Perspective on properties of renormalization schemes at high loops

TL;DR

This paper explores properties of high-loop renormalization schemes in QCD, introducing MOMt schemes that avoid even zeta functions and a new scheme for scalar  theory in six dimensions with comprehensive Laurent series absorption.

Contribution

It introduces MOMt renormalization schemes in QCD with unique properties and a novel MaxSbar scheme for scalar  theory in six dimensions, expanding the understanding of renormalization at high loops.

Findings

MOMt schemes in QCD lack even zeta functions up to five loops.

The MaxSbar scheme fully absorbs Laurent series in scalar  theory.

New insights into renormalization scheme properties at high perturbative orders.

Abstract

We report on recent work on a class of renormalization schemes in QCD, termed the MOMt schemes. None of the renormalization group functions of the eight QCD MOMt schemes involve even zetas to five loops. A new scheme is introduced for scalar $\phi^3$ theory in six dimensions where the full Laurent series in the regularizing parameter of the Green's function is absorbed into the renormalization constants. Designated as the MaxSbar scheme it is equivalent to the MOMt scheme in the critical dimension.