Strong coupling at the $τ$-mass scale from an improved vector isovector spectral function - Diogo Boito, Maarten Golterman, Kim Maltman, Santiago Peris, Marcus V. Rodrigues, Wilder Schaaf (SciPost Physics Proceedings)
We perform a precise extraction of the QCD coupling at the $τ$-mass scale, $α_s(m_τ)$, from a new vector isovector spectral function which combines ALEPH and OPAL distributions for the dominant channels, $τ→π π^0ν_τ$, $τ→ 3π π^0ν_τ$ and $τ→ π 3π^0ν_τ$, with estimates of sub-leading contributions obtained from electroproduction cross-sections using CVC, as well as BaBar results for $τ → K^-K^0ν_τ$. The fully inclusive spectral function thus obtained is entirely based on experimental data, without Monte Carlo input. From this new data set, we obtain $α_s(m_τ)=0.3077±0.0075$, which corresponds to $α_s(m_Z)=0.1171±0.0010$. This analysis can be improved on the experimental side with new measurements of the dominant $ππ^0$, $π 3π^0$, and $3π π^0$ $τ$ decay modes.