Renormalon subtraction using Fourier transform: Analyses of simplified models

TL;DR

This paper introduces a Fourier transform-based method for separating renormalons in QCD calculations, validated through toy models, and proposes a new UV renormalon resummation formula.

Contribution

It analytically examines a novel Fourier transform approach for renormalon subtraction and introduces a new UV renormalon resummation formula using simplified models.

Findings

The method effectively separates multiple renormalons in toy models.

Results align with theoretical expectations for renormalon behavior.

The new UV renormalon resummation formula shows promising validity.

Abstract

For precise QCD prediction of observables, the ambiguity due to renormalons in perturbative calculations should be appropriately separated from Wilson coefficients in the framework of the operator-product-expansion. Recently, a new method has been developed which utilizes the properties of Fourier transform to separate multiple renormalons simultaneously from the Wilson coefficients. To understand how this method works analytically, we perform a renormalon separation from various toy models with the one-loop beta function. We confirm that each of the results is consistent with the theoretical expectations. In addition, we present a new formula for the resummation of UV renormalons and study its validity using one of the toy models.