Higher-Loop Corrections to the Infrared Evolution of a Gauge Theory with Fermions

TL;DR

This paper investigates how higher-loop corrections influence the infrared behavior of a gauge theory with fermions, showing that these corrections tend to reduce the anomalous dimension compared to two-loop estimates, with implications for lattice results.

Contribution

It provides a detailed analysis of higher-loop effects on the beta function and anomalous dimension in gauge theories with fermions, extending previous two-loop results to three- and four-loop orders.

Findings

Higher-loop corrections decrease the estimated anomalous dimension at the infrared fixed point.

Three- and four-loop values of $\gamma_m$ are smaller than two-loop estimates.

Results are consistent with recent lattice simulation data.

Abstract

We consider a vectorial, asymptotically free gauge theory and analyze the effect of higher-loop corrections to the beta function on the evolution of the theory from the ultraviolet to the infrared. We study the case in which the theory contains $N_f$ copies of a fermion transforming according to the fundamental representation and several higher-dimensional representations of the gauge group. We also calculate higher-loop values of the anomalous dimension of the mass, $\gamma_m$ of $\bar\psi\psi$ at the infrared zero of the beta function. We find that for a given theory, the values of $\gamma_m$ calculated to three- and four-loop order, and evaluated at the infrared zero computed to the same order, tend to be somewhat smaller than the value calculated to two-loop order. The results are compared with recent lattice simulations.