Axion model in gauge-mediated supersymmetry breaking and a solution to the mu/Bmu problem

We present a simple supersymmetric axion model that can naturally explain the origin of the Higgs mu and Bmu terms in gauge mediation while solving the strong CP problem. To stabilize the Peccei-Quinn scale, we consider mixing between the messenger fields that communicate the supersymmetry and Peccei-Quinn symmetry breaking to the visible sector. Such mixing leads to the radiative stabilization of the Peccei-Quinn scale. In the model, a Higgs coupling to the axion superfield generates the B parameter at the soft mass scale while a small mu term is induced after the Peccei-Quinn symmetry breaking. We also explore the phenomenological and cosmological aspects of the model, which crucially depend on the saxion and axino interactions with the ordinary particles induced by the Higgs coupling to the axion superfield.