Momentum subtraction scheme renormalization group functions in the maximal Abelian gauge

Abstract

The one-loop 3-point vertex functions of QCD in the maximal Abelian gauge are evaluated at the fully symmetric point at one loop. As a consequence the theory is renormalized in the various momentum subtraction schemes, which are defined by the trivalent vertices, as well as in the $\overline{\mathrm{MS}}$ scheme. From these the two-loop renormalization group functions in the momentum schemes are derived using the one-loop conversion functions. In parallel we repeat the analysis for the Curci--Ferrari gauge, which corresponds to the maximal Abelian gauge in a specific limit. The relation between the $\ensuremath{\Lambda}$ parameters in different schemes is also provided.