The Crewther relation, schemes, gauges and fixed points

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.