The Crewther relation, schemes, gauges and fixed points

TL;DR

This paper explores the Crewther relation in different renormalization schemes and gauges at high loop order, proposing a generalized form based on renormalization group properties and fixed points in QCD.

Contribution

It introduces a generalized Crewther relation applicable beyond MSbar schemes, derived from renormalization group principles and tested across various QCD scenarios.

Findings

The generalized relation holds at fixed points in multiple schemes.

The derivation confirms scheme and gauge independence at fixed points.

Extensions of the Crewther relation are consistent with high-order QCD calculations.

Abstract

We investigate the Crewther relation at high loop order in a variety of renormalization schemes and gauges. By examining the properties of the relation in schemes other than modified minimal subtraction (MSbar) at the fixed points of Quantum Chromodynamics we propose a generalization of the Crewther relation that extends the MSbar construction of Broadhurst and Kataev. A derivation based on the properties of the renormalization group equation is provided for the generalization which is tested in various scenarios.