General Messenger Higgs Mediation

We present a general formalism for analyzing supersymmetric models where the Higgs sector directly couples to the messengers of supersymmetry breaking. Such Higgs-messenger interactions are strongly motivated by the discovery of a Higgs boson near 125 GeV, but they also raise the specter of the mu/B_mu and A/m_H^2 problems. Using our formalism, we identify new avenues to solving these problems through strong dynamics in the messenger sector or hidden sector. Although our formalism is entirely general, we show how it reproduces familiar results in two simplifying limits: one where the hidden sector consists of a single spurion, and the other where it is approximately superconformal. In the latter limit, our formalism generalizes and clarifies the scenario of hidden sector sequestering, which we show can solve both the mu/B_mu and A/m_H^2 problems uniformly.