Scheme-Independent Calculation of $\gamma_{\bar\psi\psi,IR}$ for an SU(3) Gauge Theory

TL;DR

This paper provides a scheme-independent, series expansion-based calculation of the infrared anomalous dimension of fermion bilinears in SU(3) gauge theories, offering a novel extrapolation to determine its exact value from continuum field theory.

Contribution

It introduces a new scheme-independent method to calculate the IR anomalous dimension using a series expansion in , and extrapolates to find its exact value from continuum theory.

Findings

First determination of  dependence of _{IR} in SU(3)

Comparison with n-loop and lattice results

Provides a continuum field theory estimate of _{IR}

Abstract

We present a scheme-independent calculation of the infrared value of the anomalous dimension of the fermion bilinear, $\gamma_{\bar\psi\psi,IR}$ in an SU(3) gauge theory as a function of the number of fermions, $N_f$, via a series expansion in powers of $\Delta_f$, where $\Delta_f=(16.5-N_f)$, to order $\Delta_f^4$. We perform an extrapolation to obtain the first determination of the exact $\gamma_{\bar\psi\psi,IR}$ from continuum field theory. The results are compared with calculations of the $n$-loop values of this anomalous dimension from series in powers of the coupling and from lattice measurements.