Higher-order calculation of the radiatively induced Higgs-meson mass

The mass of the Higgs meson in the standard model of the electroweak interactions has been calculated to $O\left(\alpha \right)$ by Coleman and Weinberg to be approximately 10 GeV when the gauge symmetry is broken due to radiative corrections. Motivated by the possibility of a precise determination of the weak mixing angle $\theta$ and the possibility of overlap with the $\Upsilon$ states, we calculate, in this framework, $O\left({\alpha }^2\right)$ corrections to the mass of the Higgs meson. Corrections come from the two-loop effective potential and one-loop corrections to the scalar and vector propagators and to coupling constants. We find that these contribute approximately 300 MeV to the mass. With the range of values of ${sin}^2\theta$ from the grand unified SU(5) model, the inclusion of $O\left({\alpha }^2\right)$ corrections gives 10.8±0.3 GeV for the mass, which is above the $\Upsilon$ states. The uncertainty is due to the range of values of ${sin}^2\theta$ allowed in SU(5).