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 $10\text{tev}-1000\text{tev}$. The constraint from ${\sin }^2{\theta }_W$ restricts the choices for $G_W$ and our favorite model was chosen to be $SU(4{)}_{\mathrm{PS}}\otimes SU(2{)}^4$. We review the main results of \cite{HBB}, update the original $SU(4{)}_{\mathrm{PS}}\otimes SU(2{)}^4$ model and propose two new models based on the groups $SU(4{)}_{\mathrm{PS}}\otimes SU(2{)}^3$ and $SU(4{)}_{\mathrm{PS}}\otimes SU(3{)}^2$ for which the consistency with the measured value of ${\sin }^2{\theta }_W(M_Z^2)$ determines the unification scale to be roughly $1\mathrm{TeV}$ and $3-10\mathrm{TeV}$, 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 $\text{ord}(250\text{gev})$. 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.

Comments: Main latex-file, 2 figures, 18 pages