Higher $\varepsilon$-poles and logarithms in the MS-like schemes from the algebraic structure of the renormalization group

TL;DR

This paper explores the algebraic structure underlying the renormalization group in MS-like schemes, revealing how higher epsilon-poles and logarithms relate to renormalization constants in dimensional regularization.

Contribution

It presents a unified algebraic framework connecting higher epsilon-poles and logarithms to renormalization group functions in MS-like schemes.

Findings

Derived all-loop equations for epsilon-poles and logarithms

Unified the relations using algebraic structure of the renormalization group

Provided insights into the structure of renormalization constants

Abstract

We investigate the structure of renormalization constants within the MS-like renormalization prescriptions for a version of dimensional regularization in which the dimensionful regularization parameter $\Lambda$ differs from the renormalization point $\mu$. Namely, we rewrite the all-loop equations relating coefficients at higher $\varepsilon$-poles and higher powers of $\ln\Lambda/\mu$ to the coefficients of the renormalization group functions in a simple unified form. It is argued that this form follows from the algebraic structure of the renormalization group.