We combine ALEPH and OPAL results for the spectral distributions measured in $\tau \to {\pi }^{-}{\pi }^0{\nu }_{\tau }$, $\tau \to 2{\pi }^{-}{\pi }^{+}{\pi }^0{\nu }_{\tau }$ and $\tau \to {\pi }^{-}3{\pi }^0{\nu }_{\tau }$ decays with (i) recent BABAR results for the analogous $\tau \to K^{-}{K}^0{\nu }_{\tau }$ distribution and (ii) estimates of the contributions from other hadronic $\tau$-decay modes obtained using CVC and electroproduction data, to obtain a new and more precise nonstrange, inclusive vector, isovector spectral function. The BABAR $K^{-}{K}^0$ and CVC/electroproduction results provide us with alternate, entirely data-based input for the contributions of all exclusive modes for which ALEPH and OPAL employed Monte-Carlo-based estimates. We use the resulting spectral function to determine ${\alpha }_s(m_{\tau })$, the strong coupling at the $\tau$ mass scale, employing finite energy sum rules. Using the fixed-order perturbation theory (FOPT) prescription, we find ${\alpha }_s(m_{\tau })=0.3077\pm 0.0075$, which corresponds to the five-flavor result ${\alpha }_s(M_Z)=0.1171\pm 0.0010$ at the $Z$ mass. While we also provide an estimate using contour-improved perturbation theory (CIPT), we point out that the FOPT prescription is to be preferred for comparison with other ${\alpha }_s$ determinations employing the $\overline{\mathrm{MS}}$ scheme, especially given the inconsistency between CIPT and the standard operator product expansion recently pointed out in the literature. Additional experimental input on the dominant $2\pi$ and $4\pi$ modes would allow for further improvements to the current analysis.

中文翻译：

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来自改进的τvector等矢量谱函数的强耦合

我们将ALEPH和OPAL结果结合起来，得出在 $\tau \to {\pi }^{-}{\pi }^0{\nu }_{\tau }$， $\tau \to \mathrm{2个}{\pi }^{-}{\pi }^{+}{\pi }^0{\nu }_{\tau }$ 和 $\tau \to {\pi }^{-}3{\pi }^0{\nu }_{\tau }$（i）类似的最近BABAR结果衰减$\tau \to {ķ}^{-}{ķ}^0{\nu }_{\tau }$ 分布和（ii）其他强子的贡献估计 $\tau$使用CVC和电生产数据获得的衰减模式，以获得新的且更精确的非奇异，包含向量，等向量谱函数。该巴巴尔 ${ķ}^{-}{ķ}^0$CVC /电生产结果为ALEPH和OPAL采用基于蒙特卡洛的估计的所有排他性模式的贡献为我们提供了完全基于数据的替代输入。我们使用结果谱函数来确定${\alpha }_s（{米}_{\tau }）$，在 $\tau$质量规模，采用有限的能量求和规则。使用固定阶扰动理论（FOPT）处方，我们发现${\alpha }_s（{米}_{\tau }）=0.3077\pm 0.0075$，对应于五种口味的结果 ${\alpha }_s（{\mathrm{中号}}_{ž}）=0.1171\pm 0.0010$ 在 $ž$大量的。虽然我们还使用轮廓改进的扰动理论（CIPT）提供了估计，但我们指出，与其他方法进行比较时，首选FOPT处方${\alpha }_s$ 确定采用 $\overline{\mathrm{小姐}}$方案，特别是考虑到CIPT与最近在文献中指出的标准运营商产品扩展之间的不一致。占主导地位的其他实验输入$\mathrm{2个}\pi$ 和 $4\pi$ 模式将允许对当前分析进行进一步的改进。