Four loop [formula omitted] 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 MS ¯ 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 MS ¯ β-function and construct the β-function of the evanescent operator coupling which corrects earlier computations.