Table Of ContentWEAK SCALE SUPERSYMMETRY
FromSuperfieldstoScatteringEvents
Supersymmetryhasbeenproposedasanewsymmetryofnature.Supersymmetric
models of particle physics predict new superpartner matter states for each known
particleintheStandardModel.Theexistenceofsuchsuperpartnerswillhavewide-
rangingimplications,fromtheearlyhistoryoftheUniversetowhatisobservedat
highenergyacceleratorssuchasCERN’sLHC.
Inthistext,theauthorsdeveloptheconceptsofsupersymmetryfromfirstprin-
ciples, and show how it can be incorporated into a theoretical framework for de-
scribingunifiedtheoriesofelementaryparticles.Theydevelopthetechnicaltools
of supersymmetry using four-component spinor notation familiar to high energy
experimentalistsandphenomenologists.Thetexttakesthereaderfromanabstract
formalism to a straightforward recipe for writing supersymmetric gauge theories
of particle physics, and ultimately to the calculation of cross sections and decay
rates necessary for practical applications to experiments both at colliders and for
cosmology.
This advanced text is a comprehensive, practical, and accessible introduction
to supersymmetry for experimental and phenomenological particle physicists and
graduatesstudyingsupersymmetry.SomefamiliaritywiththeStandardModeland
tree-level calculations in quantum field theory is required. Exercises and worked
examplesthatsupplementandclarifythematerialareinterspersedthroughout.
This title, first published in 2007, has been reissued as an Open
Access publication on Cambridge Core.
Howard Baer is currently the J. D. Kimel Professor of Physics at Florida
State University. He received his Ph.D. in theoretical physics from the University
of Wisconsin in 1984 and has held postdoctoral appointments at the European
LaboratoryforParticlePhysics(CERN),ArgonneNationalLaboratory,andFlorida
State University. Dr. Baer is a Fellow of the American Physical Society. He has
publishedoverahundredarticlesonthephysicsofelementaryparticles.
Xerxes TataisaprofessorintheDepartmentofPhysicsandAstronomy,Uni-
versity of Hawaii. He received his Ph.D. in theoretical high energy physics from
theUniversityofTexasatAustin.HehasdonepostdoctoralworkattheUniversity
ofOregon,theEuropeanLaboratoryforParticlePhysics(CERN),andtheUniver-
sityofWisconsin.HewasalsoavisitingscientistattheHighEnergyAccelerator
ResearchOrganization(KEK),Japan.HejoinedtheUniversityofHawaiiin1988.
Dr.Tatahaspublishedoverahundredresearcharticlesinhighenergyphysics,and
isaFellowoftheAmericanPhysicalSociety.
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WEAK SCALE SUPERSYMMETRY
From Superfields to Scattering Events
HOWARD BAER
FloridaStateUniversity
XERXES TATA
UniversityofHawaii
Published online by Cambridge University Press
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Information on this title: www.cambridge.org/9781009289849
DOI: 10.1017/9781009289801
© Howard Baer and Xerxes Tata 2022
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ToAdrienneandKalpana,Madeleine,Kashmira,andJake
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Contents
Preface pagexiv
1 TheStandardModel 1
1.1 Gaugeinvariance 1
1.2 Spontaneoussymmetrybreaking 3
1.3 BriefreviewoftheStandardModel 6
1.3.1 QCD 6
1.3.2 Theelectroweakmodel 6
2 WhatliesbeyondtheStandardModel? 11
2.1 Scalarfieldsandquadraticdivergences 12
2.2 WhyistheTeVscalespecial? 14
2.3 WhatcouldtheNewPhysicsbe? 16
3 TheWess–Zuminomodel 23
3.1 TheWess–ZuminoLagrangian 23
3.1.1 Thefieldcontent 23
3.1.2 SUSYtransformationsandinvarianceoftheaction 25
3.1.3 Thechiralmultiplet 28
3.1.4 AlgebraoftheSUSYcharges 29
3.2 QuantizationoftheWZmodel 32
3.3 InteractionsintheWZmodel 35
3.4 Cancellationofquadraticdivergences 36
3.5 Softsupersymmetrybreaking 39
4 Thesupersymmetryalgebra 41
4.1 Rotations 41
4.2 TheLorentzgroup 42
4.3 ThePoincare´ group 44
4.4 Thesupersymmetryalgebra 46
5 Superfieldformalism 49
5.1 Superfields 49
vii
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viii Contents
5.2 Representationsofsymmetrygenerators:arecap 52
5.3 RepresentationofSUSYgeneratorsasdifferentialoperators 54
5.4 Usefulθ identities 56
5.5 SUSYtransformationsofsuperfields 58
5.6 IrreducibleSUSYmultiplets 60
5.6.1 Left-chiralscalarsuperfields 61
5.6.2 Right-chiralscalarsuperfields 63
5.6.3 Thecurlsuperfield 64
5.7 Productsofsuperfields 64
5.8 Supercovariantderivatives 65
5.9 Lagrangiansforchiralscalarsuperfields 68
5.9.1 Ka¨hlerpotentialcontributionstotheLagrangiandensity 70
5.9.2 SuperpotentialcontributionstotheLagrangiandensity 72
5.9.3 Atechnicalaside 74
5.9.4 AmasterLagrangianforchiralscalarsuperfields 75
5.10 Theactionasanintegraloversuperspace 76
6 Supersymmetricgaugetheories 79
6.1 Gaugetransformationsofsuperfields 79
6.2 TheWess–Zuminogauge 84
6.2.1 Abeliangaugetransformations 84
6.2.2 Non-Abeliangaugetransformations 86
6.3 ThecurlsuperfieldintheWess–Zuminogauge 89
6.4 Constructionofgaugekineticterms 92
6.5 Couplingchiralscalartogaugesuperfields 95
6.5.1 Fayet–Iliopoulos D-term 98
6.6 AmasterLagrangianforSUSYgaugetheories 98
6.7 Thenon-renormalizationtheorem 104
7 Supersymmetrybreaking 105
7.1 SUSYbreakingbyelementaryfields 106
7.2 F-typeSUSYbreaking:theO’Raifeartaighmodel 107
7.2.1 Massspectrum:CaseA 109
7.2.2 Massspectrum:CaseB 111
7.3 D-typeSUSYbreaking 113
7.3.1 CaseA 114
7.3.2 CaseB 114
7.4 Compositegoldstinos 115
7.5 Gauginocondensation 116
7.6 Goldstinointeractions 117
7.7 Amasssumrule 118
7.7.1 Scalarcontributions 118
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Contents ix
7.7.2 Vectorcontributions 119
7.7.3 Fermioncontributions 119
7.8 Explicitsupersymmetrybreaking 121
7.9 Atechnicalaside:γ -dependentfermionmassmatrices 124
5
8 TheMinimalSupersymmetricStandardModel 127
8.1 ConstructingtheMSSM 127
8.1.1 ParameterspaceoftheMSSM 134
8.1.2 Asimplifiedparameterspace 136
8.2 Electroweaksymmetrybreaking 138
8.3 ParticlemassesintheMSSM 141
8.3.1 Gaugebosons 141
8.3.2 Matterfermions 142
8.3.3 Higgsbosons 144
8.3.4 Gluinos 148
8.3.5 Charginosandneutralinos 149
8.3.6 Squarksandsleptons 155
8.4 InteractionsintheMSSM 161
8.4.1 QCDinteractionsintheMSSM 161
8.4.2 ElectroweakinteractionsintheMSSM 164
8.4.3 InteractionsofMSSMHiggsbosons 174
8.5 Radiativecorrections 184
8.5.1 Higgsbosonmasses 184
8.5.2 Squarkmass 187
8.5.3 Charginoandneutralinomasses 187
8.5.4 YukawacouplingsandSMfermionmasses 188
8.6 ShouldthegoldstinobepartoftheMSSM? 188
9 ImplicationsoftheMSSM 190
9.1 LowenergyconstraintsontheMSSM 191
9.1.1 TheSUSYflavorproblem 191
9.1.2 TheSUSYCP violationproblem 195
9.1.3 LargeCP-violatingparametersintheMSSM? 196
9.2 Renormalizationgroupequations 199
9.2.1 Gaugecouplingsandunification 199
9.2.2 EvolutionofsoftSUSYbreakingparameters 204
9.2.3 Radiativebreakingofelectroweaksymmetry 209
9.2.4 Naturalnessconstraintonsuperparticlemasses 211
9.3 Constraintsfromb → sγ decay 214
9.4 B → μ+μ− decay 217
s
9.5 Muonanomalousmagneticmoment 220
9.6 Cosmologicalimplications 221
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