Predictions of m(b)/m(tau) and m(t) in an asymptotically nonfree theory

Abstract

We discuss an extension of the Minimal Supersymmetric Standard Model (MSSM) with 5 generations of matter superfields. The extra generations are assumed to form a generation–mirror generation pair (the 4th and anti-4th generations) enabling the extra fermions to have SU(2)_L × U(1)_Y invariant masses. Due to the contribution of the extra generations, all three running gauge couplings of SU(3)_C × SU(2)_L × U(1)_Y become asymptotically non– free while preserving gauge coupling unification at the GUT scale. We show that due to the asymptotically non–free character of the gauge couplings: (1) the top and bottom Yukawa couplings are strongly focused onto infrared fixed points as they are evolved down in scale making their values at µ = M_Z insensitive to their initial values at µ = M_GUT; (2) the model predicts R_bτ ( MZ ) ≡ Y_b/Y_τ |_{µ=M_Z} ≈ 1 .8, which is consistent with the experimental value provided we take the ratio of Yukawa couplings at the GUT scale to be R_bτ(M_GUT) = Y_b/Y_τ |_{µ=M_GUT} = 1/3; (3) the t mass prediction comes out to be m_t ≈ 180 GeV which is also consistent with experiment.