CP Violation

, by Branco, Gustavo Castelo; Lavoura, Luís; Silva, Joao Paulo

Note: Supplemental materials are not guaranteed with Rental or Used book purchases.

ISBN: 9780198503996 | 0198503997
Cover: Hardcover
Copyright: 9/23/1999

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The violation of charge-conjugation and parity symmetries is a leading area of research in particle and nuclear physics, with important implications for understanding the generation of matter in the universe. CP violation occurs during the decay of the elementary particles known as kaons and the process remains little understood. This book provides a self-contained introduction to CP violation. It outlines the underlying theory and related experiments, and its systematic approach is designed to bring beginning researchers to the forefront of the field.

I CP IN QUANTUM MECHANICS

The meaning of the discrete symmetries

(12)

Parity and time reversal in classical physics

(4)

Parity

(2)

Time reversal and T

(1)

Spin, dipole moments, and helicity

(1)

Summary

(1)

Relativistic mechanics

(1)

The meaning of P and of T

(3)

P- and T-asymmetry of the observed events

(1)

A thought experiment about T

(1)

A thought experiment about P

(1)

Summary

(1)

Charge conjugation

(1)

A thought experiment about C

(1)

Violation of C, P, and CP

(5)

The experiment of Wu et al.

(1)

The helicity of the electron neutrino

(1)

CP violation

(1)

Theoretical importance of CP violation

(1)

The discrete symmetries in quantum physics

(12)

Introduction

(1)

Definition of C and of P

(1)

How to define the operators C and P

(1)

Internal symmetries

(1)

Properties of C and of P

(3)

The operator T

(5)

Antiunitary operators

(1)

Operating rules for antiunitary transformations

(1)

Basis-dependence of K

(1)

T as an antiunitary operator

(1)

T invariance and `T conservation'

(1)

Kramers' degeneracy

(1)

CPT

(3)

P, T, and C invariance of QED

(14)

Introduction

(1)

The photon field

(1)

The Klein-Gordon field

(1)

The Dirac field

(6)

Dirac matrices

(2)

Dirac spinors

(2)

The Dirac Lagrangian

(1)

Parity

(1)

Time reversal

(1)

Charge conjugation

(1)

Field bilinears and the discrete transformations

(1)

Relative parities of a particle and its antiparticle

(1)

Electric and magnetic dipole moments

(2)

P, T, and C invariance of the strong interactions

(1)

Conclusions

(2)

Applications of the discrete symmetries

(9)

Introduction

(1)

C invariance: Furry's theorem

(1)

T invariance: the spin of the pion

(1)

2 → 2 scattering

(1)

The spin of the pion

(1)

P invariance: two-photon decay of a spin-0 particle

(1)

C- and P-parities of positronium

(2)

The intrinsic parities of mesons and baryons

(2)

Flavour and intrinsic parities

(1)

The parities of pions and kaons

(1)

The relative phase of GV and GA

(2)

T invariance

(1)

CP invariance

(1)

Weak and strong phases

(10)

Complex CP conditions

(2)

Weak phases and strong phases

(2)

CP violation and interfering amplitudes

(1)

CP violation without strong phases

(1)

Hermiticity of the transition matrix

(1)

Consequences of CPT invariance

(2)

T violation and T violation

(1)

Neutral-meson systems: mixing

(16)

Introduction

(1)

Mixing

(4)

Discrete symmetries

(2)

The mass eigenstates

(2)

Unitarity

(2)

CPT-invariant case

(2)

The case of CP conservation

(1)

The reciprocal basis

(3)

Neutral-meson systems: decays

(8)

The parameters λf

(1)

CP-violating observables

(3)

Final states which are not CP eigenstates

(1)

Classification of CP violation

(1)

Final states which are CP eigenstates

(1)

Different decay channels

(1)

The superweak theory

(3)

Basic assumption

(1)

Γ12

(1)

Source of CP violation

(1)

Other consequences

(1)

Main conclusions

(1)

The neutral-kaon system

(21)

Introduction

(1)

Special features

(2)

Unitarity bound

(1)

Leptonic asymmetry

(2)

The parameters η

(2)

Regeneration

(1)

Correlated decays

(13)

Two-pion decays

(1)

Parametrization

(2)

ω and possible ΔI = 5/2 transitions

(2)

Decay amplitudes

(1)

100

(2)

ε and ω

102

(1)

Approximations: ε

102

(1)

Approximations: ε and ω

103

(1)

Conclusions

104

(1)

Heavy neutral-mesons systems

105

(30)

Introduction

105

(2)

Tagged decays

107

(3)

Flavour-specific decays

110

(4)

Time-integrated probabilities

111

(1)

Pais-Treiman parameters

112

(1)

CP-violating asymmetries

113

(1)

The case of CP conservation in mixing

114

(4)

No direct CP violation: CP eigenstates

114

(2)

Small direct CP violation: CP eigenstates

116

(1)

No direct CP violation: CP non-eigenstates

117

(1)

Inclusive decays

118

(1)

Untagged decays

119

(2)

Correlated mesons

121

(3)

Quantum-mechanical effects with correlated states

124

(2)

Quantum mechanics of parity-odd P0-P0 pairs

124

(1)

Other quantum-mechanical effects

125

(1)

Uncorrelated mesons

126

(1)

CP violation with neutral-meson pairs

126

(9)

Decays into a single flavour-specific final state

127

(2)

Decays into two flavour-specific final states

129

(2)

Decays into a flavour-specific state and a CP eigenstate

131

(1)

Decays into two CP eigenstates

132

(3)

Experimental status of B0-B0 mixing

135

(10)

Introduction

135

(1)

Mixing variables in the B0-B0 systems

135

(2)

Experiments at the ϒ(4S)

137

(3)

Time-integrated experiments at high energy

140

(1)

Time-dependent experiments at LEP1

141

(4)

II CP VIOLATION IN THE STANDARD MODEL

Gauge structure of the standard model

145

(9)

Introduction

145

(1)

SU(2)

145

(1)

Covariant derivative

146

(1)

Self-interactions of the gauge bosons

146

(1)

Gauge interactions of the scalars

147

(1)

Gauge-fixing Lagrangian

148

(3)

Ghosts

151

(1)

Self-interactions of the scalars

152

(2)

The fermions in the standard model

154

(7)

Introduction

154

(1)

Gauge interactions of the fermions

154

(1)

The Yukawa Lagrangian

155

(1)

Generations

156

(2)

Yukawa interactions

158

(3)

Fundamental properties of the CKM matrix

161

(10)

Rephasing-invariance

161

(1)

CP violation

162

(1)

Parameter counting

163

(1)

Unitarity conditions on the moduli

164

(2)

The unitarity triangle

166

(2)

Geometrical interpretation of J

168

(1)

The parameters λα

169

(1)

Main conclusions

169

(2)

Weak-basis invariants and CP violation

171

(9)

Introduction

171

(1)

Conditions for CP invariance

171

(2)

Weak-basis transformations

173

(2)

Weak-basis invariants

175

(1)

Weak-basis-invariant conditions for CP invariance

175

(1)

Two and three generations

176

(2)

ng = 2

176

(1)

ng = 3

176

(2)

More than three generations

178

(1)

CP restrictions in a special weak basis

178

(1)

Sufficient conditions for CP invariance

178

(1)

Conclusions

179

(1)

Moduli of the CKM matrix elements

180

(7)

Introduction

180

(1)

|Vud|

180

(2)

|Vus|

182

(1)

|Vcd| and |Vcs|

183

(1)

|Vcb|

183

(1)

|Vub|/|Vcb|

184

(1)

Consequences of unitarity

185

(2)

Parametrizations of the CKM matrix

187

(11)

Introduction

187

(1)

Parametrizations with Euler angles

187

(2)

Kobayashi-Maskawa parametrization

188

(1)

Chau-Keung parametrization

188

(1)

Rephasing-invariant parametrizations

189

(4)

Branco-Lavoura parametrization

189

(1)

Bjorken-Dunietz parametrization

190

(1)

Aleksan-Kayser-London parametrization

191

(2)

Wolfenstein parametrization

193

(4)

Exact version of the parametrization

194

(2)

Parametrization with Rt and Rb

196

(1)

Main results

197

(1)

198

(9)

Introduction

198

(1)

Γ and qk/pk

198

(1)

Master formula for ε

199

(1)

The box diagram

200

(1)

QCD corrections to the |ΔS| = 2 effective Hamiltonian

201

(2)

Other contributions to M12

203

(1)

Fit of ε

204

(2)

Main conclusions

206

(1)

Mixing in the B0q-B0q systems

207

(8)

M12

207

(1)

A note on CP invariance

208

(1)

209

(1)

The mass difference in the B0d-B0d system

210

(1)

The ρ-η plane and the unitarity triangle

211

(2)

The mass difference in the B0s-B0s system

213

(1)

Main conclusions

213

(2)

KL →π0νν

215

(7)

Introduction

215

(1)

λπνν

216

(2)

Prediction of the branching ratio

218

(1)

K+ → π+νν

219

(1)

Explicit values

219

(3)

Effective Hamiltonians

222

(8)

Current-current operators

222

(2)

Penguin operators

224

(2)

The effective Hamiltonian

226

(1)

Calculating amplitudes with the effective Hamiltonian

227

(1)

Hadronic matrix elements

228

(2)

ε / ε

230

(9)

Introduction

230

(2)

Master formula for ε / ε

232

(2)

Matrix elements

234

(1)

Final result

235

(4)

III CP VIOLATION BEYOND THE STANDARD MODEL

Multi-Higgs-doublet models

239

(21)

Introduction

239

(2)

General multi-Higgs-doublet model

241

(1)

The two-Higgs-doublet model

242

(1)

The Higgs basis

243

(1)

The Higgs basis in the THDM

243

(3)

The potential

244

(1)

The Yukawa interactions

245

(1)

CP transformation

246

(1)

CP violation in the scalar potential: simple examples

247

(1)

THDM with a discrete symmetry

247

(1)

Softly broken discrete symmetry

247

(1)

Weinberg model

248

(1)

General treatment of CP violation

248

(3)

Weak-basis transformations

249

(1)

Weak-basis invariants

250

(1)

CP violation

250

(1)

CP violation in the two-Higgs-doublet model

251

(3)

I1 and I2

251

(1)

I3 and I4

252

(1)

Feynman rules and CP violation: I1 and I2

252

(2)

Feynman rules and CP violation: I3 and I4

254

(1)

Flavour-changing neutral Yukawa interactions

254

(2)

Mechanisms for natural suppression of the FCNYI

256

(2)

Natural flavour conservation

256

(1)

Non-vanishing but naturally small FCNYI

257

(1)

Main conclusions

258

(2)

Spontaneous CP violation

260

(16)

Introduction

260

(1)

CP invariance and reality of the coupling constants

261

(1)

Lee model

262

(3)

The Higgs potential

262

(2)

The Yukawa interactions

264

(1)

Effective superweak models

264

(1)

Natural flavour conservation and SCPV

265

(3)

Mechanism for generating ε

265

(2)

Symmetries of the scalar potential and SCPV

267

(1)

Branco model

268

(3)

CP-breaking vacuum

269

(1)

Scalar mass matrices

270

(1)

Model with one doublet and one singlet

271

(2)

Summary

273

(3)

Phenomenological consequences

274

(2)

Models with vector-like quarks

276

(17)

Motivation

276

(1)

The model

277

(3)

Quark spectrum

277

(1)

Mixing matrices

278

(1)

Non-unitarity of V and its relation to the FCNC

279

(1)

Natural suppression of the FCNC

280

(2)

CP-violating phases

282

(1)

The invariant approach

282

(3)

CP-invariance conditions

282

(1)

Analysis in a specific weak basis

283

(1)

Invariant CP restrictions

284

(1)

Parametrization of the CKM matrix

285

(2)

Parametrization with Euler angles and phases

285

(2)

Spontaneous CP violation: a simple model

287

(2)

Phenomenological implications

289

(3)

Experimental bounds on Zkj

289

(1)

Implications for CP asymmetries

290

(1)

Baryogenesis

291

(1)

Main conclusions

292

(1)

Massive neutrinos and CP violation in the leptonic sector

293

(17)

Introduction

293

(1)

Theoretical motivations

293

(1)

Phenomenological motivations

293

(1)

Dirac and Majorana masses

294

(3)

Dirac masses

294

(1)

Majorana masses

295

(2)

The seesaw mechanism

297

(2)

Neutrino masses in SU(2)U(1) gauge theories

299

(2)

Conditions for CP invariance

301

(2)

The case with no right-handed neutrinos

303

(6)

The CP-parities of the neutrinos

304

(1)

Two generations

305

(1)

Neutrinoless double beta decay

306

(1)

Mass-degenerate neutrinos

307

(2)

Main conclusions

309

(1)

The left-right-symmetric model

310

(19)

Overview of the model

310

(6)

Introduction

310

(1)

Gauge couplings

311

(1)

Scalar multiplets

312

(2)

Gauge-boson masses

314

(2)

Spontaneous symmetry breaking

316

(5)

The scalar potential

317

(1)

Spontaneous breaking of P

318

(1)

Spontaneous CP breaking

319

(2)

Quark masses and mixing matrices

321

(4)

Mass matrices

321

(1)

Mixing matrices and CP-violating phases

321

(2)

Manifest and pseudo-manifest left-right symmetry

323

(2)

Weak-basis invariants and CP violation

325

(2)

Conditions for CP invariance

325

(1)

Weak-basis transformations

325

(1)

CP restrictions in a special weak basis

326

(1)

Weak-basis invariants

326

(1)

Phenomenological implications

327

(1)

Main conclusions

328

(1)

The strong CP problem

329

(18)

Introduction

329

(1)

The U(1)A problem

329

(2)

Instantons

331

(3)

The strong CP problem

334

(1)

mu = 0 solution

335

(1)

Peccei-Quinn solution

336

(2)

The DFSZ model

337

(1)

Solutions with calculable and naturally small &thetas;

338

(4)

A model with spontaneous CP breaking

338

(3)

A model with spontaneous P breaking

341

(1)

Appraisal

342

(5)

IV CP VIOLATION IN B DECAYS

Introduction

347

(11)

B decays as a testing ground for the SM

347

(1)

CP-violating asymmetries

348

(2)

The parameters λf

348

(1)

Definition of the CP asymmetries

349

(1)

Decays dominated by a single weak phase

350

(1)

Penguin pollution

351

(2)

The four phases in the CKM matrix

353

(2)

SM values of ε and ε

354

(1)

Smallness of ε in models of new physics

354

(1)

Outline of Part IV

355

(3)

Some experimental issues

358

(8)

Introduction

358

(1)

Preparation of the initial state

358

(1)

Experiments at the ϒ(4S)

359

(1)

Other experiments

359

(1)

Tagged decays

359

(2)

Tagging one meson with semileptonic decays

359

(1)

Tagging neutral mesons

360

(1)

CP asymmetries at the ϒ(4S)

361

(1)

Consequences of the limits on vertexing

362

(2)

The need for asymmetric ϒ(4S) factories

362

(1)

Tracing the time dependence in the B0s-B0s system

363

(1)

Decays into lighter neutral-meson systems

364

(2)

The mixing parameters

366

(8)

Introduction

366

(2)

Extracting experimental information on q/p

366

(1)

A theoretical argument

367

(1)

An assumption about the decay amplitudes

368

(1)

qk/pk

368

(2)

The phase of M*12

369

(1)

Relating arg (qBq/pBq) to arg M*12

370

(2)

The Bd case

370

(1)

The Bs case

371

(1)

qBd/pBd and qBs/pBs

372

(1)

q/p in the SM

372

(1)

qBq/pBq in the presence of new physics

372

(1)

Main conclusions

373

(1)

Decay amplitudes: diagrammatics

374

(18)

Introduction

374

(1)

SU(3) classification of mesons

375

(1)

Final states with several possible quark-flavour contents

376

(1)

Tree-level diagrams

376

(4)

C and T diagrams

377

(1)

Classification of the decays at tree level

378

(1)

Decay channels common to B0 and B0

379

(1)

Gluonic penguins

380

(2)

Classification of decays

382

(1)

Decays into CP eigenstates

383

(4)

Diagrams involving the spectator quark

387

(2)

Quark diagrams and SU(3) symmetry

388

(1)

Electroweak penguins

389

(1)

Conclusion

390

(2)

Decay amplitudes: effective Hamiltonian

392

(6)

Effective Hamiltonian for B decays

392

(3)

On the evaluation of hadronic matrix elements

395

(1)

CP transformations

395

(3)

ΔC = 0 ΔU decays

395

(2)

ΔC ≠ 0 ≠ ΔU decays

397

(1)

CKM phases and interference CP violation

398

(11)

Parameters λf at tree level

398

(4)

B0d → π+π-

398

(1)

B0d → J/ψ Ks

399

(1)

B0s → ρKs

400

(1)

Consequences of single-phase dominance

401

(1)

New physics in the mixing and the parameters λf

402

(1)

α + β + γ = π

403

(1)

Corrections induced by the subleading amplitudes

404

(3)

General discussion

404

(1)

Decays with a tree-level contribution

405

(1)

Pure penguin decays

406

(1)

is the gold-plated decay

407

(2)

Cascade decays

409

(12)

Introduction

409

(1)

The decay chain

410

(1)

The cascade decays

411

(3)

The kaon state at time tB

411

(1)

Cascade decay rate: tK-dependence

412

(1)

Cascade decay rate: tK-integrated

413

(1)

The Kayser method to measure cos 2β

414

(1)

Decay chains with intermediate neutral-D mesons

414

(2)

λf for decays with ΔC ≠ O ≠ ΔU

416

(1)

Generalized cascade decays

417

(4)

Some methods to extract α

421

(11)

Introduction

421

(1)

The Gronau-London method

421

(4)

The Silva-Wolfenstein method

425

(3)

The Synder-Quinn method

428

(4)

Some methods to extract γ

432

(15)

Introduction

432

(1)

The Gronau-London triangle relations

433

(1)

The Gronau-London-Wyler method

434

(7)

Procedure

434

(2)

Geometrical interpretation

436

(1)

The weak phase in the SM

437

(2)

Experimental difficulties with the GLW method

439

(2)

Simple extensions of the GLW method

441

(2)

Extracting γ with self-tagging Bod modes

441

(1)

Extracting γ from D decays into non-CP eigenstates

441

(2)

The Atwood-Dunietz-Soni method

443

(1)

The Gronau-London Bod method

444

(3)

Extracting γ from

444

(1)

Extracting 2β + γ from

445

(2)

Extracting CKM phases with Bos decays

447

(7)

Introduction

447

(1)

:the silver-plated decay

448

(1)

The Aleksan-Dunietz-Kayser method

449

(2)

The Gronau-London method

451

(1)

Extracting γ from

451

(1)

Extracting -2ε + γ from

451

(1)

On the use of untagged decays

452

(2)

Discrete ambiguities

454

(5)

Statement of the problem

454

(2)

Removing the ambiguities

456

(3)

Determining the sign of cos2ø

456

(2)

Determining the sign of sinø

458

(1)

A Two notes on CP-transformation phases

459

(4)

A.1 The CP-transformation phases of the quarks in q/p

459

(2)

A.2 Cancellation of the CP-transformation phases in λf

461

(2)

B Effective Hamiltonian for |ΔS| = 2 processes

463

(6)

B.1 The box diagram of the standard model

463

(4)

B.1.1 Introduction

463

(1)

B.1.2 Writing down the diagram

463

(1)

B.1.3 Gauge independence

464

(1)

B.1.4 Effective operator

465

(1)

B.1.5 Integration

465

(1)

B.1.6 GIM mechanism

466

(1)

B.1.7 Effective Hamiltonian

466

(1)

B.2 Scalars and mixing at tree level

467

(1)

B.3 Vector bosons and mixing at tree level

468

(1)

C The vacuum-insertion approximation in mixing

469

(7)

C.1 Introduction

469

(1)

C.2 Creation and destruction operators

470

(1)

C.3 Fierz transformations

470

(2)

C.3.1 Dirac matrices

470

(1)

C.3.2 Gell-Mann matrices

471

(1)

C.3.3 Applications in the VIA

471

(1)

C.4 Vacuum insertion

472

(1)

C.5 Use of symmetries

473

(2)

C.6 fk

475

(1)

D The effective Hamiltonian for

476

(4)

D.1 Introduction

476

(1)

D.2 The diagrams in Fig. D. 1

477

(1)

D.3 The diagrams in Fig. D.2

478

(1)

D.4 Final result

479

(1)

E mixing

480

(5)

E.1 Theoretical expectations

480

(2)

E.1.1 The box diagrams

480

(1)

E.1.2 Dipenguin diagrams

481

(1)

E.1.3 Long-distance contributions

481

(1)

E.1.4 mixing beyond the standard model

482

(1)

E.2 Experimental results

482

(2)

E.3 Conclusions

484

(1)

References

485

(18)

Index

503

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CP Violation

Summary

Table of Contents

Supplemental Materials