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 written 22 years ago. In that paper, we provided a general discussion of quark-lepton unification characterized by the gauge group G_S⊗G_W with two couplings g_S and g _W and by the unification mass scales M = 10 TeV-1000 TeV. The constraint from sin² θ_W restricts the choices for G_W and our favorite model for petite unification was chosen to be SU(4)_PS ⊗SU(2)⁴. In the present paper, we review the main results of our earlier paper 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 sin² θ_W(M_Z²) determines the unification scale to be roughly 1 TeV and 3-10 TeV, respectively. The implication 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 K _L → μe is automatically absent at the 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 be made consistent with the measured value of sin ² θ_W(M_Z²) and the unification scale M = O(1 TeV) only 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 K_L → 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.