Gradient-flow renormalon subtraction and the hadronic tau decay series

TL;DR

This paper introduces a gradient flow-based method to automatically subtract infrared renormalons in QCD corrections to tau decay, resolving discrepancies between fixed-order and contour-improved series and favoring the fixed-order approach.

Contribution

It proposes using gradient flow to define gauge-invariant operators, enabling automatic renormalon subtraction and reconciling different perturbative series in tau decay analysis.

Findings

The CI series is modified to agree with the FO series after renormalon subtraction.

Gradient flow regularization leads to gauge-invariant condensates and series rearrangement.

The method confirms the preference for fixed-order perturbation theory in tau decay.

Abstract

The inconsistency between the fixed-order (FO) and contour-improved (CI) representation of the QCD corrections to the inclusive hadronic tau decay width limits the precision to which the strong coupling can be determined from this process. It has recently been shown that subtracting the infrared renormalon divergence related to the gluon condensate resolves the discrepancy. Here we suggest to employ the gradient flow to define gauge-invariant regularized operators and to use the corresponding condensates in the operator product expansion. The associated rearrangement of the perturbative series results in automatic renormalon subtraction without the need to determine explicitly the Stokes constants that normalize the divergent asymptotic series. Applying this method to the gluon condensate, we find that the CI series is modified and now agrees with the (unmodified) FO series. This conclusively demonstrates the preference for the fixed-order approach, as has been advocated long ago.