$\alpha_s$ from an improved $\tau$ vector isovector spectral function

TL;DR

This paper presents a new experimental-based method to determine the strong coupling constant $oldsymbol{ ext{alpha}_s}$ from tau decay data, addressing previous issues with duality violations and asymptotic OPE behavior.

Contribution

It introduces an improved vector isovector spectral function derived solely from experimental data, combining multiple sources and replacing Monte Carlo estimates with recent measurements.

Findings

Determined $oldsymbol{ ext{alpha}_s}(m_ au)=0.3077\pm 0.0075$

Converted to $oldsymbol{ ext{alpha}_s}(m_Z)=0.1171\pm 0.0010$

Addressed criticisms of previous approaches

Abstract

After discussing difficulties in determining $\alpha_s$ from tau decay due to the existence of Duality Violations and the associated asymptotic nature of the OPE, we describe a new determination based on an improved vector isovector spectral function, now based solely on experimental input, obtained by (i) combining ALEPH and OPAL results for $2\pi +4\pi$ and (ii) replacing $K^-K^0$ and higher-multiplicity exclusive-mode contributions, both previously estimated using Monte Carlo, with new experimental BaBar results for $K^-K^0$ and results implied by $e^+ e^-$ cross sections and CVC for the higher-multiplicity modes. We find $\alpha_s(m_\tau)=0.3077\pm 0.0075$, which corresponds to $\alpha_s(m_Z)=0.1171\pm 0.0010$. Finally, we comment on some of the shortcomings in the criticism of our approach by Pich and Rodriguez-Sanchez.