Violations of Quark-Hadron Duality in Low-Energy Determinations of $\alpha_s$

TL;DR

This paper assesses the impact of quark-hadron duality violations on determining the strong coupling constant from tau decay spectral functions, finding effects are minimal with standard methods but significant with non-protected weights.

Contribution

It provides a detailed analysis of duality violations' effects on alpha_s extraction, highlighting the robustness of standard methods and the systematic uncertainties in model-dependent approaches.

Findings

Duality violations are negligible with pinched weights.

Standard alpha_s determinations are robust against duality violations.

Model-dependent fits can have large systematic errors due to duality assumptions.

Abstract

Using the spectral functions measured in $\tau$ decays, we investigate the actual numerical impact of duality violations on the extraction of the strong coupling. These effects are tiny in the standard $\alpha_s(m_\tau^2)$ determinations from integrated distributions of the hadronic spectrum with pinched weights, or from the total $\tau$ hadronic width. The pinched-weight factors suppress very efficiently the violations of duality, making their numerical effects negligible in comparison with the larger perturbative uncertainties. However, combined fits of $\alpha_s$ and duality-violation parameters, performed with non-protected weights, are subject to large systematic errors associated with the assumed modelling of duality-violation effects. These uncertainties have not been taken into account in the published analyses, based on specific models of quark-hadron duality.