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 $μ=\mz$ insensitive to their initial values at $μ=\mgut$; (2) the model predicts $\R(\mz) \equiv Y_b/Y_τ|_{μ=\mz}\approx 1.8$, which is consistent with the experimental value provided we take the ratio of Yukawa couplings at the GUT scale to be $\R(\mgut) = Y_b/Y_τ|_{μ= \mgut} = 1/3$; (3) the $t$ mass prediction comes out to be $\mt\approx 180\,\GeV$ which is also consistent with experiment.

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

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