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arXiv 1002.2968hep-ph
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关于确定α_s(M_tau)的Renormalon模型的注记

A note on renormalon models for the determination of alpha_s(M_tau)

S. Descotes-Genon, B. Malaescu

摘要:

τ强子宽度提供了一个确定的强耦合常数α_s在低能量,因为它可以涉及到一个加权积分的阿德勒函数在复杂的能量平面。利用算子乘积展开,可以看出对alpha_s的灵敏度来自微扰贡献,它可以通过积分Adler函数的微扰展开得到。提出了两种不同的处方来执行这个积分,称为固定阶微扰理论和轮廓改进的微扰理论(FOPT和CIPT),产生不同的结果的强耦合常数。最近,模型的Adler函数的基础上renormalon演算已被提出来确定这两种方法是最准确的,通过比较所得的渐近级数与真实值的积分。我们讨论了这一假设及其自由参数的确定。我们发现,对于CIPT与FOPT的比较,这种重正马龙模型的变化可能会产生相反的结论,而且这种模型没有足够的约束来提供关于这个问题的明确答案,也不足以用于高精度地确定alpha_s(m_tau^2)。

英文摘要:

The tau hadronic width provides a determination of the strong coupling constant alpha_s at low energies, since it can be related to a weighted integral of the Adler function in the complex energy plane. Using Operator Product Expansion, one sees that the sensitivity to alpha_s comes from the perturbative contribution, which can be obtained by integrating the perturbative expansion of the Adler function. Two different prescriptions proposed to perform this integral, called Fixed-Order Perturbation Theory and Contour-Improved Perturbation Theory (FOPT and CIPT), yield different results for the strong coupling constant. Recently, models for the Adler function based on renormalon calculus have been proposed to determine which of the two methods is the most accurate, by comparing the resulting asymptotic series with the true value of the integral. We discuss the assumptions of such ansatz and the determination of their free parameters. We show that variations of this renormalon ansatz can yield opposite conclusions concerning the comparison of CIPT versus FOPT, and that such models are not constrained enough to provide a definite answer on this issue or to be exploited for a high-precision determination of alpha_s(m_tau^2).

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