Quark masses and mixing angles from universal seesaw mechanism.

Abstract

A universal seesaw mechanism is invoked to account for the observed fermion mass hierarchies. In the framework of left-right symmetry, heavy fermions (mass scale $\ensuremath{\chi}$) which are ${\mathrm{SU}(2)}_{L}\ensuremath{\bigotimes}{\mathrm{SU}(2)}_{R}$ singlets are postulated while retaining the simplest possible Higgs system: namely, ${\ensuremath{\varphi}(1,2,1)}_{+1}\ensuremath{\bigoplus}{\ensuremath{\varphi}(1,1,2)}_{+1}$ accompanied by a left-right singlet ${\ensuremath{\sigma}(1,1,1)}_{0}$ in the standard ${\mathrm{SU}(3)}_{C}\ensuremath{\bigotimes}{\mathrm{SU}(2)}_{L}\ensuremath{\bigotimes}{\mathrm{SU}(2)}_{R}\ifmmode\times\else\texttimes\fi{}{\mathrm{U}(1)}_{B\ensuremath{-}L}$ notation. Every conventional quark and lepton is accompanied by a nonmirror singlet heavy fermion, so that the associated mass matrix is doubled and has the seesaw form usually associated only with the neutrino mass matrix. In the single-generation case, the model provides a plausible explanation for the mass hierarchy ${m}_{e,u,d}\ensuremath{\sim}{10}^{\ensuremath{-}4}{M}_{W}$ and predicts ${m}_{{\ensuremath{\nu}}_{e}}{m}_{{\ensuremath{\nu}}_{R}}\ensuremath{\approx}{m}_{e}^{2}$, thus accounting for the superlightness of neutrinos. Combined with a U(1) axial symmetry, the mechanism provides a formalism in which the generations are distinguished and constraints emerge on the allowed form of mass matrices. In this paper, we consider the realistic case of three generations in a simplified version of the model in which $\mathrm{CP}$ violation does not arise from the gauge sector. Choosing the ${\mathrm{U}(1)}_{A}$ quantum numbers so that the mass matrices are of the Fritzsch type, we calculate experimentally measured Cabibbo-Kobayashi-Maskawa matrix elements ${V}_{\mathrm{us}}$, ${V}_{\mathrm{ub}}$, and ${V}_{\mathrm{cs}}$ and derive their dependence on quark mass parameters. An interesting correlation between ${V}_{\mathrm{us}}$ which measures the Cabibbo angle and ${V}_{\mathrm{ub}}$ which measures the charmless decay of the $b$ quark emerges from the model. ${V}_{\mathrm{ub}}$ is naturally suppressed if ${V}_{\mathrm{us}}=\sqrt{\frac{d}{s}}\ensuremath{-}\sqrt{\frac{u}{c}}$ to a very good approximation.