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Experimental Signatures of Low Energy Gauge Mediated Supersymmetry Breaking

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Experimental Signatures of Low Energy Gauge Mediated Supersymmetry Breaking SLAC-PUB-7104 SU-ITP-96-06 SCIPP 96-08 hep-ph/9601367 Exp erimental Signatures of Low Energy Gauge Mediated Sup ersymmetry Breaking ? ab c Savas Dimopoulos , Michael Dine , y z d e Stuart Raby , Scott Thomas a Physics Department, Stanford University, Stanford, CA 94309 b Theoretical Physics Division, CH-1211, Geneva 23, Switzerland c Santa Cruz Institute for Particle Physics, University of California, Santa Cruz, CA 95064 d Physics Department, Ohio State University, Columbus, OH 43210 e Stanford Linear Accelerator Center, Stanford, CA 94309 Abstract The exp erimental signatures for gauge mediated sup ersymmetry breaking are presented. The phenomenology asso ciated with this class of mo dels is distinctive since the gravitino is naturally the LSP. The next lightest sup ersymmetric particle NLSP can b e a gaugino, Higgsino, or right handed slepton. Decay of the NLSP to its partner plus the LSP pro ceeds through the Goldstino comp onent of the gravitino. For a signi cant range of parameters this decay can take place within the detector, and can b e measured as a displaced vertex or kink in a charged particle track. In the case that the NLSP is mostly gaugino, we identify the discovery + + mo des as e e ! + E6 , and pp ! l l + E6 . If the NLSP is a right handed T + + + slepton the discovery mo des are e e ! l l + E6 and pp ! l l + E6 . An NLSP T which is mostly Higgsino is also considered. Finally, these theories can contain scalar particles which mediate sub-millimeter range coherent forces of gravitational strength. Submitted to Physical Review Letters ? Work supp orted by the Department of Energy. y Work supp orted by the Department of Energy under contract DOE-ER-01545-646. z Work supp orted by the Department of Energy under contract DE-AC03-76SF00515. 1. Intro duction Low energy sup ersymmetry is widely viewed as a plausible solution of the hierarchy problem. If nature is sup ersymmetric, it is imp ortant to understand how sup ersymmetry is broken. It is usually assumed that sup ersymmetry breaking is communicated to ordinary elds and their sup erpartners by sup ergravity. The 11 breaking scale is then necessarily of order 10 GeV. An alternative p ossibility, which has b een less thoroughly explored, is that sup ersymmetry is broken at some lower energy scale, and that the ordinary gauge interactions act as the messengers of sup ersymmetry breaking. In this case, the scale of sup ersymmetry breaking can b e as low as 10's of TeV [1]. Indep endent of source and messenger, sup ersymmetry breaking is represented among ordinary elds the visible sector by soft sup ersymmetry breaking terms [5]. The most general soft-breaking Lagrangian is describ ed by 105 parameters beyond those of the minimal standard mo del [6]. In the conventional sup ergravity context, these are in principle all indep endent, free parameters. However, there are anumb er of constraints which these parameters must satisfy, coming from direct exp erimental searches for sup erpartners, electric dip ole moments, and the lack of avor changing neutral currents. Most mo del builders simply p ostulate a high degree of degeneracy among squarks and sleptons at a high energy scale to deal with this problem [5]. In certain classes of sup erstring theories, there are weak hints for such a universality [7,8]. Alternatively, the various exp erimental constraints might b e satis ed as a result of avor symmetries or by other means [9-11]. With gauge mediated sup ersymmetry breaking the entire soft breaking Lagrangian can b e calculated in terms of a small numb er of parameters. In addition, the regularities required to avoid avor changing neutral currents are automatically obtained since the ordinary gauge interactions do not distinguish generations. For these reasons, we b elieve the gauge-mediated p ossibility should b e taken seriously. In this letter, we discuss two striking and distinctive signatures of low energy gauge-mediated sup ersymmetry breaking. The rst is the sp ectrum of sup erpart- ner masses. These masses are functions of the gauge quantum numb ers, and are roughly in the ratio of the appropriate gauge couplings squared. In the simplest mo dels, de nite relations exist among these masses. As a result, the lightest stan- 1 dard mo del sup erpartner is almost inevitably either a neutralino or a right-handed slepton. The second imp ortant signature arises from the fact that the lightest sup ersymmetric particle LSP is the gravitino. The lightest standard mo del su- p erpartner is then the next to lightest sup ersymmetric particle NLSP. Assuming that R-parity is conserved, the principle decay of the NLSP is then to its partner plus a gravitino. The longitudinal comp onent of the gravitino { the Goldstino { 1 couples to matter with strength prop ortional to F , where F is the scale of su- p ersymmetry breaking. For a plausible range of F , the decay length can b e 100's of m to meters. The decays can therefore take place within a detector. This leads to signatures for sup ersymmetry which are distinct from the conventional minimal sup ersymmetric standard mo del MSSM, and with p otentially dramatic displaced vertices. 2. Sup erpartner Sp ectrum In gauge mediated mo dels, sup ersymmetry is broken in a messenger sector which transforms under the standard mo del gauge group. The matter elds in this sector are generally referred to as messenger quarks and leptons. Sup ersymmetry breaking is transmitted to the visible sector by ordinary gauge interactions. To 2 preserve the successful sup ersymmetric prediction of the low energy sin it is W sucient that the messengers form a GUT representation. In the simplest versions, the messenger elds are weakly coupled, and p ossess the quantum numb ers of a single 5 + 5 of SU 5, i.e. there are triplets, q andq and doublets ` and ` . They couple to a single gauge singlet eld, S , through a sup erp otential W = Sqq + S``. The eld S has non-zero exp ectation values for b oth scalar and 1 2 auxiliary comp onents, S and F .Integrating out the messenger sector then gives S rise to gaugino masses at one lo op. For F S , these masses are given by [4] S i m = c N : 2:1 i i 4 5 where c = ;c = c =1,=F =S , and for a more general messenger sector 1 2 3 S 3 N is the equivalentnumber of SU 5 5 + 5 representations. The scalar masses 2 squared arise at two-lo ops [4] " 2 2 2 2 5 Y 3 2 1 2 2 m~ =2 N C +C + : 2:2 3 2 4 4 3 2 4 4 3 where C = for color triplets and zero for singlets, C = for weak doublets 3 2 3 4 and zero for singlets, and Y is the ordinary hyp ercharge normalized as Q = T + 3 1 Y . It should b e stressed that F is not necessarily the intrinsic sup ersymmetry S 2 breaking scale, F , since the gauge singlet eld may not b e coupled directly to the sup ersymmetry breaking sector. For example, in the mo del of Ref. [4], F F . S However, it is also p erfectly p ossible that F F [12]. While F determines the S S sup erpartner masses, it is F which determines the Goldstino coupling discussed in the next section. These expressions for the masses p ossess a numb er of noteworthy features. There is a hierarchy of masses, with colored particles b eing the most massive, and SU 3 SU 2 singlet particles the lightest. The gaugino masses are in the ratio 7 : 2 : 1, just as for sup ersymmetry breaking with universal gaugino masses at a high scale. For N = 1 the squark, left handed slepton, right handed slepton, and bino partner of the hyp ercharge gauge b oson masses are in the ratio 11:6: 2:5:1:1: 1. In this case the bino is therefore the natural candidate for the NLSP. The gaugino p masses growas N, while the scalar masses growas N. For N = 2 the ab ove masses are in the ratio 10:6:2:3:1 :1:3. In this case the right handed slepton is the candidate for the NLSP. In more general mo dels the ab ove relations among the masses can b e mo di ed. 2 For example b oth 2.1 and 2.2 are corrected at O F =S . Additional mo di ca- tions can arise with several gauge singlet elds coupling to q q and `` . In the mo del with one singlet, the couplings and cancel out in the expressions for the 1 2 masses, but this is not true of the more general case. As a result, b oth the ratios of the squark and slepton masses and the ratio of these masses to gaugino masses are mo di ed. More generally scalar masses require only sup ersymmetry breaking, while gaugino masses require also that U 1 b e broken to at most R-parity.In R principle U 1 could e ectively b e broken at a lower scale than sup ersymmetry, R leading to gauginos which are much lighter than the scalars. 3 Perhaps a more interesting p ossibility is that the messenger sector is strongly coupled. Gaugino masses can then arise directly from non-p erturbative dynamics 2 in the messenger sector, m g . The scalar masses require one p erturbative 2 2 2 gauge lo op,m ~ g =4 .
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