Scheme-Independent Calculations of Anomalous Dimensions of Baryon Operators in Conformal Field Theories

TL;DR

This paper provides the first scheme-independent analytic calculations of anomalous dimensions of baryon operators at an IR fixed point in SU(3) gauge theories, demonstrating scheme independence across various renormalization schemes.

Contribution

It introduces a scheme-independent series calculation method for anomalous dimensions of baryon operators and other physical quantities at IR fixed points in gauge theories.

Findings

Scheme independence of calculated anomalous dimensions confirmed across multiple schemes.

Analytic series expansions for physical quantities at IR fixed points derived.

Results applicable to a range of gauge theories with different fermion representations.

Abstract

We present the first analytic scheme-independent series calculations of anomalous dimensions of several types of baryon operators at an infrared fixed point (IRFP) in an asymptotically free SU(3) gauge theory with $N_f$ fermions. Separately, for an asymptotically free gauge theory with a gauge group $G$ and $N_f$ fermions in a representation $R$ of $G$, we consider physical quantities at an IRFP, including the anomalous dimension of gauge-invariant fermion bilinears and the derivative of the beta function. These quantities have been calculated in series expansions whose coefficients have been proved to be scheme-independent at each order. We illustrate the scheme independence using a variety of schemes, including the RI$^\prime$ scheme and several types of momentum subtraction (MOM) schemes.