QCD coupling from an improved vector-isovector spectral function using tau decays and electroproduction data - Mansur, Lucas Morethes (2025)
The determination of the Quantum Chromodynamics (QCD) coupling, αs, from the theoretical description of inclusive τ → hadrons + ντ decays, dominated by perturbative QCD, is one of the most precise αs extractions from experimental data. In these decays, the hadronic vector and axial vector spectral functions are experimentally accessible. In this work, we produce a new and improved non-strange inclusive vector-isovector spectral function by performing a data combination, on a channel-by-channel basis, for the dominant hadronic τ decay channels using ALEPH and OPAL collaborations data for π-π0, 2π-π+π0, and π-3π0 decay modes, and the high-statistics Belle dataset for τ → π-π0 + ντ . The dominant channels are supplemented with small contributions from higher-threshold modes obtained from e+e- → hadrons cross-section data related by isospin symmetry and the Babar τ → K-K0ντ data, and, with this, we arrive at an inclusive spectral function that relies solely on experimental information, without Monte Carlo simulations inputs. With this new and improved hadronic spectral function, we perform a new αs determination at the τ-mass scale, employing finite energy sum rules. Using fixed-order perturbation theory (FOPT), we obtained α(mτ) = 0.2967(85), which corresponds to the five-flavor result α(mZ) = 0.1156(12), at Z-boson mass scale, result that agrees within 1.6σ with the PDG worlds average, α(mZ) = 0.1180(9). In addition, our combination of exclusive spectra for the dominant channels paves the way for future improvements in case new exclusive data become available and enables the use of the combined spectra in other related investigations, such as the π+π- channel contribution to the muons anomalous magnetic moment.