Confluence of constraints in gauge mediation: The 125 GeV Higgs boson and Goldilocks cosmology

Recent indications of a 125 GeV Higgs boson are challenging for gauge-mediated supersymmetry breaking, since radiative contributions to the Higgs boson mass are not enhanced by significant stop mixing. This challenge should not be considered in isolation, however, as gauge-mediated supersymmetry breaking also generically suffers from two other problems: unsuppressed electric dipole moments (EDMs) and the absence of an attractive dark matter candidate. We show that all of these problems may be simultaneously solved by considering heavy superpartners, without extra fields or modified cosmology. Multi-TeV sfermions suppress the EDMs and raise the Higgs mass, and the dark matter problem is solved by Goldilocks cosmology, in which TeV neutralinos decay to GeV gravitinos that are simultaneously light enough to solve the flavor problem and heavy enough to be all of dark matter. The implications for collider searches and direct and indirect dark matter detection are sobering, but EDMs are expected near their current bounds, and the resulting nonthermal gravitino dark matter is necessarily warm, with testable cosmological implications.