Implications of a 125 GeV Higgs boson for the MSSM and low-scale supersymmetry breaking

Recently, the ATLAS and CMS collaborations have announced exciting hints for a standard model-like Higgs boson at a mass of approximate to 125 GeV. In this paper, we explore the potential consequences for the MSSM and low-scale SUSY-breaking. As is well-known, a 125 GeV Higgs implies either extremely heavy stops (>= 10 TeV), or near-maximal stop mixing. We review and quantify these statements, and investigate the implications for models of low-scale SUSY-breaking such as gauge mediation where the A-terms are small at the messenger scale. For such models, we find that either a gaugino must be superheavy or the NLSP is long-lived. Furthermore, stops will be tachyonic at high scales. These are very strong restrictions on the mediation of supersymmetry breaking in the MSSM, and suggest that if the Higgs truly is at 125 GeV, viable models of gauge-mediated supersymmetry breaking are reduced to small corners of parameter space or must incorporate new Higgs-sector physics.