Petite Unification of Quarks and Leptons: Twenty Two Years After

Abstract

A recent surge of interest in the {\em early} unification of quarks and leptons, has prompted us to revive a paper \cite{HBB} written twenty two years ago. We provided there a general discussion of quark-lepton unification characterized by the gauge group $G_{S} \otimes G_{W}$ with two couplings $g_S$ and $g_W$ and by the unification mass scales $10\tev-1000\tev$. The constraint from $\sin^2 \theta_{W}$ restricts the choices for $G_W$ and our favorite model was chosen to be $SU(4)_{\rm PS}\otimes SU(2)^4$. We review the main results of \cite{HBB}, update the original $SU(4)_{\rm PS}\otimes SU(2)^4$ model and propose two new models based on the groups $SU(4)_{\rm PS}\otimes SU(2)^3$ and $SU(4)_{\rm PS}\otimes SU(3)^2$ for which the consistency with the measured value of $\sin^{2}\theta_{W}(M_{Z}^{2})$ determines the unification scale to be roughly $1 {\rm TeV}$ and $3-10 {\rm TeV}$, respectively. The implications of this very early unification is the existence of new quarks and leptons with charges up to 4/3 (for quarks) and 2 (for leptons) and masses $\ord(250\gev)$. Interestingly, in these models the rare decay $K_L\to \mu e$ is automatically absent at tree level and the one-loop contributions are consistent with the experimental upper bound for this decay.