Scheming in Dimensional Regularization

TL;DR

This paper explores the relationship between dimensional regularization and cutoff regularization in non-relativistic effective field theories, showing how nonminimal subtraction schemes can recover cutoff regularization.

Contribution

It demonstrates that cutoff regularization can be derived from dimensional regularization through nonminimal subtraction schemes in non-relativistic EFTs.

Findings

Nonminimal subtraction schemes relate dimensional and cutoff regularizations.

Cutoff regularization is recovered from dimensional regularization.

Power-counting in non-relativistic EFTs is discussed in alternative schemes.

Abstract

We consider the most general loop integral that appears in non-relativistic effective field theories with no light particles. The divergences of this integral are in correspondence with simple poles in the space of complex space-time dimensions. Integrals related to the original integral by subtraction of one or more poles in dimensions other than D=4 lead to nonminimal subtraction schemes. Subtraction of all poles in correspondence with ultraviolet divergences of the loop integral leads naturally to a regularization scheme which is precisely equivalent to cutoff regularization. We therefore recover cutoff regularization from dimensional regularization with a nonminimal subtraction scheme. We then discuss the power-counting for non-relativistic effective field theories which arises in these alternative schemes.