The b − τ unification in GUTs with non - chiral matter

It is shown, that the presently accepted value for b-quark mass can be obtained from the requirement of the exact b − τ unification in the both non-SUSY and SUSY non-chiral extended GUTs. Introduction. In due time the minimal SU(5) grand unification proposal [1] had ignited interest to the Grand Unified Theory (GUT) business by the calculation of the unification scale M GUT and mixing angle sin 2 θ W [2] and also by successful prediction of the b-quark and τ-lepton mass ratio, R = m b /m τ ≈ 3 [3,4]. It had been also shown, that the predicted mass ratio depends on the number of chiral quark-lepton families and that the observed ratio seems to require three such families [4,5]. At present we know that further prediction of three light families was confirmed by determination of the number of neutrino species in Z-boson decays at LEP and SLC [6]. However, we also know from the present accurate data on the Standard Model (SM) gauge couplings α S , α W and α Y , that the minimal SU(5) GUT, in which the first such predictions were made, is ruled out due to the actual non-unification of the SM running gauge couplings. This initiates one to go beyond the minimal SU(5) model. One such way is a supersymmetric (SUSY) extension of the minimal SU(5) GUT, in which gauge couplings meet each other at a single point around 10 16 GeV [7,8]. In addition to the unification of gauge couplings, the unification of the b-quark and τ-lepton Yukawa couplings appears naturally [9]. Namely, in the small tanβ (tanβ = v 2 /v 1 is the ratio of the two Higgs vacuum expectation values (VEVs)) regime one obtains, that for the presently allowed values of the electroweak parameters and the b-quark mass b − τ unification demands for the large values of the t-quark Yukawa coupling Y t = y