Renormalization Group Evolution and Infra-red Fixed Points in Minimal Supersymmetric Standard Model with Baryon and Lepton Number Violation

TL;DR

This paper analyzes the renormalization group evolution and fixed points of Yukawa and soft supersymmetry breaking couplings in the minimal supersymmetric standard model with baryon and lepton number violation, identifying stable fixed points and deriving bounds.

Contribution

It provides an analytical and numerical study of infra-red fixed points in the MSSM with baryon and lepton number violation, revealing unique stable fixed points and bounds on couplings.

Findings

Identifies a unique infra-red stable fixed point for Yukawa couplings.

Derives bounds on baryon number violating coupling $ extlambda_{233}''$.

Analyzes quasi-fixed point behavior of couplings.

Abstract

We study the renormalization group evolution and infra-red 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 infra-red stable fixed point. This corresponds to non-trivial 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 infra-red 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-fixed point behaviour, 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 behaviour, we obtain upper and lower bounds on the baryon number violating coupling $\lambda_{233}''$, as well as on the supersymmetry breaking trilinear couplings.