Strong coupling at the $\tau$-mass scale from an improved vector isovector spectral function

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Abstract
We perform a precise extraction of the QCD coupling at the \tau τ -mass scale, \alpha_s(m_\tau) α s ( m τ ) , from a new vector isovector spectral function which combines ALEPH and OPAL distributions for the dominant channels, \tau\to\pi \pi^0\nu_\tau τ → π π 0 ν τ , \tau\to 3\pi \pi^0\nu_\tau τ → 3 π π 0 ν τ and \tau\to \pi 3\pi^0\nu_\tau τ → π 3 π 0 ν τ , 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 τ → K − K 0 ν 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 \alpha_s(m_\tau)=0.3077±0.0075 α s ( m τ ) = 0.3077 ± 0.0075 , which corresponds to \alpha_s(m_Z)=0.1171±0.0010 α s ( m Z ) = 0.1171 ± 0.0010 . This analysis can be improved on the experimental side with new measurements of the dominant \pi\pi^0 π π 0 , \pi 3\pi^0 π 3 π 0 , and 3\pi \pi^0 3 π π 0 \tau τ decay modes.
Funding Information
  • Conselho Nacional de Desenvolvimento Científico e Tecnológico (309847/2018-4)
  • European Regional Development Fund (CICYTFEDER-FPA2017-86989-P)
  • Fundação de Amparo à Pesquisa do Estado de São Paulo (2015/20689-9)
  • Fundação de Amparo à Pesquisa do Estado de São Paulo (2019/16957-9)
  • Generalitat de Catalunya (2017 SGR 1069)
  • Natural Sciences and Engineering Research Council of Canada
  • U.S. Department of Energy (DE-SC0013682)

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