Index

a1 (1260) meson 449, 468 Action 46 Adjoint representation 224 Adler–Bell–Jackiw anomaly 438 Altarelli–Parisi–Gribov–Lipatov equations 505 Amputated diagram 117 – n-point function 521 Angular momentum 30, 55, 63 Annihilation and pair production 127, 249, 255 Anomalous dimension 527, 559 Anomalous magnetic moment 127, 348, 350 Anticommutation relations 79, 88 Antilinear operator 157 Antiparticle 33, 76 – mass of 180 – parity of 147, 150 Antisymmetrization 12, 78 Asymptotic freedom 278, 369, 505 – Froissart bound 431 Auxiliary variables 479, 621, 651 B factor (vacuum insertion) 387 B mesons 214, 261, 549 0 – B0 –B mixing 406, 588 Bare – charge 511, 520 – mass 485, 486 – field 487, 489 – k-point function 522 Barn (cross section unit) 15 β-decay 153–155, 163, 178, 350 β-function (see Callan–Symanzik functions) Baryons 235, 238, 245 Baryon number 5, 165 Beauty (see Bottom) Bilinear covariants 65, 181–182 Bjorken scaling 362, 366

Bohr magneton 348, 482 Bootstrap 360 Bose condensation 607 Bose–Einstein statistics 6, 12, 78 Bottom quark 5, 261 Box diagram 379, 388, 588 Branching ratio 205, 392, 573 Breit frame 370 Breit–Wigner form 251, 354 Bremsstrahlung 475, 497 Cabibbo mixing 332 Callan–Gross relation 369 Callan–Symanzik equation 520 – functions 523, 524 Canonical commutation relations 37, 45, 79 Casimir operator 225, 530 Charge conjugation – of Dirac equation 172 – of Klein–Gordon equation 170 – in field theory 169–174 – invariance 175, 177 – violation of symmetry 178 Charge conservation 164 Charge independence 186 Charge renormalization 511 Charge symmetry 185 Charm 5, 252 Charmonium 252 Chirality 83 Chiral representation 85 Circular polarization 44 CKM matrix 338, 399 Color of quarks 5, 248 Commutation relations 37, 40 Compton scattering 133 Confinement of color 279 Conserved Vector Current (CVC) 350, 435 Coulomb gauge 45, 142

658

Index

Counterterms 488, 529–535 – Lagrangian of 512 Coupling constant 8, 104 Covariant derivative 270, 274 CP asymmetry 588 CP symmetry 176, 180 – violation 389–405, 588–599 CPT theorem 178–179 Cross-section 96–102 – Compton scattering 140 – electron–proton scattering 124, 356 – Klein–Nishina 140 – Mott 126, 357 – neutrino–electron 431 – neutrino–nucleon 436, 441 – pair annihilation and production 131, 132, 259 – Rosenbluth 357 – Thomson 141 Current 32 – axial 466 – conservation of 52 – isospin 208, 309 – weak 306, 321, 328, 337 CVC (Conserved Vector Current) 350, 435 ∆I = 1/2 rule 210, 561 D mesons 253 Decay constants fπ , fρ , fK 353, 386, 460 Decay rate 103 – of muon 182, 260 – of pion 182, 461 – of τ lepton 260, 457 – of top quark 262, 265 – of vector meson 255 Deep inelastic scattering 361 Dimensional regularization 478 Dirac equation 57 – completeness of states 68, 70, 77 – covariance 60 – orthogonality of spinors 69, 76 – plane-wave solutions 66 – projection operators 70, 72 Dirac field 76 Dirac matrices 57 – representations 59, 84 – trace theorems 125 Dirac spinors 67 Dispersion relation 352 Divergence – infrared 476, 482

– ultraviolet 475, 482 Double-β decay 166 Dressed propagator 485, 486 Duality (quark–hadron) 473, 568 , 0 (CP violation) parameters 396, 399 Eightfold-way model 215, 228 Electromagnetic field 41, 45 Electron–proton scattering 118 Electroweak interaction 322–323, 335–339 Euler–Lagrange equation 47, 48 Euler’s Γ -function 478 Exclusion principle 76, 78, 193, 248 Exclusive reaction 361 – decay 576 Factorization approximation 405, 577, 583 Faddeev–Popov gauge fixing 538 Fermi coupling constant 155, 306, 350 Fermi–Dirac statistics 4, 78 Fermi–Yang model 215 Feynman–t’ Hooft gauge 385, 477 Feynman diagrams 116 Feynman rules 89, 117 – for electroweak interaction 322–323, 338–339 – for QCD 283, 534 – for QED 130, 137 – for scalar particles 117 – for loop diagrams 654 Fields – electromagnetic field 45 – energy of 36, 46 – gauge (see Gauge fields) – scalar field 25 – vector field 30, 39 Fierz transformation 87, 386, 405 Flavor of quarks 5, 263 Flavor-changing neutral current 332, 427 Flux factor 98 Fock states 36, 77 Form factor 343 Functional path integral formulation 538 Furry’s theorem 174 G parity 202, 205 γ-function (see Callan–Symanzik functions)

Index

659

γ-matrices (see Dirac matrices) Gauge – Coulomb 45 – Feynman 297 – Landau 297 – Lorentz 45 – Rξ 295 – unitary 295 Gauge (boson) field 270, 273 – propagator 282 – self-couplings 276, 318 Gauge fixing 42, 281, 295 Gauge invariance 3, 269, 273, 312 Gauge transformation 267 – Abelian 75, 217, 269–270 – global 167 – local 43, 167 – non-Abelian 30, 273 Gell-Mann matrices 223, 403 Gell-Mann–Nishijima relation 205, 214 Gell-Mann–Okubo mass relation 237, 264 Generations of fermions 2, 333 Generalized charges 4, 164 Ghost (Faddeev–Popov) 534, 538 GIM mechanism 332, 387, 427 Gluons 257, 278 Goldstone–Nambu boson 289, 298, 437 Goldberger–Treiman relation 438 Gordon decomposition 87, 347, 480 Grassmannian numbers 540 Gravitation 7 GSW electroweak theory 4, 330–340, 408

Inclusive decay 450, 568 Instantaneous Coulomb interaction 120, 142 Interaction representation 91–95 Interactions 6, 8 – current–current 305 – electroweak (see Electroweak interactions) – nuclear 197 – strong (see QCD) Invariant mass 343, 364 Inversion – in space 21, 144 – in time 155 Irreducible diagrams 485 Irreducible representations 219, 227 Isospin 188, 194, 229 – invariance 189, 197 – selection rules 208–212 – of strange particles 205–206 – weak 308

Hadron 2, 7 Hadronic currents 448 – decays 582 Heisenberg representation 28, 90 Helicity 71, 83 Heavy flavor symmetry 351, 549, 563 Heavy quark effective theory (HQET) 565 Higgs boson 9, 287, 291, 313, 327 Higgs mechanism 286, 293, 602 – self-coupling constant 609 Hypercharge – strong 206, 229 – weak 310

Lagrangian 48–50 – Dirac 73 – electromagnetism 49 – electroweak 322–323, 338–339 – Klein–Gordon 49 – QCD 278 ΛMS (QCD scale) 537 Landau gauge (see Gauge) Lattice gauge calculations 279 Leptons 4, 258, 263, 308, 333, 447 – currents 321, 448 – decays 209, 450 Lepton number 4, 165 Lifetime 7, 169, 180 Loop diagrams 388, 475, 506, 536 Loop integrals 403, 475

Inclusive reaction

361

J/ψ meson 250, 388 Jets of hadrons 262, 367 Klein–Gordon equation 31 – completeness of states 34 – negative-energy states 33 Klein–Nishina formula 140 K mesons 210, 239, 377, 380 – CP violation 389 – regeneration 383 – mass 385, 389 Kobayashi–Maskawa (KM) phase 338, 389 – CP-violating mechanism 389

660

Index

Lorentz condition 39, 43 Lorentz group 22 – generators 29, 30, 63, 75 – structure of 22 Lorentz transformations 18, 28, 53 – boost 20, 62 – rotation 19, 62 – in Dirac space 60, 65 – improper 21, 22, 144, 155 Magnetic moments of hadrons 246 Majorana neutrino 409 Mandelstam variables 100, 429 Mass renormalization 484, 485 Massless fermion 85 Masses of particles 4, 6, 7, 207, 231, 235, 253 Maxwell equations 41 Meissner effect 293, 606 Mesons 6, 176, 239, 243 Michel parameter (ρ) 455–456 Minimal coupling 119, 152 MSW effect 415, 420 Nc (number of color) 477 Nf (number of flavor) 532 Natural units 13 Neutral weak current 321, 328, 336 Neutrino 4, 260, 409 – oscillations 412, 415 – MSW effect 420 Noether’s theorem 12, 50, 75 Non-Abelian gauge transformations (see Gauge transformation) Nonleptonic (or hadronic) weak decays 210, 449 Nonrenormalizable interactions 489 Normal-ordered product 80 Nucleon–nucleon interaction 198 Octet of hadrons 233 One-particle irreducible (1PI) diagram 485 Operator product expansion 560, 569 OZI rule 241 Pair production (see Annihilation and pair production) Parity 144 (see also Inversion) – intrinsic 148–152 – transformation 147–150 – violation of 152–153 Parton 277, 362, 366, 370

Particle–antiparticle pair 147, 150, 175–176, 202, 244 Pauli matrices 59 Pauli principle (see Exclusion principle) PCT theorem (see CPT theorem) Penguin diagram 402 Phase transformation (see Gauge transformation) Phase space 99, 380, 462 – phase space integral 494 – two-body 99, 461 – three-body 141, 498 Photon–photon scattering 540 π–N interaction 197–198, 213 Polarization four-vectors 39, 44 Positronium decay 176 Potential quark model 246, 255 Principle of least action 47 Projection operators 70, 72, 281 Propagator – ghost 534 – gluon 282 – massive vector boson 297 – photon 122, 123 – scalar boson 111 – spin 1/2 134 Pseudoscalar mesons 204, 231–233 QCD (Quantum Chromodynamics) 9, 267, 277 QED (Quantum Electrodynamics) 119, 142, 271, 481, 506 Quanta 8 Quantum (radiative) effects 475 Quantization of fields 34, 40, 45, 79 Quark 2, 230, 263, 333 – distributions 371 – self-energy 484 R (in e+ e− annihilation) 249, 472 Radiative corrections 475 Regularization – dimensional 478 – Pauli–Villars 479, 508 Renormalization 268, 277, 475, 484 Renormalized – charge 511 – field 484, 485 – Green’s function 522 – mass 484, 485 – vertex 490

Index Renormalization group equation 518, 521, 527, 558 ρ(770) meson 256, 352 Rotations 19 Running coupling constant 506, 536 Rutherford scattering 344 Sakata model 215 Scalar fields 25, 105 Scaling (Bjorken) 277, 362, 366 Scattering – electron–proton 118 – pion 112 – neutrino–electron 429 – neutrino–nucleon 435 Scattering matrix 95 Schr¨ odinger equation 17 Schr¨ odinger picture 28, 90 Screening effect 517 Sea quarks 366 Self-energy – gluon 531 – quark 484, 529 Semileptonic weak decays 212, 448 Spectator model 550, 569 Spin – spin 1/2 63, 82 – spin 1 30, 55 Spin and statistics 78, 179 Spinors 66–67, 85 Spontaneous symmetry breaking 284, 293 Standard model (see GSW Electroweak theory) Strangeness 167, 205 – -changing neutral current 427 – oscillations 377, 380 – regeneration 377, 383 Strong coupling constant αs (q2 ) 536 Strong interactions (see QCD) Structure functions 362, 364 SU(2) 215, 216, 308 SU(2)×U(1) 311 SU(3) 215, 222, 264, 278 SU(3)×SU(2)×U(1) 340 SU(4) 253 SU(6) 242 Sum rules – in dispersion relation 352 – for quark distributions 372 Supersymmetry 611 Symmetries 9–12

661

τ lepton 258–260 – decay rate 260, 457 – decay energy spectrum 455 – semileptonic decay 460, 465 Technicolor 612 Time-ordered product 94 Time reversal or inversion 155–162 – test of invariance 162–163 Top quark 262, 265, 388, 601 Trace theorems 125 Translations 26, 53 Tree diagrams 117, 449, 475, 550 Truth (see Top quark) U(1) 216, 269, 310 U-gauge (see Gauge, unitary) U-spin 223, 264 Uehling effect 518 Uncertainty principle 8 Unitarity – bound 431 – gauge 295 – of CKM matrix 401, 593 – of S-matrix 541 – role of ghosts 546 Υ particle 261 V-spin 223 V–A coupling 155, 308, 323, 339 Vacuum polarization 403, 507 Vacuum condensate 285 Valence quarks 367 Vector boson (see W boson, Z boson) Vector mesons 205, 231, 240, 256 Vertex – corrections to 476–477 – renormalization of 490 W boson 8, 315, 341, 385 Ward–Takahashi identity 491, 503 Weak interaction (see also Electroweak interaction) – classification 209, 305, 448 Weinberg angle 316, 446 Weinberg sum rules 469 Weyl spinor 84 Wolfenstein parameterization of CKM matrix 399 Yang–Mills theory 275 Yukawa coupling 313, 327, 334 Z boson

8, 316, 340, 448