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Report of the Supersymmetry Theory Subgroup Report of the Supersymmetry Theory Subgroup J. Amundson (Wisconsin), G. Anderson (FNAL), H. Baer (FSU), J. Bagger (Johns Hopkins), R.M. Barnett (LBNL), C.H. Chen (UC Davis), G. Cleaver (OSU), B. Dobrescu (BU), M. Drees (Wisconsin), J.F. Gunion (UC Davis), G.L. Kane (Michigan), B. Kayser (NSF), C. Kolda (IAS), J. Lykken (FNAL), S.P. Martin (Michigan), T. Moroi (LBNL), S. Mrenna (Argonne), M. Nojiri (KEK), D. Pierce (SLAC), X. Tata (Hawaii), S. Thomas (SLAC), J.D. Wells (SLAC), B. Wright (North Carolina), Y. Yamada (Wisconsin) ABSTRACT Spacetime supersymmetry appears to be a fundamental in- gredient of superstring theory. We provide a mini-guide to some of the possible manifesta- tions of weak-scale supersymmetry. For each of six scenarios These motivations say nothing about the scale at which nature we provide might be supersymmetric. Indeed, there are additional motiva- tions for weak-scale supersymmetry. a brief description of the theoretical underpinnings, Incorporation of supersymmetry into the SM leads to a so- the adjustable parameters, lution of the gauge hierarchy problem. Namely, quadratic divergences in loop corrections to the Higgs boson mass a qualitative description of the associated phenomenology at future colliders, will cancel between fermionic and bosonic loops. This mechanism works only if the superpartner particle masses comments on how to simulate each scenario with existing are roughly of order or less than the weak scale. event generators. There exists an experimental hint: the three gauge cou- plings can unify at the Grand Uni®cation scale if there ex- I. INTRODUCTION ist weak-scale supersymmetric particles, with a desert be- The Standard Model (SM) is a theory of spin- 1 matter tween the weak scale and the GUT scale. This is not the 2 fermions which interact via the exchange of spin-1 gauge case with the SM. bosons, where the bosons and fermions live in independent rep- Electroweak symmetry breaking is a derived consequence resentations of the gauge symmetries. Supersymmetry (SUSY) of supersymmetry breaking in many particle physics mod- is a symmetry which establishes a one-to-one correspondence between bosonic and fermionic degrees of freedom, and pro- els with weak-scale supersymmetry, whereas electroweak vides a relation between their couplings [1]. Relativistic quan- symmetry breaking in the SM is put in ªby hand.º The tum ®eld theory is formulated to be consistent with the symme- SUSY radiative electroweak symmetry-breaking mecha- m 150 200 nism works best if the top quark has mass t tries of the Lorentz/PoincarÂe group ± a non-compact Lie alge- m = GeV. The recent discovery of the top quark with t bra. Mathematically, supersymmetry is formulated as a gener- 4:4 176 GeV is consistent with this mechanism. alization of the Lorentz/PoincarÂe group of space-time symme- tries to include spinorial generators which obey speci®c anti- As a bonus, many particle physics models with weak- commutation relations; such an algebra is known as a graded scale supersymmetry contain an excellent candidate for Lie algebra. Representations of the SUSY algebra include both cold dark matter (CDM): the lightest neutralino. Such a bosonic and fermionic degrees of freedom. CDM particle seems necessary to describe many aspects of The hypothesis that nature is supersymmetric is very com- cosmology. pelling to many particle physicists for several reasons. Finally, there is a historical precedent for supersymmetry. In It can be shown that the SUSY algebra is the only non- 1928, P. A. M. Dirac incorporated the symmetries of the Lorentz trivial extension of the set of spacetime symmetries which group into quantum mechanics. He found as a natural conse- forms one of the foundations of relativistic quantum ®eld quence that each known particle had to have a partner particle theory. ± namely, antimatter. The matter-anti-matter symmetry wasn't revealed until high enough energy scales were reached to create If supersymmetry is formulated as a local symmetry, then a positron. In a similar manner, incorporation of supersymme- one is necessarily forced into introducing a massless spin-2 try into particle physics once again predicts partner particles for (graviton) ®eld into the theory. The resulting supergravity all known particles. Will nature prove to be supersymmetric at theory reduces to Einstein's general relativity theory in the the weak scale? In this report, we try to shed light on some of appropriate limit. the many possible ways that weak-scale supersymmetry might Theory subgroup conveners. be revealed by colliders operating at suf®ciently high energy. 655 masses, (C. Kolda, S. Martin and S. Mrenna) Boson ®elds Fermionic partners Gauge multiplets models with non-universal GUT-scale soft SUSY-breaking a a (3) g g~ SU terms, (G. Anderson, R. M. Barnett, C. H. Chen, J. Gunion, i i ~ (2) W W SU J. Lykken, T. Moroi and Y. Yamada) ~ B B U (1) Matter multiplets two MSSM scenarios which use the large parameter free- j ~ dom of the MSSM to ®t to various collider zoo events, (G. L =(~; e~ ) (; e ) Scalar leptons L L + c ~ Kane and S. Mrenna) R =~e e L R j ~ ~ Q =(~u ;d ) (u; d) L L Scalar quarks L R models with parity violation, (H. Baer, B. Kayser and X. c ~ U =~u u L R Tata)and c ~ ~ D=d d R L j 0 ~ ~ H (H ; H ) Higgs bosons L models with gauge-mediated low energy SUSY breaking 1 1 1 j + 0 ~ ~ H (H ; H ) L (GMLESB), (J. Amundson, C. Kolda, S. Martin, T. Moroi, 2 2 2 S. Mrenna, D. Pierce, S. Thomas, J. Wells and B. Wright). Table I: Field content of the MSSM for one generation of quarks and leptons. Each section contains a brief description of the model, quali- tative discussion of some of the associated phenomenology, and ®nally some comments on event generation for the model under discussion. In this way, it is hoped that this report will be a start- A. Minimal Supersymmetric Standard Model ing point for future experimental SUSY searches, and that it will provide a ¯avor for the diversity of ways that weak-scale super- The simplest supersymmetric model of particle physics which symmetry might manifest itself at colliding beam experiments. is consistent with the SM is called the Minimal Supersymmet- We note that a survey of some additional models is contained in ric Standard Model (MSSM). The recipe for this model is to Ref. [2], although under a somewhat different format. start with the SM of particle physics, but in addition add an ex- tra Higgs doublet of opposite hypercharge. (This ensures can- cellation of triangle anomalies due to Higgsino partner contri- II. MINIMAL SUPERGRAVITY MODEL butions.) Next, proceed with supersymmetrization, following well-known rules to construct supersymmetric gauge theories. The currently most popular SUSY model is the minimal super- At this stage one has a globally supersymmetric SM theory. gravity (mSUGRA) model [3, 4]. Here one assumes that SUSY Supersymmetry breaking is incorporated by adding to the La- is broken spontaneously in a ªhidden sector,º so that some aux- 10 2 M M ' (10 GeV ) Pl grangian explicit soft SUSY-breaking terms consistent with the iliary ®eld(s) get vev(s) of order Z . symmetries of the SM. These consist of scalar and gaugino mass Gravitational ± strength interactions then automaticallytransmit SUSY breaking to the ªvisible sector,º which contains all the B terms, as well as trilinear (A terms) and bilinear ( term) scalar SM ®elds and their superpartners; the effective mass splitting in 100 interactions. The resulting theory has > parameters, mainly from the various soft SUSY-breaking terms. Such a model is the the visible sector is by construction of order of the weak scale, most conservative approach to realistic SUSY model building, as needed to stabilize the gauge hierarchy. In minimal super- but the large parameter space leaves little predictivity. What is gravity one further assumes that the kinetic terms for the gauge needed as well is a theory of how the soft SUSY-breaking terms and matter ®elds take the canonical form: as a result, all scalar arise. The fundamental ®eld content of theMSSM is listed in Ta- ®elds (sfermions and Higgs bosons) get the same contribution 2 A m to their squared scalar masses, and that all trilinear param- ble 1, for one generation of quark and lepton (squark and slep- 0 A ton) ®elds. Mixings and symmetry breaking lead to the actual eters have the same value 0 , by virtueof an approximate global (n) physical mass eigenstates. U symmetry of the SUGRA Lagrangian [4]. Finally, mo- The goal of this report is to create a mini-guide to some of tivated by the apparent uni®cation of the measured gauge cou- 16 M ' 2 10 the possible supersymmetric models that occur in the literature, plings within the MSSM [5] at scale GUT GeV, one and to provide a bridge between SUSY model builders and their assumes that SUSY-breaking gaugino masses have a common m M GUT =2 experimental colleagues. The following sections each contain value 1 at scale . In practice, since little is known M M Planck a brief survey of six classes of SUSY-breaking models studied about physics between the scales GUT and , one of- M A at this workshop; contributing group members are listed in ital- ten uses GUT as the scale at which the scalar masses and ics. We start with the most popular framework for experimental parameters unify. We note that R parity is assumed to be con- searches, the paradigm served within the mSUGRA framework. This ansatz has several advantages. First, it is very econom- minimal supergravity model (mSUGRA) (M. Drees and M.
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