Revisiting gravitino dark matter in thermal leptogenesis
  In this paper, we revisit the gravitino dark matter scenario in the presence of the bilinear $R$-parity violating interaction. In particular, we discuss a consistency with the thermal leptogenesis. For a high reheating temperature required for the thermal leptogenesis, the gravitino dark matter tends to be overproduced, which puts a severe upper limit on the gluino mass. As we will show, a large portion of parameter space of the gravitino dark matter scenario has been excluded by combining the constraints from the gravitino abundance and the null results of the searches for the superparticles at the LHC experiments. In particular, the models with the stau (and other charged slepton) NLSP has been almost excluded by the searches for the long-lived charged particles at the LHC unless the required reheating temperature is somewhat lowered by assuming, for example, a degenerated right-handed neutrino mass spectrum. 
Masahiro Ibe, Motoo Suzuki, Tsutomu T. Yanagida
hep-ph