Predictions of $m_b/m_{\tau }$ and $m_t$ in an Asymptotically Non-Free Theory

Abstract

We discuss an extention of the Minimal Supersymmetric Standard Model (MSSM) with the 4th and anti-4th generations which have $SU(2{)}_L\times U(1{)}_Y$ invariant masses. Due to the the extra generations, all three running gauge couplings 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 $\mu =\text{mz}$ insensitive to their initial values at $\mu =\text{mgut}$; (2) the model predicts $\mathbb{R}(\text{mz})\equiv Y_b/Y_{\tau }{|}_{\mu =\text{mz}}\approx 1.8$, which is consistent with the experimental value provided we take the ratio of Yukawa couplings at the GUT scale to be $\mathbb{R}(\text{mgut})=Y_b/Y_{\tau }{|}_{\mu =\text{mgut}}=1/3$; (3) the $t$ mass prediction comes out to be $\text{mt}\approx 180\text{GeV}$ which is also consistent with experiment.

Comments: 20 pgs. 7 figures. Latex2e. othersym.sty, suceqn.sty included