从$τ$衰变得到$α_s$：新的QCD微扰展开式中的轮廓改进和固定阶求和
$α_s$ from $τ$ decays: contour-improved versus fixed-order summation in a new QCD perturbation expansion
摘要：
在一个新的QCD微扰展开的框架下，通过研究轮廓改进（CI）和固定阶（FO）重整化群求和，我们考虑了从$τ$强子衰变中确定$α_s$.新的扩展功能，取代的权力的耦合，定义的解析连续的博雷尔复平面，通过最佳的保角映射。使用的物理模型最近讨论的Beneke和Jamin，我们表明，新的CIPT接近真实的结果，具有很大的精度时，微扰阶数增加，而新的FOPT给出了一个不太准确的描述在该地区的虚数存在于扩展的运行耦合大。使用新的展开式，标准CI和FO求和之间的$α_s(m_τ^2)$中的0.024差异减少到仅0.009。由新的CIPT预测了$α_s(m_τ^2)= 0.320 ^{+0.011}_{-0.009}$，与标准FOPT的结果基本一致，但有更坚实的理论基础。
英文摘要：
We consider the determination of $α_s$ from $τ$ hadronic decays, by investigating the contour-improved (CI) and the fixed-order (FO) renormalization group summations in the frame of a new perturbation expansion of QCD, which incorporates in a systematic way the available information about the divergent character of the series. The new expansion functions, which replace the powers of the coupling, are defined by the analytic continuation in the Borel complex plane, achieved through an optimal conformal mapping. Using a physical model recently discussed by Beneke and Jamin, we show that the new CIPT approaches the true results with great precision when the perturbative order is increased, while the new FOPT gives a less accurate description in the regions where the imaginary logarithms present in the expansion of the running coupling are large. With the new expansions, the discrepancy of 0.024 in $α_s(m_τ^2)$ between the standard CI and FO summations is reduced to only 0.009. From the new CIPT we predict $α_s(m_τ^2)= 0.320 ^{+0.011}_{-0.009}$, which practically coincides with the result of the standard FOPT, but has a more solid theoretical basis.
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