用ALEPH $τ$衰变数据在Borel-Laplace求和规则中使用改进的算子乘积展开，并确定pQCD耦合
Using improved Operator Product Expansion in Borel-Laplace Sum Rules with ALEPH $τ$ decay data, and determination of pQCD coupling
摘要：
在V+A通道无奇异半强$τ$衰变的双箍缩Borel-Laplace求和规则和有限能量求和规则中，我们对Adler函数采用改进的截断算子乘积展开（OPE），其中包含两类具有$D=6$维数的项.高阶微扰QCD项的$D=0$部分的Adler函数的产生进行使用的renormalon激励的anterior纳入领先的UV renormalon和前两个领先的IR renormalon。求和规则的截断$D=0$部分由固定阶扰动理论（FO）的两个变体、Borel重算的主值（PV）和轮廓改进扰动理论（CI）来评估。对于实验V+A通道谱函数，我们使用ALEPH $τ$ -衰变数据。我们指出，截断的FO和PV评估方法正确的帐户的Renormalon结构的求和规则，而这不是截断的CI评估的情况。我们提取了两种FO方法和PV方法的平均值的${\overline {\rm MS}}$耦合$α_s(m_τ^2) = 0.3235^{+0.0138}_{-0.0126}$ [ $α_s(M_Z^2)=0.1191 \pm 0.0016$ ]的值，我们认为这是我们的主要结果。如果我们在平均值中还包括CI提取，则值将为$α_s(m_τ^2) = 0.3299^{+0.0232}_{-0.0225}$ [ $α_s(M_Z^2)=0.1199^{+0.0026}_{-0.0028}$ ]。这项工作是我们以前工作的扩展和改进[Eur.Phys.J.C81（2021）10，930]，其中我们对截断OPE使用了更简单（和广泛使用）的形式，并且其中$α_s(M_Z^2)$的提取值略低。
英文摘要：
We use improved truncated Operator Product Expansion (OPE) for the Adler function, involving two types of terms with dimension $D=6$, in the double-pinched Borel-Laplace Sum Rules and Finite Energy Sum Rules for the V+A channel strangeless semihadronic $τ$ decays. The generation of the higher order perturbative QCD terms of the $D=0$ part of the Adler function is carried out using a renormalon-motivated ansatz incorporating the leading UV renormalon and the first two leading IR renormalons. The trunacted $D=0$ part of the Sum Rules is evaluated by two variants of the fixed-order perturbation theory (FO), by Principal Value of the Borel resummation (PV), and by contour-improved perturbation theory (CI). For the experimental V+A channel spectral function we use the ALEPH $τ$-decay data. We point out that the truncated FO and PV evaluation methods account correctly for the renormalon structure of the Sum Rules, while this is not the case for the truncated CI evaluation. We extract the value of the ${\overline {\rm MS}}$ coupling $α_s(m_τ^2) = 0.3235^{+0.0138}_{-0.0126}$ [$α_s(M_Z^2)=0.1191 \pm 0.0016$] for the average of the two FO methods and the PV method, which we consider as our main result. If we included in the average also CI extraction, the value would be $α_s(m_τ^2) = 0.3299^{+0.0232}_{-0.0225}$ [$α_s(M_Z^2)=0.1199^{+0.0026}_{-0.0028}$]. This work is an extension and improvement of our previous work [Eur.Phys.J.C81 (2021) 10, 930] where we used for the truncated OPE a more naive (and widely used) form and where the extracted values for $α_s(M_Z^2)$ were somewhat lower.
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