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 (GMSB), 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 GMSB also
generically suffers from two other problems: unsuppressed electric dipole
moments 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 non-thermal gravitino
dark matter is necessarily warm, with testable cosmological implications.
