Four loop MSbar mass anomalous dimension in the Gross-Neveu model

TL;DR

This paper calculates the four-loop mass anomalous dimension in the two-dimensional Gross-Neveu model within the MSbar scheme, addressing the effects of evanescent operators and correcting previous three-loop beta-function results.

Contribution

It provides the first four-loop computation of the mass anomalous dimension in this model, including the treatment of evanescent operators and correction of earlier three-loop beta-function calculations.

Findings

Four-loop mass anomalous dimension computed.

Evanescent operator effects properly incorporated.

Previous three-loop beta-function results corrected.

Abstract

We compute the four loop term of the mass anomalous dimension in the two dimensional Gross-Neveu model in the MSbar scheme. The absence of multiplicative renormalizability which results when using dimensional regularization means that the effect of the evanescent operator, which first appears at three loops in the 4-point Green's function, has to be properly treated in the construction of the renormalization group function. We repeat the calculation of the three loop MSbar beta-function and construct the beta-function of the evanescent operator coupling which corrects earlier computations.