On the seven-loop renormalization of Gross-Neveu model

A bstract The presence of an infinite number of marginal four-fermion operators is a key characteristic of the two-dimensional Gross-Neveu model. In this study, we investigate the structure of UV divergences in this model, and by symmetry argument we found that the renormalizability only requires a subset of evanescent operators. We perform a 7-loop renormalization computation of beta function for the corresponding evanescent operator, and confirm its non-trivial contribution to UV divergences. By integrating infrared rearrangement, dimensional shifting, and large momentum expansion techniques, we systematically reduce the two-dimensional tensor integrals in the four-fermion correlation functions into four-dimensional scalar integrals. These scalar integrals are subsequently evaluated using the graphical function method, which marks the first application of the method to models with fermionic fields. Our result represents the first time that beta functions have been computed analytically beyond 5-loop in a model with spinning particles.