A new determination of higher-order QCD corrections to hadronic τ decays

We employ Levin-type sequence transformations to accelerate the convergence of the perturbative fixed-order expansion of the QCD correction δ (0) in terms of the strong coupling α s . The method efficiently resums the series, yielding a stable and self-consistent determination of higher-order QCD corrections to hadronic τ decays, consistent with existing results. We find δ Levin-FOPT ( 0 ) = 0.2089 ± 0.0040 ± 0 . 0060 α s , and predict c 5 , 1 = 278 − 19 + 27 , c 6 , 1 = 3375 − 209 + 489 , c 7 , 1 = ( 2 . 03 − 0.25 + 0.41 ) × 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 τ decays.