$\sin^2\theta_W(M_Z)$ ~in the MSSM and Unification of Couplings

Abstract

We calculate ~$\sin^2\theta(M_Z)$ ~in the MSSM in terms of ~ $\alpha_{EM}$, ~$G_F$, ~$m_t$, ~$\tan\beta$ ~and SUSY mass parameters with the same accuracy as the present calculations of ~$\sin^2\theta(M_Z)$ ~in the SM. We compare the results with the standard leading logarithmic approximation used for SUSY threshold corrections and find important differences in the case of light sparticles. We give approximate formulae connecting coupling constants in the SM and in the MSSM and comment on process dependence of such formulae. The obtained values of the MSSM couplings ~$\alpha_i(M_Z)$ ~are used to investigate gauge coupling unification in the minimal SUSY ~SU(5) ~model. Our non-logarithmic corrections lower the predicted value of the Higgs triplet mass. The interplay between the supersymmetric and GUT thresholds in achieving unification for the coupling constants in the range of the experimentally acceptable values is quantified.