A new determination of higher-order QCD corrections to hadronic $\tau$ decays

We employ $\mathit{\text{Levin-type}}\mathit{\text{sequence}}\mathit{\text{transformations}}$ to accelerate the convergence of the perturbative fixed-order expansion of the QCD correction ${\delta }^{(0)}$ in terms of the strong coupling ${\alpha }_s$. The method efficiently resums the series, yielding a stable and self-consistent determination of higher-order QCD corrections to hadronic $\tau$ decays, consistent with existing results. We find ${\delta }_{\text{Levin-FOPT}}^{(0)}=0.2089\pm 0.0040\pm {0.0060}_{{\alpha }_s}$, and predict $c_{5,1}=278_{-19}^{+27},c_{6,1}=3375_{-209}^{+489},c_{7,1}=(2.03_{-0.25}^{+0.41})\times {10}^4\mathrm{.}$ Our results demonstrate that Levin-type transformations provide an efficient framework for analyzing asymptotic perturbative series, and studying the higher order perturbative behaviour of the hadronic $\tau$ decays.