The strong coupling from an improved $\tau$ vector isovector spectral function

Abstract

We combine ALEPH and OPAL results for the spectral distributions measured in $\tau \to {\pi }^{-}{\pi }^0{\nu }_{\tau }$, $\tau \to 2{\pi }^{-}{\pi }^{+}{\pi }^0{\nu }_{\tau }$ and $\tau \to {\pi }^{-}3{\pi }^0{\nu }_{\tau }$ decays with (i) recent BaBar results for the analogous $\tau \to K^{-}{K}^0{\nu }_{\tau }$ distribution and (ii) estimates of the contributions from other hadronic $\tau$-decay modes obtained using CVC and electroproduction data, to obtain a new and more precise non-strange, inclusive vector, isovector spectral function. The BaBar $K^{-}{K}^0$ and CVC/electroproduction results provide us with alternate, entirely data-based input for the contributions of all exclusive modes for which ALEPH and OPAL employed Monte-Carlo-based estimates. We use the resulting spectral function to determine ${\alpha }_s(m_{\tau })$, the strong coupling at the $\tau$ mass scale, employing finite energy sum rules. Using the fixed-order perturbation theory (FOPT) prescription, we find ${\alpha }_s(m_{\tau })=0.3077\pm 0.0075$, which corresponds to the five-flavor result ${\alpha }_s(M_Z)=0.1171\pm 0.0010$ at the $Z$ mass. While we also provide an estimate using contour-improved perturbation theory (CIPT), we point out that the FOPT prescription is to be preferred for comparison with other ${\alpha }_s$ determinations employing the $\overline{\mathrm{MS}}$ scheme, especially given the inconsistency between CIPT and the standard operator product expansion recently pointed out in the literature. Additional experimental input on the dominant $2\pi$ and $4\pi$ modes would allow for further improvements to the current analysis.

38 pages, 8 figures, published version

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• Violation of Quark-Hadron Duality (The missing oscillation in the OPE)