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

Preprint number: CP3-Origins-2016-55 DNRF90
Authors: Gongjun Choi (YITP Stony Brook), Thomas A. Ryttov (CP3-Origins & DIAS), and Robert Shrock (YITP Stony Brook)

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.