论文标题
使用$τ$衰减数据的Borel-Laplace Sum规则，使用具有改进的异常尺寸的OPE
Borel-Laplace Sum Rules with $τ$ decay data, using OPE with improved anomalous dimensions
论文作者
论文摘要
我们对无固定的semihadronic $τ$ -DECAY数据的双齿轮borel-laplace QCD总规则进行数值分析。 $ d = 0 $对总和规则中理论轮廓积分的贡献由（截断的）固定订单扰动理论方法（FO）以及Borel集成的主要价值（PV）评估。我们用于完整的Adler函数运算符产品扩展（OPE），其中包含$ \ sim \ sim \ langle o_d \ rangle $ dimension $ d = 2 n $，其中$ 2 \ leq n \ leq n \ leq 5 $（v+a）-CHANNEL和$ 2 \ leq n \ leq N \ leq 7 $ for V-Channel数据。在我们以前的作品[1,2]中，仅分析了（V+A） - 通道数据。在这项工作中，也进行了一组新的V通道数据的分析。此外，$ d = 0 $部分功能的重统计动力构造在$ u = 3 $红外肾上腺肾上腺术领域得到了改善，通过涉及有关两个主要非智能值$ k^{（j）} =γ^{（1）}（1）}（O_6^{（O_6^{（j）} {（j）} {（j）} {（j）} {（j））/β0$的$ k^{（j）} =γ^{（j）} = fiff有效的信息。此外，ADLER函数的OPE现在具有主体异常维度（$ \ simα_s^{k^{（1）}} $）的d = 6贡献，并且更高维度的术语（零异常维度）。通过复制几个双钉动量矩$ a^{（2，n）} $的（中央）实验值（中央）实验值来进行$α_s$的提取值的交叉检查。 （MSBAR）耦合的平均最终提取值为：$α_s（M_τ^2）= 0.3169^{+0.0070} _ { - 0.0096} $，对应于$ afiman_s（m_z^2）= 0.1183^{+0.0009} {+0.0009} _ {-0.0009} _ {-0.0009 _ {-0.000012}。
We perform numerical analysis of double-pinched Borel-Laplace QCD sum rules for the strangeless semihadronic $τ$-decay data. The $D=0$ contribution to the theoretical contour integral in the sum rules is evaluated by the (truncated) Fixed Order perturbation theory method (FO) and by the Principal Value (PV) of the Borel integration. We use for the full Adler function the Operator Product Expansion (OPE) with the terms $\sim \langle O_D \rangle$ of dimension $D=2 n$ where $2 \leq n \leq 5$ for the (V+A)-channel, and $2 \leq n \leq 7$ for the V-channel data. In our previous works [1,2], only the (V+A)-channel data was analysed. In this work, the analysis of a new set of V-channel data is performed as well. Further, a renormalon-motivated construction of the $D=0$ part of the Adler function is improved in the $u=3$ infrared renormalon sector, by involving the recently known information on the two principal noninteger values $k^{(j)}=γ^{(1)}(O_6^{(j)})/β_0$ of the effective leading-order anomalous dimensions. Additionally, the OPE of the Adler function has now the D=6 contribution with the principal anomalous dimension ($\sim α_s^{k^{(1)}}$), and terms of higher dimension (with zero anomalous dimension). Cross-checks of the obtained extracted values of $α_s$ and of the condensates were performed by reproduction of the (central) experimental values of several double-pinched momenta $a^{(2,n)}$. The averaged final extracted values of the (MSbar) coupling are: $α_s(m_τ^2) = 0.3169^{+0.0070}_{-0.0096}$, corresponding to $α_s(M_Z^2)=0.1183^{+0.0009}_{-0.0012}$.
