Speaker
Description
The extraction of the QCD coupling, $\alpha_s$, from hadronic tau decays relies on experimental determinations of the relevant inclusive spectral functions. In this work, we produce a new inclusive vector-isovector spectral function combining information from several experiments. We obtain contributions from the dominant decay modes, $\pi^-\pi^0$, $2\pi^-\pi^+\pi^0$, and $\pi^-3\pi^0$, adding to the ALEPH and OPAL data used in our previous analyses, for the first time in this update, the high-statistics Belle $\tau \to \pi^-\pi^0 \nu_\tau$ results. Smaller contributions from other higher-threshold modes are obtained using BaBar data for $\tau \to K^-K^0 \nu_\tau$ and $e^+e^- \to \rm{hadrons}$ cross section input, related to the corresponding $\tau$ distributions by CVC, for other modes. This allows us to construct a new complete vector-isovector spectral function that relies solely on experimental data, without the need of Monte-Carlo inputs. This is then used to perform a new $\alpha_s$ determination, employing our previously developed strategy based on finite energy sum rules. We find, at the $Z$-mass scale, $\alpha_s(m_Z^2) =0.1159(14)$. The lower central value and larger error, compared with the result of our previous works, are mainly due to updated HFLAV branching-fractions inputs. The impact of Belle data for the dominant $2\pi$ channel and the inclusion of the CLEO spectrum in the analysis are also discussed.