Renormalization group evolution and infrared fixed points in the minimal supersymmetric standard model with baryon and lepton number violation

We study the renormalization group evolution and infrared stable fixed points of the Yukawa couplings and the soft supersymmetry breaking trilinear couplings of the minimal supersymmetric standard model with baryon and lepton number and R-parity! violation involving the heaviest generations. We show analytically that in the Yukawa sector there is only one infrared stable fixed point. This corresponds to nontrivial fixed point for the top-, bottom-quark Yukawa couplings and the B violating coupling $\lambda^{"}_{233}$, and a trivial one for the $\tau $ -Yukawa coupling. All other possible fixed points are either unphysical or unstable in the infrared region. We then carry out an analysis of the renormalization group equations for the soft supersymmetry breaking trilinear couplings, and determine the corresponding fixed points for these couplings. We also study the quasi-fixedpoint behavior, both algebraically and with numerical solutions of the evolution equations, of the third generation Yukawa couplings and the baryon number violating coupling, and those of the soft supersymmetry breaking trilinear couplings. From the analysis of the fixed point behavior, we obtain upper and lower bounds on the baryon number violating coupling $\lambda^{"}_{233}$, as well as on the supersymmetry breaking trilinear couplings