Unraveling duality violations in hadronic tau decays

TL;DR

This paper addresses potential Duality Violations (DVs) that challenge the reliability of the Operator Product Expansion (OPE) in hadronic $\tau$ decays used to determine $\alpha_s$ and condensates. It introduces a physically motivated vector-meson resonance model with finite widths to study how DVs arise, derives the OPE and DV structures within this model, and tests the standard moments method (with pinched weights) against it. The authors find that DVs can induce a non-negligible systematic error in $\alpha_s$ unless higher-dimension condensates (up to $D=10$) and DV effects are properly accounted for; their results motivate a DV-aware, data-driven fitting approach. They propose an iterative two-step method that separates modeling of DVs from the extraction of OPE coefficients, showing improved control over DV-induced systematics in the model and outlining how this could be applied to real data, albeit with challenges like correlated errors and running of $\alpha_s$. Overall, the work highlights the importance of explicitly modeling DVs to obtain robust, precise QCD parameters from tau decays and offers a practical path toward reducing associated uncertainties.

Abstract

There are some indications from recent determinations of the strong coupling constant alpha_s and the gluon condensate that the Operator Product Expansion may not be accurate enough to describe non-perturbative effects in hadronic tau decays. This breakdown of the Operator Product Expansion is usually referred to as being due to ``Duality Violations.'' With the help of a physically motivated model, we investigate these duality violations. Based on this model, we argue how they may introduce a non-negligible systematic error in the current analysis, which employs finite-energy sum rules with pinched weights. In particular, this systematic effect might affect the precision determination of alpha_s from tau decays. With a view to a possible future application to real data, we present an alternative method for determining the OPE coefficients that might help estimating, and possibly even reducing, this systematic error.

Figures (4)

• Figure 1: Analytical structure of $\Pi(q^2)$ on the complex $q^2$ plane. The solid curve with an arrow shows the contour to which Cauchy's theorem is applied.
• Figure 2: Experimental data for the spectral function for the vector channel from the ALEPH collaboration ALEPHAlephdata. In blue, we show the curve given by the model defined in Eq. (\ref{['themodel']}) with values for the parameters as given by Eq. (\ref{['param']}).
• Figure 3: Comparison between the exact spectral function (black solid curve) and the iterative fit described in Sec. \ref{['sec:IIF']} (blue dashed curve).
• Figure 4: The contour used to evaluate Eq. (\ref{['fullD']}), see text.