The strong coupling from an improved $τ$ vector isovector spectral function

We combine ALEPH and OPAL results for the spectral distributions measured in $τ\toπ^-π^0ν_τ$, $τ\to 2π^-π^+π^0ν_τ$ and $τ\toπ^-3π^0ν_τ$ decays with (i) recent BaBar results for the analogous $τ\to K^- K^0ν_τ$ distribution and (ii) estimates of the contributions from other hadronic $τ$-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 $α_s(m_τ)$, the strong coupling at the $τ$ mass scale, employing finite energy sum rules. Using the fixed-order perturbation theory (FOPT) prescription, we find $α_s(m_τ)=0.3077\pm 0.0075$, which corresponds to the five-flavor result $α_s(M_Z)=0.1171\pm 0.0010$ 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 $α_s$ determinations employing the $\overline{\rm MS}$ 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 $2π$ and $4π$ modes would allow for further improvements to the current analysis.

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