Crewther's Relation in Different Schemes
October 11, 2023
January 22, 2024
We examine Crewther’s relation at high loop order in perturbative QCD and demonstrate how the
relation is accommodated in gauge-parameter dependent schemes where the running of the gauge
parameter has to be explicitly considered. Motivated by ensuring that the conformal properties
of the relation are preserved at all the critical points of QCD, including the Banks-Zaks and
its infra-red stable twin, we demonstrate the necessity of an additional term in the relation for
describing gauge running in the minimal momentum subtraction scheme (mMOM) and argue for
its inclusion for all gauge-parameter dependent schemes.
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