Weak mixing angle and grand unified gauge theories

We discuss the role of sin2theta/sub W/ (theta/sub W/ = weak mixing angle) in the Weinberg-Salam SU(2) x U(1) model. A definition of the renormalized value of sin2theta/sub W/ is given, the effects of radiative corrections are considered, and the possibility of precisely determining this parameter experimentally is examined. Within the framework of grand unified gauge theories, we derive an expression for the effective quantity sin2theta/sub W/(M/sub W/) which can be compared with experiment. Our results are illustrated for the Georgi-Glashow SU(5) model and their implications regarding the predicted lifetime of the proton tau/sub p/ are discussed. For sin2theta/sub W/(M/sub W/) approx. = 0.21--0.20, values consistent with neutral--current measurements, we estimate that the SU(5) model predicts tau/sub p/ approx. = 1030--1033 yr, a range that is not very far from the present experimental bound. We also show that by increasing the number of scalar multiplets, the model can accommodate larger values for sin2theta/sub W/