Infrared Zero of $\beta$ and Value of $\gamma_m$ for an SU(3) Gauge Theory at the Five-Loop Level

TL;DR

This paper computes the five-loop infrared zero of the beta function and the anomalous dimension of fermion bilinear in an SU(3) gauge theory, enhancing precision in understanding its infrared behavior.

Contribution

It provides the first five-loop calculation of the IR zero of the beta function and the anomalous dimension for SU(3) gauge theories, using both direct beta function analysis and Padé approximants.

Findings

Calculated the five-loop IR zero of the beta function as a function of fermion number.

Determined the five-loop anomalous dimension at the IR zero.

Compared results from different analytical methods for consistency.

Abstract

We calculate the value of the coupling at the infrared zero of the beta function of an asymptotically free SU(3) gauge theory at the five-loop level as a function of the number of fermions. Both a direct analysis of the beta function and analyses of Pad\'e approximants are used for this purpose. We then calculate the value of the five-loop anomalous dimension, $\gamma_m$, of the fermion bilinear at this IR zero of the beta function.