Gradient-flow renormalon subtraction and the hadronic tau decay series

Martin Beneke, Hiromasa Takaura

Research output: Contribution to journalConference articlepeer-review


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.

Original languageEnglish
Article number062
JournalProceedings of Science
StatePublished - 22 Jan 2024
Event16th International Symposium on Radiative Corrections: Applications of Quantum Field Theory to Phenomenology, RADCOR 2023 - Crieff, Scotland, United Kingdom
Duration: 28 May 20232 Jun 2023


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