Low $α_{strong}(M_Z)$, Intermediate Scale SUSY SO(10) GUT and Its Implications

We show that one of the ways of obtaining consistency between the idea of supersymmetric grand unification and an apparent low value of $\alpha_{strong}(M_Z)\simeq .11$ indicated by several low energy experiments is to have an intermediate scale corresponding to a local $B-L$ symmetry breaking around the mass scale of $10^{10}$ to $10^{12}$ GeV. We discuss the realization of this idea within the framework of supersymmetric $SO(10)$ grand unified theories with spectra of particles derivable from simple superstring-inspired versions of this model. We then study the $b-\tau$ mass unification within this class of models and show that due to the influence of new gauge and Yukawa interactions beyond the intermediate scale, the prediction of the $b$-quark mass comes out well within the presently accepted values. We also discuss an un-orthodox class of SUSY models inspired by some theoretical considerations having two pairs of Higgs doublets at low energy and show that they also can lead to unification with intermediate scales and low $\alpha_{s}(M_Z)$ as desired.