Beta Function and Anomalous Dimensions

TL;DR

This paper presents a method to determine all-order beta function coefficients using two-loop data and universal anomalous dimensions, enabling accurate predictions of fermion mass anomalous dimensions at infrared fixed points.

Contribution

It introduces a novel approach to derive the all-order beta function coefficients from limited perturbative data and universal anomalous dimensions.

Findings

Beta function coefficients can be determined from two-loop and universal anomalous dimensions.

Predicted anomalous dimensions at infrared fixed points agree with lattice results.

Method enhances understanding of non-perturbative effects in gauge theories.

Abstract

We demonstrate that it is possible to determine the coefficients of an all-order beta function linear in the anomalous dimensions using as data the two-loop coefficients together with the first one of the anomalous dimensions which are universal. The beta function allows to determine the anomalous dimension of the fermion masses at the infrared fixed point, and the resulting values compare well with the lattice determinations.