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

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.