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 $\alpha_s(m_\tau)=0.3077\pm0.0075$, which corresponds to $\alpha_s(m_Z)=0.1171\pm0.0010$. 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.