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

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 $\mathcal{O}({\Lambda }_{\mathrm{QCD}}^4)$ renormalon from the Adler function, the $\mathcal{O}({\Lambda }_{\mathrm{QCD}}^2)$ renormalon from the $B\to X_{u}l\bar{\nu }$ decay width, and the $\mathcal{O}({\Lambda }_{\mathrm{QCD}})$ and $\mathcal{O}({\Lambda }_{\mathrm{QCD}}^2)$ 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 ${\bar{\Lambda }}_{\mathrm{FTRS}}=0.495\pm 0.053\text{GeV}$ and$({\mu }_{\pi }^2{)}_{\mathrm{FTRS}}=-0.12\pm 0.23{\text{GeV}}^2$ for the non-perturbative parameters of HQET. We explain the formulation and analyses in detail.

Comments: 67 pages, 14 figures, More discussions, figures and references added in revision