${\alpha }_s$ from an improved $\tau$ vector isovector spectral function

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.

Comments: Contribution to the proceedings of The XVth Quark Confinement and the Hadron Spectrum Conference, August 1st-6th, 2022, Univ. of Stavanger, Norway