The strong coupling from hadronic $\tau$ decays: a critical appraisal

TL;DR

This paper critically evaluates methods for determining the strong coupling constant from hadronic tau decays, highlighting issues with one approach that neglects non-perturbative effects and endorsing another that explicitly models these effects for more reliable results.

Contribution

It provides a critical comparison of two analysis approaches, demonstrating the reliability of a method that explicitly accounts for non-perturbative effects in tau decay data.

Findings

The approach neglecting duality violations is unreliable due to uncontrolled OPE truncation.

Explicit modeling of duality violations yields consistent and reliable strong coupling determinations.

The second approach passes all self-consistency tests and is more trustworthy.

Abstract

Several different analysis methods have been developed to determine the strong coupling via finite-energy sum-rule analyses of hadronic $\tau$ decay data. While most methods agree on the existence of the well-known ambiguity in the choice of a resummation scheme due to the slow convergence of QCD perturbation theory at the $\tau$ mass, there is an ongoing controversy over how to deal properly with non-perturbative effects. These are small, but not negligible, and include quark-hadron "duality violations" (i.e., resonance effects) which are not described by the operator product expansion (OPE). In one approach, an attempt is made to suppress duality violations enough that they might become negligible. The number of OPE parameters to be fit, however, then exceeds the number of available sum rules, necessitating an uncontrolled OPE truncation, in which a number of higher-dimension OPE contributions in general present in QCD are set to zero by hand. In the second approach, truncation of the OPE is avoided by construction, and duality violations are taken into account explicitly, using a physically motivated model. In this article, we provide a critical appraisal of a recent analysis employing the first approach and demonstrate that it fails to properly account for non-perturbative effects, making the resulting determination of the strong coupling unreliable. The second approach, in contrast, passes all self-consistency tests, and provides a competitive determination of the strong coupling from $\tau$ decays.