Subtracting IR Renormalons from Wilson Coefficients: Uniqueness and power dependences on ${\Lambda }_{\mathrm{QCD}}$

Abstract

In the context of OPE and using the large-${\beta }_0$ approximation, we propose a method to define Wilson coefficients free from uncertainties due to IR renormalons. We first introduce a general observable $X(Q^2)$ with an explicit IR cutoff, and then we extract a genuine UV contribution $X_{\mathrm{UV}}$ as a cutoff-independent part. $X_{\mathrm{UV}}$ includes power corrections $\sim ({\Lambda }_{\mathrm{QCD}}^2/Q^2{)}^n$ which are independent of renormalons. Using the integration-by-regions method, we observe that $X_{\mathrm{UV}}$ coincides with the leading Wilson coefficient in OPE and also clarify that the power corrections originate from UV region. We examine scheme dependence of $X_{\mathrm{UV}}$ and single out a specific scheme favorable in terms of analytical properties. Our method would be optimal with respect to systematicity, analyticity and stability. We test our formulation with the examples of the Adler function, QCD force between $Q\bar{Q}$, and $R$-ratio in $e^{+}{e}^{-}$ collision.

55 pages, 11 figures, 1 table. v3: version published in PRD

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• C-parameter Distribution at N${}^3$LL${}^{\prime }$ including Power Corrections
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Cited by in corpus (9)

• Superasymptotic and hyperasymptotic approximation to the operator product expansion
• Determination of ${\alpha }_s$ from static QCD potential with renormalon subtraction
• Strong coupling constant and quark masses from lattice QCD
• Renormalons beyond the Borel plane
• Formulation for renormalon-free perturbative predictions beyond large-${\beta }_0$ approximation
• Renormalon-free definition of the gluon condensate within the large-${\beta }_0$ approximation
• Renormalon free part of an ultrasoft correction to the static QCD potential
• Resurgent representation of the Adler function in the large-${\beta }_0$ approximation of QCD
• UV contributions to energy of a static quark-antiquark pair in large ${\beta }_0$ approximation