The mu problem and the axion in gauge mediation

Abstract

We revisit the idea of generating the Higgs mu parameter through a spontaneously broken Peccei-Quinn (PQ) symmetry in a gauge-mediated supersymmetry breaking scenario. For the messenger scale of gauge mediation higher than the PQ scale, the setup naturally generates mu similar to m(soft) and the Higgs soft parameter B less than or similar to O(m(soft)) with the CP phase of B aligned to the phase of gaugino masses, while giving the PQ scale v(PQ) similar to root m(soft)Lambda, where m(soft) denotes the gauge-mediated gaugino or sfermion masses and Lambda is the cutoff scale which can be identified as the Planck scale or the grand unified theory scale. The PQ sector of the model results in distinctive cosmology including a late thermal inflation. We discuss the issue of dark matter and baryogenesis in the resulting thermal inflation scenario, and find that a right amount of gravitino dark matter can be produced together with a successful Affleck-Dine leptogenesis, when the gravitino mass m(3/2) = O(100) keV.