Scalar mass stability bound in a simple Yukawa-theory from renormalisation group equations

TL;DR

This paper uses functional renormalisation group equations to analyze the stability bounds of scalar mass in a simple Yukawa model, considering non-perturbative effects and irrelevant operators.

Contribution

It introduces a non-perturbative approach to determine scalar mass stability bounds in a Yukawa theory using FRG equations with a composite fermion background.

Findings

Extended the stability bound analysis beyond perturbation theory.

Showed the impact of irrelevant operators on the scalar mass bound.

Provided a systematic method to explore the effective potential evolution.

Abstract

Functional Renormalisation Group (FRG) equations are constructed for a simple Yukawa-model with discrete chiral symmetry, including also the effect of a nonzero composite fermion background beyond the conventional scalar condensate. The evolution of the effective potential of the model, generically depending on two invariants, is explored with help of power series expansions. Systematic investigation of the effect of a class of irrelevant operators on the lower (stability) bound allows a non-perturbative extension of the maximal cut-off value consistent with any given mass of the scalar field.