The Standard Model and Beyond (Series in High Energy Physics, Cosmology and Gravitation)

651 Pages·2017·6.828 MB·English

by  Paul Langacker

The Standard Model
and Beyond
S E C ON D E DI T ION
Series in High Energy Physics, Cosmology, and Gravitation
Series Editors: Brian Foster, Oxford University, UK
Edward W Kolb, Fermi National Accelerator Laboratory, USA
This series of books covers all aspects of theoretical and experimental high energy physics,
cosmology and gravitation and the interface between them. In recent years the fields of particle
physics and astrophysics have become increasingly interdependent and the aim of this series
is to provide a library of books to meet the needs of students and researchers in these fields.
Other recent books in the series:
The Standard Model and Beyond, Second Edition
Paul Langacker
An Introduction to Beam Physics
Martin Berz, Kyoko Makino, and Weishi Wan
Neutrino Physics, Second Edition
K Zuber
Group Theory for the Standard Model of Particle Physics and Beyond
Ken J Barnes
The Standard Model and Beyond
Paul Langacker
Particle and Astroparticle Physics
Utpal Sakar
Joint Evolution of Black Holes and Galaxies
M Colpi, V Gorini, F Haardt, and U Moschella (Eds)
Gravitation: From the Hubble Length to the Planck Length
I Ciufolini, E Coccia, V Gorini, R Peron, and N Vittorio (Eds)
The Galactic Black Hole: Lectures on General Relativity and Astrophysics
H Falcke, and F Hehl (Eds)
The Mathematical Theory of Cosmic Strings: Cosmic Strings in the Wire Approximation
M R Anderson
Geometry and Physics of Branes
U Bruzzo, V Gorini, and U Moschella (Eds)
Modern Cosmology
S Bonometto, V Gorini, and U Moschella (Eds)
Gravitation and Gauge Symmetries
M Blagojevic
Gravitational Waves
I Ciufolini, V Gorini, U Moschella, and P Fré (Eds)
Series in High Energy Physics, Cosmology, and Gravitation
The Standard Model
and Beyond
S E C ON D E DI T ION
Paul Langacker
Institute for Advanced Study
Princeton, New Jersey, USA
CRC Press
Taylor & Francis Group
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Boca Raton, FL 33487-2742
© 2017 by Taylor & Francis Group, LLC
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Printed on acid-free paper
Version Date: 20170509
International Standard Book Number-13: 978-1-4987-6321-9 (Hardback)
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Library of Congress Cataloging-in-Publication Data
Names: Langacker, P., author.
Title: The standard model and beyond / Paul Langacker.
Other titles: Series in high energy physics, cosmology, and gravitation.
Description: Second edition. | Boca Raton, FL : CRC Press, Taylor & Francis
Group, [2017] | Series: Series in high energy physics, cosmology and
gravitation | Includes bibliographical references and index.
Identifiers: LCCN 2016057676| ISBN 9781498763219 (hardback ; alk. paper) |
ISBN 1498763219 (hardback ; alk. paper) | ISBN 9781315170626 (e-book) |
ISBN 1315170620 (e-book)
Subjects: LCSH: Standard model (Nuclear physics)
Classification: LCC QC794.6.S75 L36 2017 | DDC 539.7/2--dc23
LC record available at https://lccn.loc.gov/2016057676
Visit the Taylor & Francis Web site at
http://www.taylorandfrancis.com
and the CRC Press Web site at
http://www.crcpress.com
Contents
Preface xi
hapter
C 1(cid:4) Notation and Conventions 1
1.1 PROBLEMS 5
hapter
C 2(cid:4) Review of Perturbative Field Theory 7
2.1 CREATIONANDANNIHILATIONOPERATORS 7
2.2 LAGRANGIANFIELDTHEORY 9
2.3 THEHERMITIANSCALARFIELD 9
2.3.1 The Lagrangian and Equations of Motion 10
2.3.2 The Free Hermitian Scalar Field 10
2.3.3 The Feynman Rules 11
2.3.4 Kinematics and the Mandelstam Variables 13
2.3.5 The Cross Section and Decay Rate Formulae 15
2.3.6 Loop E(cid:11)ects 21
2.4 THECOMPLEXSCALARFIELD 23
2.4.1 U(1) Phase Symmetry and the Noether Theorem 24
2.5 ELECTROMAGNETICANDVECTORFIELDS 26
2.5.1 Massive Neutral Vector Field 28
2.6 ELECTROMAGNETICINTERACTIONOFCHARGEDPIONS 29
2.7 THEDIRACFIELD 34
2.7.1 The Free Dirac Field 35
2.7.2 Dirac Matrices and Spinors 36
2.8 QEDFORELECTRONSANDPOSITRONS 43
2.9 SPINEFFECTSANDSPINORCALCULATIONS 48
2.10 THEDISCRETESYMMETRIESP,C,CP,T,ANDCPT 49
2.11 TWO-COMPONENTNOTATIONANDINDEPENDENTFIELDS 60
2.12 QUANTUMELECTRODYNAMICS(QED) 63
2.12.1 Higher-Order E(cid:11)ects 63
2.12.2 The Running Coupling 66
2.12.3 Tests of QED 69
2.12.4 The Role of the Strong Interactions 74
2.13 OPERATORDIMENSIONSANDCLASSIFICATION 80
v
vi Contents
2.14 MASSANDKINETICMIXING 80
2.15 PROBLEMS 82
hapter
C 3(cid:4) Lie Groups, Lie Algebras, and Symmetries 89
3.1 BASICCONCEPTS 89
3.1.1 Groups and Representations 89
3.1.2 Examples of Lie Groups 91
3.1.3 More on Representations and Groups 92
3.2 GLOBALSYMMETRIESINFIELDTHEORY 96
3.2.1 Transformation of Fields and States 96
3.2.2 Invariance (Symmetry) and the Noether Theorem 98
3.2.3 Isospin and SU(3) Symmetries 103
3.2.4 Chiral Symmetries 111
3.2.5 Discrete Symmetries 113
3.3 SYMMETRYBREAKINGANDREALIZATION 114
3.3.1 A Single Hermitian Scalar 114
3.3.2 A Digression on Topological Defects 117
3.3.3 A Complex Scalar: Explicit and Spontaneous Symmetry
Breaking 117
3.3.4 Spontaneously Broken Chiral Symmetry 120
3.3.5 Field Rede(cid:12)nition 121
3.3.6 The Nambu-Goldstone Theorem 122
3.3.7 Boundedness of the Potential 124
3.3.8 Example: Two Complex Scalars 125
3.4 PROBLEMS 127
hapter
C 4(cid:4) Gauge Theories 135
4.1 THEABELIANCASE 136
4.2 NON-ABELIANGAUGETHEORIES 137
4.3 THEHIGGSMECHANISM 141
4.4 THER GAUGES 144
(cid:24)
4.5 ANOMALIES 151
4.6 PROBLEMS 153
hapter
C 5(cid:4) The Strong Interactions and QCD 157
5.1 THEQCDLAGRANGIAN 159
5.2 EVIDENCEFORQCD 161
5.3 SIMPLEQCDPROCESSES 165
5.4 THERUNNINGCOUPLINGINNON-ABELIANTHEORIES 170
5.4.1 The RGE Equations for an Arbitrary Gauge Theory 170
5.5 DEEPINELASTICSCATTERING 173
Contents vii
5.5.1 Deep Inelastic Kinematics 173
5.5.2 The Cross Section and Structure Functions 175
5.5.3 The Simple Quark Parton Model (SPM) 178
5.5.4 Corrections to the Simple Parton Model 182
5.6 OTHERSHORTDISTANCEPROCESSES 186
5.7 THESTRONGINTERACTIONSATLONGDISTANCES 187
5.8 THESYMMETRIESOFQCD 188
5.8.1 Continuous Flavor Symmetries 188
5.8.2 The (3(cid:3);3)+(3;3(cid:3)) Model 190
5.8.3 The Axial U(1) Problem 194
5.8.4 The Linear (cid:27) Model 197
5.8.5 The Nonlinear (cid:27) Model 199
5.9 OTHERTOPICS 200
5.10 PROBLEMS 201
hapter
C 6(cid:4) Collider Physics 205
6.1 BASICCONCEPTS 206
6.1.1 The Cross Section and Luminosity 206
6.1.2 Collider Kinematics 208
6.1.3 Soft Processes in Hadron-Hadron Scattering 212
6.2 HADRON-HADRONSCATTERINGATSHORTDISTANCES 213
6.3 PROBLEMS 221
hapter
C 7(cid:4) The Weak Interactions 223
7.1 ORIGINSOFTHEWEAKINTERACTIONS 223
7.2 THEFERMITHEORYOFCHARGEDCURRENTWEAKINTERACTIONS 228
7.2.1 (cid:22) Decay 232
7.2.2 (cid:23) e(cid:0) (cid:23) e(cid:0) 237
e e
!
7.2.3 (cid:25) and K Decays 238
7.2.4 Nonrenormalization of Charge and the Ademollo-Gatto The-
orem 245
7.2.5 (cid:12) Decay 247
7.2.6 Hyperon Decays 251
7.2.7 Heavy Quark and Lepton Decays 252
7.3 PROBLEMS 255
hapter
C 8(cid:4) The Standard Electroweak Theory 257
8.1 THESTANDARDMODELLAGRANGIAN 257
8.2 SPONTANEOUSSYMMETRYBREAKING 261
8.2.1 The Higgs Mechanism 262
8.2.2 The Lagrangian in Unitary Gauge after SSB 263
viii Contents
8.2.3 E(cid:11)ective Theories 276
8.2.4 The R Gauges 277
(cid:24)
8.3 THEZ,THEW,ANDTHEWEAKNEUTRALCURRENT 279
8.3.1 Purely Weak Processes 280
8.3.2 Weak-Electromagnetic Interference 289
8.3.3 Implications of the WNC Experiments 296
8.3.4 Precision Tests of the Standard Model 297
8.3.5 The Z-Pole and Above 305
8.3.6 Implications of the Precision Program 314
8.4 GAUGESELF-INTERACTIONS 320
8.5 THEHIGGS 323
8.5.1 Theoretical Constraints 323
8.5.2 Higgs Properties, Searches, and Discovery 328
8.5.3 Implications of the Higgs Discovery 335
8.6 THECKMMATRIXANDCP VIOLATION 339
8.6.1 The CKM Matrix 340
8.6.2 CP Violation and the Unitarity Triangle 343
8.6.3 The Neutral Kaon System 344
8.6.4 Mixing and CP Violation in the B System 356
8.6.5 Time Reversal Violation and Electric Dipole Moments 361
8.6.6 Flavor Changing Neutral Currents (FCNC) 364
8.7 PROBLEMS 367
hapter
C 9(cid:4) Neutrino Mass and Mixing 373
9.1 BASICCONCEPTSFORNEUTRINOMASS 374
9.1.1 Active and Sterile Neutrinos 374
9.1.2 Dirac and Majorana Masses 374
9.1.3 Extension to Two or More Families 380
9.1.4 The Propagators for Majorana Fermions 384
9.2 EXPERIMENTSANDOBSERVATIONS 385
9.2.1 Neutrino Counting 385
9.2.2 Neutrino Mass Constraints 387
9.2.3 Neutrinoless Double Beta Decay 389
9.2.4 Relic Neutrinos 390
9.2.5 Electromagnetic Form Factors 390
9.3 NEUTRINOOSCILLATIONS 392
9.3.1 Oscillations in Vacuum 392
9.3.2 The Mikheyev-Smirnov-Wolfenstein (MSW) E(cid:11)ect 394
9.3.3 Oscillation Experiments 396
9.3.4 Possible Sterile Neutrinos 407
9.4 THESPECTRUM 410
Contents ix
9.5 MODELSOFNEUTRINOMASS 413
9.5.1 General Considerations 414
9.5.2 Dirac Masses 415
9.5.3 Majorana Masses 416
9.5.4 Mixed Mass Models 419
9.5.5 Textures and Family Symmetries 420
9.6 IMPLICATIONSOFNEUTRINOMASS 422
9.7 PROBLEMS 423
hapter
C 10(cid:4) Beyond the Standard Model 425
10.1 THENEEDFORNEWPHYSICS 425
10.1.1 Problems with the Standard Model 426
10.1.2 New Ingredients for Cosmology and Particles 432
10.2 SUPERSYMMETRY 438
10.2.1 Implications of Supersymmetry 439
10.2.2 Formalism 443
10.2.3 Supersymmetric Interactions 453
10.2.4 Supersymmetry Breaking and Mediation 461
10.2.5 The Minimal Supersymmetric Standard Model (MSSM) 463
10.2.6 Further Aspects of Supersymmetry 475
10.3 EXTENDEDGAUGEGROUPS 478
10.3.1 SU(2) U(1) U(1)0 Models 479
(cid:2) (cid:2)
10.3.2 SU(2) SU(2) U(1) Models 487
L R
(cid:2) (cid:2)
10.4 GRANDUNIFIEDTHEORIES(GUTS) 492
10.4.1 The SU(5) Model 493
10.4.2 Beyond the Minimal SU(5) Model 500
10.5 PROBLEMS 502
ppendix
A A(cid:4) Canonical Commutation Rules 507
ppendix
A B(cid:4) Derivation of a Simple Feynman Diagram 511
ppendix
A C(cid:4) Unitarity,thePartialWaveExpansion,andtheOptical
Theorem 513
Appendix D(cid:4) Two, Three, and n-Body Phase Space 515
ppendix
A E(cid:4) Calculation of the Anomalous Magnetic Moment of the
Electron 519
ppendix
A F(cid:4) Breit-Wigner Resonances 523