Predictions of supersymmetric grand unified theories

Abstract

Renormalization effects are analyzed for a class of supersymmetric grand unified theories which contain the standard $\mathrm{SU}{(3)}_{c}\ifmmode\times\else\texttimes\fi{}\mathrm{SU}{(2)}_{L}\ifmmode\times\else\texttimes\fi{}\mathrm{U}(1)$ model. Predictions for ${{sin}^{2}\stackrel{^}{\ensuremath{\theta}}}_{W}({m}_{W})$ and the proton lifetime are obtained as functions of ${\ensuremath{\Lambda}}_{\stackrel{-}{\mathrm{MS}}}$ ($\stackrel{-}{\mathrm{MS}}$ is the modified minimal-subtraction scheme), ${N}_{H}$ (number of relatively light Higgs doublets), and $\ensuremath{\mu}$ (the scale of supersymmetry breaking). For realistic input parameters we find $0.23<~{sin}^{2}{\stackrel{^}{\ensuremath{\theta}}}_{W}({m}_{W})<~0.26$ and ${10}^{38}\ensuremath{\gtrsim}{\ensuremath{\tau}}_{p}\ensuremath{\gtrsim}{10}^{29}$ yr. Loop effects that could render the larger predicted values of ${{sin}^{2}\stackrel{^}{\ensuremath{\theta}}}_{W}({m}_{W})$ consistent with experiment are described.