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arXiv 1005.2674hep-ph
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用ALEPH $τ$衰变数据检验夸克-强子对偶性概念

Testing the Concept of Quark-Hadron Duality with the ALEPH $τ$ Decay Data

B. A. Magradze

备注：
33 pages, 1 postscript figure, 14 Tables. Abstract corrected, two new Tables 1 and 7 added, numbers in Eqs. 43,45,47,52 corrected, numbers in Tables 4,5,6,9,10 corrected, new references [15,16,17,18,21,46,48,50,51] added, presentation of the material improved. see also arXiv: 1112.5958 [hep-ph](2011) a Revised version of the article published in Few-Body Syst(2010) 48:143-169; Erratum: Few Body Syst. 2012 Online First
发表信息：
Few Body Syst.48:143-169,2010. Few Body Syst. 48: Few Body Syst. 53, 365-367, 2012
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摘要：

本文提出了一种从矢量通道中的$τ$轻子强子衰变率中提取强耦合常数$α_s$数值的改进方法。我们采用夸克-强子对偶的概念，特别是引入一个边界能量平方$s_{\rm p}>0$，在闵可夫斯基空间\cite{BLR,Rafa,PPR}的微扰QCD连续的开始。为了近似$s>s_{\rm p}$区域中的强子谱函数，我们使用五阶解析微扰理论（APT）。我们的方法的一个新特点是，它使我们能够同时从数据中提取QCD尺度参数$Λ_{\bar{\rm MS}}$和边界能量平方$s_{\rm p}$。我们仔细地确定这些参数的实验误差来自不变质量平方分布的误差。对于$\bar{\rm MS}$方案耦合常数，我们得到了$α_s(m^{2}_τ)=0.308\pm 0.014_{\rm exp.}$。我们表明，我们的数值分析是更稳定的高阶修正比标准的。二元点$s_{\rm p}$的提取值对微扰理论修正$s_{\rm d}= 1.71\pm 0.05_{\rm exp}\pm 0.00_{\rm th}\,\, {\rm GeV^{2}}$的稳定性令人惊讶。此外，我们使用最终ALEPH结果重新计算了红外区域的“实验”Adler函数。还确定了该函数的不确定度。

英文摘要：

We propose a modified procedure for extracting the numerical value for the strong coupling constant $α_s$ from the $τ$ lepton hadronic decay rate into non-strange particles in the vector channel. We employ the concept of the quark-hadron duality specifically, introducing a boundary energy squared $s_{\rm p}>0$, the onset of the perturbative QCD continuum in Minkowski space \cite{BLR,Rafa,PPR}. To approximate the hadronic spectral function in the region $s>s_{\rm p}$, we use Analytic Perturbation Theory (APT) up to the fifth order. A new feature of our procedure is that it enables us to extract from the data simultaneously the QCD scale parameter $Λ_{\bar{\rm MS}}$ and the boundary energy squared $s_{\rm p}$. We carefully determine the experimental errors on these parameters which come from the errors on the invariant mass squared distribution. For the $\bar{\rm MS}$ scheme coupling constant, we obtain $α_s(m^{2}_τ)=0.308\pm 0.014_{\rm exp.}$. We show that our numerical analysis is more stable against higher-order corrections than the standard one. The extracted value for the duality point $s_{\rm p}$ is found surprisingly stable against perturbation theory corrections $s_{\rm d}= 1.71\pm 0.05_{\rm exp}\pm 0.00_{\rm th}\,\, {\rm GeV^{2}}$.Additionally, we recalculate the "experimental" Adler function in the infrared region using final ALEPH results. The uncertainty on this function is also determined.

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