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

Properly separating and subtracting renormalons in the framework of the op- erator 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 O(ΛQCD4) renormalon from the Adler function, the O(ΛQCD2) renormalon from the B → X_ulν¯ decay width, and the O(Λ_QCD) and O(ΛQCD2) 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 Λ ¯ _FTRS = 0.495 ± 0.053 GeV and (μπ2)_FTRS = −0.12 ± 0.23 GeV² for the non-perturbative parameters of HQET. We explain the formulation and analyses in detail.