x
19.4 Flux quantization in a superconductor . . . . . . . . . . . . . 268
19.5 ’t Hooft’s gauges . . . . . . . . . . . . . . . . . . . . . . . . . 271
19.6 Spontaneously broken local SU(2) × U(1) symmetry . . . . . 275
Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 279
VIII Weak Interactions and the Electroweak Theory281
20 Introduction to the Phenomenology of Weak Interactions
283
20.1 Fermi’s ‘current–current’ theory of nuclear β-decay, and its generalizations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284
20.2 Parity violation in weak interactions, and V-A theory . . . . 287
20.2.1 Parity violation . . . . . . . . . . . . . . . . . . . . . . 287
20.2.2 V-A theory: chirality and helicity . . . . . . . . . . . . 288
20.3 Lepton number and lepton flavours . . . . . . . . . . . . . . 293
20.4 The universal current × current theory for weak interactions of
leptons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 296
20.5 Calculation of the cross section for ν μ + e
−
→ μ
− + ν e . . . . 298
20.6 Leptonic weak neutral currents . . . . . . . . . . . . . . . . . 302
20.7 Quark weak currents . . . . . . . . . . . . . . . . . . . . . . 304
20.7.1 Two generations . . . . . . . . . . . . . . . . . . . . . 304
20.7.2 Deep inelastic neutrino scattering . . . . . . . . . . . . 308
20.7.3 Three generations . . . . . . . . . . . . . . . . . . . . 317
20.8 Non-leptonic weak interactions . . . . . . . . . . . . . . . . . 324
Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325
21 CP Violation and Oscillation Phenomena
329
21.1 Direct CP violation in B decays . . . . . . . . . . . . . . . . 330
21.2 CP violation in B meson oscillations . . . . . . . . . . . . . 335
21.2.1 Time-dependent mixing formalism . . . . . . . . . . . 336
21.2.2 Determination of the angles α(φ 2 ) and β(φ 1 ) of the unitarity triangle . . . . . . . . . . . . . . . . . . . . . . . 339
21.3 CP violation in neutral K-meson decays . . . . . . . . . . . 345
21.4 Neutrino mixing and oscillations . . . . . . . . . . . . . . . . 350
21.4.1 Neutrino mass and mixing . . . . . . . . . . . . . . . . 350
21.4.2 Neutrino oscillations: formulae . . . . . . . . . . . . . 353
21.4.3 Neutrino oscillations: experimental results . . . . . . . 358
21.4.4 Matter effects in neutrino oscillations . . . . . . . . . 361
21.4.5 Further developments . . . . . . . . . . . . . . . . . . 363
Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 364
22 The Glashow–Salam–Weinberg Gauge Theory of Electroweak
Interactions
367
22.1 Difficulties with the current–current and ‘naive’ IVB models
367
22.1.1 Violations of unitarity . . . . . . . . . . . . . . . . . . 368
22.1.2 The problem of non-renormalizability in weak interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 374
19.4 Flux quantization in a superconductor . . . . . . . . . . . . . 268
19.5 ’t Hooft’s gauges . . . . . . . . . . . . . . . . . . . . . . . . . 271
19.6 Spontaneously broken local SU(2) × U(1) symmetry . . . . . 275
Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 279
VIII Weak Interactions and the Electroweak Theory281
20 Introduction to the Phenomenology of Weak Interactions
283
20.1 Fermi’s ‘current–current’ theory of nuclear β-decay, and its generalizations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284
20.2 Parity violation in weak interactions, and V-A theory . . . . 287
20.2.1 Parity violation . . . . . . . . . . . . . . . . . . . . . . 287
20.2.2 V-A theory: chirality and helicity . . . . . . . . . . . . 288
20.3 Lepton number and lepton flavours . . . . . . . . . . . . . . 293
20.4 The universal current × current theory for weak interactions of
leptons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 296
20.5 Calculation of the cross section for ν μ + e
−
→ μ
− + ν e . . . . 298
20.6 Leptonic weak neutral currents . . . . . . . . . . . . . . . . . 302
20.7 Quark weak currents . . . . . . . . . . . . . . . . . . . . . . 304
20.7.1 Two generations . . . . . . . . . . . . . . . . . . . . . 304
20.7.2 Deep inelastic neutrino scattering . . . . . . . . . . . . 308
20.7.3 Three generations . . . . . . . . . . . . . . . . . . . . 317
20.8 Non-leptonic weak interactions . . . . . . . . . . . . . . . . . 324
Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325
21 CP Violation and Oscillation Phenomena
329
21.1 Direct CP violation in B decays . . . . . . . . . . . . . . . . 330
21.2 CP violation in B meson oscillations . . . . . . . . . . . . . 335
21.2.1 Time-dependent mixing formalism . . . . . . . . . . . 336
21.2.2 Determination of the angles α(φ 2 ) and β(φ 1 ) of the unitarity triangle . . . . . . . . . . . . . . . . . . . . . . . 339
21.3 CP violation in neutral K-meson decays . . . . . . . . . . . 345
21.4 Neutrino mixing and oscillations . . . . . . . . . . . . . . . . 350
21.4.1 Neutrino mass and mixing . . . . . . . . . . . . . . . . 350
21.4.2 Neutrino oscillations: formulae . . . . . . . . . . . . . 353
21.4.3 Neutrino oscillations: experimental results . . . . . . . 358
21.4.4 Matter effects in neutrino oscillations . . . . . . . . . 361
21.4.5 Further developments . . . . . . . . . . . . . . . . . . 363
Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 364
22 The Glashow–Salam–Weinberg Gauge Theory of Electroweak
Interactions
367
22.1 Difficulties with the current–current and ‘naive’ IVB models
367
22.1.1 Violations of unitarity . . . . . . . . . . . . . . . . . . 368
22.1.2 The problem of non-renormalizability in weak interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 374