Precise SU(5) Predictions for ${{{sin}^2\theta }_{\mathrm{W}}}^{\exp }$, $m_W$, and $m_Z$

Radiative corrections to $\nu$-induced neutral-current scattering are computed for an arbitrary $G\supset {\left[\mathrm{SU}\mathrm{}\right(3\left)\right]}_c\otimes {\left[\mathrm{SU}\mathrm{}\right(2\left)\right]}_L\otimes \mathrm{U}\mathrm{}\left(1\right)\mathrm{}$. Application to the Georgi-Glashow SU(5) model with a single superheavy mass leads, for ${\Lambda }_{\overline{\mathrm{MS}}}$ (the mass scale of quantum chromodynamics) = 0.4 GeV, to the precise predictions ${{{sin}^2\theta }_{\mathrm{W}}}^{({\nu }_{\mu };l)}\mathrm{}\left(0\right)=0.2104\mathrm{}$ for ${\nu }_{\mu }$-lepton scattering at $q^2=0\mathrm{}$ and ${{{sin}^2\theta }_{\mathrm{W}}}^{(\nu ;h)}(-20\mathrm{} \mathrm{Ge}{\mathrm{V}}^2)=0.2098\mathrm{}$ for deep-inelastic $\nu$-hadron scattering. This result, together with our previous radiative corrections to $m_W{sin\theta }_{\mathrm{W}}$, gives the SU(5) predictions $m_W=84.36\mathrm{}$ GeV and $m_Z=94.91\mathrm{}$ GeV.