Renormalisation Group determination of scalar mass bounds in a simple Yukawa-model

TL;DR

This paper uses the Functional Renormalisation Group to determine scalar mass bounds in a simple Yukawa model, considering scalar and fermionic backgrounds, and finds results consistent with previous studies, indicating small systematic errors.

Contribution

It introduces a method that incorporates composite fermionic backgrounds into FRG calculations for scalar mass bounds, enhancing previous scalar-only approaches.

Findings

Results agree with previous scalar condensate studies

Small systematic errors due to truncation are supported

Scalar mass bounds are determined across the stability range

Abstract

The scalar mass is determined in the simplest scalar-fermion Yukawa-model in the whole range of stability of the scalar potential. Two versions of the Functional Renormalisation Group (FRG) equations are solved, where also composite fermionic background is taken into account. The close agreement of the results with previous studies taking into account exclusively the effect of the scalar condensate, supports a rather small systematic truncation error of FRG due to the omission of higher dimensional operators.