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

Understand

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.