Fermion Masses in a Supersymmetric SU(4)xSU(2)_LxSU(2)_R Model

Abstract

We calculate quark and lepton masses and quark mixing angles in the framework of a supersymmetric SU(4)$\otimes$SU(2)$_L\otimes$SU(2)$_R$ model where the gauge group is broken at 10$^{16}$ GeV. The model predicts third family top-bottom-tau Yukawa unification, as in minimal SO(10). The other smaller Yukawa couplings are assumed to arise from non-renormalisable operators suppressed by powers of some heavy scale. We perform a systematic operator analysis of the model in order to find the minimum set of operators which describe the low energy quark and lepton masses, and quark mixing angles consistent with low-energy phenomenology. A novel feature of the model is the possibility of asymmetric texture zeroes in the Yukawa matrices at the scale of the new physics. Successful predictions are obtained for $m_t$, $\tan β$, $m_s/m_μ$, $m_d/m_e$ and $V_{ub}$ in terms of a CP violating phase $ϕ$. For example, we predict $\tan β= 35-65$, $m_t = 130 - 190$ GeV, and $|V_{ub}|>0.0040$.