Infra-red stable fixed points of R-parity violating Yukawa couplings in supersymmetric models

TL;DR

This paper analyzes the infrared fixed points of R-parity violating Yukawa couplings in supersymmetric models, finding that only one coupling approaches a stable fixed point, which conflicts with observed top quark mass data.

Contribution

It provides an analytical study of the renormalization group equations for R-parity violating couplings, identifying the unique stable fixed point and its phenomenological implications.

Findings

Only the B-violating coupling λ''_{233} reaches a stable fixed point.

Other fixed points are either unphysical or unstable.

The fixed point predicts a top-quark mass incompatible with experimental data.

Abstract

We investigate the infra-red stable fixed points of the Yukawa couplings in the minimal version of the supersymmetric standard model 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 these couplings together with the top- and b-quark Yukawa couplings. We show that only the B-violating coupling $\lambda^{''}_{233}$ approaches a non-trivial infra-red stable fixed point, whereas all other non-trivial fixed point solutions are either unphysical or unstable in the infra-red region. However, this fixed point solution predicts a top-quark Yukawa coupling which is incompatible with the top quark mass for any value of $\tan\beta$.