On the Question of a Possible Infrared Zero in the Beta Function of the Finite-$N$ Gross-Neveu Model

TL;DR

This paper examines the four-loop beta function of the finite-N Gross-Neveu model to determine if it shows an infrared zero, using Padé approximants and scheme dependence analysis, and finds no robust evidence for such a zero.

Contribution

The study provides a detailed four-loop analysis of the beta function in the finite-N Gross-Neveu model, including scheme dependence and Padé approximants, to assess the presence of an infrared zero.

Findings

No robust evidence for an infrared zero in the reliable coupling range

Padé approximants do not indicate an infrared fixed point

Scheme dependence analysis supports the absence of an infrared zero

Abstract

We investigate whether the beta function of the finite-$N$ Gross-Neveu model, as calculated up to the four-loop level, exhibits evidence for an infrared zero. As part of our analysis, we calculate and analyze Pad\'e approximants to this beta function and evaluate effects of scheme dependence. From our study, we find that in the range of coupling where the perturbative calculation of the four-loop beta function is reliable, it does not exhibit robust evidence for an infrared zero.