Early [formula omitted] unification of quarks and leptons

Abstract

We discuss various aspects of the early petite unification (PUT) of quarks and leptons based on the gauge group G PUT = SU ( 4 ) PS ⊗ SU ( 2 ) L ⊗ SU ( 2 ) R ⊗ SU ( 2 ) H . This unification takes place at the scale M = O ( 1 – 2 TeV ) and gives the correct value of sin 2 θ W ( M Z 2 ) without the violation of the upper bound on the K L → μ e rate and the limits on FCNC processes. These properties require the existence of three new generations of unconventional quarks and leptons with charges up to 4 / 3 (for quarks) and 2 (for leptons) and masses O ( 250 GeV ) in addition to the standard three generations of quarks and leptons. The horizontal group SU ( 2 ) H connects the standard fermions with the unconventional ones. We work out the spontaneous symmetry breaking (SSB) of the gauge group G PUT down to the SM gauge group, generalize the existing one-loop renormalization group (RG) analysis to the two-loop level including the contributions of Higgs scalars and Yukawa couplings, and demonstrate that the presence of three new generations of heavy unconventional quarks and leptons with masses O ( 250 GeV ) is consistent with astrophysical constraints. The NLO and Higgs contributions to the RG analysis are significant while the Yukawa contributions can be neglected.