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arXiv 1306.0985hep-ph
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用非幂次QCD微扰理论研究τ强子宽度的强耦合

Strong coupling from the tau hadronic width by non-power QCD perturbation theory

I. Caprini

备注：
Plenary talk at the International Workshop on Determination of the Fundamental Parameters of QCD, Singapore, March 2013. To be published in Mod. Phys. Lett. A
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摘要：

从QCD中微扰展开式的发散性质出发，利用Borel平面共形映射的级数加速技术，定义了一种新的Adler函数的非幂微扰展开式，它同时实现了重整化群求和并具有驯服的高阶行为.新的扩展功能，取代标准的权力的耦合，是奇异的耦合平面的原点，并有分歧的微扰扩展，类似于扩展功能本身。面对新的微扰展开与标准的最近在文献中研究的特定模型，我表明，他们近似在一个令人印象深刻的方式准确的阿德勒函数和谱函数的时刻。应用于$τ$强子宽度，${\overline{\rm MS}}$方案中的轮廓改进和重整化群求和的非幂展开导致预测$α_s(M_τ^2)= 0.3192~^{+ 0.0167}_{-0.0126}$，其转化为$α_s(M_Z^2)= 0.1184~^{+0.0020}_{-0.0016}$。

英文摘要：

Starting from the divergent character of the perturbative expansions in QCD and using the technique of series acceleration by the conformal mappings of the Borel plane, I define a novel, non-power perturbative expansion for the Adler function, which simultaneously implements renormalization-group summation and has a tamed large-order behaviour. The new expansion functions, which replace the standard powers of the coupling, are singular at the origin of the coupling plane and have divergent perturbative expansions, resembling the expanded function itself. Confronting the new perturbative expansions with the standard ones on specific models investigated recently in the literature, I show that they approximate in an impressive way the exact Adler function and the spectral function moments. Applied to the $τ$ hadronic width, the contour-improved and the renormalization-group summed non-power expansions in the ${\overline{\rm MS}}$ scheme lead to the prediction $α_s(M_τ^2)= 0.3192~^{+ 0.0167}_{-0.0126}$, which translates to $α_s(M_Z^2)= 0.1184~^{+0.0020}_{-0.0016}$.

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