Petite Unification of Quarks and Leptons: Twenty Two Years After

A recent surge of interest in the novel ideas of Large Extra Dimensions and their implications, such as the early unification of quarks and leptons, has prompted us to revive a paper [1] written twenty two years ago. In that paper, we provided a general discussion of quark-lepton unification characterized by the gauge group GS ⊗ GW with two couplings gS and gW and by the unification mass scales M = 10 TeV− 1000 TeV. The constraint from sin θW restricts the choices for GW and our favorite model for the Petite Unification (PUT) was chosen to be SU(4)PS ⊗ SU(2) . In the present paper, we review the main results of [1] and propose two new models based on the groups SU(4)PS ⊗ SU(2) 3 and SU(4)PS ⊗ SU(3) 2 for which the consistency with the measured value of sin θW (M 2 Z) determines the unification scale to be roughly 1 TeV and 3 − 10 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 O(250 GeV). Interestingly, in these models the rare decay KL → μe is automatically absent at tree level and the one-loop contributions are consistent with the experimental upper bound for this decay. On the other hand the original SU(4)PS ⊗SU(2) 4 model can only be made consistent with the measured value of sin θW (M 2 Z) and the unification scale M = O(1 TeV), provided there exist at least nine ordinary quark and lepton generations, with four generations in the case of the supersymmetric version. Moreover, the solution to the KL → μe problem is not as natural as in the two other scenarios. We comment on the recent papers on early unification in the context of Large Extra Dimensions.