Gradient-flowed operator product expansion without IR renormalons

Abstract

A long-standing problem concerns the question how to consistently combine perturbative expansions in QCD with power corrections in the context of the operator product expansion (OPE), since the former exhibit ambiguities due to infrared renormalons, which are of the same order as the power corrections. We propose to use the gradient flow time $1/\sqrt{t}$ as a factorization scale and to express the OPE in terms of IR renormalon-free subtracted perturbative expansions and unambiguous matrix elements of gradient-flow regularized local operators. We show on the example of the Adler function and its leading power correction from the gluon condensate that this method dramatically improves the convergence of the perturbative expansion. We employ lattice data on the action density to estimate the gradient-flowed gluon condensate, and obtain the Adler function with non-perturbative accuracy and significantly reduced theoretical uncertainty, enlarging the predictivity at low $Q^2$. When applied to the hadronic decay width of the tau lepton, the method resolves the long-standing discrepancy between the fixed-order and contour-improved approach in favour of the fixed-order treatment.