Radiative corrections tosin2θWto leading logarithm in theW-boson mass

The renormalization group is used to sum radiative corrections to weak neutral-current and charged-current processes to leading logarithm in the $W$-boson mass. Strong and electromagnetic corrections to ${{sin}^2\theta }_W\left(M_W\right)$ determined from deep-inelastic neutrino-nucleon scattering and polarized $e\mathrm{D}$ experiments are computed. The leading-logarithm corrections produce a decrease in ${{sin}^2\theta }_W\left(M_W\right)$ from its uncorrected value by 0.015 in our analysis of deep-inelastic scattering and 0.009 in the polarized $e\mathrm{D}$ analysis. The $W$- and $Z$-boson masses are predicted to be 82.6 and 93.4 GeV. The results we quote are suitable for a direct comparison with predictions from grand unified theories.