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arXiv 1202.2672hep-phhep-exhep-lat
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用改进的固定阶微扰理论确定$α_s(M_τ^2)$

Determination of $α_s(M_τ^2)$ from Improved Fixed Order Perturbation Theory

Gauhar Abbas, B. Ananthanarayan, Irinel Caprini

摘要:

我们重新审视了$α_s(M_τ^2)$的提取从QCD微扰修正强子$τ$分支比,使用改进的固定阶微扰理论的基础上的显式求和的所有重整化群可访问的矩阵,提出了一段时间以前的文献。在这种方法中,在QCD Adler函数的展开中耦合的功率乘以一组函数$D_n$,其自身依赖于耦合并且可以通过迭代地求解微分方程序列而以封闭形式写出。我们发现,新的扩展有一个改进的行为在复杂的能量平面相比,标准的固定阶微扰理论(FOPT),是类似的,但不完全相同的轮廓改进微扰理论(CIPT)。在${\bar{\rm MS}}$方案$ α_s(M_τ^2)= 0.338 \pm 0.010$中,我们得到了五项微扰展开式,并以最近文献中报道的$τ$轻子的微扰对强子宽度的贡献的精确值作为输入.

英文摘要:

We revisit the extraction of $α_s(M_τ^2)$ from the QCDperturbative corrections to the hadronic $τ$ branching ratio, using an improved fixed-order perturbation theory based on the explicit summation of all renormalization-group accessible logarithms, proposed some time ago in the literature. In this approach, the powers of the coupling in the expansion of the QCD Adler function are multiplied by a set of functions $D_n$, which depend themselves on the coupling and can be written in a closed form by iteratively solving a sequence of differential equations. We find that the new expansion has an improved behavior in the complex energy plane compared to that of the standard fixed-order perturbation theory (FOPT), and is similar but not identical to the contour-improved perturbation theory (CIPT). With five terms in the perturbative expansion we obtain in the ${\bar{\rm MS}}$ scheme $ α_s(M_τ^2)= 0.338 \pm 0.010$, using as input a precise value for the perturbative contribution to the hadronic width of the $τ$ lepton reported recently in the literature.

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