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We discuss the lightest Higgs boson mass in the minimal supersymmetric Standard Model with “pure gravity mediation”. By requiring that the model provides the observed dark matter density, we find that the lightest Higgs boson is predicted to be below 132 GeV. We also find that the upper limit on the lightest Higgs boson mass becomes 128 GeV, if we further assume thermal leptogenesis mechanism as the origin of baryon asymmetry of universe. The interrelations between the Higgs boson mass and the gaugino masses are also discussed.
Ibe et al. (Tue,) studied this question.