Delta expansion and Wilson fermion in the Gross-Neveu model: Compatibility with linear divergence and continuum limit from inverse-mass expansion

TL;DR

This paper uses delta-expansion on the Gross-Neveu model with Wilson fermions to study dynamical mass generation, confirming continuum scaling and estimating the mass in the continuum limit.

Contribution

It demonstrates the compatibility of delta-expansion with mass renormalization and continuum limit in the Gross-Neveu model with Wilson fermions.

Findings

Delta-expansion is compatible with mass renormalization.

Continuum scaling of the bare coupling is confirmed.

Estimated dynamical mass converges to the exact value for certain Wilson parameters.

Abstract

We apply the $\delta$-expansion to the Gross-Neveu model in the large $N$ limit with Wilson fermion and investigate dynamical mass generation from inverse-mass expansion. The dimensionless mass $M$ defined via the effective potential is employed as the expansion parameter of the bare coupling constant $\beta$ which is partially renormalized by the subtraction of linear divergence. We show that $\delta$-expansion of the $1/M$ series of $\beta$ is compatible with the mass renormalization. After the confirmation of the continuum scaling of the bare coupling without fermion doubling, we attempt to estimate dynamical mass in the continuum limit and obtain the results converging to the exact value for values of Wilson parameter $r\in (0.8,1.0)$.