ThEORy ANCJ PhENOMENoLoqy oF
Sparticles An account of four-dimensional A/=1 supersymmetry in High Energy Physics
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ThEORy ANCI PhENOMENoloqy of
Sparticles An account of four-dimensional A/=1 supersymmetry in High Energy Physics
Manuel Drees University of Bonn
Rohini Godbole Indian Institute of Science, Bangalore
Probir Roy Tata Institute of Fundamental Research, Mumbai
\Hp World Scientific NEW JERSEY • LONDON • SINGAPORE • BEIJING • SHANGHAI • HONGKONG • TAIPEI • CHENNAI
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THEORY AND PHENOMENOLOGY OF SPARTICLES Copyright © 2004 by World Scientific Publishing Co. Pte. Ltd. All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the Publisher.
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To those of our parents who are living and the memory of those who are not.
"d-T^H, * I T % T "
"Die Theorie ist ein Werkzeug das wir durch Anwendung erproben"
' % ^ r i W F T = T ' -«h>J|K
'Die Logik der Forschung' - Karl Popper
"Truth via existence"
'The Atomic Code' - Kariada
"Theory is a tool which we test through applications" 'The logic of scientific research' - Karl Popper
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Preface Supersymmetry (or SUSY in short) is a proposed invariance under generalized spacetime transformations linking fermions and bosons. One can say without exaggeration that it is one of the most strikingly beautiful recent ideas in Physics. Ever since the codification of the spinstatistics theorem in the nineteen thirties, most physicists had developed an attitude towards fermions and bosons that can be summed up in a Kiplingesque adage: a fermion is a fermion, a boson is a boson and ne'er the twain shall meet. Supersymmetry breaks this attitude and makes them meet. It enables a fermion to transform into a boson and vice versa. It admits supermultiplets with fermionic and bosonic members. The couplings of those members get related and their masses are split by supersymmetry breaking effects. Historically, supersymmetry originated at the beginning of the nineteen seventies through aesthetic reasoning rather than from factual evidence. (Earlier formulations, motivated by hadronic resonances and strings, had not been complete). The greater ultraviolet convergence of supersymmetric field theories and the nonrenormalization of some of their couplings immediately generated much formal interest. The close link between local supersymmetry transformations and gravity also attracted a lot of attention. However, the obviously different physical properties of the known fermions and bosons made it appear initially that any connection of supersymmetry with phenomena in particle physics might be remote. Yet astonishingly, within just about a decade of its first mathematical formulation, the situation in this respect changed dramatically. A very plausible reason was found, namely the stability of the observed weak interaction scale ~ 102 GeV vis-a-vis much higher scales, for the existence of broken supersymmetry in the real world. This led to the anticipation of new sparticles, superpartners of the old particles with an intra-supermultiplet mass splitting Ma ~ 10 2 -10 3 GeV, possibly within the study reach of current or foreseeable high energy accelerators. Soon afterwards, with the birth of superstring theory, came additional theoretical motivation for supersymmetry as a low energy legacy of Planck scale physics. Three decades after the inception of supersymmetry, the literature today is flush with phenomenological papers anticipating the experimental discovery of softly broken N=l supersymmetry in the near future. The key new feature of this phenomenology is the predicted occurrence of sparticles. For each known elementary particle (including the confined quarks and gluons) there is supposedly at least one sparticle. It differs in spin from the particle by 1/2 and is endowed with opposite statistics, a mass difference of the order of Ms and couplings strictly related to the known particle couplings. When produced in the laboratory, sparticles are expected to exhibit unusual and unique kinematic behavior and decay patterns enabling the unambiguous confirmation of supersymmetry. Many calculations have been performed on sparticle production and major experiments are planned for detecting such signals. One of the major goals of the Large Hadron Collider, now being constructed in Geneva at CERN, is to discover these sparticles. Furthermore, precision study of the properties of the latter has been stated as a reason to propose the construction of high luminosity, high energy lepton colliders. Supersymmetry also enables one to connect the unification of fundamental forces at high energies with phenomena studied in the laboratory. This comes about through the extrapolation of scale dependent 'running' coupling strengths of strong, weak and electromagnetic interacvn
Vlll
Preface
tions, obtained from experiments performed at presently accessible energies, to much higher energy scales. The construction of supersymmetric grand unified theories has been an ambitious step towards the above unification. The relation between such theories and a higher dimensional superstring theory, which supposedly describes nature at and above Planckian energies (~ 10 18 GeV), has been the subject of much study too. A further possible role for supersymmetry would be in linking particle physics with large scale structure in cosmology. This is envisaged with the lightest sparticle, expected in the minimal scenario to be stable, being the leading candidate for the cold component of cosmological nonbaryonic dark matter which is supposed to constitute nearly 86% of the total mass of matter in the Universe. Supersymmetric field theories are most easily formulated in terms of spinorial supercharges. This needs an extension of our usual spacetime to superspace. In addition to the four spacetime coordinates, a pair of conjugate spinorial coordinates are included in the minimal version of superspace. The densities of the spinorial supercharge and its conjugate, which take fermions into bosons and vice versa, are generalized local functions (distributions) of superspace coordinates. Together with the generators of the Poincare group, these charges form a graded Lie algebra: the super-Poincare algebra. A supersymmetric system is one whose action is invariant under infinitesimal transformations of this algebra. Just as quantum fields can be defined in our usual spacetime, so can superfields be defined in superspace as polynomials in the spinorial coordinates with ordinary bosonic and fermionic fields as coefficients. The beauty and power of supersymmetry in a field theoretic context are best appreciated through the superfield formalism set up in superspace. Furthermore, the link between theoretical and phenomenological aspects of supersymmetry appears clearest when expressed in this language. It is this link that the present work aspires to bring into a clear view. The aim of this book is to provide the reader with an introductory, pedagogical and userfriendly treatment of those observational and unifying aspects of softly broken N=l supersymmetry in (3+1) dimensions that fall within a phenomenological ambit. However, we have tried to make it self-contained by including the requisite superfield formalism in the beginning (Part One). There are several excellent texts in the market (cited in the Bibliography) with expositions of these aspects. Our effort in this direction is not supposed to be in competition with them, but is only meant to help the uninitiated reader learn enough formalism to be able to understand the phenomenological consequences of supersymmetry which are dealt with in Part Two. We provide an introduction to the subject in C h . l by sketching the historical development of supersymmetry ideas in quantum field theory leading to the supersymmetric resolution of the naturalness (or, more specifically in terms of an overlying grand unified theory, the gauge hierarchy) problem which plagues the Standard Model of particle interactions. We then attempt to impart - in terms of one loop corrections in a toy model - a bird's eye view of naturalness and nonrenormalization in supersymmetric field theory. The pedagogical part of the book, written in the style of a textbook with more or less complete derivations, starts with Part One entitled "Supersymmetry Formalism". It is structured as follows. The preliminary ideas and tools of the subject are introduced in a quantum mechanical setting in Ch.2. The JV=1 supersymmetry algebra in (3+1) dimensions is derived and the contents of simple supermultiplets are discussed in Ch.3. In Ch.4 we start considering supersymmetry in a field theoretic context by introducing free superfields. Interacting superfields are
Preface
IX
treated in Ch.5 with discussions of the Wess-Zumino model, supersymmetric quantum electrodynamics (SQED), supersymmetric quantum chromodynamics (SQCD) and supersymmetric chiral gauge theory (SxGT). In Ch.6, supersymmetric perturbation theory is treated in superspace by means of supergraphs and the nonrenormalization theorem is explained with this methodology; one loop /?- and 7-functions are also derived. Ch.7 contains a treatment of supersymmetry breaking, both of the explicit and of the spontaneous kinds, with special reference to the goldstino in the latter case. We change gears after this. Part Two, entitled "Supersymmetry Phenomenology" and written more like a research monograph, does not always include derivations in which case suitable references are given. This part is devoted to a discussion of the supersymmetrization of the Standard Model as well as of the new phenomena that are consequently predicted to occur above the electroweak energy scale. The basic structure of the simplest extension, known as the Minimal Supersymmetric Standard Model (MSSM), is outlined in Ch.8 which introduces the various new sparticle fields and their couplings that become necessary on account of exact supersymmetry. We discuss the soft explicit breaking of supersymmetry and the mass mixing among various sparticles with the same charge in Ch.9; physical mass eigenstate sparticles as well as the interaction vertices in which they participate are also enumerated. Ch.10 describes the Higgs sector of the MSSM with Higgs mass spectra plus couplings including radiative corrections and highlights relations that follow from the supersymmetric identification of Higgs quartic self couplings with gauge couplings. Possible constraints on the soft supersymmetry breaking parameters in the MSSM from high scale physics are discussed in C h . l l . The origin of the said parameters from gravity mediation between observable and hidden sector superfields is discussed in detail in Ch.12; the latter also contains an annex presenting a brief introduction to the essential features of N=l supergravity that are used in this chapter. The gauge mediation mechanism of supersymmetry breaking and related models are discussed in Ch.13. A critique of the MSSM is given in Ch.14 along with a survey of some proposed alternative scenarios. Issues related to present and future collider searches for sparticles and supersymmetric Higgs bosons, including limits already obtained, are covered in Ch.15. Ch.16 is devoted to a discussion of the cosmological consequences of supersymmetry with a focus on supersymmetric Dark Matter, gravitino cosmology and baryogenesis. The concluding Ch.17 discusses the future prospects of the entire supersymmetric scenario, in particular its viability in relation to forthcoming experiments by quantitatively specifying the amounts of fine tuning that get introduced as lower bounds on the masses of the yet unobserved sparticles keep getting pushed upwards. We would like to make some disclaimers by stating what this book is not. First, we have not gone into nonperturbative aspects of supersymmetry such as the vacuum structure or phases of a supersymmetric gauge theory. Specifically, we have chosen to omit any serious treatment of dynamical supersymmetry breaking though we refer to and discuss it occasionally. Second, though this book has been written with a phenomenological ethos, it is not a comprehensive account }f all phenomenological aspects of four dimensional supersymmetry. For the sake of keeping the length reasonable, we have not given any significant coverage to indirect phenomenological probes of supersymmetry, referring to them only sketchily. These include additional MSSM contributions to CP violation, possible supersymmetric implications for heavy flavor physics as well as detailed discussions of supersymmetric loop corrections in the MSSM interrelated with con-
X
Preface
straints from precision electroweak data. An informative review of these topics may be found in the article by Eigen, Gaitskell, Kribs and Matchev cited in the Bibliography at the end. We have also avoided any significant discussion of the interface between unified supersymmetric theories and String Theory. Finally, though we mention some braneworld scenarios, we have not gone in detail into supersymmetric models with extra dimensions. Coming to the Chapter References, our selection has been illustrative (and hence subjective) rather than comprehensive. While these references are by no means complete, we have tried to list most relevant review article collections and books in the Bibliography at the end. Apologies are made for any omissions that may have occured here. A word also about the motivation behind writing this book. Our intent has not been to 'sell' supersymmetry at laboratory energies. We have chosen to present a specific minimal model (and its extensions) for the supersymmetric stabilization of the electroweak scale, after setting up the requisite formalism. We discuss its strengths and weaknesses as well as those of its features t h a t open it to experimental confirmation or demolition in forthcoming colliders. One can then judge for oneself how desirable it all is. We shall deem our effort as worthwhile if the practioners of phenomenlogical as well as theoretical supersymmetry find this work useful and if a beginner is motivated by reading it towards the pursuit of research in this direction. It has taken several years to write this book. All of us, in the interim, have utilized visits to various institutes, departments and laboratories for the purpose of writing it. We have also benefited immensely from interactions with many colleagues: theorists and experimentalists alike. We acknowledge fruitful discussions and/or research collaborations on the subject with H. Baer, S. Banerjee, G. Belanger, T. Bhattacharya, G. Bhattacharyya, F. Borzumati, F. Boudjema, B. Brahmachari, U. Chattopadhyay, D. Choudhury, S.R. Das, A. Datta, D. Denegri, M. Dittmar, D.A. Dicus, A. Djouadi, D.K. Ghosh, G.F. Giudice, M. Gliick, M. Guchait, K. Hamaguchi, S. Heinemeyer, J. Kalinowski, R. Kaul, A. Kundu, E. Ma, N.K. Mondal, P. Majumdar, S.P. Martin, S. Mukhi, B. Mukhopadhyaya, P. Nath, M.M. Nojiri, G. Polesello, S. Raychaudhuri, E. Reya, D.P. Roy, S. Roy, U. Sarkar, S. Sen Gupta, M. Sher, K. Sridhar, X. Tata, S.P. Trivedi, T. Vachaspati, D. Wyler and Y. Yamada. We are grateful to high energy theory groups at the Tata Institute of Fundamental Research (Mumbai), the Centre for High Energy Physics of the Indian Institute of Science (Bangalore), Technical University (Munich), Laboratoire d'Annecy de Physique des Particules, Oxford University, University of California (Riverside), University of Hawaii (Manoa), University of Wisconsin (Madison), the Kavli Institute of Theoretical Physics (Santa Barbara), UNESP (Sao Paolo), Korea Institute of Advanced Studies (Seoul), College of William and Mary (Williamsburg) as well as at the CERN, DESY, INFN (Frascati) and Thomas Jefferson Laboratories for their hospitality. We are indebted to G.V. Ogale for preparing the latexscript and to R.S. Pawar for drawing the line diagrams with xfig. Additional secretarial assistance from R.N. Bathija and M.R. Shinde is acknowledged. We thank S. Raychaudhuri for designing the cover and A. Mukherjee for help in adjusting figure postscript files as well as in preparing the index. Spring 2004
M.D. R.M.G. P.R.
Contents
Preface
vii
Some Tips on Using This Book
xvii
MSSM Sparticles and Lower Mass Bounds
xix
Acronyms and Abbreviations
xxi
Notation, Conventions and Basic Superfield Definitions
xxiii
INTRODUCTION A N D OVERVIEW
Chapter 1. Supersymmetry: W h y and How
3
1.1 History and motivation
3
1.2 Quadratic divergence and unnaturalness
8
1.3 Naturalness, nonrenormalization, supersymmetry References
10 15
PART ONE SUPERSYMMETRY FORMALISM
Chapter 2. Preliminaries
19
2.1 Grassmann elements and variables
19
2.2 Supersymmetric harmonic oscillator
22
2.3 Glimpse of superspace
25
2.4 Supersymmetry and spacetime transformations
27
References
28
xii
Contents
Chapter 3. Algebraic Aspects 3.1 Supersymmetry algebra 3.2 Two component notation 3.3 Particle supermultiplets References
C h a p t e r 4. Free Superfields in S u p e r s p a c e 4.1 General superfield in superspace 4.2 Chiral covariant derivatives 4.3 Left and right chiral superfields 4.4 Vector superfields 4.5 Matter parity and .R-parity References
C h a p t e r 5. I n t e r a c t i n g Superfields 5.1 System of interacting chiral superfields 5.2 Abelian gauge interactions 5.3 Supersymmetric quantum electrodynamics (SQED) 5.4 Nonabelian gauge interactions 5.5 Supersymmetric quantum chromodynamics (SQCD) 5.6 Supersymmetric chiral gauge theory (S%GT) References
C h a p t e r 6. S u p e r s p a c e P e r t u r b a t i o n T h e o r y a n d S u p 6.1 Nonrenormalization of superpotential terms 6.2 Functional methods in superspace 6.3 Functional formulation of superfield theory 6.4 GRS Feynman rules for the Wess-Zumino model
Contents
xm
6.5 Feynman rules for nonabelian supergauge theories
112
6.6 Sample one loop supergraph calculations
120
6.7 The nonrenormalization theorem
125
6.8 One loop infinities and
ft-,7-functions
6.9 Renormalization group evolution
128 133
References
136
C h a p t e r 7. G e n e r a l A s p e c t s of S u p e r s y m m e t r y B r e a k i n g
137
7.1 Initial remarks
137
7.2 Spontaneous supersymmetry breaking: some generalities
138
7.3 The goldstino
141
7.4 Model of F-type supersymmetry breaking
145
7.5 Model of .D-type supersymmetry breaking
149
7.6 Dynamical model of supersymmetry breaking
150
7.7 Soft explicit supersymmetry breaking
152
7.8 The general mass sum rule
155
References
157
PART TWO SUPERSYMMETRY
PHENOMENOLOGY
C h a p t e r 8. B a s i c S t r u c t u r e of t h e M S S M
161
8.1 Brief review of the Standard Model
161
8.2 Superfields of the MSSM
164
8.3 Supersymmetric part of the MSSM
171
8.4 Some non-Higgs vertices of the MSSM
174
References
182
Contents
XIV
Chapter 9. Soft S u p e r s y m m e t r y Breaking in t h e M S S M
183
9.1 The content of £ S O F T
183
9.2 Electroweak gauginos and higgsinos
187
9.3 Chargino and neutralino interactions with gauge bosons
194
9.4 Masses and mixing patterns of sfermions
196
9.5 The flavor problem in supersymmetry
202
9.6 Interactions of sfermions with gauge bosons
206
9.7 Fermion-sfermion-gaugino/higgsino interactions
208
9.8 Quartic sfermion vertices
214
References
Chapter 10. Higgs B o s o n s in t h e M S S M
217
219
10.1 Higgs potential in the MSSM
219
10.2 Spontaneous breakdown and VEVs
220
10.3 Higgs masses at the tree level
222
10.4 Higgs-particle vertices
226
10.5 Higgs-sparticle vertices
229
10.6 Radiative effects on MSSM Higgs particles
240
References
Chapter 11. Evolution from Very High Energies
249
251
11.1 The need for a high scale
251
11.2 The running of gauge couplings in the SM and the MSSM
253
11.3 Derivation of the remaining RGE equations
257
11.4 Application to the MSSM
265
References
272
Contents Chapter 12. Gravity M e d i a t e d S u p e r s y m m e t r y Breaking
x 273
12.1 General remarks
273
12.2 N=l supergravity broken in the hidden sector
275
12.3 mSUGRA and its parameters
283
12.4 Phenomenology with mSUGRA
287
12.5 Beyond mSUGRA
297
12.6 Quantum effects and extra dimensions
307
12.7 Annex to Ch.12: A brief discussion of 7V=1 supergravity theory
314
References
Chapter 13. Gauge M e d i a t e d S u p e r s y m m e t r y Breaking
320
323
13.1 The basic ingredients
323
13.2 The minimal model mGMSB
329
13.3 Nonminimal messenger sector
333
13.4 The n and B\x problems
335
13.5 Direct messenger-matter coupling
338
13.6 Flavor symmetries for the GMSB scenario
339
References
Chapter 14. B e y o n d t h e M S S M
342
343
14.1 Motivation and outline
343
14.2 The next-to-the-minimal supersymmetric standard model
344
14.3 Introduction to imparity violation
355
14.4 Phenomenological limits on trilinear ff couplings
362
14.5 Bilinear Rp violation
367
14.6 Neutrino masses in supersymmetric theories
375
References
380
cvi
Contents
Chapter 15. S u p e r s y m m e t r y at Colliders
385
15.1 Introduction
385
15.2 Signals of charginos and neutralinos
389
15.3 Signals of sleptons
406
15.4 Signals of gluinos and squarks
416
15.5 The quest for supersymmetric Higgs bosons
429
15.6 Collider signals in the presence of Rp violation
442
References
Chapter 16. Supersymmetric Cosmology
448
455
16.1 Introductory comments
455
16.2 Standard Big Bang cosmology
456
16.3 Dark matter as a supersymmetric Big Bang relic
462
16.4 Cosmology of the gravitino
479
16.5 Baryogenesis
486
References Chapter 17. Conclusion: W i s h List, R o a d m a p and Fine Tuning References
498 501 506
Appendix A: Sparticle Vertices in the MSSM
507
Appendix B: Higgs Vertices in the MSSM
522
Bibliography
531
Index
539
Some Tips on Using This Book The reader's familiarity with basic quantum field theory and the Standard Model of particle interactions at a textbook level (e.g. Peskin and Schroeder, opere citato, Bibliography), has been assumed. The introductory Ch.l is largely for motivation and can be more easily followed by those already with some exposure to supersymmetry. The uninitiated reader, who may find it difficult to follow this chapter fully, is advised to browse through it first and come back for serious reading after finishing the more formal and pedagogical Part One. The latter, comprising Chs. 2-7, is a must for beginners. However, Ch.6 may be omitted by the less theoretically inclined reader who will then need to accept the nonrenormalization theorem and the Renormalization Group Evolution equations on faith. A cautionary note is that our conventions in describing supersymmetry transformations as well as a four component spinor in terms of its two component parts are different from those of Wess and Bagger, op. cit., Bibl. However, our Feynman rules are those of Haber and Kane, loco citato, Bibl. Those, who already know supersymmetric field theory but would like to apprise themselves of the phenomenological consequences of softly broken N—l supersymmetry in four dimensions, need only skim through Part One. That would be mainly to familiarize them'-es with our notation and the Feynman rules of SQED, SQCD and SxGT. They can then "v go to Part Two, consisting of Chs. 8-16. Chs. 8-10 describe the MSSM largely in "low" energy context and form the backbone of our phenomenological discussions. Again, those - who are already familiar with "low" energy MSSM but would like to see the links between high scale physics and laboratory signatures, cosmological aspects and nonminimal scenarios - may browse though these chapters and go directly to Ch.ll. Ch.15 may be omitted without loss of continuity by readers uninterested in collider signals of supersymmetry. A similar statement can be made for the cosmological discussions of Ch.16. A final tip on references: using those given at the end of each chapter and the review articles/books cited in the Bibliography, a more complete set can be obtained by literature survey through the SPIRES database http://www.slac.stanford.edu/spires/hep/. Corrections A list of corrections (including typographical errors) will be posted on the website with the url 'http://www.th.physik.uni-bonn.de/Groups/Drees/book' and will be updated from time to time. The cooperation of readers in pointing out additional errors in the book to
[email protected] will be much appreciated.
xvn
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MSSM sparticles and lower mass bounds 1 Sfermions
Lower mass bound (GeV)
Bosinos
Lower mass bound (GeV)
250 -do-do-do-
9
gluino
300 {trig = Mg) 195 (otherwise)
X?
lightest neutralino
59 (mSUGRA) 40 (otherwise)
u d c s
u-squark d-squark c-squark s-squark
i
stop
135 (fi)
b
sbottom
91 (Si)
xl
next lightest neutralino
62.4
e
selectron
99 (eR)
xl
second heaviest neutralino
99.9
>>e
e-sneutrino
45
x\
heaviest neutralino
-do-
M
smuon
95 {jiR)
xt
lighter chargino
103 (gauginolike) 99 (higgsinolike)
Vp.
mu-sneutrino
80 (n)
xt
heavier chargino
-do-
45
G
3
f
stau
i>T
tau-sneutrmo
45
3
gravitino
1.0 x 10~ 1 4
1
M. Schmitt in Supersymmetric Particle Searches, Review of Particle Physics, Particle Data Group, Phys. Rev. D66 (2002) 010001. Other assumptions, which go into the extraction of these bounds, are detailed in this review which also contains some recent improvements in older bounds plus stronger constraints in the plane of two sparticle masses (e.g. Mjo vs m^, cf. Ch.15). 2
All are expected to have masses in the sub-TeV to a few TeV range, though the gravitino G could be much lighter or somewhat heavier. Two mass diagonal states f\ 2 exist for each charged sfermion / , being orthogonal combinations of mixed left (/L) and right (JR) chiral sfermion fields. However, the mixing is expected to be significant only for third generation sfermions. For any sfermion / , the corresponding antisfermion will be denoted by / . Uncharged sfermions (sneutrinos) are purely left chiral and uncharged bosinos are Majorana fermions. An axino a will also be called for as the superpartner of the axion a in case the latter is included in the Standard Model. 3
We shall sometimes use the symbol ej to denote a charged slepton, i being a generation index and equal to 1,2,3 for the selectron, smuon, stau respectively. Also, q and I will be used generically to stand for an electroweak doublet squark and a similar slepton respectively.
xix
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Acronyms and Abbreviations AD ALEPH AMSB ATLAS BB BBN BR BSM CDF CDM CERN CKM c.l.
CM CMS CMB CMSSM CMSSM
D0 DR DR DELPHI DESY DY EDM
n
Ej1
IfT em
EW FCNC FN FRW FP FSR GF GIM GMSB GRS GUT HDM HERA ISR JLC L3
Affleck-Dine (Mechanism) Apparatus (detector) for L E P Physics Anomaly Mediated Supersymmetry Breaking A Toroidal LHC A p p a r a t u s (Detector)
Big Bang Big Bang Nucleosynthesis Branching Ratio Beyond Standard Model Collider Detector at Fermilab Cold Dark Matter Organization of European Nuclear Research (Geneva) Cabibbo-Kobayashi-Maskawa (Matrix) Confidence Level Center of Mass Compact Muon Solenoid (LHC Detector) Cosmic Microwave Background Constrained Minimal Supersymmetric Model Constrained Minimal Supersymmetric Model (Modified) A detector at the TEVATRON, Fermilab Dimensional Reduction (Regularization procedure) Modified Dimensional Reduction DEtector with Lepton, P h o t o n & Hadron Identification (at L E P ) Deutsches Elektronen Synchrotron (Hamburg) Drell-Yan (Process) Electric Dipole Moment Missing Energy Transverse Energy Missing Transverse Energy Electromagnetic Electroweak Flavor Changing Neutral Current Frogatt-Nielsen (Fields, Superfields) Friedmann-Robertson-Walker (Metric) Faddeev-Popov (Ghost) Final State Radiation Gauge Fixed Glashow-Iliopoulos-Maiani (Mechanism) Gauge Mediated Supersymmetry Breaking Grisaru-Rocek-Siegel (Rules) Grand Unified Theory Hot Dark Matter Hadron Elektron Ring Anlage (Device), Hamburg Initial State Radiation Joint Linear Collider (Proposed) A Detector at L E P xxi
xxii
Acronyms and Abbreviations LC LEP LHC LSP LO L-R AcDM MACHO MS MSSM mGMSB mSUGRA MSW NLSP NLC NLO NMSSM OPAL OS, SF PyP-2 c.o.m. QCD QED QFT Ftp
9v
# p MSSM RGE RPC S X GT sFG SLC SM SQED SQCD
ss SSB STr SUGRA SUSY SYM TESLA TEV-I (II) UA1 VEV WIMP WZ YM
Linear Collider Large Electron Positron (Ring) Large Hadron Collider (CERN) Lightest Supersymmetric Particle Leading Order Left-Right Cosmological Constant plus CDM (Model) MAssive Compact Halo Object Modified Minimal Subtraction (Renormalization scheme) Minimal Supersymmetric Standard Model Minimal gauge mediated supersymmetry breaking (Model) Minimal Supergravity (Model) Mikhayev-Smirnov-Wolfenstein (Effect) Next Lightest Supersymmetric Particle Next Linear Collider (Proposed) Next-to-the Leading Order Next-to-the Minimal Supersymmetic Standard Model Omni Purpose Apparatus (Detector) for LEP Opposite Sign, Same Flavor Center of Mass Frame of the Partons P\ and P2 Quantum Chromodynamics Quantum Electrodynamics Quantum Field Theory .R-parity .R-parity Violating Extended MSSM with # p Interactions Renormalization Group Evolution .R-parity Conserving Supersymmetric Chiral Gauge Theory Super-Feynman Gauge Stanford Linear Collider Standard Model Supersymmetric Quantum Electrodynamics Supersymmetric Quantum Chromodynamics Salam-Strathdee (Propagators) Spontaneous Supersymmetry Breaking Supertrace Supergravity Supersymmetry Super-Yang-Mills (theory) TeV Energy Superconducting Linear Accelerator (Proposed) Run I (II) at the TEVATRON Underground Area 1 (CERN Experiment) Vacuum Expectation Value Weakly Interacting Massive Particle Wess-Zumino (Supermultiplet, Model, Gauge) Yang-Mills (Theory)
Notation, Conventions and Basic Superfield Definitions Natural units c = h = 1. a;** = spacetime coordinate =
(t,x).
rf" = flat Minkowski metric ( 1 , - 1 , - 1 , - 1 ) = i f V
rj^.
= *£ = diag(l, 1,1,1).
(•livap is t h e Levi-Civita tensor density with £0123 = 1a _
d
cm _ _ J L
X[3 M ]y = ^ X f y F -
\(d»X)Y.
Mpi = (87rG Ne wton)- 1/2 - 2.43 x 10 1 8 GeV. K = \/87rGNewton = Mpt
[X, Y] = XY[X,Y]+ = XY +
.
YX. YX.
Pfi = generators of four translations = id^ on incoming waves. M^v = generators of homogenous Lorentz transformations. 4> = complex scalar field. A^ or A™ = real gauge field, abelian or nonabelian. T" = internal symmetry generator. g = gauge coupling. ip = Dirac four spinor. ipc = charge conjugate of ip = C-ipT. XM — Majorana four spinor = A ^ . a, b = four component spinor sub-indices in t h e ( | , 0 ) © (0, \) representation. ipa = spinor component of ip.
xxiv
Notation, Conventions and Basic Superfield Definitions
Pi = - ( 1 — 75) : left chiral projector. PR — o(l "*" Ts) • right chiral projector. A,B = two spinor indices in the (^,0) representation. A,B = two spinor indices in the (0, ^) representation. 0
1\ n
eAB = i
/0 I j eAB = I
„ I , CAQ = (
- 1 \ n ]'
me
. . , ,1 „, * n c l n * n e (510) representation space.
. J: metric in the (0, | ) representation space.
#,e = Grassmann coordinate two component spinor in the (|,0) representation. S,e = Grassmann coordinate two component spinor in the (0, | ) representation. 9 A , 8B = component of 6,9.
a - d ~d9A'a
dA
»A _ d 5A = JL a - d ~ deA' ~ deA,0A~ &*•
QA = —i(dA -\-io>\J)Bdll):
spinorial supercharge in the (5,0) representation.
QA = —i(BA + ioilAB9Bdll): £1 Xi \ C =
tw0
spinorial supercharge in the (0, 5) representation.
component spinors in the (|, 0) representation.
£,, Xi \C = two component spinors in the (0, \) representation. Cx = CAXA, Cx =
(AXA-
