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Cambridge University Press 978-1-107-40426-7 - The Standard Model: A Primer C. P. Burgess and Guy D. Moore Index More information

Index

2π counting, 156 Anomalous magnetic moment of a proton, 322 1 ∆I = 2 Rule, 356 Anomaly matching, 365 ∆ baryon, 302 Anti-fundamental representation, 491 Λ baryon, 302 Antiparticles, 14 Ω baryon, 302 Antisymmetry of the baryonic wave function, Σ baryon, 302 301 Σ∗ baryon, 302 Asymmetries, left-right, 199 Θ3, and electric dipole moments, 464 Asymmetry, forward-backward, 200 Ξ baryon, 302 Asymptotic freedom, 454 Ξ gauges, 506 Atmospheric neutrino oscillations, 402 Ξ∗ baryon, 302 Axioms of field theory, 7 γ5, convention for, 518 Axion, 459 ΛQCD, 278 Axion potential, 467 ρ parameter, 236 Axions, as cold dark matter, 468 SUc(3) SUL(2) UY (1), 54 × × B-L conservation, 104 A terms, Supersymmetry breaking, 450 B-L symmetry, gauged, 108 Abelian Higgs model, 41 BaBar experiment, 229 Accidental conservation laws, in the standard Barn, 197 model, 96 Baryon masses, 300 Accidental symmetries, 239, 241 Baryon masses, and chiral symmetry breaking, Accidental symmetries, and the Fermi theory, 316 241 Baryon number, 96, 286 Accidental symmetry, 68 Baryon number, anomalies, 102 Action, 12 Baryon number, of QCD bound states, 287 Ademollo-Gatto theorem, 324, 361 Baryons, 71, 281 Adjoint Higgs models, 107 Baryons, and flavor symmetry, 300 Adjoint representation, 490 Baryons, defined, 281 Altarelli-Parisi (DGLAP) equations, 347 Baryons, octet and decuplet, 302 Angular momentum operators, 497 Baryons, valence quark content of, 302 Annihilation operators, 4, 13, 21 Baryons, wave function antisymmetry, 301 Annihilation to photons, 216 Basic principles, 7 Anomalies, 96 Belle experiment, 229 Anomalies, and π0 decay, 297, 363 Beta decay, double, 416 Anomalies, and Qe + Qp, 101 Bhabha scattering, 223 Anomalies, and Qν , 101 Bjorken x, 331 Anomalies, and baryon number, 102 Bloch-Nordsieck resummation, 221 Anomalies, and lepton number, 103 Boosts, generator of, 498 Anomalies, and neutrino stability, 154 Boson decays, 127 Anomalies, between electromagnetism and Bottomonium, 285 chiral symmetries, 297 Bound states, 113 Anomalies, gauge, 99 Bound states, b¯b, 199 Anomalies, involving the Lorentz group, 102 Bound states, cc¯, 199

534

Index 535

Bound states, of heavy quarks, 284 Conservation of lepton number, 96 Bound states, strongly interacting, 75 Conserved vector current, 324 Branching fraction, 137 Conventions, and γ5, 518 Branching fractions, for Z0 bosons, 138 Corrections near a resonance, 202 Branching fractions, in W ± decays, 145 Cosmological constant problem, 436 Branching ratios of the τ lepton, 159 Cosmological constant problem., 437 Breaking of UV (3) symmetry by masses, 295 Coulomb barrier, 325 Breit frame, 331 Coupling constants, 484 Breit-Wigner lineshape, 205 Couplings, fermion-Z0 boson, 137 Breit-Wigner resonance, 207 Couplings, gluon-fermion, 75 Covariant derivative, 39 C symmetry, 74, 76, 78, 80, 82, 85 Covariant derivatives of standard modelfields, C symmetry, and QCD bound states, 287 58 C symmetry, broken by Z and W couplings, 89 CP symmetry, 459 C, definition, 86 CP symmetry, broken by Cabbibo angle, 81 Kobayashi–Maskawamatrix phases, 89 Callan-Gross sum rule, 337 CP violation, 399 Canonical form: fermions, 23 CP violation, in neutrino physics, 399 Canonical form: scalars, 17 Creation operators, 4, 13, 21 Casimir, in SUc(3), 345 Cross section, 112 Causality, 14 Cross-section, 122 Center of mass frame, 190 Crossed graphs, 212 CERN, 202 Crossing symmetry, 14, 211, 216 Charge conjugation symmetry, 86 CTEQ collaboration, 348 Charge radius of the proton, 323 Cubic electroweak interactions, 77 Charged current interactions, 78, 154, 235 Current conservation, 215 Charged current interactions, and W ± boson Custodial SU(2) symmetry, 66 decay, 143 Charged current interactions, and Fermi D term, supersymmetric, 445 theory, 235 Decay rate, of a polarized Z0 boson, 136 Charmonium, 285 Decay rate, of the Z0 boson, 135 Cherenkov radiation, 224 Decay rates, 122 Chern-Simons number, 460 Decay, of the − lepton, 155 Chiral Lagrangian, 310 Decay, of the τ − lepton, 158 Chiral perturbation theory, 279 Decays, of elementary bosons, 127 Chiral symmetry, 103, 290, 292, 320 Decays, of leptons, 153 Chiral symmetry breaking, and baryon Decoupling, 435 masses, 316 Deep inelastic scattering, 330 Chiral symmetry, and spectral degeneracies, Deep inelastic scattering, kinematics, 330 297 Delta baryon, 302 Chiral symmetry, broken by electromagnetism, Density matrix, 129 296 DGLAP (Altarelli-Parisi) equations, 347 Chiral symmetry, explicit breaking, 294 Dilepton, 338 Chiral symmetry, spontaneous breaking, 304 Dimension 5 operators in the standard model, Circular polarization, 28 424 CKM matrix, 79 Dirac conjugate, 22, 504 Clifford algebra, 504, 518 Dirac field, 69 Cluster decomposition, 7 Dirac neutrino, 395 Cold dark matter, 468 Dirac neutrino masses, 413 Collinear photon emission, 218 Dirac neutrinos, 409 Color, 54 Dirac spinor, 69, 503 Color confinement, 282 Dirac traces, 131 Commutation relations, 38 Dirac traces, evaluation, 131 Compton scattering, 214 Discrete symmetries, 85 Confinement, 282 Divergences, soft, 346 Confinement hypothesis, 282 Divergent soft photon corrections, 220 Confinement scale, Λc, 283 Double beta decay, neutrinoless, 416 Confinement, linear, 283 Drell-Yan process, 338 Conservation laws, and stable particles, 153 Drell-Yan process, differential cross-section, Conservation laws, approximate, 239 340 Conservation of baryon number, 96 Dyadics, of fermion spinors, 130

536 Index

Dynkin index, 478 Feynman rules, vertices for the standard model, 175 Effective Lagrangian, 231 Field strength, 27 Effective Lagrangians, 231 Fields, Dirac, 69 Effective theory, of QED with hadrons, 320 Fields, transformation under a symmetry, 487 Electric charge, 39 Fiertz identity, 52, 225 Electric charge, and anomalies, 101 Fiertz rearrangements, 471 Electric dipole moment, for the neutron, 464 Flavor change, absent in Z couplings, 84 Electric dipole moments, and Θ3, 464 Flavor changing, 81 electromagnetic breaking of chiral symmetry, Flavor changing neutral currents, 73, 84 296 Flavor changing, absent in strong interactions, Electromagnetic interactions, 83 75 Electromagnetism, as a symmetry of the Flavor octet mesons, 298 vacuum, 64 Flavor problem, 469 Electron charge, 83 Flavor singlet mesons, 298 Electron number, 96 Fock space, 4 Electroweak interactions, 76 Forward-backward asymmetry, 200 Elementary boson decays, 127 Forward-backward asymmetry, on resonance, Endpoint, 169 206 eta’ meson, mass, 313 Fragmentation, 343 Evolution equations for PDF’s, 347 Fragmentation function, 343 Expansion, in large MW , 163 Free quarks, non-observation, 282 Experimental values, of masses, 484 Fundamental representation, 491 External lines, Feynman rules, 172 GF , the Fermi coupling constant, 164 F term, supersymmetric, 445 Gamma matrices, 22, 504 Factorization, 206, 329 Gamma matrices, Hermiticity of, 518 Factorization, on resonance, 207 Gauge anomalies, 99 Fadeev-Popov ghosts, 506 Gauge bosons, 38 Families, 54 Gauge choice, and Feynman rules, 174 Fermi coupling constant, 164 Gauge choice, unitary, 43 Fermi effective theory, 225 Gauge coupling unification, 478 Fermi Lagrangian, 235 Gauge fixing, 62 Fermi statistics–and signs in interference Gauge group, of the standard model, 54 terms, 212 Gauge invariance, 30, 215 Fermi theory, 231, 233 Gauge, renormalizable ξ, 506 Fermi theory of neutral currents, 236 Gauge, unitary, 62, 506 Fermi theory of the weak interactions, 423 Gaugino, 443 Fermi theory, and accidental symmetries, 241 Gaugino Yukawa couplings, 445 Fermion electroweak couplings, Feynman Gell Mann–Okubo mass relation, 317 rules, 178 Gell-Mann matrices, 44 Fermion loops, minus sign associated with, 179 Generators of Lorentz group, 497 Fermion masses, 69 Ghosts, 506 Fermionic content of the standard model, 56 Ghosts, Feynman rules, 513 Fermionic fields: canonical form, 23 GIM mechanism, 376, 377, 398 Fermions, charges in the standard model, 56 GIM mechanism, leptons, 410 Fermions, Dirac, 69 Global symmetries, and Yukawa interactions, Feynman gauge, 174, 506 94 Feynman graph, symmetry factor, 179 Glueballs, 71 Feynman rules, 153, 172, 507 Gluon, 45 Feynman rules, and metric convention, 521 Gluon emission, and gauge invariance, 217 Feynman rules, combinatorial factors, 175 Gluon self-couplings, Feynman rules, 176 Feynman rules, for external lines, 172 Gluon-fermion coupling, Feynman rules, 177 Feynman rules, for incoming lines, 172 Gluon-fermion couplings, 75 Feynman rules, for internal lines, 173 Gluons, 54, 74 Feynman rules, for outgoing lines, 173 Gluons, self-couplings, 74 Feynman rules, ghosts, 513 Goldberger-Treiman relation, 363 Feynman rules, ghosts and unphysical scalars, Goldstone boson, 305 508 Goldstone’s Theorem, 306 Feynman rules, ordering of spinorial indices, Grand Unified Theories, 472, 475 173 Group theory, 486

Index 537

Gyroscopic ratio, of protons and neutrons, 322 Interactions, between W and Z bosons, 76 Interactions, charged current, 78 Hadron-hadron collisions, 338 Interactions, electromagnetic, 83 Hadronic heavy quark pair production, 340 Interactions, electroweak, 76 Hadronic scattering, 319 Interactions, electroweak cubic, 77 Hadronization, 343 Interactions, electroweak quartic, 77 Hadrons, 54, 70, 75, 140 Interactions, gluon self, 74 Hadrons, light, 290 Interactions, gluon-fermion, 75 Hamiltonian, 3 Interactions, Higgs self, 72 Hamiltonian, of a free system, 6 Interactions, Higgs-fermion, 73 Hamiltonian, physical constraints on, 7 Interactions, Higgs-gauge boson, 72 Heaviside function, 116, 162 Interactions, neutral current, 82, 83 Heavy particles, and nonrenormalizable Interactions, nonrenormalizable, 233 interactions, 233 Interactions, strong, 75 Heavy quark effective theory, 325 Interactions: scalar, 36 Heavy quark pair production, hadronic, 340 Interactions: scalar-spinor, 36 Heavy quarks, bound states, 284 Interference, 212 Helicity conservation, 136 Interference and minus signs, 180 Helicity suppression, 411 Internal lines, Feynman rules, 173 Helicity, and angular distributions of final Internal symmetry, 32 states, 136 Inverted hierarchy of neutrino masses, 403 Hierarchy problem, 439 Irreducible representation, 489 Higgs boson decays, and longitudinal gauge Isospin, 295 boson polarizations, 149 Higgs boson mass, 63, 74 J/ψ particle, 284 Higgs boson, decays, 146 Jets, 329 Higgs boson, decays into bosons, 148 Jets, and collinear radiation, 343 Higgs boson, decays into fermions, 147 Josephson effect, 252 Higgs field, 60 Higgs mechanism, 43 KL decays, 73 Higgs self-couplings, 72 Kinematics, 188 Higgs self-couplings, Feynman rules, 175 Kinematics, in deep inelastic scattering, 330 Higgs-fermion couplings, 73 Klein-Gordon equation, 16 Higgs-fermion couplings, Feynman rules, 176 Kobayashi-Maskawa matrix, 79 Higgs-gauge boson couplings, 72 Higgs-gauge boson couplings, Feynman rules, Lab frame, 189 175 Lagrangian, 12 Higgsino, 444 Lagrangian density, 13 Higgsstrahlung, 228, 429 Lagrangian terms, involving the Higgs boson, Higher order corrections, 141 60 Higher order corrections, parametric Lagrangian, of a spin-0 field, 18 estimates, 141 Lagrangian, of a spin-1 field, 27 Hilbert space, 3, 113 Lagrangian, of a spin-1/2 field, 25 Hilbert space, and symmetries, 486 Lagrangian, of the standard model, 58 Hypercharge, 54 Lambda baryon, 302 Landau gauge, 174, 506 Inclusive reactions, 275 Landau pole, 455 Incoming lines, Feynman rules, 172 Large extra dimensions, 441 Infinite momentum frame, 331 Large logarithms, 217 Initial state radiation, 221, 344 Large mass expansion, 163, 231 Initial state radiation, and PDF evolution, 344 Lattice QCD, 278 Instanton, 461 Left-handed spinor, 501 Interaction Hamiltonian, 128 Left-right asymmetry, 199 Interaction Hamiltonian, and temporal gauge Left-right asymmetry, on resonance, 206 field components, 128 LEP collider, 183, 197, 208, 228 Interactions, 35 LEP I experiment, 202 Interactions, W -fermion, 78 LEP II experiment, 429 Interactions, Z-fermion, 82, 83 Lepton number, 96 Interactions, Z-fermion coupling strengths, 84 Lepton number, anomalies, 103 Interactions, and gauge invariance, 37 Leptons, 54, 75 Interactions, and vector particles, 37 Levi-Civita tensor, 132

538 Index

Lie algebra, 38, 488 Meson masses, and SU(3) flavor symmetry, Lie algebra, for the Lorentz group, 498 298 Lie groups, 487 Meson masses, related by chiral symmetry Lifetime, of the − lepton, 157 breaking, 313 Lifetime, of the τ − lepton, 159 Mesons, 71, 281, 298 Linear confinement, 283 Mesons, defined, 281 Linear potential, and confinement, 283 Metric convention, 9, 22 Lineshape, 205 Metric convention, and Feynman rules, 521 LMA oscillations, 402 Metric conventions, 517 Local symmetry, 486 Microcausality, 8 Locality, 8, 12 Minimal Supersymmetric Standard Model locality, 7 (MSSM), 443 Loop corrections, 242 Minus signs, in interference between diagrams, Loops, 242 180 Lorentz covariance, and gauge boson Mixing, between φ and ω mesons, 316 propagators, 162 MNS matrix, 399 Lorentz group, 493 MRST collaboration, 348 Lorentz group representations, 14, 19 MSW effect, 404 Lorentz group, and anomalies, 102 MSW oscillations, adiabatic, 407 Lorentz group, generators, 497 MSW resonance, 407 Lorentz group, Lie algebra, 498 mu Decays, 155 Lorentz group, representations, 499 muon decay rate, computed value, 168 Lorentz group: reducible representations, 20 muon lifetime, 157 Lorentz invariance, 13, 162 Muon number, 96 Lorentz invariance, of time ordering operation, Muon-hadron production ratio R, 198 117 Møller scattering, 212 Lorentz symmetry, 8 Møller wave operators, 114 Lorentz transformation, orthochronous, 496 Lorentz transformation, proper, 496 Nanobarn, 197 Low energy expansion, 231 Neutral K system, 73 LSP (lightest supersymmetric particle), 447 Neutral current interactions, 82, 83, 128 LSP as dark matter candidate, 448 Neutral current interactions, and Z0 decay, Luminosity, 197 128 Neutral currents, 236 Magnetic moment, of a proton, 322 Neutral currents, and Fermi theory, 236 Majorana mass, 397, 420 Neutral pion decay, 363 Majorana neutrino, 397 Neutral pion decay, and broken axial Majorana notation, 501, 502 symmetry, 297 Majorana spinor, 20 Neutrino beam oscillations, 402 Majorana spinors, identities, 46 Neutrino CP violation, 82 Mandelstam variables, 188, 209 Neutrino mass, 70, 82 Mandelstam variables, kinematically allowed Neutrino mass, absent in the standard model, ranges, 191 70 Mass formula, for mesons, 313 Neutrino masses, 105, 425 Mass relations, for baryons, 317 Neutrino masses, Dirac, 413 Mass relations, Gell Mann–Okubo, 317 Neutrino masses, experimental values, 402 Mass shell, 201 Neutrino masses, upper and lower bounds, 404 Mass, A boson, 65 Neutrino oscillations, 393, 400 Mass, W boson, 64 Neutrino, right handed, 57, 70 Mass, Z boson, 65 Neutrino, sterile, 419 Mass, fermions, 69 Neutrinoless double beta decay, 416 Mass, Higgs boson, 63, 74 Neutrinos propagating through solar medium, Mass, Majorana, 397 404 Mass, neutrino, 70 Neutrinos, pseudo-Dirac, 413 Masses of the baryons, 300 neutron, 302 Masses, of particles, 484 Neutron decay, 361 Matrix element, 117 Neutron electric dipole moment, 464 Matrix element for Z0 decay, 128 Noether current, 32 Meson decays, 351 Noether current, and gauge couplings, 38 Meson decays, nonleptonic, 353 Noether’s theorem, 13, 32 Meson mass formula, 313 Nonabelian symmetries, 38

Index 539

Nonleptonic meson decays, 353 Proton, charge radius, 323 Nonrenormalizable interactions, 233, 422 Proton, magnetic moment, 322 Nonrenormalizable operators, and the Pseudo-Dirac neutrinos, 413 standard model, 424 Pseudo-Goldstone boson, 305 Normal hierarchy of neutrino masses, 403 pseudo-Goldstone boson, 308 Nucleon-pion scattering, 363 Pseudoscalar, 505 Numerical values, of couplings, 484 Pseudoscalar mesons, 299 Pseudovector mesons, 299 O(3,1), 494 Oblique electroweak corrections, 266 QCD, 44, 276 Omega baryon, 302 QCD bound states, quantum numbers, 285 order parameter, 306 QCD Lagrangian, 276 Orthochronous, 496 QCD vacuum, and topology, 460 Oscillation length, 401 QCD vacuum, spontaneously breaks chiral Outgoing lines, Feynman rules, 173 symmetry, 304 QED, 276 P symmetry, 74, 76, 78, 80, 82, 85, 459 QED Lagrangian, 276 P symmetry, and QCD bound states, 287 QED, including hadrons, 320 P symmetry, broken by Z and W couplings, 89 Quadratic Casimir CF, 345 Parameters of the standard model, 61 Quantum Chromodynamics (QCD), 275 Parametric estimates, 139, 156 Quantum electrodynamics, 39 Parity, 496 Quantum numbers, of QCD bound states, 285 Parity, definition, 85 quark, 44 Particle data book, 284 Quarkonia, 284 Particle Data Group, 79 Quarkonium, 285 Particle Data Group, parameterization of Quarks, 54 CKM matrix, 79 Quarks, valence and sea, 335 Particle masses, 484 Quartic electroweak interactions, 77 Parton distribution functions (PDF’s), 334 Partons, 328, 329 R parity, 447 Pascos-Wolfenstein ratio, 387 Rξ gauge, 174 Pauli matrices, 20, 58 Radiative corrections, 217 PDF’s, 334 Radiative corrections, and the Z line shape, PDF’s: approximate scale independence, 344 222 PDF’s: scale dependence, 344 Rapidity, 339 pentaquark, 281 Reactor neutrino oscillations, 402 Pentaquarks, 303 Redundant effective interactions, 481 Perturbative expansion, breakdown for low Reflection positivity, 466 energy QCD, 278 Regge theory, 320 Phase space, 138 Renormalizability, 9, 15, 422 Phase space integrals, three body, 165 Representation theory, 488 Photon, 54 Representation, adjoint, 490 Photon emission, collinear, 218 Representation, irreducible, 489 Photon exchange, 196 Representation, singlet or trivial, 489 Photons, as external states, 214 Representations, and Lie algebra, 489 Pion decay constant, from decay rates, 352 Representations, of the Lorentz group, 499 Pion decay, neutral, 363 Resonance, Z, 205 Pion scattering, 356 Resonances, 202 Pions, as pseudo-Goldstone bosons, 308 Resonances, hadronic, 320 PMNS matrix, 262, 399 Rho parameter, 236 Poincaréalgebra, 498 rho parameter, 242 Poincare invariance, 8 Right handed neutrinos, 57, 105 Polarization vectors, 28 Right-handed spinor, 501 Polarizations, summed over, 214 Rotations, generator of, 498 Polarized Z0 boson decay rate, 136 Precision electroweak measurements, 266 S matrix, in terms of interaction Hamiltonian, Propagator, 161 117 Propagator, Feynman rules, 507 s-channel process, 194, 210 Propagators, near resonance, 202 S-matrix, 111, 114 Proper Lorentz transformation, 496 Scalar fields: canonical form, 17 proton, 302 Scalar fields: vacuum energy, 19

540 Index

Scalar particles, 16 Strangeness, 286, 296 Scalar representation, 499 String tension, in QCD, 283 Scalar self-interactions, 36 Strong CP problem, 459, 460 Scalar-spinor interactions, 36 Strong interactions, 54, 74, 75 Scattering process, s channel, 194 Strong interactions, and bound states, 75 Scattering states, 112 Structure constants, 488 Sea quarks, 335 Structure functions, 332 Seesaw mechanism, 414, 426 Structure functions, in terms of PDF’s, 336 Seesaw neutrino masses, 477 Structure functions, spin dependent, 333 Self-energy corrections, 203 SU(2) symmetry, custodial, 66 semi-leptonic decays, 351 SU(3) Flavor, 298 Sigma baryon, 302 SU(3) SU(2) U(1), 54 × × Sigma∗ baryon, 302 SU(5) grand unified model, 475 Singlet representation, 489 SU(N), representation theory, 491 SLAC, 202 Sum rule, Callan-Gross, 337 SLC experiment, 202 Supernova 1987A, 224 Slepton, 444 Superpotential, 445 SO(10) grand unified models, 477 Supersymmetric D-term, 445 SO(3,1), 494 Supersymmetric F term, 445 Soft photon emission, 220 Supersymmetry, 438, 442 Soft singularities, 346 Supersymmetry breaking, 448 Soft-Pion Scattering, 349 Supersymmetry breaking A terms, 450 Solar neutrino oscillations, 402 Supersymmetry, and gauge coupling Solar neutrinos, 394 unification, 480 Spectral degeneracies, and chiral symmetry, Symmetries, 486 297 Symmetries of the standard model, 90 Spectral relations, 33 Symmetries, accidental, 85, 241 Spin average, in initial state, 129 Symmetries, and the standard model, 85 Spin dependent structure functions, 333 Symmetries, as a group, 487 Spin-1 particles, 26 Symmetries, C, P, and T, 74, 76, 78, 80, 82, 85 Spin-1 particles, massive, 26 Symmetries, continuous global, 90 Spin-1 particles, massless, 28 Symmetries, discrete, 85 Spin-half particles, 19 Symmetry breaking vacuum, 42 Spin-Statistics Theorem, 15 Symmetry factor, of a Feynman diagram, 179 Spinor, 500 Symmetry factor, of a Feynman graph, 179 Spinor fields, 19 Symmetry transformation, 486 Spinor, Dirac, 69 Symmetry transformation, and fields, 487 spinor, Majorana, 20 Symmetry, accidental, 68 spinor, Weyl, 20 Symmetry, CP, 459 Spinorial indices, ordering in Feynman rules, Symmetry, local, 486 173 Symmetry, P, 459 Spinors, Majorana versus Dirac, 55 Symmetry, spontaneously broken, 35 Splitting functions, 347 Symmetry: broken by the ground state, 34 Spontaneous breaking of chiral symmetry, 304 Spontaneous symmetry breaking, 41, 43 T matrix, 117 Spontaneously broken symmetry, 35 T symmetry, 74, 76, 78, 80, 82, 85 Squark, 444 t-channel process, 210 Stability, 9, 15 T-matrix element, 117 Stability of neutrinos, 153 Tachyons, 41 Stability of the electron, 153 Tachyons, absent about correct vacuum, 42 standard model fields, covariant derivatives, 58 tau decay rate, computed value, 168 standard model gauge group, 54 tau decay, branching ratios, 159 standard model Lagrangian, 58, 60 tau decays, 158 standard model, continuous symmetries, 90 tau lifetime, 159 standard model, fermionic content, 56 Tau number, 96 standard model, parameters, 61 Technicolor models, 441 Step function, 116, 162 Technicolor models., 258 Step function, integral representation, 162 Tensor product, 490 Sterile neutrino, 419 Tensor product, of spinor fields, 503 Sterile neutrino bounds, 414 Tensor, totally antisymmetric, 132 Sterile neutrinos, 409 Theta vacua, 461

Index 541

Thompson scattering, 386 Weak interactions, 54 Three body phase space integrations, 165 Weak mixing angle, 65 Time dependent perturbation theory, 115 Weak universality, 81 Time ordering operator, 116 Weinberg angle, 65 Time reversal, 496 Wess-Zumino term, 366 Time reversal, deﬁnition, 85 Weyl notation, 502 Top quark decay, 151 Weyl spinor, 20, 501 Top quark, decay width, 151 Wick rotation, 522 Top quark, virtual, 238 Wolfenstein parameterization, 80 Topological susceptibility, 467 Topology, and QCD vacuum, 460 X boson, of grand uniﬁed theories, 477 Total derivative, in the Lagrangian, 460 x, Bjorken, 331 Trace theorems, 132 Xi baryon, 302 Translation invariance, 13 Xi gauges, 506 Trivial representation, 489 Xi∗ baryon, 302 Triviality, 454 Triviality bounds, on Higgs mass, 74 Yukawa couplings, 36 Triviality problem, 455 Yukawa couplings, and global symmetries, 94 Twist, 337 Yukawa couplings, from a superpotential, 445 Two Higgs doublet models, 106 Z boson decay, 127

UA(1) anomaly, 293 Z boson pole, imaginary part, 203 UL(3) UR(3) approximate symmetry, 292 Z boson, couplings to fermions, 137 × UV (3) breaking, 295 Z bosons, 54 U(1), representation theory, 490 Z charges of the fermions, 84 U(3) chiral symmetry, 104 Z decay rate, 135 Uncrossed graphs, 212 Z decay, and hadronic ﬁnal states, 140 Unitarity, 7, 12 Z lifetime, 138 Unitarity bounds, on Higgs mass, 74 Z pole line shape, 223 Unitary gauge, 43, 62, 506 Z resonance, 205 Unitary gauge, and Feynman rules, 174 Z width, 138 Unphysical scalars, Feynman rules, 508 Z width, and higher order corrections, 141 Upsilon particle, 284 Z width, parametric estimate, 139 Z-fermion coupling strengths, 84 Vacuum alignment, in the MSSM, 451 Z-fermion interactions, 82, 83 Vacuum energy: scalars, 19 vacuum expectation value, 42 Vacuum, symmetry breaking, 42 Valence quarks, 335 Vector particles, 26 Vector particles, massive, 26 Vector particles, massless, 28 Vector representation, 499 Vertex, Feynman rules involving ghosts, 513 Vertices, for unphysical scalars, 508 vev, 42 Virtual Higgs exchange, 237 Virtual particles, 153 Virtual top quark eﬀects, 238

W boson decay, 143 W boson decay, interaction Hamiltonian, 143 W boson mass, 64 W boson mass, and renormalization, 251 W bosons, 54 W decay width, 143 W decay, branching fractions, 145 W lifetime, 145 W-fermion interactions, 78 Wave packets, 118 wave packets, 112