Bare Higgs mass at Planck scale

Abstract

We compute one- and two-loop quadratic divergent contributions to the bare Higgs mass in terms of the bare couplings in the Standard Model. We approximate the bare couplings, defined at the ultraviolet cutoff scale, by the $\overline{\mathrm{MS}}$ ones at the same scale, which are evaluated by the two-loop renormalization group equations for the Higgs mass around 126 GeV in the Standard Model. We obtain the cutoff scale dependence of the bare Higgs mass, and examine where it becomes zero. We find that when we take the current central value for the top quark pole mass, 173 GeV, the bare Higgs mass vanishes if the cutoff is about ${10}^{23}\text{ }\text{ }\mathrm{GeV}$. With a $1.3\text{ }\text{ }\ensuremath{\sigma}$ smaller mass, 170 GeV, the scale can be of the order of the Planck scale.