On power corrections in the dispersive approach

TL;DR

The paper develops a dispersive framework for QCD power corrections based on an infrared-regular universal coupling, emphasizing Minkowskian observables and an analytic connection to Euclidean quantities. It proves infrared renormalon cancellation within this setup and provides a clear separation of infrared and ultraviolet power corrections, including potential unconventional $1/Q^2$ UV effects and channel-dependent behavior. It also explores non-perturbative ansätze for the running coupling (QED-inspired and Analytic Perturbation Theory based) and discusses renormalization-scheme issues, arguing for a conceptually RS-invariant dressed skeleton expansion. Together, these results offer a systematic approach to quantify and interpret power corrections in QCD and their impact on precision determinations of $\alpha_s$.

Abstract

Power corrections in QCD (both conventional and unconventional ones arising from the ultraviolet region) are discussed within the infrared finite coupling-dispersive approach. It is shown how power corrections in Minkowskian quantities can be derived from the corresponding ones in associated Euclidean quantities through analyticity, allowing a parametrization in term of the Euclidean coupling and a renormalon-free perturbative expansion. It is argued that one should in general expect coefficients functions computed in the true non-perturbative vacuum to differ from the standard perturbative ones, even without assuming new physics. A phenomenology of $1/Q^2$ terms arising from eventual new physics of ultraviolet origin is also set-up. Models for non-perturbative contributions to the (universal) QCD coupling are suggested. Issues of renormalization scheme dependence are commented upon.