Impacts of the Higgs mass on vacuum stability, running fermion masses and two-body Higgs decays

The latest results of the ATLAS and CMS experiments indicate 116 GeV \lesssim M_H \lesssim 131 GeV and 115 GeV \lesssim M_H \lesssim 127 GeV, respectively, for the mass of the Higgs boson in the standard model (SM) at the 95% confidence level. In particular, both experiments point to a preferred narrow mass range M_H \simeq (124 ... 126) GeV. We examine the impact of this preliminary result of M_H on the SM vacuum stability by using the two-loop renormalization-group equations (RGEs), and arrive at the cutoff scale \Lambda_VS \sim 4 \times 10^{12} GeV (for M_H = 125 GeV, M_t = 172.9 GeV and \alpha_s(M_Z) = 0.1184) where the absolute stability of the SM vacuum is lost and some kind of new physics might take effect. We update the values of running lepton and quark masses at some typical energy scales, including the ones characterized by M_H, 1 TeV and \Lambda_VS, with the help of the two-loop RGEs. The branching ratios of some important two-body Higgs decay modes, such as H \to b\bar{b}, H \to \tau^+ \tau^-, H\to \gamma\gamma, H\to W^+ W^- and H \to Z Z, are also recalculated by inputting the values of relevant particle masses at M_H.