2-loop supersymmetric renormalization group equations including R -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 ${\ensuremath{\alpha}}_{S}{(M}_{Z})$ predicted from unification can be reduced by 5% with respect to the R-parity conserving case, bringing it to within $2\ensuremath{\sigma}$ of the observed value. Bottom-tau Yukawa unification becomes potentially valid for any value of $\mathrm{tan}\ensuremath{\beta}\ensuremath{\sim}2\char21{}50$. The prediction of the top Yukawa coupling from the low $\mathrm{tan}\ensuremath{\beta}$ infrared quasi-fixed point can be lowered by up to $10%$, raising $\mathrm{tan}\ensuremath{\beta}$ up to a maximum of 5 and relaxing experimental constraints upon the quasi-fixed scenario. For heavy scalar fermion masses $O(1\mathrm{}\mathrm{TeV})$ the limits on the higher family $\ensuremath{\Delta}L\ensuremath{\ne}0$ operators from perturbative unification are competitive with the indirect laboratory bounds. We calculate the dependence of these bounds upon $\mathrm{tan}\ensuremath{\beta}$.