2-loop supersymmetric renormalization group equations includingR-parity violation and aspects of unification

We present the complete 2-loop renormalization group equations of superpotential parameters for the supersymmetric standard model including the full set of R-parity violating superpotential couplings. We use these equations to do a study of (a) gauge coupling unification, (b) bottom-tau unification, (c) the fixed-point structure of the top quark Yukawa coupling, and (d) two-loop bounds from perturbative unification. The value of ${\alpha }_S{(M}_Z)$ predicted from unification can be reduced by 5% with respect to the R-parity conserving case, bringing it to within $2\sigma$ of the observed value. Bottom-tau Yukawa unification becomes potentially valid for any value of $\tan \beta \sim 2–50$. The prediction of the top Yukawa coupling from the low $\tan \beta$ infrared quasi-fixed point can be lowered by up to $10\%$, raising $\tan \beta$ up to a maximum of 5 and relaxing experimental constraints upon the quasi-fixed scenario. For heavy scalar fermion masses $O\left(1\mathrm{}\mathrm{}\mathrm{TeV}\right)$ the limits on the higher family $\Delta L\ne 0$ operators from perturbative unification are competitive with the indirect laboratory bounds. We calculate the dependence of these bounds upon $\tan \beta$.