# A gauge mediation scenario with hidden sector renormalization in MSSM 

$^{1}$Institute of Experimental and Applied Physics, Czech Technical University in Prague, Horsk´ a 3a/22, 128 00 Prague 2, Czech Republic 

Masato Arai, 1, ∗ Shinsuke Kawai, 2, 3, † and Nobuchika Okada 4, ‡ 

2 Institute for the Early Universe (IEU), 11-1 Daehyun-dong, Seodaemun-gu, Seoul 120-750, Korea 

$^{3}$Department of Physics, Sungkyunkwan University, Suwon 440-746, Korea 

4 Department of Physics and Astronomy, University of Alabama, Tuscaloosa, AL35487, USA 

(Dated: June 15, 2018) 

We study the hidden sector effects to the mass renormalization of a simplest gauge-mediated supersymmetry breaking scenario. We point out that possible hidden sector contributions render the soft scalar masses smaller, resulting in drastically different sparticle mass spectrum at low energy. In particular, in the 5 + ¯ 5 minimal gauge mediated supersymmetry breaking with high messenger scale (that is favored by the gravitino cold dark matter scenario), we show that stau can be the next lightest superparticle for moderate values of hidden sector self coupling. This provides a very simple theoretical model of long-lived charged next lightest superparticles, that imply distinctive signals in ongoing and upcoming collider experiments. 

The minimal supersymmetric standard model (MSSM) is an attractive framework of a theory beyond the stan- dard model. It resolves some of the shortcomings of the standard model and at the same time makes falsifi- able predictions for upcoming experiments. The presence of dark matter, for an instance, has been consolidated by numerous cosmological and astrophysical observations [1]. According to the best-fit Λ-cold dark matter (the ‘concordance’) model, the major part of the energy den- sity of the present universe is dark energy and dark mat- ter, neither of them is explained by the standard model. While dark energy is likely to be of gravitational origin, dark matter is readily accommodated in MSSM; as the lightest superparticle (LSP) is protected by R-parity, it is an ideal candidate of dark matter. 

Among competing supersymmetry breaking scenarios of MSSM, the gauge-mediated supersymmetry breaking (GMSB) [2] is advantageous for natural suppression of flavor-changing neutral currents and CP violation. In GMSB the LSP is gravitino. Cosmological model build- ing with successful structure formation favors cold dark matter, which, in the case of gravitino dark matter, yields gravitino mass lower bound m$_{3}$$_{/}$$_{2}$ ≳ 100 keV. Gravitino LSP of this mass range is realized by GMSB models with sufficiently high messenger scale (see also Section 3). For this reason we will be concerned with the high messen- ger scale GMSB scenario in this paper. The interaction of gravitino with the standard model particles is Planck- suppressed. While this makes gravitino an ideal candi- date of dark matter, it also makes its direct detection rather difficult. A more direct telltale of supersymmetry is from the next lightest superparticle (NLSP), which, 

## I. INTRODUCTION 

in the case of GMSB, is either the lightest neutralino or the lightest charged slepton(s). In the high messen- ger scale GMSB, the NLSP is long-lived, behaving as quasi-stable particles, and the distinction of whether the NLSP is neutralino or slepton leads to entirely different physics. In the ‘minimal’ GMSB scenario based on the N$_{5}$ = 1 (the sum of the Dynkin indices) 5 + ¯ 5 messen- gers which are representations of the SU (5) gauge group [3, 4], the NLSP is neutralino. The long-lived neutralino NLSP scenario is strongly constrained by the big-bang nucleosynthesis (BBN) [5], leading to severe constraints on both gravitino and neutralino masses. Assuming non- thermal production of gravitino dark matter combined with the BBN bound, the neutralino mass is constrained to be larger than TeV scale. In contrast, if the gravitino dark matter is of thermal origin the neutralino mass can be smaller. In any case, the long-lived neutralino be- haves like stable particles in collider experiments and the physics is similar to that of neutralino LSP. If the NLSP is charged slepton(s), on the other hand, we expect en- tirely different signals. A natural candidate for a charged NLSP is the lightest scalar tau (stau). While the stau NLSP scenario is also constrained by BBN [5], the restric- tions on the gravitino and stau masses are not so tight as the neutralino NLSP case. In collider experiments, charged particles like stau leave tracks in detectors, al- lowing direct observations of the NLSP. It would also be possible to make a precise measurement of its mass, and the absence of missing energy (such as due to neutrino) would facilitate detailed study of various processes in- volving stau [6–10]. In GMSB, stau NLSP is obtained in models with larger N$_{5}$ [3, 4] or messengers belonging to larger gauge groups [11]. The messenger index N$_{5}$ , however, cannot be taken to be arbitrarily large as it is constrained by the condition that the successful gauge group unification must be preserved. In the case of sim- ple multiple SU (5) messengers, for example, the possible range of N$_{5}$ is roughly N$_{5}$ ≲ 10 for the messenger masses ≈ 10 10 GeV. For too large N$_{5}$ the gauge couplings diverge before the unification. 

