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Renormalization group equation (RGE) of the Higgs mass up to one-loop orderis derived in $R_\xi$ gauge with dimensional regularization method (DREG) baseon MS (or $\bar{\rm{MS}}$) scheme. Scale-dependent properties of the Higgs massup to two-loop level are investigated. The result gives the positive Higgs massup to energy scale around the Planck scale. While following the vacuumstability argument, the Higgs mass need to be negative above the energy scale$10^{10}$ GeV for $M_{t}=173.3$ GeV. The conflict is induced by therenormalization of vacuum energy value(VEV).

RGE of the Higgs mass in the context of the SM