Muon g-2 in MSSM Gauge Mediation Revisited

The Higgs boson of 125 GeV requires large stop masses, leading to the large $\mu$-parameter in most cases of gauge mediation. On the other hand, the explanation for the muon $g-2$ anomaly needs small slepton and neutralino/chargino masses. Such disparity in masses may be obtained from a mass splitting of colored and non-colored messenger fields. However, even if the required small slepton and neutralino/chargino masses are realized, all parameter regions consistent with the muon g-2 are excluded by the recent updated ATLAS result on the wino search in the case that the messenger fields are in ${\bf 5}+\bar {\bf 5}$ representations of SU(5). It is also revealed that the messenger fields in ${\bf 10} + \overline{\bf 10}$ or ${\bf 24}$ representation can not explain the muon g-2 anomaly. We show, giving a simple example model, that the above confliction is solved if there is an additional contribution to the Higgs soft mass which makes the $\mu$-parameter small. We also show that the required Higgs B-term for the electroweak symmetry breaking is consistently generated by radiative corrections from gaugino loops.