CP VIOLATION Why didn’t the matter in our Universe annihilate with antimatter immediately after its creation? The study of CP violation may help to answer this fundamental question. Reflecting the explosion of new results over the last decade, this second edition has been substantially expanded. From basic principles to the front-line of research, this account presents the information and theoretical tools necessary to understand this phenomenon. Charge conjugation, parity and time reversal are introduced, before describing the Kobayashi–Maskawa (KM) theory for CP violation and examining our understanding of CP violation in kaon decays. Following chapters reveal how the discovery of B mesons provided a new laboratory to study CP violation with KM theory predicting large asymmetries, and discuss how these predictions have been confirmed since the first edition of this book. This led to M. Kobayashi and T. Maskawa receiving the 2008 Nobel Prize for Physics. Later chapters describe the search for a new theory of nature’s fundamental dynamics. The observation of neutrino oscillations provides opportunities to reveal CP violation in the lepton sector, which might drive baryogenesis in a Big Bang Universe. The impor- tance of close links with experiment is stressed, and numerous problems are included. This book is suitable for researchers in high energy, atomic and nuclear physics and in the history and philosophy of science. Ikaros Bigi was born in Munich, Germany. Following undergraduate and postgraduate studies at the Universities of Munich, Oxford and Stanford, he has taught and researched at the Max-Planck Institute for Physics, CERN, RWTH Aachen, UCLA, the University of Oregon, SLAC and the University of Notre Dame. He is a former scholarship student of the Mazi- milianeum Foundation and Scholarship Foundation of the German People and has been appointed both a Heisenberg Fellow and a Max-Kade Fellow. Ichiro Sanda was born in Tokyo, and at the age of 14 accompanied his father who was transferred to the United States on business. After a bach- elor’s degree in physics from the University of Illinois and a Ph.D. from Princeton University, he taught and researched at Columbia University, Fermilab and Rockefeller University. In 1992, after 34 years in the US, he went to Japan as a Professor of physics at Nagoya University. He is now the Chairman of the physics department at Kanagawa University. He is a winner of the 10th Inoue Prize (1993) and the 43rd Nishina Memorial Prize (1997). Both prizes have been awarded for his work in CP violation, and on B physics. Since 1980 the authors have written 14 papers together. In their first paper they explained the special role for CP violation played by certain B meson decays; among them was the channel B → ψKS, where the first CP asymmetry outside K decays was established in 2001. In 2004 they were jointly awarded the J. J. Sakurai Prize by the American Physical Society ‘for pioneering theoretical insights that pointed the way to the very fruitful experimental study of CP violation in B decays, and for continuing contributions to the field of CP and heavy flavor physics’. CAMBRIDGE MONOGRAPHS ON PARTICLE PHYSICS NUCLEAR PHYSICS AND COSMOLOGY 28 General Editors: T. Ericson, P. V. Landshoff 1. K. Winter (ed.): Neutrino Physics 2. J. F. Donoghue, E. Golowich and B. R. Holstein: Dynamics of the Standard Model 3. E. Leader and E. Predazzi: An Introduction to Gauge Theories and Modern Particle Physics, Volume 1: Electroweak Interactions, the ‘New Particles’ and the Parton Model 4. E. Leader and E. Predazzi: An Introduction to Gauge Theories and Modern Particle Physics, Volume 2: CP-Violation, QCD and Hard Processes 5. C. Grupen: Particle Detectors 6. H. Grosse and A. Martin: Particle Physics and the Schr¨odinger Equation 7. B. Anderson: The Lund Model 8. R. K. Ellis, W. J. Stirling and B. R. Webber: QCD and Collider Physics 9. I. I. Bigi and A. I. Sanda: CP Violation 10. A. V. Manohar and M. B. Wise: Heavy Quark Physics 11.R.K.Bock,H.Grote,R.Fr¨uhwirth and M. Regler: Data Analysis Techniques for High- Energy Physics, Second edition 12. D. Green: The Physics of Particle Detectors 13. V. N. Gribov and J. Nyiri: Quantum Electrodynamics 14. K. Winter (ed.): Neutrino Physics, Second edition 15. E. Leader: Spin in Particle Physics 16. J. D. Walecka: Electron Scattering for Nuclear and Nucleon Scattering 17. S. Narison: QCD as a Theory of Hadrons 18. J. F. Letessier and J. Rafelski: Hadrons and Quark-Gluon Plasma 19. A. Donnachie, H. G. Dosch, P. V. Landshoff and O. Nachtmann: Pomeron Physics and QCD 20. A. Hoffmann: The Physics of Synchroton Radiation 21. J. B. Kogut and M. A. Stephanov: The Phases of Quantum Chromodynamics 22. D. Green: High PT Physics at Hadron Colliders 23. K. Yagi, T. Hatsuda and Y. Miake: Quark-Gluon Plasma 24. D. M. Brink and R. A. Broglia: Nuclear Superfluidity 25. F. E. Close, A. Donnachie and G. Shaw: Electromagnetic Interactions and Hadronic Structure 26. C. Grupen and B. A. Shwartz: Particle Detectors, Second edition 27. V. Gribov: Strong Interactions of Hadrons at High Energies 28. I. I. Bigi and A. I. Sanda: CP Violation, Second edition CP VIOLATION I. I. BIGI Physics Department, University of Notre Dame du Lac A. I. SANDA Physics Department, Kanagawa University CAMBRIDGE UNIVERSITY PRESS Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo, Delhi, Dubai, Tokyo Cambridge University Press The Edinburgh Building, Cambridge CB2 8RU, UK Published in the United States of America by Cambridge University Press, New York www.cambridge.org Information on this title: www.cambridge.org/9780521847940 © I. Bigi and A. Sanda 2009 This publication is in copyright. Subject to statutory exception and to the provision of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published in print format 2009 ISBN-13 978-0-511-58069-7 eBook (NetLibrary) ISBN-13 978-0-521-84794-0 Hardback Cambridge University Press has no responsibility for the persistence or accuracy of urls for external or third-party internet websites referred to in this publication, and does not guarantee that any content on such websites is, or will remain, accurate or appropriate. Dedicated to Colette and Hiroko Contents Preface to the second edition page xvii Preface to the first edition xix Part I Basics of CP violation 1 1 Prologue 3 2 Prelude: C, P and T in classical dynamics 12 2.1 Classical mechanics 13 2.1.1 Parity 13 2.1.2 Time reversal 14 2.2 Electrodynamics 16 2.2.1 Charge conjugation 17 2.2.2 Parity 17 2.2.3 Time reversal 17 2.3 R´esum´e 19 Problems 19 3 C, P and T in non-relativistic quantum mechanics 21 3.1 Parity 22 3.2 Charge conjugation 25 3.3 Time reversal 26 3.4 Kramers’ degeneracy 30 3.5 Detailed balance 32 3.6 Electric dipole moments 33 3.6.1 The neutron EDM 33 3.6.2 Water molecules and atoms 35 3.6.3 Dumb-bells 36 3.6.4 Schiff’s theorem 37 ix x Contents 3.7 R´esum´e 38 Problems 38 4 C, P and T in relativistic quantum theories 41 4.1 Notation 42 4.2 Spin-1 fields 43 4.3 Spin-0 fields 46 4.3.1 Parity 46 4.3.2 Charge conjugation 47 4.3.3 Time reversal 47 4.4 Spin-1/2 fields 48 4.4.1 Parity 49 4.4.2 Charge conjugation 51 4.4.3 Time reversal 52 4.5 CP and CPT transformations 53 4.6 Some consequences of the CPT theorem 56 4.7 ♠ Back to first quantization ♠ 58 4.8 ♠ Phase conventions for C and P ♠ 59 4.9 ♠ Internal symmetries ♠ 60 4.10 The role of final state interactions 62 4.10.1 T invariance and Watson’s theorem 62 4.10.2 Final state interactions and partial widths 64 4.10.3 ♠ T symmetry and final state interactions ♠ 67 4.11 R´esum´e and outlook 69 Problems 70 5 The arrival of strange particles 73 5.1 The discovery of strange particles 73 5.2 The θ − τ puzzle 75 1 5.3 The ΔI = 2 rule 76 5.4 The existence of two different neutral kaons 77 0 5.5 CP invariant K0 − K oscillations 79 5.6 Regeneration – which is heavier: KL or KS? 83 5.7 The quiet before the storm 84 5.8 The discovery of CP violation 85 Problems 89 6 Quantum mechanics of neutral particles 90 6.1 The effective Hamiltonian 90 6.2 Constraints from CPT, CP and T 93 6.3 Spherical coordinates 93 6.4 ♠ On phase conventions ♠ 95 6.5 ♠ ΔM and ΔΓ ♠ 97 6.6 Master equations of time evolution 99 6.7 CP violation: classes (A), (B) and (C) 102 6.8 ♠ On the sign of the CP asymmetry ♠ 106 Contents xi 6.9 What happens if you don’t observe the decay time? 107 6.10 Regeneration 108 6.11 The Bell–Steinberger inequality 110 0 6.12 R´esum´eonP 0 − P oscillations 111 Problems 113 Part II Theory and experiments 115 7 The quest for CP violation in K decays – a marathon 117 7.1 The landscape 117 7.2 KL → ππ decays 121 7.2.1 Decay amplitudes 121 7.2.2 Constraints on AI and AI 124 i 7.2.3 Relating to M − 2 Γ 125 7.2.4 The phase of 126 7.3 Semileptonic decays 127 7.4 ♠ P⊥ in K → πμν decays ♠ 129 7.5 ♠ K → 3π ♠ 133 0 7.5.1 KS → 3π 133 + − 0 7.5.2 KS → π π π 133 7.5.3 K± → π±π+π− 138 7.6 ♠ Hyperon decays ♠ 138 7.7 The bard’s song 141 Problems 141 8 The KM implementation of CP violation 143 8.1 A bit of history 143 8.2 The Standard Model 145 8.2.1 QCD 146 8.2.2 The Glashow–Salam–Weinberg model 147 8.3 The KM ansatz 149 8.3.1 The mass matrices 149 8.3.2 Parameters of consequence 149 8.3.3 Describing weak phases through unitarity triangles 151 8.4 A tool kit 154 8.4.1 The angles of the unitarity triangle 156 8.5 The pundits’ judgement 157 Problems 158 9 The theory of KL → ππ decays 160 9.1 The ΔS = 1 non-leptonic Lagrangian 160 9.2 Evaluating matrix elements 164 9.3 Chiral