GMSB with Light Stops

Gauge mediated supersymmetry breaking (GMSB) is an elegant mechanism to transmit supersymmetry breaking from the hidden to the MSSM observable sector, which solves the supersymmetric flavor problem. However the smallness of the generated stop mixing requires superheavy stops to reproduce the experimental value of the Higgs mass. Two possible ways out are: i) To extend GMSB by direct superpotential messenger-MSSM Yukawa couplings to generate sizeable mixing, thus reintroducing the flavor problem; ii) To extend the MSSM Higgs sector with singlets and/or triplets providing extra tree-level corrections to the Higgs mass. Singlets will not get any soft mass from GMSB and triplets will contribute to the $\rho$ parameter which could be an issue. In this paper we explore the second way by introducing extra supersymmetric triplets with hypercharges $Y=(0,\pm 1)$, with a tree-level custodial $SU(2)_L\otimes SU(2)_R$ global symmetry in the Higgs sector protecting the $\rho$ parameter: a supersymmetric generalization of the Georgi-Machacek model, dubbed as supersymmetric custodial triplet model (SCTM). The renormalization group running from the messenger to the electroweak scale mildly breaks the custodial symmetry. We will present realistic low-scale scenarios (with the NLSP being a Bino-like neutralino or the right-handed stau) based on general (non-minimal) gauge mediation and consistent with all present experimental data. Their main features are: i) Light ($\sim 1$ TeV) stops; ii) Exotic couplings ($H^\pm W^\mp Z$ and $H^{\pm\pm} W^\mp W^\mp$) absent in the MSSM and proportional to the triplets VEV, $v_\Delta$; and, iii) A possible (measurable) universality breaking of the Higgs couplings $\lambda_{WZ}=r_{WW}/r_{ZZ}\neq 1$