Gauge invariance and renormalization schemes in quantum chromodynamics

Abstract

A general analysis of the Slavnov-Taylor identity connecting the triple gluon and ghost-ghost-gluon vertices and its consequences for two momentum subtraction (symmetric and asymmetric) renormalization schemes are given. It is shown that in the asymmetric scheme proposed in this paper the relation $Z_3 Z_{1^{ - 1} } = \tilde Z_8 \tilde Z_{1^{ - 1} }$follows directly from the identity for a simple and natural definition of the renormalization constants. Explicit one-loop expressions for the renormalization constants $\left( {Z_1 ,Z_3 ,\tilde Z_1 \tilde Z_3 } \right)$in an arbitrary covariant gauge, including quark masses are given in support of the general analysis.