Constraints on Baryon-Nonconserving Yukawa Couplings in a Supersymmetric Theory

Abstract

The 1-loop evolution of couplings in the minimal supersymmetric standard model, extended to include baryon nonconserving $(B\!\!\!/)$ operators through explicit $R$-parity violation, is considered keeping only $B\!\!\!/$ superpotential terms involving the maximum possible number of third generation superfields. If all retained Yukawa couplings $Y_i$ are required to remain in the perturbative domain $(Y_i < 1)$ upto the scale of gauge group unification, upper bounds ensue on the magnitudes of the $B\!\!\!/$ coupling strengths at the supersymmetry breaking scale, independent of the model of unification. They turn out to be similar to the corresponding fixed point values reached from a wide range of $Y_i$ (including all $Y_i$ greater than unity) at the unification scale. The coupled evolution of the top and $B\!\!\!/$ Yukawa couplings results in a reduction of the fixed point value of the former.