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