Scheme-independent series for anomalous dimensions of higher-spin operators at an infrared fixed point in a gauge theory

Thomas A Ryttov,Robert Shrock

doi:10.1103/physrevd.101.076018

Thomas A Ryttov, Robert Shrock

Open Access

https://doi.org/10.1103/physrevd.101.076018

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Abstract

We consider an asymptotically free vectorial gauge theory, with gauge group $G$ and $N_f$ fermions in a representation $R$ of $G$, having an infrared fixed point of the renormalization group. We calculate scheme-independent series expansions for the anomalous dimensions of higher-spin bilinear fermion operators at this infrared fixed point up to $O(\Delta_f^3)$, where $\Delta_f$ is an $N_f$-dependent expansion variable. Our general results are evaluated for several special cases, including the case $G={\rm SU}(N_c)$ with $R$ equal to the fundamental and adjoint representations.

Highlights

An asymptotically free gauge theory with sufficiently many massless fermions evolves from the deep ultraviolet (UV) to an infrared fixed point (IRFP) of the renormalization group at a zero of the beta function
We present scheme-independent series expansions of the anomalous dimensions of gauge-invariant higher-spin operators that are bilinear in the fermion fields, up to OðΔ3fÞ inclusive, at the infrared fixed point, where Δf is an Nf-dependent expansion variable defined below, in Eq (1.8)
IV we present our scheme-independent calculations of the anomalous dimensions of these higherspin Wilson operators for a general gauge group G and fermion representation R

Summary

INTRODUCTION

An asymptotically free gauge theory with sufficiently many massless fermions evolves from the deep ultraviolet (UV) to an infrared fixed point (IRFP) of the renormalization group at a zero of the beta function. We present scheme-independent series expansions of the anomalous dimensions of gauge-invariant higher-spin operators that are bilinear in the fermion fields, up to OðΔ3fÞ inclusive, at the infrared fixed point, where Δf is an Nf-dependent expansion variable defined below, in Eq (1.8). In previous work we have calculated scheme-independent expansions for anomalous dimensions of several types of gauge-invariant operators at an IRFP in an asymptotically free gauge theory [34,35,36,37,38,39,40].

CALCULATIONAL METHODS

General

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VIII. CONCLUSIONS