Vacuum structure and stability of a singlet fermion dark matter model with a singlet scalar messenger

We consider the issue of vacuum stability and triviality bound of the singlet extension of the Standard Model (SM) with a singlet fermion dark matter (DM). In this model, the singlet scalar plays the role of a messenger between the SM sector and the dark matter sector. This model has two Higgs-like scalar bosons, and is consistent with all the data on electroweak precision tests, thermal relic density of DM and its direct detection constraints. We show that this model is stable without hitting Landau pole up to Planck scale for 125GeV Higgs boson. We also perform a comprehensive study of vacuum structure, and point out that a region where electroweak vacuum is the global minimum is highly limited. In this model, both Higgs-like scalar bosons have reduced couplings to the SM weak gauge bosons and the SM fermions, because of the mixing between the SM Higgs boson and the singlet scalar. There is also a possibility of their invisible decay(s) into a pair of DM's. Therefore this model would be disfavored if the future data on the (sigma . B)(VV) or (sigma . B)(f (f) over bar) with V = gamma, W, Z and f = b, tau turn out larger than the SM predictions.