Upper Bound On Gluino Mass From Thermal Leptogenesis

Thermal leptogenesis requires the reheating temperature $T_R \gsim 3\times 10^{9}$ GeV, which contradicts a recently obtained constraint on the reheating temperature, $T_R \lsim 10^6$ GeV, for the gravitino mass of 100 GeV-10 TeV. This stringent constraint comes from the fact that the hadronic decays of gravitinos destroy very efficiently light elements produced by the Big-Bang nucleosynthesis. However, it is not applicable if the gravitino is the lightest supersymmetric particle (LSP). We show that this solution to the gravitino problem works for the case where the next LSP is a scalar charged lepton or a scalar neutrino. We point out that there is an upper bound on the gluino mass as $m_{\rm gluino} \lsim 1.8$ TeV so that the energy density of gravitino does not exceed the observed dark matter density $\Omega_{\rm DM}h^2\simeq 0.11$.