Non-thermal Higgsino dark matter, heavy gravitino and 125 GeV Higgs boson in modulus/anomaly-mediated supersymmetric models

If the lightest supersymmetric particle (LSP) is Higgsino-like, the thermal relic density is lower than the observed dark matter content for a LSP mass in the sub-TeV region. We outline constraints arising from the Fermi Gamma-ray Telescope data and LSP production from gravitino decay that must be satisfied by a successful nonthermal Higgsino scenario. We show that in a generic class of models where anomaly- and modulus-mediated contributions to supersymmetry breaking are of comparable size, Higgsino arises as the only viable sub-TeV dark matter candidate if gravitinos are heavy enough to decay before the onset of big bang nucleosynthesis. The correct relic density can be obtained via modulus decay in these models. As an explicit example, we consider a modulus sector in effective field theory (D = 4, N = 1 supergravitiy arising from type IIB Kachru-Kallosh-Linde-Trivedi compactification). Within this class of mirage mediation models, heaviness of the gravitino forces a sub-TeV Higgsino LSP and gives a Higgs mass around 125 GeV. In this example, the constraints from direct detection experiments are also satisfied.