Renormalon subtraction in OPE using Fourier transform: Formulation and application to various observables

TL;DR

This paper introduces a Fourier transform-based method (FTRS) for subtracting multiple renormalons in QCD observables, improving the precision of operator product expansion calculations.

Contribution

The FTRS method enables simultaneous subtraction of multiple renormalons using Fourier transform properties, aligning with principal-value prescriptions and enhancing convergence.

Findings

Successfully subtracted renormalons from various QCD observables.

Achieved consistent non-perturbative parameter estimates with theoretical expectations.

Demonstrated improved convergence and reduced scale dependence in analyses.

Abstract

Properly separating and subtracting renormalons in the framework of the operator product expansion (OPE) is a way to realize high precision computation of QCD effects in high energy physics. We propose a new method (FTRS method), which enables to subtract multiple renormalons simultaneously from a general observable. It utilizes a property of Fourier transform, and the leading Wilson coefficient is written in a one-parameter integral form whose integrand has suppressed (or vanishing) renormalons. The renormalon subtraction scheme coincides with the usual principal-value prescription at large orders. We perform test analyses and subtract the ${\cal O}(\Lambda_{\rm QCD}^4)$ renormalon from the Adler function, the ${\cal O}(\Lambda_{\rm QCD}^2)$ renormalon from the $B\to X_ul\bar{\nu}$ decay width, and the ${\cal O}(\Lambda_{\rm QCD})$ and ${\cal O}(\Lambda_{\rm QCD}^2)$ renormalons from the $B,\,D$ meson masses. The analyses show good consistency with theoretical expectations, such as improved convergence and scale dependence. In particular we obtain $\bar{\Lambda}_{\rm FTRS}=0.495\pm0.053~\text{GeV}$ and$ (\mu_\pi^2)_{\rm FTRS}=-0.12\pm 0.23~\text{GeV}^2$ for the non-perturbative parameters of HQET. We explain the formulation and analyses in detail.