Scheme-independent calculations of anomalous dimensions of baryon operators in conformal field theories

John A Gracey,Robert Shrock,Thomas A Ryttov

doi:10.1103/physrevd.97.116018

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.

Highlights

In conformal field theories, quantities of particular interest are the scaling dimensions, DO, of gauge-invariant operators, O
We shall focus on the determination of γO in perturbation theory at a fixed point of the renormalization group (RG)
In addition to demonstrating explicitly that different schemes yield the same values of coefficients in the scheme-independent expansion of γΦcomp;IR of the form (1.7), this work showed that (i) the series (1.7) converges to the exact expression everywhere where the latter applies, i.e., in the non-Abelian Coulomb phase (NACP), (ii) for a fixed Nf in the NACP, a finite truncation of the series (1.7) to order OðΔpf Þ approaches the exact expression exponentially rapidly, and (iii) throughout the entire NACP, one achieves excellent accuracy of a few percent even with a series calculated to a modest order of n 1⁄4 4, i.e., OðΔ4fÞ

Summary

INTRODUCTION

Quantities of particular interest are the scaling dimensions, DO, of gauge-invariant operators, O. In addition to demonstrating explicitly that different schemes yield the same values of coefficients in the scheme-independent expansion of γΦcomp;IR of the form (1.7), this work showed that (i) the series (1.7) converges to the exact expression everywhere where the latter applies, i.e., in the NACP, (ii) for a fixed Nf in the NACP, a finite truncation of the series (1.7) to order OðΔpf Þ approaches the exact expression exponentially rapidly, and (iii) throughout the entire NACP, one achieves excellent accuracy of a few percent even with a series calculated to a modest order of n 1⁄4 4, i.e., OðΔ4fÞ These scheme-independent calculations of anomalous dimensions in an N 1⁄4 1 supersymmetric gauge theory improved upon conventional scheme-dependent series expansions in powers of αIR [75,76] (see [77])

BARYON OPERATORS

SCHEME-INDEPENDENT SERIES EXPANSION FOR ANOMALOUS DIMENSION

UNITARITY BOUNDS ON ANOMALOUS DIMENSIONS OF BARYONIC OPERATORS

SCHEMES FOR ILLUSTRATIVE CALCULATIONS

VIII. SCHEME-INDEPENDENT EXPANSION OF β0IR

CONCLUSIONS