Elementary Particle Physics: Foundations of the Standard Model V2

647 Pages·2013·14.915 MB·English

by  Yorikiyo Nagashima

YorikiyoNagashima
ElementaryParticlePhysics
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Yorikiyo Nagashima
Elementary Particle Physics
Volume 2: Foundations of the Standard Model
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V
Contents
Preface XI
Acknowledgments XV
ColorPlates XVII
PartOne ElectroweakDynamics 1
1 TheStandardModel 3
1.1 Introduction 3
1.2 WeakChargeandSU(2)(cid:1)U(1)Symmetry 4
1.3 SpontaneousSymmetryBreaking 10
1.3.1 AnIntuitivePictureofSpontaneousSymmetryBreaking 10
1.3.2 HiggsMechanism 12
1.3.3 UnitaryGauge 14
1.3.4 MassGeneration 15
1.4 GaugeInteractions 18
1.5 HiggsInteractions 22
1.6 FeynmanRulesofElectroweakTheory 23
1.7 RolesoftheHiggsinGaugeTheory 28
2 NeutralCurrent 39
2.1 DiscoveryoftheNeutralCurrent 39
2.2 ν(cid:2)eScattering 41
2.3 νN ! νCX 49
2.4 ParityViolationintheElectromagneticProcesses 54
2.4.1 AtomicProcess 54
2.4.2 Polarizede(cid:2)D Scattering 58
2.5 ElectroweakUnificationatHighQ2 64
2.6 Asymmetryinthee(cid:1)eC ! ll,cc,bb 66
2.7 AsymmetryinqCq! lCl 76
3 W 81
3.1 DiscoveryofW,Z 81
3.2 BasicFormulas 87
3.2.1 DecayWidth 87
VI Contents
3.2.2 HadronicProductionof W,Z 89
3.3 PropertiesofW 93
3.3.1 AsymmetryofDecayLeptonsfromW,Z 93
3.3.2 SpinofW,Z 95
3.3.3 MassofW 96
3.3.4 DecayWidthofW 99
3.3.5 TripleGaugeCoupling 103
4 PhysicsatZResonance 109
4.1 BornApproximation 110
4.2 ImprovedBornApproximation 114
4.3 ExperimentalArrangements 125
4.3.1 Detectors 125
4.3.2 LuminosityMonitor 127
4.3.3 EnergyDetermination 128
4.3.4 HeavyQuarkTagging 135
4.4 Observations 142
4.4.1 EventCharacteristics 142
4.4.2 Mass,WidthsandBranchingRatios 143
4.4.3 InvisibleWidth 145
4.4.4 Asymmetries 147
4.5 WeinbergAngleand(cid:1)Parameter 155
5 PrecisionTestsoftheElectroweakTheory 157
5.1 InputParameters 157
5.2 Renormalization 161
5.2.1 Prescription 161
5.2.2 Self-EnergyofGaugeBosons 164
5.3 µDecay 170
5.3.1 ∆r,(cid:1),∆α 170
5.3.2 RunningElectromagneticConstant 174
5.3.3 ResidualCorrectionsandNumericalEvaluation 175
5.4 ImprovedBornApproximation 176
5.4.1 γ(cid:2)Z Mixing 177
5.4.2 αorG ? 178
F
5.4.3 VertexCorrection 180
5.5 EffectiveWeinbergAngle 181
5.6 WeinbergAngleintheMS Scheme 182
5.7 BeyondtheStandardModel 187
6 Cabibbo–Kobayashi–MaskawaMatrix 193
6.1 OriginoftheCKMMatrix 193
6.2 CKMMatrixElements 198
6.3 TheUnitarityTriangle 205
6.4 FormalismoftheTwoNeutralMesonSystem 207
6.4.1 MassMatrix,MixingandCPParameters 207
Contents VII
6.4.2 CPParametersoftheKMeson 210
6.4.3 MixingintheB0(cid:2)B0System 211
6.4.4 D0(cid:2)D0Mixing 220
6.5 TheoreticalEvaluationoftheMassMatrix 224
6.5.1 MassMatrixoftheKMeson 225
6.5.2 MassMatrixoftheBMeson 229
6.6 CPViolationintheBSector 232
6.6.1 IndirectCPViolation 232
6.6.2 DirectCPViolation 233
6.6.3 CPViolationinInterference 238
6.6.4 CoherentB0B0Production 240
6.7 ExtractionoftheCKMPhases 246
6.7.1 UsingB0(cid:2)B Mixing 246
6.7.2 PenguinPollution 248
6.7.3 ExperimentsattheB-factory 249
6.8 TestofUnitarity 253
6.8.1 RareDecaysoftheKMeson 253
6.8.2 GlobalFitoftheUnitarityTriangle 256
6.9 CPViolationbeyondtheStandardModel 257
PartTwo QCDDynamics 259
7 QCD 261
7.1 FundamentalsofQCD 264
7.1.1 Lagrangian 264
7.1.2 TheFeynmanRules 267
7.1.3 GaugeInvarianceandtheGluonSelf-Coupling 269
7.1.4 StrengthoftheColorCharge 272
7.1.5 QCDVacuum 274
7.2 RenormalizationGroupEquation 279
7.2.1 RunningCouplingConstant 279
7.2.2 AsymptoticFreedom 282
7.2.3 ScaleDependenceofObservables 286
7.2.4 RunningMass 289
7.2.5 QuarkMasses 294
7.3 GluonEmission 296
7.3.1 EmissionProbability 297
7.3.2 CollinearandInfraredDivergence 301
7.3.3 LeadingLogarithmicApproximation 303
7.3.4 TransverseKick 305
8 DeepInelasticScattering 307
8.1 Introduction 307
8.2 ThePartonModelRevisited 311
8.2.1 StructureFunctions 314
8.2.2 EquivalentPhotons 317
VIII Contents
8.3 QCDCorrections 319
8.3.1 VirtualComptonScattering 319
8.3.2 Factorization 321
8.3.3 PowerExpansionoftheEvolutionEquation 326
8.3.4 CascadeBranchingofthePartons 328
8.4 DGLAPEvolutionEquation 330
8.4.1 GluonDistributionFunction 330
8.4.2 RegularizationoftheSplittingFunction 332
8.4.3 FactorizationScheme 335
8.5 SolutionstotheDGLAPEquation 337
8.5.1 MethodofMoments 337
8.5.2 DoubleLogarithm 343
8.5.3 MonteCarloGenerators 347
8.6 Drell–YanProcess 351
8.6.1 FactorizationinHadronScattering 358
9 JetsandFragmentations 361
9.1 PartonsandJets 361
9.1.1 FragmentationFunction 363
9.1.2 JetShapeVariables 367
9.1.3 ApplicationsofJetVariables 372
9.1.4 JetSeparation 375
9.2 PartonShowerModel 380
9.3 HadronizationModels 384
9.3.1 IndependentFragmentationModel 385
9.3.2 StringModel 389
9.3.3 ClusterModel 392
9.3.4 ModelTests 393
9.4 TestoftheAsymptoticFreedom 398
9.4.1 InclusiveReactions 398
9.4.2 JetEventShapes 408
9.4.3 SummaryoftheRunningα (Q2) 415
s
10 Gluons 417
10.1 GaugeStructureofQCD 417
10.1.1 SpinoftheGluon 417
10.1.2 Self-CouplingoftheGluon 421
10.1.3 SymmetryofQCD 423
10.2 ColorCoherence 424
10.2.1 AngularOrdering 425
10.2.2 StringEffect 428
10.3 FragmentationatSmallx 430
10.3.1 DGLAPEquationwithAngularOrdering 430
p
10.3.2 α DependenceandN D1PoleintheAnomalousMoment 433
s
10.3.3 MultiplicityDistribution 434
10.3.4 HumpbackDistribution:MLLA 435
Contents IX
10.4 GluonFragmentationFunction 441
10.5 GluonJetsvs.QuarkJets 445
11 JetsinHadronReactions 451
11.1 Introduction 451
11.2 JetProductionwithLarge p 452
T
11.3 2!2Reaction 456
11.3.1 KinematicsandCrossSection 456
11.3.2 JetProductionsComparedwithpQCD 460
11.4 JetClusteringinHadronicReactions 464
11.4.1 ConeAlgorithm 466
11.4.2 k Algorithm 468
T
11.5 ReproducibilityoftheCrossSection 469
11.5.1 ScaleDependence 469
11.5.2 PartonDistributionFunction 470
11.6 MultijetProductions 472
11.7 SubstructureofthePartons? 474
11.8 VectorParticleProduction 475
11.8.1 DirectPhotonProduction 476
11.8.2 W: p Distribution 479
T
11.9 HeavyQuarkProduction 484
11.9.1 CrossSections 484
11.9.2 ComparisonswithExperiments 489
11.9.3 TopQuarkProduction 496
AppendixA GammaMatrixTracesandCrossSections 501
AppendixB FeynmanRulesfortheElectroweakTheory 507
AppendixC RadiativeCorrectionstotheGaugeBosonSelf-Energy 513
AppendixD ’tHooft’sGauge 525
AppendixE FierzTransformation 531
AppendixF Collins–SoperFrame 535
AppendixG MultipoleExpansionoftheVertexFunction 537
AppendixH SU(N) 543
AppendixI UnitarityRelation 551
AppendixJ σModelandtheChiralPerturbationTheory 563
AppendixK SplittingFunction 573
AppendixL AnswerstotheProblems 583
References 591
Index 607