SLAC-PUB-8442 April 2000 UCSD/PTH-00-10 The Superpartner Spectrum of Gaugino Mediation Martin Schmaltz x and Witold Skiba y xStanford Linear Accelerator Center Stanford University, Stanford, CA 94309 yDepartment of Physics, University of California at San Diego, La Jolla, CA 92093 Submitted to Physical Review D Stanford Linear Accelerator Center, Stanford University, Stanford, CA 94309 Work supported by Department of Energy contract DE–AC03–76SF00515. SLAC-PUB-8442 UCSD/PTH-00-10 hep-ph/yymmnnn The Sup erpartner Sp ectrum of Gaugino Mediation x y Martin Schmaltz and Witold Skiba x SLAC, Stanford University, Stanford, CA 94309 [email protected] y Department of Physics, University of California at San Diego, La Jol la, CA 92093 [email protected] Abstract We compute the sup erpartner masses in a class of mo dels with gaugino mediation or no-scale b oundary conditions at a scale b etween the GUT and Planck scales. These mo dels are comp elling b ecause they are simple, solve the sup ersymmetric avor and CP problems, satisfy all constraints from colliders and cosmology, and predict the sup erpartner masses in terms of very few parameters. Our analysis includes the renormalization group evolution of the soft-breaking terms ab ove the GUT scale. We show that the running ab ove the GUT scale is largely mo del indep endent and nd that a phenomenologically viable sp ectrum is obtained. 1 I. INTRODUCTION The soft-breaking terms in the Minimal Sup ersymmetric Standard Mo del MSSM need to have a very sp ecial form for the mo del to be viable. Generic mass matrices for the squarks and sleptons lead to unacceptably rapid avor-changing and lepton-numb er-violating pro cesses. Similarly, the tri-linear soft-breaking breaking A-terms also require ne tuning for the MSSM to agree with exp eriment. It is imp ortant to explore mo dels which naturally solve the avor ne-tuning problem. The rates for avor-changing pro cesses induced by the soft masses are prop ortional to the ratios of the o -diagonal mass squares to the diagonal ones. In order to make such ratios small one needs to minimize the o -diagonal terms or increase the avor-preserving masses. Examples of natural scenarios are gauge mediation [1,2] and anomaly mediation [3], which pro duce diagonal mass matrices due to the universality of the gauge coupling, and e ective sup ersymmetry [4], which p ostulates large soft masses for the rst two generations, for which the exp erimental constraints are most stringent. The p opular minimal sup ergravity [5] mo del do es not contain a solution to the avor problem, instead one simply assumes that the higher-dimensional op erators which pro duce the scalar masses are avor preserving. It has b een noticed that in \gaugino-dominated" mo dels the avor problem is less se- vere [6]. If at a high scale gaugino masses are larger than other soft parameters at that scale, then at low energies the soft masses consist of large avor-conserving masses with smaller avor-violating comp onents. This is b ecause the renormalization group running induces p ositive! universal soft scalar masses prop ortional to the gaugino masses. The generated scalar masses are avor universal b ecause couplings to gauginos are generation-indep endent. The most app ealing gaugino-dominated scenarios have no soft masses for squarks and slep- tons and no A-terms at a high scale M . Since at the high scale there are no masses BC and no A-terms, the only sources of avor violation are the Yukawa matrices, thus the sup ersymmetric avor problem is solved by a \sup er-GIM" mechanism [7]. Gaugino domination also alleviates the sup ersymmetric CP problem b ecause the only sources for new phases are the gaugino masses, , and B . Two phases can b e rotated away by eld re-de nitions, leaving only one p ossible new phase. For the sp ecial case B =0 the sup ersymmetric CP problem is solved automatically. In fact, the sp ecial b oundary conditions with vanishing sup erpartner masses and A- terms are theoretically well motivated. They arise, for example, in no-scale sup ergravity [8] or in the recently constructed higher-dimensional \gaugino mediation" mo dels [9{11]. In gaugino mediation the MSSM matter elds are con ned to a brane in higher dimensions. Sup ersymmetry is assumed to break on a distant parallel brane. Extra dimensional lo cality forbids direct couplings between the two branes and thereby suppresses all soft masses which involve MSSM matter elds squark and slepton masses, A-terms. Gauge elds and gauginos propagate in the bulk and couple directly to sup ersymmetry breaking, allowing for the generation of gaugino masses. 2 Extra-dimensional lo cality only forbids scalar masses at energies large compared to the compacti cation scale M . At long distances the theory is four-dimensional and masses are BC generated from renormalization as usual. The compacti cation scale in gaugino mediation corresp onds to a free parameter. Gauge coupling uni cation motivates us to cho ose M > BC M , and an upp er limit on M is given by the length scale at which Nature b ecomes GU T BC non-lo cal, presumably the string scale or Planck scale. In no-scale sup ergravity the scale M at which soft scalar masses vanish is related to the string scale. In the following we will BC treat M as a free parameter sub ject to the constraint M M M , and refer BC GU T BC P l anck to the b oundary condition of vanishing scalar masses and A terms as gaugino mediation. Clearly this scenario is very app ealing and it is crucial to ask if it is phenomenologically viable. For the particular choice of M = M one nds that the stau is the lightest BC GU T sup erpartner LSP which is problematic b ecause the calculated relic abundance of stable staus exceeds exp erimental limits by many orders of magnitude. This observation is often conceived as a failure of no-scale mo dels and has motivated construction of mo dels with new elds at intermediate scales to mo dify the renormalization group equations. In this pap er we rep eat the analysis for general M M and nd the good news that the BC GU T problematic stau-LSP is very sp ecial to M M . For compacti cation scales slightly BC GU T higher than M the stau mass gets a large new contribution from running in the uni ed GU T theory ab ove M which lifts its mass ab ove the mass of the Bino. This results in a very GU T satisfying cosmological picture with a Bino-LSP. Usually, the renormalization ab ove the GUT scale is ignored see, however, Refs. [12{15]. There are two seemingly go o d reasons for this negligence, we nd that b oth are invalid. The rst reason given is that logM =M is negligibly small compared to logM =M . BC GU T GU T w eak However, we nd that the smallness of the logarithm is comp ensated for bymuch larger group theory factors which arise in GUT theories. In particular, the right-handed sleptons receive only very small contributions from running b elow the GUT scale b ecause they carry only hyp ercharge, but ab ove M they are uni ed into a much larger representation with large GU T corresp onding group theory factors. The second reason is that the renormalization group equations ab ove M are necessarily mo del-dep endent. Obviously, GUTs have more elds GU T than just the MSSM multiplets and the adjoint eld needed to break the GUT symmetry to the Standard Mo del gauge group. For example, there must b e additional multiplets that guarantee the splitting of the doublet and triplet Higgs elds. All such new GUT-scale elds app ear with mo del-dep endent SUSY couplings. However, this do es not necessarily imply that the running of all soft parameters ab ove the GUT scale is mo del dep endent. As we will demonstrate in gaugino mediation most of the soft masses decouple from the unknown physics and many predictions can be made in a mo del-indep endent fashion. In the next two sections we describ e the renormalization group analysis ab ove Section I I and b elow Section III M in detail. We nd that the number of mo del-indep endent GU T predictions that can b e obtained is related to the form of the b oundary conditions at M . BC General gaugino mediation b oundary conditions allow arbitrary soft Higgs masses [10,16], 3 a B-term and gaugino masses at the scale M . We show that in this case the sp ectrum BC of the rst two generations and the ratios of gaugino masses can be predicted. When only M and B are non-zero at M one can also predict third generation scalar masses. BC 1=2 Finally, when B is also set to zero one obtains the b oundary conditions of Minimal Gaugino Mediation [11]. In this case the entire sup erpartner sp ectrum can be predicted in terms of just two parameters: M and M . We conclude in Section IV. BC 1=2 II. RENORMALIZATION ABOVE THE GUT SCALE In this section we discuss the renormalization of soft mass parameters ab ove the grand 16 uni cation scale, which we take to be M =2 10 GeV.