$\alpha_s(m_Z)$, intermediate scales and Fermion masses in supersymmeric theories; two-loop results

Abstract

One way to generate an intermediate scale being consistent with gauge coupling unification is to add new Higgs scalars above the intermediate scale. We classify such scenarios according to their degree of departure from minimal supersymmetric standard model. Thereafter, we summarize the results of a two-loop renormalization group analysis of the gauge and the Yukawa sectors of such scenarios, and their sensitivity to the {\it input} $\alpha_3(m_Z)$. The presence of an adjoint color octet above the intermediate scale can raise the gauge coupling unification scale to the $string$ scale, acommodate a suitable intermediate scale, provide a left-handed $\tau$-neutrino$ mass of the order of few electron volts and also have the right prediction of the ratio of $m_b /m_\tau$.