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AN INTRODUCTION TO THE STANDARD MODEL OF
PARTICLE PHYSICS
SecondEdition
The Standard Model of particle physics is the mathematical theory that describes
theweak,electromagneticandstronginteractionsbetweenleptonsandquarks,the
basicparticlesoftheStandardModel.
The new edition of this introductory graduate textbook provides a concise but
accessible introduction to the Standard Model. It has been updated to account for
thesuccessesofthetheoryofstronginteractions,andtheobservationsonmatter–
antimatterasymmetry.Ithasbecomeclearthatneutrinosarenotmass-less,andthis
bookgivesacoherentpresentationofthephenomenaandthetheorythatdescribes
them.Itincludesanaccountofprogressinthetheoryofstronginteractionsandof
advances in neutrino physics. The book clearly develops the theoretical concepts
fromtheelectromagneticandweakinteractionsofleptonsandquarkstothestrong
interactionsofquarks.
This textbook provides an up-to-date introduction to the Standard Model for
graduatestudentsinparticlephysics.Eachchapterendswithproblems,andhintsto
selectedproblemsareprovidedattheendofthebook.Themathematicaltreatments
are suitable for graduates in physics, and more sophisticated mathematical ideas
aredevelopedinthetextandappendices.
noel cottinghamandderek greenwoodaretheoreticiansworkinginthe
H.H.WillsPhysicsLaboratoryattheUniversityofBristol.Theyhavepublishedtwo
undergraduate texts with Cambridge University Press, Electricity and Magnetism
(1991)andAnIntroductiontoNuclearPhysics,nowinitssecondedition(2001).
AN INTRODUCTION TO THE
STANDARD MODEL OF
PARTICLE PHYSICS
Second Edition
W. N. COTTINGHAM and D. A. GREENWOOD
UniversityofBristol,UK
CAMBRIDGEUNIVERSITYPRESS
Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo
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/9780521852494
©W.N.CottinghamandD.A.Greenwood2007
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 2007
ISBN-13 978-0-511-27377-3 eBook (EBL)
ISBN-10 0-511-27377-0 eBook (EBL)
ISBN-13 978-0-521-85249-4 hardback
ISBN-10 0-521-85249-8 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
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Contents
Prefacetothesecondedition page xi
Prefacetothefirstedition xiii
Notation xv
1 Theparticlephysicist’sviewofNature 1
1.1 Introduction 1
1.2 TheconstructionoftheStandardModel 2
1.3 Leptons 3
1.4 Quarksandsystemsofquarks 4
1.5 Spectroscopyofsystemsoflightquarks 5
1.6 Morequarks 10
1.7 Quarkcolour 11
1.8 Electronscatteringfromnucleons 16
1.9 Particleaccelerators 17
1.10 Units 18
2 Lorentztransformations 20
2.1 Rotations,boostsandproperLorentztransformations 20
2.2 Scalars,contravariantandcovariantfour-vectors 22
2.3 Fields 23
2.4 TheLevi–Civitatensor 24
2.5 Timereversalandspaceinversion 25
3 TheLagrangianformulationofmechanics 27
3.1 Hamilton’sprinciple 27
3.2 Conservationofenergy 29
3.3 Continuoussystems 30
3.4 ALorentzcovariantfieldtheory 32
3.5 TheKlein–Gordonequation 33
3.6 Theenergy–momentumtensor 34
3.7 Complexscalarfields 36
v
vi Contents
4 Classicalelectromagnetism 38
4.1 Maxwell’sequations 38
4.2 ALagrangiandensityforelectromagnetism 39
4.3 Gaugetransformations 40
4.4 SolutionsofMaxwell’sequations 41
4.5 Spaceinversion 42
4.6 Chargeconjugation 44
4.7 Intrinsicangularmomentumofthephoton 44
4.8 Theenergydensityoftheelectromagneticfield 45
4.9 Massivevectorfields 46
5 TheDiracequationandtheDiracfield 49
5.1 TheDiracequation 49
5.2 LorentztransformationsandLorentzinvariance 51
5.3 Theparitytransformation 54
5.4 Spinors 54
5.5 Thematrices(cid:1)(cid:2) 55
5.6 MakingtheLagrangiandensityreal 56
6 FreespacesolutionsoftheDiracequation 58
6.1 ADiracparticleatrest 58
6.2 TheintrinsicspinofaDiracparticle 59
6.3 Planewavesandhelicity 60
6.4 Negativeenergysolutions 62
6.5 TheenergyandmomentumoftheDiracfield 63
6.6 DiracandMajoranafields 65
6.7 TheE>>mlimit,neutrinos 65
7 Electrodynamics 67
7.1 Probabilitydensityandprobabilitycurrent 67
7.2 TheDiracequationwithanelectromagneticfield 68
7.3 Gaugetransformationsandsymmetry 70
7.4 Chargeconjugation 71
7.5 Theelectrodynamicsofachargedscalarfield 73
7.6 ParticlesatlowenergiesandtheDiracmagneticmoment 73
8 Quantisingfields:QED 77
8.1 Bosonandfermionfieldquantisation 77
8.2 Timedependence 80
8.3 Perturbationtheory 81
8.4 Renornmalisationandrenormalisablefieldtheories 83
8.5 Themagneticmomentoftheelectron 87
8.6 QuantisationintheStandardModel 89
Contents vii
9 Theweakinteraction:lowenergyphenomenology 91
9.1 Nuclearbetadecay 91
9.2 Piondecay 93
9.3 Conservationofleptonnumber 95
9.4 Muondecay 96
9.5 Theinteractionsofmuonneutrinoswithelectrons 98
10 Symmetrybreakinginmodeltheories 102
10.1 GlobalsymmetrybreakingandGoldstonebosons 102
10.2 LocalsymmetrybreakingandtheHiggsboson 104
11 Massivegaugefields 107
11.1 SU(2)symmetry 107
11.2 Thegaugefields 109
11.3 BreakingtheSU(2)symmetry 111
11.4 Identificationofthefields 113
12 TheWeinberg–Salamelectroweaktheoryforleptons 117
12.1 LeptondoubletsandtheWeinberg–Salamtheory 117
12.2 LeptoncouplingtotheW± 120
12.3 LeptoncouplingtotheZ 121
12.4 Conservationofleptonnumberandconservationofcharge 122
12.5 CPsymmetry 123
12.6 MasstermsinL:anattemptedgeneralisation 125
13 ExperimentaltestsoftheWeinberg–Salamtheory 128
13.1 Thesearchforthegaugebosons 128
13.2 TheW± bosons 129
13.3 TheZboson 130
13.4 Thenumberofleptonfamilies 131
13.5 Themeasurementofpartialwidths 132
13.6 Left–rightproductioncross-sectionasymmetryandlepton
decayasymmetryoftheZboson 133
14 Theelectromagneticandweakinteractionsofquarks 137
14.1 ConstructionoftheLagrangiandensity 137
14.2 QuarkmassesandtheKobayashi–Maskawamixingmatrix 139
14.3 TheparameterisationoftheKMmatrix 142
14.4 CPsymmetryandtheKMmatrix 143
14.5 Theweakinteractioninthelowenergylimit 144
15 ThehadronicdecaysoftheZandWbosons 147
15.1 HadronicdecaysoftheZ 147
15.2 Asymmetryinquarkproduction 149
15.3 HadronicdecaysoftheW± 150
viii Contents
16 Thetheoryofstronginteractions:quantumchromodynamics 153
16.1 AlocalSU(3)gaugetheory 153
16.2 Colourgaugetransformationsonbaryonsandmesons 156
16.3 LatticeQCDandasymptoticfreedom 158
16.4 Thequark–antiquarkinteractionatshortdistances 161
16.5 Theconservationofquarks 162
16.6 Isospinsymmetry 162
16.7 Chiralsymmetry 164
17 Quantumchromodynamics:calculations 166
17.1 LatticeQCDandconfinement 166
17.2 LatticeQCDandhadrons 169
17.3 PerturbativeQCDanddeepinelasticscattering 171
+ −
17.4 PerturbativeQCDande e colliderphysics 173
18 TheKobayashi–Maskawamatrix 176
18.1 Leptonicweakdecaysofhadrons 176
18.2 |V |andnuclear(cid:3)decay 178
ud
18.3 Moreleptonicdecays 179
18.4 CPsymmetryviolationinneutralkaondecays 180
18.5 BmesondecaysandBo,B¯o mixing 182
18.6 TheCPTtheorem 183
19 Neutrinomassesandmixing 185
19.1 Neutrinomasses 185
19.2 Theweakcurrents 186
19.3 Neutrinooscillations 187
19.4 TheMSWeffect 190
19.5 NeutrinomassesandtheStandardMoael 191
19.6 ParameterisationofU 191
19.7 Leptonnumberconservation 192
19.8 Sterileneutrinos 193
20 Neutrinomassesandmixing:experimentalresults 194
20.1 Introduction 194
20.2 K2K 196
20.3 Chooz 198
20.4 KamLAND 198
20.5 Atmosphericneutrinos 200
20.6 Solarneutrinos 200
20.7 SolarMSWeffects 203
20.8 Futureprospects 204
21 Majorananeutrinos 206
21.1 Majorananeutrinofields 206
