$\alpha_s$ from the updated ALEPH data for hadronic $\tau$ decays

TL;DR

This paper determines the strong coupling constant $oldsymbol{ ext{α}_s}$ at the $ au$ mass scale using updated ALEPH spectral data, applying a self-consistent analysis to improve precision and compare perturbation theories.

Contribution

It introduces a self-consistent analysis method for extracting $ ext{α}_s$ from $ au$ decay data, incorporating updated ALEPH spectral functions and comparing fixed order and contour improved perturbation theories.

Findings

$ ext{α}_s^{ m FO}(m_ au^2)=0.296 ext{±}0.010$ from FOPT

$ ext{α}_s^{ m CI}(m_ au^2)=0.310 ext{±}0.014$ from CIPT

Evolved $ ext{α}_s$ at $M_Z$ scale: 0.1165±0.0012 (FOPT), 0.1185±0.0015 (CIPT)

Abstract

We extract the strong coupling $\alpha_s(m_\tau^2)$ from the recently updated ALEPH non-strange spectral functions obtained from hadronic $\tau$ decays. We apply a self-consistent analysis method, first tested in the analysis of OPAL data, to extract $\alpha_s(m_\tau^2)$ and non-perturbative contributions. The analysis yields $\alpha_s^{\rm FO}(m_\tau^2)=0.296\pm0.010 $, using Fixed Order Perturbation Theory (FOPT), and $\alpha^{\rm CI}_s(m_\tau^2)= 0.310\pm0.014$, using Contour Improved Perturbation Theory (CIPT). The weighted average of these results with those previously obtained from OPAL data give $\alpha_s^{\rm FO}(m_\tau^2)=0.303\pm 0.009$ and $\alpha_s^{\rm CI}(m_\tau^2)=0.319\pm 0.012$, which gives, after evolution to the $Z$ boson mass scale, $\alpha^{\rm FO}_s(m_Z^2)=0.1165\pm0.0012 $ and $\alpha_s^{\rm CI}(m_Z^2)=0.1185\pm0.0015 $, respectively. We observe that non-perturbative effects limit the accuracy with which $\alpha_s$ can be extracted from $\tau$ decay data.