Higgs Mediation with Strong Hidden Sector Dynamics

We present a simple model that achieves $m_h\approx 126$ GeV in the MSSM with large $A$-terms and TeV-scale stops through a combination of gauge mediation and Higgs-messenger interactions. The $\mu$/$B_\mu$ and $A$/$m_H^2$ problems are both solved by a common mechanism -- partial sequestering from strong hidden sector dynamics. Using the framework of General Messenger Higgs Mediation, we explicitly calculate the soft masses in terms of the vacuum expectation values, operator dimensions and OPE coefficients of the strongly-coupled hidden sector. Along the way, we also present a general analysis of the various constraints on sequestered Higgs mediation models. The phenomenology of such models is similar to gaugino mediation, but with large $A$-terms. The NLSP is always long-lived and is either the lightest stau or the Higgsino. The colored states are typically out of reach of the 8 TeV LHC, but may be accessible at 14 TeV, especially if the NLSP is the lightest stau.