Petite unification of quarks and leptons

Abstract

A general discussion of a quark-lepton unification characterized by the gauge group ${G}_{S}\ensuremath{\bigotimes}{G}_{W}$ with two coupling constants ${g}_{S}$ and ${g}_{W}$ and by the unification mass scale $M={10}^{5\ifmmode\pm\else\textpm\fi{}1}$ GeV is presented. The choice of ${G}_{W}$ is quite restricted by the measured value of ${{sin}^{2}\ensuremath{\theta}}_{W}$. The minimal model of such a unification turns out to be $\mathrm{SU}{(4)}_{\mathrm{PS}}\ensuremath{\bigotimes}\mathrm{SU}{(2)}_{L}\ensuremath{\bigotimes}\mathrm{SU}{(2)}_{R}\ensuremath{\bigotimes}\mathrm{SU}{(2)}_{{L}^{\ensuremath{'}}}\ensuremath{\bigotimes}\mathrm{SU}{(2)}_{{R}^{\ensuremath{'}}}$, where the first three factors constitute the well-known Pati-Salam group. The presence of $\mathrm{SU}{(2)}_{{L}^{\ensuremath{'}}}\ensuremath{\bigotimes}\mathrm{SU}{(2)}_{{R}^{\ensuremath{'}}}$ is required by the measured value of ${{sin}^{2}\ensuremath{\theta}}_{W}$ and it implies the existence of mirror fermions whose masses may range from 20-30 GeV to a few TeV. The lightest mirror fermion might be relatively long lived when compared to an ordinary sequential heavy fermion. The model accommodating all known quark and lepton generations gives the correct ${{sin}^{2}\ensuremath{\theta}}_{W}\ensuremath{\approx}0.22$ and at the same time can be made consistent with the experimental bounds on rare transitions induced by leptoquark exchanges.