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

Understand

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.