No-$\pi$ schemes for multi-coupling theories

TL;DR

This paper demonstrates that in multi-coupling theories, even complex zeta-function terms can be eliminated from beta-functions through coupling redefinitions, effectively changing the renormalisation scheme.

Contribution

It introduces a method to remove zeta-function terms from beta-functions in multi-coupling theories via coupling redefinitions, applicable up to high loop orders.

Findings

Zeta-function terms can be removed from beta-functions in general theories.

The removal corresponds to a scheme change, such as to a momentum subtraction scheme.

Applicable to theories where beta-functions are determined by anomalous dimensions.

Abstract

We show that even $\zeta$-functions may be removed from the $\beta$-functions of general multi-coupling theories up to high loop order by means of coupling redefinitions. For theories whose $\beta$-function is determined by the anomalous dimensions of the fields, such as supersymmetric theories, this corresponds to a renormalisation scheme change to a momentum subtraction scheme.