Explicit no-${\pi }^2$ renormalization schemes in QCD at five loops

Abstract

We examine a variety of renormalization schemes in QCD based on its $3$-point vertices where the $\beta$-functions, gluon, ghost, quark and quark mass anomalous dimensions in each scheme do not depend on ${\zeta }_4$ or ${\zeta }_6$ in an arbitrary linear covariant gauge at five loops. We comment on the $C$-scheme.

Comments: 40 latex pages, anc directory contains electronic version of the renormalization group functions, coupling constant and gauge parameter maps, and the conversion functions for each scheme; label typos corrected in data file