Ultraviolet and Infrared Divergences in Implicit Regularization: a Consistent Approach

TL;DR

This paper extends Implicit Regularization, originally designed for ultraviolet divergences, to also handle infrared divergences, introducing a new independent infrared scale and demonstrating the method's consistency through examples.

Contribution

It introduces a consistent extension of Implicit Regularization to treat infrared divergences alongside ultraviolet ones, including the emergence of an independent infrared scale.

Findings

Implicit Regularization can be adapted for infrared divergences.

A new infrared scale appears independently of the ultraviolet scale.

The method is validated through illustrative examples.

Abstract

Implicit Regularization is a 4-dimensional regularization initially conceived to treat ultraviolet divergences. It has been successfully tested in several instances in the literature, more specifically in those where Dimensional Regularization does not apply. In the present contribution we extend the method to handle infrared divergences as well. We show that the essential steps which rendered Implicit Regularization adequate in the case of ultraviolet divergences have their counterpart for infrared ones. Moreover we show that a new scale appears, typically an infrared scale which is completely independent of the ultraviolet one. Examples are given.