Infra-red stable fixed points of Yukawa couplings in non-minimal supersymmetric standard model with R-parity violation

TL;DR

This paper investigates the infrared fixed points of Yukawa couplings in a non-minimal supersymmetric model with R-parity violation, finding that only specific baryon-number violating couplings approach stable fixed points, but these are incompatible with observed top quark mass.

Contribution

It provides an analytical study of the renormalization group equations and fixed point structure in NMSSM with R-parity violation, highlighting the limitations for realistic top quark mass predictions.

Findings

No simultaneous non-trivial fixed points for all couplings.

Only the baryon-number violating coupling approaches a stable fixed point.

Fixed point solutions are incompatible with the observed top quark mass.

Abstract

We study the renormalization group evolution and the infra-red stable fixed points of the Yukawa couplings of the non-minimal supersymmetric standard model (NMSSM) with R-parity violation. Retaining only the R-parity violating couplings of higher generations, we analytically study the solutions of the renormalization group equations of all the couplings of the model. We find that there are no simultaneous non-trivial infra-red fixed points for all the couplings of the model, and that the infra-red fixed point structure of the model is similar to the MSSM with R-parity violation. In particular, we show that only the baryon number violating coupling $\lambda^{''}_{233}$, together with top- and bottom-quark Yukawa couplings, approaches a non-trivial infra-red stable fixed point. However, this fixed point solution predicts a top-quark Yukawa coupling which is incompatible with the top quark mass for any value of $\tan\beta$.