikiborg, Kbk, Tpbradbury, Phys, Bevo, Topbanana, JonathanDP81, AnonMoos, Bcorr, Jerzy, BenRG, Slawojarek, Phil Boswell, Donarreiskoffer, Robbot, Josh Cherry, ChrisO~enwiki, Owain, Iwpg, Goethean, Altenmann, Nurg, Lowellian, Merovingian, Rursus, Caknuck, Hadal, Alba, Mattflaschen, David Gerard, M-Falcon, Giftlite, Graeme Bartlett, Harp, ShaneCavanaugh, Lethe, Herbee, Jrquinlisk, Xerxes314, Ds13, Fleminra, Dratman, Muzzle, Varlaam, Jason Quinn, Foobar, DÅ‚ugosz, Golbez, Bodhitha, Mmm~enwiki, Aughtandzero, Quadell, Selva, Kaldari, Fred Stober, Johnflux, RetiredUser2, Thincat, Elektron, Bbbl67, Icairns, J0m1eisler, Cructacean, Tdent, TJSwoboda, JohnArmagh, Safety Cap, ProjeX, [email protected], Mike Rosoft, Chris Howard, Jkl, Discospinster, Rich Farmbrough, FT2, Qutezuce, Vsmith, Pie4all88, Kooo, David Schaich, Xgenei, Mal~enwiki, Dbachmann, Mani1, Bender235, ESkog, RJHall, Ylee, Pt, El C, Lycurgus, Lars~enwiki, Laurascudder, Art LaPella, Bookofjude, Brians, TheMile, Dragon76, Smalljim, C S, Reuben, La goutte de pluie, Rangelov, Sasquatch, Bawolff, Tritium6, Eritain, HasharBot~enwiki, Jumbuck, Yoweigh, Alansohn, Andrew Gray, JohnAlbertRigali, Axl, Sligocki, Kocio, Mlm42, Tom12519, Chuckupd, Atomicthumbs, Wtmitchell, KapilTagore, Endersdouble, Dirac1933, DrGaellon, Falcorian, Itinerant, DarTar, Joriki, Reinoutr, Linas, Mindmatrix, Jamsta, Sburke, Benbest, Jonburchel, Thruston, TotoBaggins, GregorB, J M Rice, CharlesC, Waldir, Christopher Thomas, Karam.Anthony.K, Tevatron~enwiki, SqueakBox, Ashmoo, Fleisher, Kbdank71, GrundyCamellia, Drbogdan, Rjwilmsi, Nightscream, Koavf, Strait, XP1, Martaf, BlueMoonlet, MZMcBride, Mike Peel, NeonMerlin, R.e.b., Jehochman, Bubba73, Afterwriting, A Man In Black, Splarka, RobertG, Nihiltres, Norvy, Itinerant1, Gurch, Mark J, Nimur, [email protected], ElfQrin, DannyDaWriter, Goudzovski, Diza, Consumed Crustacean, Srleffler, Sbove, Chobot, DVdm, Bgwhite, Zentropa, Bambaiah, Wester, Hairy Dude, Huw Powell, Wikky Horse, Pip2andahalf, RussBot, Jacques Antoine, Bhny, JabberWok, Hellbus, Archelon, Eleassar, Rsrikanth05, Salsb, Big Brother 1984, NawlinWiki, Folletto, Buster79, Trovatore, Neutron, SCZenz, Daniel Mietchen, Gadget850, Bota47, Karl Andrews, Dna-webmaster, Jezzabr, Thor Waldsen, Crisco 1492, Deeday-UK, Daniel C, WAS 4.250, Paul Magnussen, Closedmouth, D'Agosta, Bondegezou, Netrapt, Egumtow, LeonardoRob0t, Ilmari Karonen, NeilN, Kgf0, Maryhit, Dragon of the Pants, SmackBot, Nahald, Moeron, Ashley thomas80, Slashme, InverseHypercube, Melchoir, Cinkcool, Baad, Jagged 85, Nickst, Frymaster, AnOddName, ZerodEgo, Giandrea, Gilliam, Ohnoitsjamie, Skizzik, Carl.bunderson, Aurimas, Dauto, JCSantos, TimBentley, RevenDS, Jprg1966, Rick7425, Cadmasteradam, Roscelese, Epastore, DHN-bot~enwiki, Sbharris, Eusebeus, Scwlong, Modest Genius, Famspear, V1adis1av, Rhodesh, Fiziker, Lantrix, Grover cleveland, Jmnbatista, Robma, Flyguy649, Jgwacker, Daqu, Mesons, Rezecib, Martijn Hoekstra, Pulu, BullRangifer, Andrew c, Gildir, Kendrick7, Marcus Brute, Vina-iwbot~enwiki, Yevgeny Kats, Frglee, TriTertButoxy, CIS, SashatoBot, Lambiam, Mukadderat, Hi2lok, Kuru, Khazar, Shirifan, Eikern, Tktktk, JorisvS, DMurphy, Mgiganteus1, Bjankuloski06en~enwiki, IronGargoyle, Aardvark23, Loadmaster, Smith609, Deceglie, Hvn0413, Xiphoris, Norm mit, Keith-264, Kencf0618, Britannica~enwiki, Paul venter, Newone, Twas Now, GDallimore, Benplowman, Airstrike~enwiki, Chetvorno, DKqwerty, Harold f, JForget, Laplacian, Er ouz, Jtuggle, Banedon, Ruslik0, Krioni, McVities, Keithh, Rotiro, Yaris678, Slazenger, Cydebot, Martinthoegersen, Gogo Dodo, Anonymi, Lewisxxxusa, Mat456, Jlmorgan, Hippypink, Michael C Price, Quibik, AndersFeder, Raoul NK, PKT, Thijs!bot, Keraunos, Anupam, Headbomb, Kathovo, James086, Hcobb, D.H, Logicat, Jomoal99, Northumbrian, Oreo Priest, JitendraS, -dennis~enwiki, Widefox, Seaphoto, Orionus, QuiteUnusual, Readro, Hsstr8, Tlabshier, Tim Shuba, Yellowdesk, TuvicBot, JAnDbot, Asmeurer, Tigga, Jde123, Roman à clef, Zekemurdock, Mcorazao, Mozart998, Kborland, Bongwarrior, NeverWorker, Ronstew, Marcel Kosko, Jpod2, J mcandrews, Walter Wpg, Trugster, JMBryant, Vanished user ty12kl89jq10, CodeCat, Allstarecho, Brian Fenton, JaGa, GermanX, Alangarr, WLU, TimidGuy, Mr Shark, Pagw, Andre.holzner, Sigmundg, Ben MacDui, David Nicoson, Anaxial, JTiago, CommonsDelinker, Leyo, Gah4, Fconaway, Oddz, Tgeairn, J.delanoy, Fatka, Pharaoh of the Wizards, Maurice Carbonaro, Stephanwehner, Foober, Aveh8, McSly, Memory palace, NewEnglandYankee, Policron, 83d40m, Usp, Lamp90, Austinian, Izno, SoCalSuperEagle, Robprain, Cuzkatzimhut, Deor, Schucker, VolkovBot, Off-shell, ABF, Eliga~enwiki, JohnBlackburne, AlnoktaBOT, Tburket, Davidwr, Philip Trueman, Spemble, TXiKiBoT, Quatschman, The Original Wildbear, Gwib, Fatram, Kipb9, Andrius.v, Matan568, Nxavar, Nafhan, Photonh2o, Impunv, Peterbullockismyname, Cerebellum, Martin451, Praveen pillay, LoverOfArt, Abdullais4u, Justinrossetti, Cgwaldman, Bcody80, BotKung, Tennisnutt92, Dirkbb, Antixt, Francis Flinch, Moose-32, Ptrslv72, TheBendster, Masterofpsi, Jonbutterworth, Adrideba, SieBot, StAnselm, Manyugarg, PlanetStar, Jor63, Meldor, OlliffeObscurity, Jdcanfield, Yintan, Abhishikt, Flyer22, Graycrow, Infestor, Hrishirise, Cablehorn, Arthur Smart, Aperseghin, Mattmeskill, Gobbledygeek, Cthomas3, Steven Zhang, Nskillen, Sunrise, Afernand74, Jimtpat, Iknowyourider, StaticGull, Jfromcanada, MvL1234, Sphilbrick, Nergaal, Denisarona, Escape Orbit, Quinling, Martarius, PhysicsGrad2013, ClueBot, Victor Chmara, The Thing That Should Not Be, TomRed, Alyjack, Infrasonik, Mx3, Master1228, Drmies, Frmorrison, Loves martyr, Polyamorph, Nobaddude, Sjdunn9, Kitsunegami, Ktr101, Excirial, Joeyfjj, Wmlschlotterer, Pawan ctn, Lartoven, Artur80, Sun Creator, BobertWABC, PeterTheWall, Nondisclosure, M.O.X, SchreiberBike, JasonAQuest, Another Believer, Scf1984, 1ForTheMoney, Anoopan, Wnt, Darkicebot, TimothyRias, XLinkBot, Rreagan007, Resonance cascade, JinJian, Jabberwoch, Hess88, Hybirdd, Tayste, Addbot, Proofreader77, Mortense, Jacopo Werther, DBGustavson, DOI bot, Betterusername, Ocdnctx, OttRider, Cgd8d, Leszek Jańczuk, WikiUserPedia, NjardarBot, Download, LaaknorBot, AndersBot, Favonian, AgadaUrbanit, HandThatFeeds, Tide rolls, Lightbot, ScAvenger, SPat, Zorrobot, Jarble, ScienceApe, Luckas-bot, Yobot, Chreod, EchetusXe, Nsbinsnj, Evans1982, Amble, Now dance, fu.cker, dance!, Anypodetos, Nallimbot, Trinitrix, SkepticalPoet, Pulickkal, Fernandosmission, Apollo reactor, Csmallw, AnomieBOT, Novemberrain94, 1exec1, Jim1138, JackieBot, Gc9580, LlywelynII, Materialscientist, Citation bot, Brightgalrs, Onesius, ArthurBot, Northryde, LilHelpa, 82 CHAPTER 9. HIGGS BOSON Xqbot, Konor org, Noonehasthisnameithink, Engineering Guy, Yutenite, Newzebras, Universalsuffrage, DeadlyMETAL, Tomdo08, Professor J Lawrence, Br77rino, Srich32977, Arni.leibovits, StevenVerstoep, ProtectionTaggingBot, Vdkdaan, Omnipaedista, RibotBOT, Kyng, Waleswatcher, WissensDürster, Ace111, Kristjan.Jonasson, MerlLinkBot, Ernsts, Chaheel Riens, A. di M., A.amitkumar, Markdavid2000, , Dave3457, FrescoBot, Weyesr1, Paine Ellsworth, Kenneth Dawson, Cdw1952, CamB424, CamB4242, Steve Quinn, N4tur4le, Jc odcsmf, Cannolis, Dolyn, Citation bot 1, Openmouth, Gil987, OriumX, Biker Biker, Gautier lebon, Pinethicket, Edderso, Boson15, Jonesey95, Three887, CarsonsDad, Calmer Waters, Jusses2, RedBot, BiObserver, Aknochel, Meier99, Trappist the monk, Puzl bustr, Proffsl, Higgshunter, Mary at CERN, Periglas, Zanhe, Lotje, Callanecc, Comet Tuttle, Jdigitalbath, Vrenator, SeoMac, ErikvanB, Tbhotch, Minimac, Coolpranjal, Mean as custard, RjwilmsiBot, TjBot, Olegrog, 123Mike456Winston789, Weaselpit, Newty23125, Techhead7890, Tesseract2, Skamecrazy123, Northern Arrow, Mukogodo, J36miles, EmausBot, John of Reading, WikitanvirBot, Stryn, Dadaist6174, Nuujinn, Montgolfière, Fotoni, GoingBatty, RA0808, Bengt Nyman, Bt8257, Gimmetoo, KHamsun, LHC Tommy, Slightsmile, NikiAnna, TeeTylerToe, Dekker451, Hhhippo, Evanh2008, JSquish, Kkm010, ZéroBot, John Cline, Liquidmetalrob, Fæ, Bollyjeff, Érico Júnior Wouters, StringTheory11, Stevengoldfarb, Opkdx, Quondum, AndrewN, Tbushman, Makecat, Timetraveler3.14, Foonle77, Tolly4bolly, Wiggles007, Irenan, Nobleacuff, Brandmeister, Baseballrocks538, Chris81w, Inswoon, Donner60, Ontyx, Angelo souti, ChuispastonBot, ChiZeroOne, Ninjalectual, Exsmokey, Herk1955, I hate whitespace, Rocketrod1960, Whoop whoop pull up, Ajuvr, Petrb, Grapple X, ClueBot NG, Perfectlight, Aaron Booth, Gareth Griffith-Jones, Siswick, MelbourneStar, Gilderien, PhysicsAboveAll, Manu.ajm, Muon, Parcly Taxel, O.Koslowski, Widr, Mohd. Toukir Hamid, Diyar se, Helpful Pixie Bot, Popcornduff, Aesir.le, Bibcode Bot, 2001:db8, Lowercase sigmabot, BG19bot, Scottaleger, Mcarmier, Jibu8, Loupatriz67, Dave4478, Frze, Ervin Goldfain, Reader505, Mark Arsten, Lovetrivedi, BarbaraMervin, Silvrous, Drcooljoe, Cadiomals, Joydeep, Altaïr, Piet De Pauw, Jeancey, Sovereign8, Visuall, Ownedroad9, Brainssturm, Jw2036, Writ Keeper, DPL bot, Nickni28, Philpill691, Lee.boston, Scientist999, Benjiboy187, Duxwing, Cengime, Skiret girdet njozet, GRighta, Downtownclaytonbrown, Diasjordan, Ghsetht, Marioedesouza, BattyBot, 1narendran, LORDCOTTINGHAM2, NO SOPA, Tchaliburton, Wijnburger, StarryGrandma, Mdann52, Dilaton, Magikal Samson, Samuelled, Dja1979, Georgegroom, BecurSansnow, EuroCarGT, MSUGRA, Rhlozier, Pscott558, Turullulla, Blueprinteditor, Misterharris~enwiki, AstroDoc, Bigbear213, Dexbot, Randomizer3, Daggerbot, DoctorLazarusLong, Caroline1981, Nitpicking polisher, SoledadKabocha, Gsmanu007, Windows.dll, Mogism, Prabal123koirala, Abitoby, Clidog, Rongended, Darryl from Mars, Cerabot~enwiki, MuonRay, TheTruth72, Capt. Mohan Kuruvilla, Gatheringstorm2, Jason7898, Mumbai999999, SkepticalKid, Cjean42, Nmrzuk, Lugia2453, Mafuee, Frosty, SFK2, Thegodparticlebook, Rijensky, Mishra866868, Rockstar999999999, Toddbeck911, Nilaykumar07, Thepalerider2012, WikiPhysTech, The Anonymouse, Ahmar Saeed, Pincrete, Apidium23, Prahas.wiki, Exenola, Pdotpwns, Epicgenius, Fireballninja, Greengreengreenred, , Technogeek101, NicoPosner, Apurva Godghase, Durfyy, Soumya Mittal, American In Brazil, SaifAli13, Qwerkysteve, Spatiandas, Retroherb, Tango303, Hoppeduppeanut, Redplain, Shaelote, Quadrum, AntiguanAcademic, Simpsonojsim, Agyeyaankur, DavidLeighEllis, Ethanthevelociraptor, Qfang12, Comp.arch, Eletro1903, E8xE8, HeineBOB, Depthdiver, Jaaron95, Mfb, Anrnusna, Stamptrader, Man of Steel 85, Cteirmn, AiraCobra, MyNameIsn'tElvis, Meganlock8, Sxxximf, Drsoumyadeepb, 22merlin, Ndidi Okonkwo Nwuneli, Monkbot, Dialga5555, Fred1810, Akro7, Pewpewpewpapapa, BradNorton1979, 21bhargav, Whistlemethis, Thinking Skeptically, Amk365, Gagnonlg, L21234, TheNextMessiah, Naterealm224, Joey van Helsing, Adrian Lamplighter, Arnab santra, Gemadi, BATMAN1021, Mercedes321, DrKitts, KasparBot and Anonymous: 951 9.13.2 Images • File:2-photon_Higgs_decay.svg Source: https://upload.wikimedia.org/wikipedia/commons/3/32/2-photon_Higgs_decay.svg License: CC BY-SA 3.0 Contributors: Own work Original artist: Parcly Taxel • File:4-lepton_Higgs_decay.svg Source: https://upload.wikimedia.org/wikipedia/commons/b/b2/4-lepton_Higgs_decay.svg License: CC BY-SA 3.0 Contributors: Own work Original artist: Parcly Taxel • File:AIP-Sakurai-best.JPG Source: https://upload.wikimedia.org/wikipedia/commons/2/2b/AIP-Sakurai-best.JPG License: Public domain Contributors: Own work Original artist: self • File:Ambox_important.svg Source: https://upload.wikimedia.org/wikipedia/commons/b/b4/Ambox_important.svg License: Public domain Contributors: Own work, based off of Image:Ambox scales.svg Original artist: Dsmurat (talk · contribs) • File:Asymmetricwave2.png Source: https://upload.wikimedia.org/wikipedia/commons/0/0d/Asymmetricwave2.png License: CC BY 3.0 Contributors: Own work Original artist: TimothyRias • File:Beta_Negative_Decay.svg Source: https://upload.wikimedia.org/wikipedia/commons/8/89/Beta_Negative_Decay.svg License: Public domain Contributors: This vector image was created with Inkscape. Original artist: Joel Holdsworth (Joelholdsworth) • File:Bohr-atom-PAR.svg Source: https://upload.wikimedia.org/wikipedia/commons/5/55/Bohr-atom-PAR.svg License: CC-BY-SA3.0 Contributors: Transferred from en.wikipedia to Commons. Original artist: Original uplo:JabberWok]] at en.wikipedia • File:CERN_LHC_Tunnel1.jpg Source: https://upload.wikimedia.org/wikipedia/commons/f/fc/CERN_LHC_Tunnel1.jpg License: CC BY-SA 3.0 Contributors: Own work Original artist: Julian Herzog (website) • File:Charmed-dia-w.png Source: https://upload.wikimedia.org/wikipedia/en/6/6d/Charmed-dia-w.png License: Fair use Contributors: http://www.bnl.gov/bnlweb/history/charmed.asp Original artist: ? • File:Commons-logo.svg Source: https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg License: ? Contributors: ? Original artist: ? • File:Elementary_particle_interactions.svg Source: https://upload.wikimedia.org/wikipedia/commons/4/4c/Elementary_particle_ interactions.svg License: Public domain Contributors: en:Image:Interactions.png Original artist: en:User:TriTertButoxy, User:Stannered • File:Enrico_Fermi_1943-49.jpg Source: https://upload.wikimedia.org/wikipedia/commons/d/d4/Enrico_Fermi_1943-49.jpg License: Public domain Contributors: This media is available in the holdings of the National Archives and Records Administration, cataloged under the ARC Identifier (National Archives Identifier) 558578. Original artist: Department of Energy. Office of Public Affairs • File:Feynman_Diagram_Y-3g.PNG Source: https://upload.wikimedia.org/wikipedia/commons/1/1c/Feynman_Diagram_Y-3g.PNG License: CC BY-SA 3.0 Contributors: Own work Original artist: DrHjmHam • File:Feynmann_Diagram_Gluon_Radiation.svg Source: https://upload.wikimedia.org/wikipedia/commons/1/1f/Feynmann_ Diagram_Gluon_Radiation.svg License: CC BY 2.5 Contributors: Non-Derived SVG of Radiate_gluon.png, originally the work of SilverStar at Feynmann-diagram-gluon-radiation.svg, updated by joelholdsworth. Original artist: Joel Holdsworth (Joelholdsworth) 9.13. TEXT AND IMAGE SOURCES, CONTRIBUTORS, AND LICENSES 83 • File:Gamma-ray-microscope.svg Source: https://upload.wikimedia.org/wikipedia/commons/6/63/Gamma-ray-microscope.svg License: CC-BY-SA-3.0 Contributors: Own work Original artist: Radeksonic • File:Hadron_colors.svg Source: https://upload.wikimedia.org/wikipedia/commons/e/e4/Hadron_colors.svg License: CC BY-SA 3.0 Contributors: • Hadron_colors.png Original artist: Hadron_colors.png: Army1987 • File:Higgs,_Peter_(1929)_cropped.jpg Source: https://upload.wikimedia.org/wikipedia/commons/2/21/Higgs%2C_Peter_%281929% 29_cropped.jpg License: CC BY-SA 2.0 de Contributors: Mathematisches Institut Oberwolfach (MFO), http://owpdb.mfo.de/detail?photo_ id=12812 Original artist: Gert-Martin Greuel • File:Higgs-Mass-MetaStability.svg Source: https://upload.wikimedia.org/wikipedia/commons/7/70/Higgs-Mass-MetaStability.svg License: CC BY-SA 3.0 Contributors: Transferred from en.wikipedia to Commons. Original artist: Folletto at English Wikipedia • File:HiggsBR.svg Source: https://upload.wikimedia.org/wikipedia/commons/0/07/HiggsBR.svg License: CC BY-SA 3.0 Contributors: Own work Original artist: TimothyRias • File:Higgsdecaywidth.svg Source: https://upload.wikimedia.org/wikipedia/commons/3/36/Higgsdecaywidth.svg License: CC BY-SA 3.0 Contributors: Own work Original artist: TimothyRias • File:Lepton-interaction-vertex-eeg.svg Source: https://upload.wikimedia.org/wikipedia/commons/b/b5/ Lepton-interaction-vertex-eeg.svg License: CC BY 3.0 Contributors: Own work Original artist: TimothyRias • File:Lepton_isodoublets_fixed.png Source: https://upload.wikimedia.org/wikipedia/en/9/93/Lepton_isodoublets_fixed.png License: CC-BY-SA-3.0 Contributors: I (HEL (talk)) created this work entirely by myself. Original artist: HEL (talk) • File:Light-wave.svg Source: https://upload.wikimedia.org/wikipedia/commons/a/a1/Light-wave.svg License: CC-BY-SA-3.0 Contributors: No machine readable source provided. Own work assumed (based on copyright claims). Original artist: No machine readable author provided. Gpvos assumed (based on copyright claims). • File:Light_cone_colour.svg Source: https://upload.wikimedia.org/wikipedia/commons/5/56/Light_cone_colour.svg License: Public domain Contributors: Own work Original artist: Incnis Mrsi 10:15, 4 June 2008 (UTC) • File:Light_dispersion_of_a_mercury-vapor_lamp_with_a_flint_glass_prism_IPNr°0125.jpg Source: https://upload.wikimedia. org/wikipedia/commons/1/1f/Light_dispersion_of_a_mercury-vapor_lamp_with_a_flint_glass_prism_IPNr%C2%B00125.jpg License: CC BY-SA 3.0 at Contributors: Own work Original artist: D-Kuru • File:Mecanismo_de_Higgs_PH.png Source: https://upload.wikimedia.org/wikipedia/commons/4/44/Mecanismo_de_Higgs_PH.png License: CC-BY-SA-3.0 Contributors: ? Original artist: ? • File:Meson_nonet_-_spin_0.svg Source: https://upload.wikimedia.org/wikipedia/commons/c/c0/Meson_nonet_-_spin_0.svg License: Public domain Contributors: Image:Noneto mesônico de spin 0.png Original artist: User:E2m, User:Stannered • File:Meson_nonet_-_spin_1.svg Source: https://upload.wikimedia.org/wikipedia/commons/1/13/Meson_nonet_-_spin_1.svg License: Public domain Contributors: Image:Noneto mesônico de spin 1.png Original artist: User:E2m, User:Stannered • File:Muon-Electron-Decay.svg Source: https://upload.wikimedia.org/wikipedia/en/6/6f/Muon-Electron-Decay.svg License: Cc-by-sa3.0 Contributors: ? Original artist: ? • File:Murray_Gell-Mann.jpg Source: https://upload.wikimedia.org/wikipedia/commons/8/87/Murray_Gell-Mann.jpg License: CC BY 2.0 Contributors: http://flickr.com/photos/jurvetson/414368314/ Original artist: jurvetson of flickr.com • File:Nobel_Prize_24_2013.jpg Source: https://upload.wikimedia.org/wikipedia/commons/5/5f/Nobel_Prize_24_2013.jpg License: CC BY 2.0 Contributors: Flickr: IMG_7469 Original artist: Bengt Nyman • File:Office-book.svg Source: https://upload.wikimedia.org/wikipedia/commons/a/a8/Office-book.svg License: Public domain Contributors: This and myself. Original artist: Chris Down/Tango project • File:One-loop-diagram.svg Source: https://upload.wikimedia.org/wikipedia/commons/5/57/One-loop-diagram.svg License: CC-BYSA-3.0 Contributors: Self-made (Originally uploaded on en.wikipedia) Original artist: Originally uploaded by JabberWok (Transferred by grondemar) • File:Portal-puzzle.svg Source: https://upload.wikimedia.org/wikipedia/en/f/fd/Portal-puzzle.svg License: Public domain Contributors: ? Original artist: ? • File:QCDphasediagram.svg Source: https://upload.wikimedia.org/wikipedia/commons/b/bc/QCDphasediagram.svg License: CC BYSA 3.0 Contributors: Own work Original artist: TimothyRias • File:Quark_masses_as_balls.svg Source: https://upload.wikimedia.org/wikipedia/commons/b/b5/Quark_masses_as_balls.svg License: CC BY-SA 3.0 Contributors: Own work Original artist: Incnis Mrsi • File:Quark_structure_proton.svg Source: https://upload.wikimedia.org/wikipedia/commons/9/92/Quark_structure_proton.svg License: CC BY-SA 2.5 Contributors: Own work Original artist: Arpad Horvath • File:Quark_weak_interactions.svg Source: https://upload.wikimedia.org/wikipedia/commons/6/66/Quark_weak_interactions.svg License: Public domain Contributors: Derivative work, from public down work uploaded to en.wikipedia. original Original artist: • Original work: [1] • File:Question_book-new.svg Source: https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg License: Cc-by-sa-3.0 Contributors: Created from scratch in Adobe Illustrator. Based on Image:Question book.png created by User:Equazcion Original artist: Tkgd2007 • File:Right_left_helicity.svg Source: https://upload.wikimedia.org/wikipedia/commons/a/a9/Right_left_helicity.svg License: Public domain Contributors: en:Image:Right left helicity.jpg Original artist: en:User;HEL, User:Stannered 84 CHAPTER 9. HIGGS BOSON • File:SatyenBose1925.jpg Source: https://upload.wikimedia.org/wikipedia/commons/f/fe/SatyenBose1925.jpg License: Public domain Contributors: Picture in Siliconeer Original artist: Unknown • File:Speakerlink-new.svg Source: https://upload.wikimedia.org/wikipedia/commons/3/3b/Speakerlink-new.svg License: CC0 Contributors: Own work Original artist: Kelvinsong • File:Spontaneous_symmetry_breaking_(explanatory_diagram).png Source: https://upload.wikimedia.org/wikipedia/commons/a/a5/ Spontaneous_symmetry_breaking_%28explanatory_diagram%29.png License: CC BY-SA 3.0 Contributors: Own work Original artist: FT2 • File:Standard_Model_of_Elementary_Particles.svg Source: https://upload.wikimedia.org/wikipedia/commons/0/00/Standard_ Model_of_Elementary_Particles.svg License: CC BY 3.0 Contributors: Own work by uploader, PBS NOVA [1], Fermilab, Office of Science, United States Department of Energy, Particle Data Group Original artist: MissMJ • File:Stimulatedemission.png Source: https://upload.wikimedia.org/wikipedia/commons/8/8a/Stimulatedemission.png License: CC-BYSA-3.0 Contributors: en:Image:Stimulatedemission.png Original artist: User:(Automated conversion),User:DrBob • File:Strong_force_charges.svg Source: https://upload.wikimedia.org/wikipedia/commons/b/b6/Strong_force_charges.svg License: CC BY-SA 3.0 Contributors: Own work, Created from Garret Lisi’s Elementary Particle Explorer Original artist: Cjean42 • File:Stylised_Lithium_Atom.svg Source: https://upload.wikimedia.org/wikipedia/commons/e/e1/Stylised_Lithium_Atom.svg License: CC-BY-SA-3.0 Contributors: based off of Image:Stylised Lithium Atom.png by Halfdan. Original artist: SVG by Indolences. Recoloring and ironing out some glitches done by Rainer Klute. • File:Symmetricwave2.png Source: https://upload.wikimedia.org/wikipedia/commons/1/1d/Symmetricwave2.png License: CC BY 3.0 Contributors: Own work Original artist: TimothyRias • File:Vertex_correction.svg Source: https://upload.wikimedia.org/wikipedia/commons/8/87/Vertex_correction.svg License: Public domain Contributors: ? Original artist: User:Harmaa • File:VisibleEmrWavelengths.svg Source: https://upload.wikimedia.org/wikipedia/commons/e/e2/VisibleEmrWavelengths.svg License: Public domain Contributors: created by me Original artist: maxhurtz • File:Wave_packet.svg Source: https://upload.wikimedia.org/wikipedia/commons/f/ff/Wave_packet.svg License: Public domain Contributors: Self made, based on Image:Photon paquet onde.png. Released in the public domain. Original artist: Oleg Alexandrov • File:Wikinews-logo.svg Source: https://upload.wikimedia.org/wikipedia/commons/2/24/Wikinews-logo.svg License: CC BY-SA 3.0 Contributors: This is a cropped version of Image:Wikinews-logo-en.png. Original artist: Vectorized by Simon 01:05, 2 August 2006 (UTC) Updated by Time3000 17 April 2007 to use official Wikinews colours and appear correctly on dark backgrounds. Originally uploaded by Simon. • File:Wiktionary-logo-en.svg Source: https://upload.wikimedia.org/wikipedia/commons/f/f8/Wiktionary-logo-en.svg License: Public domain Contributors: Vector version of Image:Wiktionary-logo-en.png. Original artist: Vectorized by Fvasconcellos (talk · contribs), based on original logo tossed together by Brion Vibber • File:Young_Diffraction.png Source: https://upload.wikimedia.org/wikipedia/commons/8/8a/Young_Diffraction.png License: Public domain Contributors: ? Original artist: ? 9.13.3 Content license • Creative Commons Attribution-Share Alike 3.0