Supersymmetry in particle physics: an elementary introduction

238 Pages·2007·0.935 MB·English

by  Ian Aitchison

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SUPERSYMMETRY IN PARTICLE PHYSICS
Supersymmetry has been a central topic in particle physics since the early 1980s,
and represents the culmination of the search for fundamental symmetries that has
dominated particle physics for the last 50 years. Traditionally, the constituents
of matter (fermions) have been regarded as essentially different from the parti-
cles (bosons) that transmit the forces between them. In supersymmetry, however,
fermionsandbosonsareunified.
Thisisthefirsttextbooktoprovideasimplepedagogicalintroductiontowhathas
been a formidably technical field. The elementary and practical treatment brings
readerstothefrontierofcontemporaryresearch,inparticular,totheconfrontation
with experiments at the Large Hadron Collider. Intended primarily for first-year
graduate students in particle physics, both experimental and theoretical, this vol-
ume will also be of value to researchers in experimental and phenomenological
supersymmetry.Supersymmetrictheoriesareconstructedthroughanintuitive‘trial
anderror’approach,ratherthanbeingformalanddeductive.Thebasicelementsof
spinor formalism and superfields are introduced, allowing readers to access more
advanced treatments. Emphasis is placed on physical understanding, and on de-
tailed,explicitderivationsofallimportantsteps.Manyshortexercisesareincluded
makingforavaluableandaccessibleself-studytool.
Ian Aitchison is Emeritus Professor of Physics at the University of Oxford.
Hisresearchinterestsincludetime-dependenteffectivetheoriesofsuperconductors,
fieldtheoriesatfinitetemperatureandtopologicalaspectsofgaugetheories.

SUPERSYMMETRY IN
PARTICLE PHYSICS
An Elementary Introduction
IAN J. R. AITCHISON
DepartmentofPhysics,UniversityofOxford,
TheRudolfPeierlsCentreforTheoreticalPhysics
and
StanfordLinearAcceleratorCenter,
StanfordUniversity
CAMBRIDGEUNIVERSITYPRESS
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Published in the United States of America by Cambridge University Press, New York
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© I. Aitchison 2007
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-13 978-0-511-35460-1 eBook (EBL)
ISBN-10 0-511-35460-6 eBook (EBL)
ISBN-13 978-0-521-88023-7 hardback
ISBN-10 0-521-88023-8 hardback
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ForDanny

Contents
Preface pageix
Acknowledgements xiii
1 Introductionandmotivation 1
1.1 TheSMfine-tuningproblem 3
1.2 Threequantitativeindications 11
1.3 Theoreticalconsiderations 12
2 Spinors:Weyl,DiracandMajorana 16
2.1 SpinorsandLorentztransformations 18
2.2 Constructinginvariantsand4-vectorsoutof2-component
(Weyl)spinors 21
2.3 AmorestreamlinednotationforWeylspinors 25
2.4 Diracspinorsusingχ-(orL-)typespinorsonly 31
2.5 Majoranaspinors 33
3 IntroductiontosupersymmetryandtheMSSM 41
3.1 Simplesupersymmetry 41
3.2 AfirstglanceattheMSSM 47
4 Thesupersymmetryalgebraandsupermultiplets 50
4.1 OnewayofobtainingtheSU(2)algebra 50
4.2 Supersymmetrygenerators(‘charges’)andtheiralgebra 53
4.3 Thesupersymmetrycurrent 58
4.4 Supermultiplets 61
4.5 Asnag,andtheneedforasignificantcomplication 65
5 TheWess–Zuminomodel 70
5.1 Interactionsandthesuperpotential 70
5.2 CancellationofquadraticdivergencesintheW–Zmodel 77
6 Superfields 88
6.1 SUSYtransformationsonfields 88
6.2 AdifferentialoperatorrepresentationoftheSUSYgenerators 93
vii
viii Contents
6.3 Chiralsuperfields,andtheir(chiral)componentfields 95
6.4 Productsofchiralsuperfields 97
6.5 Atechnicalannexe:otherformsofchiralsuperfield 100
7 Vector(orgauge)supermultiplets 106
7.1 ThefreeAbeliangaugesupermultiplet 106
7.2 Non-Abeliangaugesupermultiplets 109
7.3 Combiningchiralandgaugesupermultiplets 112
8 TheMSSM 120
8.1 Specificationofthesuperpotential 120
8.2 TheSMinteractionsintheMSSM 125
8.3 GaugecouplingunificationintheMSSM 129
8.4 R-parity 135
9 SUSYbreaking 137
9.1 BreakingSUSYspontaneously 137
9.2 SoftSUSY-breakingterms 144
9.3 RGEevolutionoftheparametersinthe(softlybroken)MSSM 149
10 TheHiggssectorandelectroweaksymmetrybreakingintheMSSM 154
10.1 Thescalarpotentialandtheconditionsfor
electroweaksymmetrybreaking 154
10.2 Thetree-levelmassesofthescalarHiggsstatesintheMSSM 158
10.3 TheSMfine-tuningproblemrevisited,intheMSSM 164
10.4 Tree-levelcouplingsofneutralHiggsbosonstoSMparticles 166
11 SparticlemassesintheMSSM 173
11.1 Gluinos 173
11.2 Neutralinos 174
11.3 Charginos 177
11.4 Squarksandsleptons 179
12 Somesimpletree-levelcalculationsintheMSSM 185
12.1 Sparticledecays 185
12.2 Sparticleproductionprocesses 195
12.3 Signaturesandsearches 208
12.4 BenchmarksforSUSYsearches 210
References 214
Index 219