标题： 一种对$α_s (M_τ^2)$的新测定以及强子$τ$衰变的高阶QCD修正 显示英文标题

标题： A new determination of $α_s (M_τ^2)$ and higher-order QCD corrections to hadronic $τ$ decays

摘要： We employ \textit{莱文型序列变换} to accelerate the convergence of the perturbative fixed-order expansion of the QCD correction $\delta^{(0)}$ in terms of the strong coupling $\alpha_s$, and of the inverted series expressing $\alpha_s$ in powers of $\delta^{(0)}$. The method efficiently resums the divergent inverted series, yielding a stable and self-consistent determination of the strong coupling at the $\tau$ mass scale. It also provides reliable estimates of higher-order QCD corrections to hadronic $\tau$ decays, consistent with existing results. 我们找到$\alpha_s^{\text{Levin-FOPT}} = 0.3159 \pm 0.0018 \, \pm 0.0023 \, $，并预测$c_{5,1} = 269^{+47}_{-45}, \quad c_{6,1} = 3185^{+117}_{-279}, \quad c_{7,1} = (1.9^{+0.9}_{-0.8}) \times 10^4.$。我们的结果表明，Levin型变换为分析渐近微扰级数和提高从强子$\tau$衰变中提取$\alpha_s(M_\tau^2)$提供了一个高效的框架。 显示英文摘要

摘要： 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 $\alpha_s$, and of the inverted series expressing $\alpha_s$ in powers of $\delta^{(0)}$. The method efficiently resums the divergent inverted series, yielding a stable and self-consistent determination of the strong coupling at the $\tau$ mass scale. It also provides reliable estimates of higher-order QCD corrections to hadronic $\tau$ decays, consistent with existing results. We find $\alpha_s^{\text{Levin-FOPT}} = 0.3159 \pm 0.0018 \, \pm 0.0023 \, $, and predict $c_{5,1} = 269^{+47}_{-45}, \quad c_{6,1} = 3185^{+117}_{-279}, \quad c_{7,1} = (1.9^{+0.9}_{-0.8}) \times 10^4.$ Our results demonstrate that Levin-type transformations provide an efficient framework for analyzing asymptotic perturbative series and improving the extraction of $\alpha_s(M_\tau^2)$ from hadronic $\tau$ decays.