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

Abstract

We employ \textit{Levin-type sequence 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 $c_{5,1}=278_{-19}^{+27},c_{6,1}=3375_{-209}^{+489},c_{7,1}=(2.03_{-0.25}^{+0.41})\times 10^4.$ 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.

Comments: 20 pages, 1 figure, title slightly modified, accepted version in Phys.Lett.B