Strong coupling at the $\tau$-mass scale from an improved vector isovector spectral function

Abstract

We perform a precise extraction of the QCD coupling at the $\tau$-mass scale, ${\alpha }_s(m_{\tau })$, from a new vector isovector spectral function which combines ALEPH and OPAL distributions for the dominant channels, $\tau \to \pi {\pi }^0{\nu }_{\tau }$, $\tau \to 3\pi {\pi }^0{\nu }_{\tau }$ and $\tau \to \pi 3{\pi }^0{\nu }_{\tau }$, with estimates of sub-leading contributions obtained from electroproduction cross-sections using CVC, as well as BaBar results for $\tau \to K^{-}{K}^0{\nu }_{\tau }$. The fully inclusive spectral function thus obtained is entirely based on experimental data, without Monte Carlo input. From this new data set, we obtain ${\alpha }_s(m_{\tau })=0.3077\pm 0.0075$, which corresponds to ${\alpha }_s(m_Z)=0.1171\pm 0.0010$. This analysis can be improved on the experimental side with new measurements of the dominant $\pi {\pi }^0$, $\pi 3{\pi }^0$, and $3\pi {\pi }^0$ $\tau$ decay modes.

Comments: 11 pages, 4 figures. Contribution to the Proceedings of "The 16th International Workshop on Tau Lepton Physics (TAU2021) (Virtual Edition)", from September 27th to October 1st 2021, Indiana University