Scaling of the coupling in the covariant ghost free gauge

TL;DR

This paper investigates the effects of a quadratic gauge on the perturbative behavior of SU(N) Yang-Mills theory by calculating the one-loop beta function, exploring differences from the standard theory.

Contribution

It provides the first calculation of the one-loop beta function in the quadratic gauge, extending previous non-perturbative analyses to the perturbative regime.

Findings

Beta function calculated at one loop in quadratic gauge

Results suggest potential deviations from standard Yang-Mills theory

Implications for understanding gauge coupling behavior in different regimes

Abstract

I introduced the quadratic gauge for $SU(N)$ Yang-Mills theory and demonstrated its substantial implications in the non-perturbative theory in my previous works. An interesting case is to understand its implications in a perturbative regime and ask whether they differ anyway from the well established theory in this regime. Here I aim to calculate the beta function at one loop level in the same gauge.