Fermion masses, mixing angles, and supersymmetric SO(10) unification.

Abstract

We reanalyze the problem of fermion masses in supersymmetric SO(10) grand unified models. In the minimal model, both low energy Higgs doublets belong to the same 10 representation of SO(10), implying the unification not only of the gauge but also of the third generation Yukawa couplings. These models predict large values of tan\ensuremath{\beta}\ensuremath{\sim}50. In this paper we study the effects of departing from the minimal conditions in order to see if we can find models with a reduced value of tan\ensuremath{\beta}. In order to maintain pre- dictability, however, we try to do this with the addition of only one new parameter. We still assume that the fermion masses arise from interactions of the spinor representations with a single 10 representation, but this 10 now only contains a part of the two light Higgs doublets. This enables us to introduce one new parameter \ensuremath{\omega}=${\ensuremath{\lambda}}_{\mathit{b}}$/${\ensuremath{\lambda}}_{\mathit{t}}$. For values of \ensuremath{\omega}\ensuremath{\ll}1 we can in principle reduce the value of tan\ensuremath{\beta}. In fact, \ensuremath{\omega} is an overall factor which multiplies the down quark and charged lepton Yukawa matrices. Thus the theory is still highly constrained. We show that the first generation quark masses and the CP-violation parameter ${\mathrm{\ensuremath{\epsilon}}}_{\mathit{K}}$ are sufficient to yield strong constraints on the phenomenologically allowed models. In the end, we find that large values of tan\ensuremath{\beta} are still preferred.