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.