CP Violation

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

• ISBN13: 9780198503996
• ISBN10: 0198503997
• Format: Hardcover
• Copyright: 1999-09-23
• Publisher: Clarendon Press

Summary

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.

Table of Contents

I CP IN QUANTUM MECHANICS
The meaning of the discrete symmetries	3	(12)
Parity and time reversal in classical physics	3	(4)
Parity	3	(2)
Time reversal and T	5	(1)
Spin, dipole moments, and helicity	5	(1)
Summary	6	(1)
Relativistic mechanics	6	(1)
The meaning of P and of T	7	(3)
P- and T-asymmetry of the observed events	8	(1)
A thought experiment about T	8	(1)
A thought experiment about P	9	(1)
Summary	9	(1)
Charge conjugation	10	(1)
A thought experiment about C	10	(1)
Violation of C, P, and CP	10	(5)
The experiment of Wu et al.	11	(1)
The helicity of the electron neutrino	11	(1)
CP	12	(1)
CP violation	13	(1)
Theoretical importance of CP violation	14	(1)
The discrete symmetries in quantum physics	15	(12)
Introduction	15	(1)
Definition of C and of P	15	(1)
How to define the operators C and P	15	(1)
Internal symmetries	16	(1)
Properties of C and of P	16	(3)
The operator T	19	(5)
Antiunitary operators	19	(1)
Operating rules for antiunitary transformations	20	(1)
Basis-dependence of K	21	(1)
T as an antiunitary operator	21	(1)
T invariance and `T conservation'	22	(1)
Kramers' degeneracy	23	(1)
CPT	24	(3)
P, T, and C invariance of QED	27	(14)
Introduction	27	(1)
The photon field	27	(1)
The Klein-Gordon field	28	(1)
The Dirac field	29	(6)
Dirac matrices	29	(2)
Dirac spinors	31	(2)
The Dirac Lagrangian	33	(1)
Parity	33	(1)
Time reversal	33	(1)
Charge conjugation	34	(1)
CP	34	(1)
Field bilinears and the discrete transformations	35	(1)
Relative parities of a particle and its antiparticle	35	(1)
Electric and magnetic dipole moments	36	(2)
P, T, and C invariance of the strong interactions	38	(1)
Conclusions	39	(2)
Applications of the discrete symmetries	41	(9)
Introduction	41	(1)
C invariance: Furry's theorem	41	(1)
T invariance: the spin of the pion	42	(1)
2 → 2 scattering	42	(1)
The spin of the pion	43	(1)
P invariance: two-photon decay of a spin-0 particle	43	(1)
C- and P-parities of positronium	44	(2)
The intrinsic parities of mesons and baryons	46	(2)
Flavour and intrinsic parities	46	(1)
The parities of pions and kaons	47	(1)
The relative phase of GV and GA	48	(2)
T invariance	48	(1)
CP invariance	49	(1)
Weak and strong phases	50	(10)
Complex CP conditions	50	(2)
Weak phases and strong phases	52	(2)
CP violation and interfering amplitudes	54	(1)
CP violation without strong phases	55	(1)
Hermiticity of the transition matrix	56	(1)
Consequences of CPT invariance	57	(2)
T violation and T violation	59	(1)
Neutral-meson systems: mixing	60	(16)
Introduction	60	(1)
Mixing	60	(4)
Discrete symmetries	64	(2)
The mass eigenstates	66	(2)
Unitarity	68	(2)
CPT-invariant case	70	(2)
The case of CP conservation	72	(1)
The reciprocal basis	73	(3)
Neutral-meson systems: decays	76	(8)
The parameters λf	76	(1)
CP-violating observables	77	(3)
Final states which are not CP eigenstates	77	(1)
Classification of CP violation	78	(1)
Final states which are CP eigenstates	79	(1)
Different decay channels	79	(1)
The superweak theory	80	(3)
Basic assumption	80	(1)
Γ12	81	(1)
Source of CP violation	81	(1)
Other consequences	82	(1)
Main conclusions	83	(1)
The neutral-kaon system	84	(21)
Introduction	84	(1)
Special features	84	(2)
Unitarity bound	86	(1)
Leptonic asymmetry	87	(2)
The parameters η	89	(2)
Regeneration	91	(1)
Correlated decays	92	(13)
Two-pion decays	95	(1)
Parametrization	95	(2)
ω and possible ΔI = 5/2 transitions	97	(2)
Decay amplitudes	99	(1)
ε	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)
ε	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)
Γ	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