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

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 $1\mathrm{/}M$ 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 $r\in (0.8,1.0)$.