Strong Coupling Constant from $\tau$ Decay within a Dispersive Approach to Perturbative QCD

TL;DR

This paper introduces a dispersive approach to extract the strong coupling constant from tau decay data, utilizing quark-hadron duality and comparing with existing perturbative methods, resulting in systematically lower alpha_s values.

Contribution

The paper develops a novel dispersive framework for alpha_s extraction from tau decays, incorporating quark-hadron duality and self-consistent determination of the duality point and coupling.

Findings

Systematically lower alpha_s values compared to previous methods.

Stable duality point s_d around 1.7 GeV^2 across data sets.

Alpha_s at M_Z^2 consistent with world averages.

Abstract

We present a new dispersive framework for the extraction of the strong coupling constant $\alpha_s$ from $\tau$-lepton decays. A new feature of our procedure is the use of the quark-hadron duality on the limited region $s_{\rm d}<s<m_{\tau}^{2}$. The duality point $s_{\rm d}$ and the $\bar{\rm MS}$ strong coupling constant $\alpha_{s}(m_{\tau}^{2})$ are self-consistently extracted from the $\tau$ data for the non-strange vector spectral function. We use 2005 ALEPH and 1998 OPAL experimental data on the vector spectral function. We compare the new framework with the contour improved perturbation theory up to order $\alpha_s^{5}$. The new procedure yields systematically lower values for $\alpha_s$. From the 2005 ALEPH data, we obtain $\alpha_{s}(m_{\tau}^{2})=0.308\pm 0.014_{\rm exp}\pm 0.005_{\rm th}$ which corresponds to $\alpha_{s}(M_{\rm_{z}}^{2})=0.1170\pm 0.0018_{\rm exp}\pm 0.0007_{\rm th}\pm 0.0005_{\rm ev}$. The extracted value for the duality point $s_{\rm d}$ is found surprisingly stable against perturbation theory corrections $s_{\rm d}= 1.71\pm 0.05_{\rm exp}\pm 0.00_{\rm th}\,\, {\rm GeV^{2}}$. From the 1998 OPAL data, we obtain $\alpha_{s}(m_{\tau}^{2})=0.290\pm 0.023_{\rm exp}$ and $s_{\rm d}=1.68\pm 0.10_{\rm exp}\,\, {\rm GeV^{2}}$.