Formulation for renormalon-free perturbative predictions beyond large-${\beta }_0$ approximation

Abstract

We present a formulation to give renormalon-free predictions consistently with fixed order perturbative results. The formulation has a similarity to Lee's method in that the renormalon-free part consists of two parts: one is given by a series expansion which does not contain renormalons and the other is the real part of the Borel integral of a singular Borel transform. The main novel aspect is to evaluate the latter object using a dispersion relation technique, which was possible only in the large-${\beta }_0$ approximation. Here, we introduce an "ambiguity function," which is defined by inverse Mellin transform of the singular Borel transform. With the ambiguity function, we can rewrite the Borel integral in an alternative formula, which allows us to obtain the real part using analytic techniques similarly to the case of the large-${\beta }_0$ approximation. We also present detailed studies of renormalization group properties of the formulation. As an example, we apply our formulation to the fixed-order result of the static QCD potential, whose closest renormalon is already visible.

43 pages, 15 figures, version to appear in JHEP, minor modifications to v2

References in corpus (6)

• The five-loop beta function of Yang-Mills theory with fermions
• The five-loop Beta function for a general gauge group and anomalous dimensions beyond Feynman gauge
• Fermionic contributions to the three-loop static potential
• The bottom quark mass from the ${\rm Y}(1S)$ system at NNNLO
• Analytic three-loop static potential
• Superasymptotic and hyperasymptotic approximation to the operator product expansion

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• Renormalon subtraction in OPE using Fourier transform: Formulation and application to various observables
• Renormalon Subtraction in OPE by Dual Space Approach: Nonlinear Sigma Model and QCD
• Renormalon subtraction using Fourier transform: Analyses of simplified models
• Renormalons in static QCD potential: review and some updates
• Determination of HQET nonperturbative matrix elements with renormalon subtraction using Fourier transform