Alessio Maiezza, Juan Carlos Vasquez
We study the QCD Adler function in the energy region $\approx 0.7-2.5$ GeV, in which the non-perturbative effects become dominant. Our analysis is a renormalon-based evaluation using transseries within the resurgence of the Renormalization-Group-Equation and does not require the Operator-Product-Expansion.
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We compute non-perturbative contributions to the Adler function, the derivative of the vacuum polarization function in gauge theory, using resurgence methods and Borel-summed gauge field propagators. At 2-loop, to order $1/N_f$, we construct the full 2-parameter transseries and perform the sum over the non-perturbative sectors. We then introduce a convolution-based method to derive the transseries structure of product series, which can also be used to study higher orders in the expansion in $1/N_f$. We compute 3-loop planar diagrams, at order $1/N_f^2$, and for each diagram study the asymptoti…
The Adler function D is found {\em exactly} in supersymmetric QCD. Our exact formula relates D(Q^2) to the anomalous dimension of the matter superfields γ(α_s(Q^2)). En rout we prove another theorem: the absence of the so-called singlet contribution to D. While such singlet contributions are present in individual supergraphs, they cancel in the sum.
Adler function in the analytic approach to QCD
利用最近导出的Adler函数D（Q^2）的积分表示，研究了D（Q^2）的低能行为.这种表示体现了对D（Q^2）的非微扰约束，特别地，它保留了由于非零π介子质量的影响。的阿德勒函数计算内开发的方法，利用其微扰近似作为唯一的额外输入。所得结果与实验预言的Adler函数在整个能量范围内一致，并对高圈数修正具有显著的稳定性。
Two renormalization group invariant quantities in quantum chromodinamics (QCD), defined in Euclidean space,namely, Adler D-function of electron-positron annihilation to hadrons and Bjorken polarized deep-inelastic scattering sum rule, are considered. It is shown, that the 5-th order corrections to them in $\overline{MS}$-like renormalization prescriptions, proportional to Riemann $ζ$-function $ζ\left(4\right)$, can be restored by the transition to the C-scheme, with the $β$-function, analogous to Novikov, Shifman, Vainshtein and Zakharov exact $β$-function in $\mathcal{N}=1$ supersymmetric gau…
I discuss similarities and differences between the resurgence program in quantum mechanics and the operator product expansion in strongly coupled Yang-Mills theories. In ${\mathcal N}=1$ super-Yang-Mills renormalons possess peculiar features that make them different from renormalons in QCD. Their conventional QCD interpretation does not seem to be applicable in supersymmetric Yang-Mills in a straightforward manner.
We formulate a way to separate UV and IR contributions to the Adler function and discuss how $Λ_\mathrm{QCD}^2/Q^2$ dependence is encoded in the UV contribution within perturbative QCD.
We describe the Adler function in Quantum Chromodynamics using a transseries representation within a resurgent framework. The approach is based on a Borel-Ecalle resummation of the infrared renormalons combined with an effective running for the strong coupling. The new approach is flexible enough to give values in agreement with the current Adler function determinations. We then apply our finding to the muon's anomalous magnetic moment studying the possibility of saturating, solely in terms of the vacuum polarization function, the current discrepancy between the best Standard Model value for t…
Resurgent representation of the Adler function in the large-$β_0$ approximation of QCD
本文利用复苏数学框架和Borel变换的逆Mellin变换，推导出QCD大-$\eta_0$近似下Adler函数的紧凑复苏表示，该表示在整个复动量平面有效，并用于计算标准模型中$\ au$轻子的强子宽度。
Large-order Behaviour of the QCD Adler D-function in Planar Approximation
在只保留平面费曼图的近似下，我们考虑了与QCD真空极化Adler D-函数相关的领先紫外（UV）重正子奇异性的结构。这种“平面近似”导致了一些简化，特别是四个费米子算子的四个潜在贡献中的三个被证明是不存在的。对于含$N_f$夸克味的SU（N）QCD，我们能够得到与$N_f^{n-r} N^r$成比例的微扰系数部分的主导$n\to\infty$行为的完全归一化结果.
Strong decays and Adler selfconsistency condition in two-dimensional QCD
在二维QCD的t Hooft模型框架下研究了强介子衰变。特别注意的是支付的过程中涉及的最终状态和低能定理已被检查，包括“阿德勒零”。它明确表明，在手征极限的任何三介子衰变振幅至少有一个π顶点消失相同的外部动量的任何值。确定了缀饰矢量流和轴矢量流顶点的沃德恒等式，并讨论了它们与π介子顶点的关系。
A new representation of the Adler function for lattice QCD
我们讨论了格点量子色动力学计算强子真空极化和相应的Adler函数的几个方面。我们实现了一个表示先前得出的，它允许一个访问这些现象学上的重要功能的一组连续的虚拟，无论当前的风味结构。其次，我们提出了一个理论分析的有限尺寸的影响，我们的特定表示的阿德勒函数，算子乘积展开在大动量和小动量的欧几里得相关的频谱表示的基础上。最后，风味结构的电磁电流相关器进行分析，其中最近的理论估计的威克断开图的贡献是独立重新推导和确认。
A novel integral representation for the Adler function
在QCD解析方法的一般框架下，导出了电子正电子湮没成强子的Adler D函数和R比的新的积分表示。这些表示捕获的非微扰信息编码的色散关系的D-功能，由于类空和类时域之间的相互关系的影响，以及由于非零π质量的影响。后者在这一分析中起着至关重要的作用，迫使阿德勒函数在红外极限中消失。在开发的方法中的D-函数计算采用其微扰近似作为唯一的额外输入。在整个动量范围$0 \le Q^2 < \infty$内，所得结果与实验预言的Adler函数相当吻合。
We consider the two-fold expansion in powers of the conformal anomaly and of the strong coupling $α_s$ for the non-singlet contributions to Adler $D$-function and Bjorken polarized sum rule calculated previously in the $\MSbar$-scheme at the four-loop level. This representation provides relations between definite terms of different loop orders appearing within the $\{β\}$-expansion of these quantities. Supposing the validity of this two-fold representation at the five-loop order and using these relations, we obtain some $\mathcal{O}(α_s^5)$ corrections to the $D$-function, to the $R$-ratio of …
The contribution from hadronic vacuum polarisation effects is responsible for a large fraction of the theoretical uncertainty in the running of the QED coupling. The current level of uncertainty has become a limitation for electroweak precision tests. We use lattice QCD simulations with two flavours of O$(a)$ improved Wilson fermions to determine the Adler function in a broad range of the momentum transfer $Q^2$. The running of the QED coupling, including valence contributions from $u$, $d$, $s$ and $c$ quarks, is compared to phenomenological results at intermediate $Q^2$ values. In the large …
Adler function from R^{e^+e^-} measurements: experiments vs QCD theory
实验动机QCD分析的行为的阿德勒D-函数在欧几里德区域描述。它强调，通过考虑$b$ -夸克质量依赖的$α_s^2$ -效果得到更好的理论预测和实验激发的行为的D-函数在大的欧几里得动量转移之间的协议。对QCD预言的更详细的分析，包括夸克和胶子凝聚的信息，需要更精确的关于$e^+e^-\to{hadrons}$的数据，特别是在$E<M_{J/Ψ}$和$M_{J/Ψ}<E<3.6 GeV$区域。本文概述了用实验测定D函数来检验广义Crewther关系的方法。
We compute the nonsinglet Adler $D$-function and the coefficient function for Bjorken polarized sum rules $S^{Bjp}$ at order $O(α_s^4)$ in an extended QCD model with arbitrary number of fermion representations. The Crewther-Broadhurst-Kataev (CBK) relation in this order is confirmed.
Comment on "Infrared freezing of Euclidean QCD observables"
最近，P. M。Brooks和C. J. Maxwell [Phys. Rev. D{ \bf 74} 065012（2006）]声称，在欧几里德Adler ${\cal D}$函数的骨架展开中，在$Q^2=Λ^2$处的单环耦合的朗道极点不存在于前导单链项中。此外，在这种近似中，沿着欧几里得轴具有连续性，并且具有平滑的红外冻结，这些属性已知由“真正的”阿德勒函数满足。我们发现，在这些结果的推导中至关重要的是使用修改后的波莱尔求和，这同时导致损失的另一个基本属性的真正的阿德勒函数：解析隐含的Källen-Lehmann表示。
Adler function, Bjorken polarized sum rule: confirmation of elements of the $\{β\}$-expansion and the diagrams
本研究在标准QCD框架下独立验证了非单态Adler函数、Bjorken极化求和规则的$\u003cβ\u003e$-展开式元素至N⁴LO阶的既有结果，还提出基于朴素非阿贝尔化推广、用少量特定类型费曼图估算高阶QCD计算结果的方法。
Perturbative expansion of the QCD Adler function improved by renormalization-group summation and analytic continuation in the Borel plane
我们研究了最近提出的重整化群改进的微扰QCD中Adler函数展开式的高阶行为，该展开式以解析封闭的形式总结了从重整化群不变性可获得的主导矩阵。膨胀是第一次书面作为一个有效的一系列的权力的一个回路耦合，其领导在博雷尔平面的奇点被证明是相同的标准的“轮廓改进”的膨胀。利用Borel平面上解析延拓的保角映射技巧，定义了一类改进的展开式，它既实现了级数的重整化群不变性，又提供了级数的高阶性态.详细的数值研究的具体模型的Adler函数表明，新的扩展有显着的收敛性能的高阶。利用这些展开式从$τ$轻子的强子宽度确定强耦合，我们得到了由非微扰修正引起的不确定性的保守估计，$α_s(M_τ^2)= 0.3189^{+ 0.0173}_{-0.0151}$，它转化为$α_s(M_Z^2)= 0.1184^{+0.0021}_{-0.0018}$。
We derive explicit expressions for the elements of the $\{ β\}$-expansion for the nonsinglet Adler $D_A$-function and Bjorken polarized sum rules $S^{Bjp}$ in the N$^4$LO using recent results by Chetyrkin for these quantities computed within extended QCD including any number of fermion representations. We discuss the properties of the $\{ β\}$-expansion for $D_A$ and $S^{Bjp}$ at higher orders which follow from the Crewther [1] and the Broadhurst-Kataev [2] relation.
The decomposed photon anomalous dimension in QCD and the $\{β\}$-expanded representations for the Adler function
本文研究QCD中Adler函数及光子反常维度在O(α^4_s)阶的{β}展开，论证了γ(α_s)需按β函数系数分解，并比较了\overline{MS}与PMC/BLM近似的理论及现象学后果。
Chiral lagrangians and the QCD string
我们提出了一种推导QCD低能有效作用量的方法，假定强相互作用的长距离性质可以用弦论描述。我们绕过通常的问题，快子的存在和缺乏足够的阿德勒零使用西格玛模型的方法，其中包括正确的（手征非不变）QCD真空以上的激发。二维共形不变性则意味着O（p^4）有效拉格朗日系数为零。我们讨论如何超越这个限制。
Adler Function, Bjorken Sum Rule, and the Crewther Relation to Order alpha_s^4 in a General Gauge Theory
我们首次计算了极化电子-核子散射中α_s^4阶对比约肯求和规则的贡献，以及在一般色规范群的情况下α_s^4阶对（非单重态）阿德勒函数的贡献。我们确认在相同的顺序（广义）Crewther关系，它提供了一个强有力的测试，我们以前得到的结果的正确性：QCD阿德勒功能和五圈β功能淬火QED。特别是，一个不合理的贡献成比例的zeta_3在后者的数量的外观被确认。我们得到了与有效强耦合常数相关的公度标度方程，该方程是从比约肯求和规则和α_s阶阿德勒函数^[4]推导出来的。
QCD Running Coupling Constant in the Timelike Region
利用Adler $D$函数的非微扰展开和色散关系，提出了一种构造类时区QCD有效耦合常数的新方法.
Using the analytical $\rm{\overline{MS}}$-scheme three-loop contribution to the perturbative Coulomb-like part of the static color potential of heavy quark-antiquark system, we obtain the analytical expression for the fourth-order $β$-function in the gauge-invariant effective V-scheme in the case of the generic simple gauge group. Also we present the Adler function of electron-positron annihilation into hadrons and the coefficient function of the Bjorken polarized sum rule in the V-scheme up to $α^4_s$ terms. We demonstrate that at this level of PT in this effective scheme the $β$-function is …
Perturbative QCD corrections to hadronic $τ$ decays and $e^+e^-$ annihilation into hadrons below charm are obtained from the Adler function, which at present is known in the chiral limit to five-loop accuracy. Extractions of the strong coupling, $α_s$, from these processes suffer from an ambiguity related to the treatment of unknown higher orders in the perturbative series. In this work, we exploit the method of Padé approximants and its convergence theorems to extract information about higher-order corrections to the Adler function in a systematic way. First, the method is tested in the large…
We present an updated version of a QCD coupling which fulfills various physically motivated conditions: at high momenta it practically coincides with the perturbative QCD (pQCD) coupling; at intermediate momenta it reproduces correctly the physics of the semihadronic tau decay; and at very low momenta it is suppressed as suggested by large-volume lattice calculations. An earlier presented analysis is updated here in the sense that the Adler function, in the regime $|Q^2| \lesssim 1 \ {\rm GeV}^2$, is evaluated by a renormalon-motivated resummation method. This Adler function is then used here …
Testing non-perturbative strong interaction effects via the Adler function
基于现有的e^+e^-数据，我们给出了由电磁流相关器导出的Adler函数的非微扰估计，并与微扰QCD（pQCD）的理论预言进行了比较.比较的欧几里得区域，pQCD应该是最好的工作。我们强调，这样的比较只有在考虑到微扰预测的确切质量依赖性时才有意义，微扰预测可用于领先和领先（两个回路）顺序。为了在强耦合的演化过程中也能得到正确的物理质量依赖关系，我们利用最近计算的双圈模型，采用了新的β函数方法。三圈效应，这是可作为一系列的扩展低和高的动量传递，包括通过使用Pade改进。我们讨论了可能的限制，非微扰效应所建议的算子乘积展开。
Expansion functions in perturbative QCD and the determination of $α_s(M_τ^2)$
传统的微扰QCD耦合幂级数的收敛半径为零，不能再现像$α_s=0$上的Adler函数那样的QCD微扰子的奇异性。使用保角映射的Borel平面的技术，结合“软化”的领导奇点，我们定义了一组新的扩展功能，类似于扩展相关器，并在零耦合共享相同的奇异性。研究了几种不同的保形映射和实现Borel平面上Adler函数第一分支点的已知性质的不同方法，包括重整化群重正化的轮廓改进（CI）和固定阶（FO）两种形式.我们证明了一组新的CI展开式的显着收敛性质，并使用它们来确定强耦合的强子$τ$衰变宽度。通过对这个集合取平均值，并对误差进行保守处理，我们得到$α_s(M_τ^2)= 0.3195^{+ 0.0189}_{- 0.0138}$。
The Euclidean Adler Function and its Interplay with $Δα^{\mathrm{had}}_{\mathrm{QED}}$ and $α_s$
本文综合微扰 QCD、幂次修正、$e^+e^-$ 色散数据与格点结果，比较约 2 GeV 欧几里得 Adler 函数，并评估其对 $α_s$ 及重整化群方程检验的约束能力。
A variant of QCD with the coupling suppressed in the infrared (IR) regime, as suggested by large-volume lattice calculations of the Landau-gauge gluon and ghost dressing functions, is considered. The coupling is further restricted by the condition of approximate coincidence with perturbative QCD in the high momentum regime, and by the $τ$-lepton semihadronic decay rate in the intermediate momentum regime, the rate which is evaluated by a renormalon-motivated resummation method. The obtained coupling turns out to be free of Landau singularities. The $D=4,6$ condensate values of the Adler functi…
The present calculations in perturbative QCD reach the order $α_s^4$ for several correlators calculated to five loops, and the huge computational difficulties make unlikely the full six-loop calculation in the near future. This situation has practical consequences, in particular the treatment of the higher orders of the perturbation series for the current-current correlator of light quarks is one of the main sources of errors in the extraction of the strong coupling from hadronic $τ$ decays. Several approximate estimates of the next coefficients of the corresponding Adler function have been pr…
The analytical singlet $α_s^4$ QCD contributions into the $e^+e^-$-annihilation Adler function and the generalized Crewther relations
考虑了非单重态和矢量夸克流通道中的广义Crewther关系。他们遵循双重应用的运营商产品的扩展方法相同的轴向矢量三角形振幅在两个地区，毗邻的角度侧$(x,y)$（或$p^2,q^2$）。我们假设，广义Crewther关系在这两个运动学制度的结果在存在相同的微扰表达式的两个产品的系数函数的湮灭和深度非弹性散射过程中的非单态和矢量通道。考虑到$S_{GLS}$的四阶结果和广义Crewther关系中共形对称破坏的微扰效应，我们得到了单重态$α_s^4$对$D_A^{V}$ -函数的修正的解析贡献.它的后验比较与最近的结果直接的单重四阶修正的评估$D_A^{V}$ -函数证明的预测和获得的$ζ_3^2$ -单重项的贡献的一致性。它们可以从原始Crewther关系式在共形不变极限下得到。与以前的看法相反，规范模型中微扰级数中出现的$zeta_3$ -项与共形对称性并不矛盾，可以认为是规则性的。我们的预测和获得的四阶修正之间的Banks-Zaks动机的关系被提及。这证实了Baikov-Chetyrkin-Kuhn的预期，即矢量流通道中的广义Crewther关系得到了额外的单重态贡献，在微扰理论的这个顺序中，它与QCD $β$函数的第一个系数成比例。
Impact of the pion mass on nonpower expansion for QCD observables
本文在QCD四圈水平解析方法的框架内提出了一组新的函数，它们构成了物理观测量的大质量非幂展开的基础。采用Adler函数的色散关系，考虑了$π$介子质量的影响.不为零的π介子质量实质上修改了低能时的泛函展开。具体地说，类空函数的影响下的质量的$π$介子在红外域低于几个GeV的，而类时函数获得的特征plateaulike行为低于2 π阈值。与此同时，在所考虑的非零π介子质量的情况下，无质量非幂次展开的所有吸引人的特征仍然存在。
The running fine structure constant alpha(E) via the Adler function
我们提出了一个最新的分析精确测定的有效精细结构常数，并讨论了未来的改进前景。我们主张使用由Adler函数监控的确定，这使得我们能够以最佳的良好控制的方式利用微扰QCD。再加上能量高达几个GeV的强子截面测量的长期计划，以与Z质量M_Z相当的精度确定α（M_Z）应该是可行的。目前，α（E）在E>1 GeV时是SM的基本参数中最不精确的。尽管由于新的BaBar独家数据而取得了重大进展，但1.4至2.4 GeV区域仍然是问题最多的区域，因此，预计VEPP-2000和弗拉斯卡蒂可能的"高能“选择DAFNE-2将在减少不确定性方面迈出重要一步。最新评估结果为Delta α ^{（5）}_{had}（M_Z^2）= 0.027515 +/- 0.000149或α ^{-1}（M_Z）=128.957 +/- 0.020。
Strong coupling from the tau hadronic width by non-power QCD perturbation theory
从QCD中微扰展开式的发散性质出发，利用Borel平面共形映射的级数加速技术，定义了一种新的Adler函数的非幂微扰展开式，它同时实现了重整化群求和并具有驯服的高阶行为.新的扩展功能，取代标准的权力的耦合，是奇异的耦合平面的原点，并有分歧的微扰扩展，类似于扩展功能本身。面对新的微扰展开与标准的最近在文献中研究的特定模型，我表明，他们近似在一个令人印象深刻的方式准确的阿德勒函数和谱函数的时刻。应用于$τ$强子宽度，${\overline{\rm MS}}$方案中的轮廓改进和重整化群求和的非幂展开导致预测$α_s(M_τ^2)= 0.3192~^{+ 0.0167}_{-0.0126}$，其转化为$α_s(M_Z^2)= 0.1184~^{+0.0020}_{-0.0016}$。
Improved Evaluation of the NNLO QCD Effects in the Tau Decay, $e^{+}e^{-}$ Annihilation into Hadrons and Deep-Inelastic Sum Rules
本文提出了一种系统的方法来分析次首阶QCD预言中重整化方案的不确定性，该方法基于一个条件，该条件消除了在展开系数的特征方案不变组合的表达式中引起大的相消的方案。利用这种方法，我们证明了对τ轻子衰变的QCD修正相对于方案的变化是相当稳定的，只要使用一个改进的公式，其中包括在复能量平面上用积分下的Adler函数数值计算围道积分。给出了τ衰变校正的优化预测。它表明，在QCD修正的情况下，$e^{+}e^{-}$湮没成强子的常规扩展有相当大的方案依赖，即使在大的能量。然而，当QCD修正被表示为围道积分时，获得了相当大的改进，在积分下的Adler函数，以这种方式表示大的$π^{2}$贡献。在极化结构函数的Bjorken求和规则的修正的情况下，发现对于$n_{f}=4$，它们对方案的改变不敏感。然而，$n_{f}=3$的表达被发现是强烈的计划依赖于在较低的能量。
Timelike and spacelike QCD characteristics of the $e^+e^-$ annihilation process
我们认为阿德勒$D$ -函数，这是定义在类空区域，和$e^+e^-$湮灭比涂抹，根据波焦，奎因和温伯格方法，这是确定的类时参数。我们表明，该方法的非微扰$a$ -膨胀允许一个描述这些欧几里得和闵可夫斯基特性的过程中的$e^+e^-$湮灭到最低的能量尺度。
Expansions of $τ$ hadronic spectral function moments in a nonpower QCD perturbation theory with tamed large order behavior
强子谱函数的矩对于从$τ$轻子的强子衰变中提取强耦合$α_s$和其它QCD参数具有重要意义。受最近对标准固定阶和轮廓改进的微扰理论中的大类矩的分析的启发，我们考虑了这些矩在QCD非幂微扰理论框架中的微扰行为，该框架由共形映射的级数加速技术定义，同时实现重整化群求和并具有驯服的高阶行为。最近提出的两个模型的Adler函数产生的扰动系列的高阶系数和预测的时刻，需要测试的性质的扰动扩展的精确值。我们表明，轮廓改进的非幂微扰理论和重整化群求和的非幂微扰理论有很好的收敛性能的一个大类的时刻，所谓的“参考模型”，包括时刻，描述不佳的标准扩展。这些结果提供了额外的支持的Adler函数的描述中的一个小数目的占主导地位的renormalons的可扩展性。
Estimates of higher-order contributions for perturbative series in QCD, in view of their asymptotic nature, are delicate, though indispensable for a reliable error assessment in phenomenological applications. In this work, the Adler function and the scalar correlator are investigated, and models for Borel transforms of their perturbative series are constructed, which respect general constraints from the operator product expansion and the renormalisation group. As a novel ingredient, the QCD coupling is employed in the so-called $C$-scheme, which has certain advantages. For the Adler function, …
In a recent work by some of us it was shown that the long-standing discrepancy between the QCD perturbation series for the inclusive hadronic tau decay rate computed in the CIPT and FOPT expansion approaches can be understood from the fact that CIPT has an infrared (IR) sensitivity that it not compatible with the standard form of the operator production expansion (OPE). For concrete IR renormalon models for the QCD Adler function the resulting CIPT-FOPT discrepancy, the asymptotic separation, can be calculated analytically from the Borel representation of the CIPT series expansion. If the know…
Optimization of perturbation series in QCD for physical quantities using the renormalization group: necessary conditions and partial results
本文探索利用QCD重整化群数值优化物理量微扰级数的方法，应用于Bjorken极化求和规则的系数函数和Adler函数，并讨论不同优化技术的后果。
Higher-order QCD perturbation theory in different schemes: From FOPT to CIPT to FAPT
在分数阶解析微扰理论（FAPT）中，给出了标量$D_S$和矢量$D_V$相关器的Adler函数的非幂级数展开式的重新计算结果。第一个可观测量可以用来确定标量希格斯玻色子到底-反底对的衰变宽度$Γ_{H\to b\bar{b}}$，而第二个可观测量则与$e^+e^-$湮灭截面有关。将所得估计值与固定阶（FOPT）和轮廓改进摄动理论（CIPT）的估计值进行了比较，找出了它们之间的差异。我们证明，虽然FAPT和CIPT是概念上不同的，他们产生相同的结果。这些扩展的收敛特性进行了讨论和预测提取的一系列的$R_S$和$D_V$使用一个和两个循环耦合运行，并利用适当的生成函数的扰动系列的系数。
An analytic method of describing $R$-related quantities in QCD
一个基于QCD分析方法的模型，包括阈值奇异性的总和，并考虑到轻夸克质量的非微扰特性，被应用于寻找强子对不同物理量的贡献。结果表明，建议的模型使我们能够很好地描述这样的对象作为强子贡献的μ子的反常磁矩，强子轻子$τ$ -衰变宽度的比率在矢量通道，阿德勒$D$ -功能，涂抹$R_Δ$ -功能，和强子贡献的精细结构常数的演变。
We present a determination of the perturbative QCD (pQCD) coupling using the V+A channel ALEPH $τ$-decay data. The determination involves the double-pinched Borel-Laplace Sum Rules and Finite Energy Sum Rules. The theoretical basis is the Operator Product Expansion (OPE) of the V+A channel Adler function in which the higher order terms of the leading-twist part originate from a model based on the known structure of the leading renormalons of this quantity. The applied evaluation methods are contour-improved perturbation theory (CIPT), fixed-order perturbation theory (FOPT), and Principal Value…
The massive analytic invariant charge in QCD
研究了最近提出的QCD大质量解析运行耦合模型的低能行为。这种运行的耦合没有非物理的奇异性，并且在没有质量的情况下显示红外增强。由于最轻强子的质量的影响的列入是通过采用色散关系的阿德勒D功能。非零π介子质量的存在驯服了上述增强，导致原点处的运行耦合有限值。此外，有效电荷在类时畴的低能区获得了“类平台”行为。这个平台被发现是在协议与一些现象学模型的强运行耦合。发展的不变电荷被应用于处理包含$τ$轻子衰变的实验数据。由于π介子质量的影响在这里也起着重要的作用，影响从这些数据中提取的QCD尺度参数$Λ$的值。最后，大量的解析运行耦合进行了比较所产生的Schwinger-Dyson方程的研究，其红外有限性是由于一个动态生成的胶子质量的有效耦合。定性地描述了前耦合对手征对称性破缺的可能影响。
The absence of QCD $β$-function factorization property of the generalized Crewther relation in the 't Hooft $\bar{MS}$-based scheme
我们应用t Hooft $\bar{MS}$方案研究了QCD推广的Crewther关系对归一化非单重态微扰对$e^+e^-$湮灭Adler函数和极化轻子-核子深度非弹性散射过程的Bjorken求和规则的贡献的乘积的方案依赖性.我们证明了在从纯$\bar{MS}$ -格式变换到't Hooft格式之后，这个关系式的特征$\bar{MS}$ -格式理论性质，即$β$ -函数在其共形对称破缺部分的因式分解，消失了.本文还提到了在$\mathcal{N}=1$ SUSY QED模型中应用这一处方的另一个“非舒适”的理论结果。它示出，内的t Hooft计划的展开的格林函数的朗伯函数是简化的高阶微扰理论。这可以被认为是't Hooft方案的吸引人的特征，它在高阶微扰唯象学应用中表现出来。
The Crewther-Broadhurst-Kataev (CBK) relation connects the Bjorken function for deep-inelastic sum rules (or the Gross - Llewellyn Smith function) with the Adler function for electron-positron annihilation in QCD; it has been checked to hold up to four loops in perturbation theory. Here we study non-perturbative terms in the CBK relation using a holographic dual theory that is believed to capture properties of QCD. We show that for the large invariant momenta the perturbative CBK relation is exactly satisfied. For the small momenta non-perturbative corrections enter the relation and we calcula…
At order $α_s^4$ in perturbative quantum chromodynamics, even-integer $ζ$-function values are present in Euclidean physical correlation functions like the scalar quark correlation function or the scalar gluonium correlator. We demonstrate that these contributions cancel when the perturbative expansion is expressed in terms of the so-called $C$-scheme coupling $\hatα_s$ which has recently been introduced in Ref. [1]. It is furthermore conjectured that a $ζ_4$ term should arise in the Adler function at order $α_s^5$ in the $\overline{\rm MS}$-scheme, and that this term is expected to disappear i…
We consider a phenomenologycal parametrization of the QCD running coupling which arises from the dispersion relation respecting the holomorphic properties of the physical QCD observables in the complex momentum plane. The parameters are fixed by the following requirements: 1) at enough high energies, it reproduces the underlying perturbative coupling, 2) at intermediate energy momenta, it reproduces the experimental semihadronic tau decay ratio, and 3) in the deep IR regime, it satisfies the qualitative properties coming from recent lattice results. Finally, we apply this new coupling to low-e…
Dispersive approach to QCD and inclusive tau lepton hadronic decay
本文将QCD的色散方法应用于研究包含τ轻子的强子衰变。这种方法为强子真空极化函数、相关的R函数和Adler函数提供了统一的积分表示。这些表示占本质上的非微扰约束，这起源于手头上的功能的运动学限制，并保留由于强子化的影响，这在低能量的强相互作用过程的分析中发挥了宝贵的作用。色散的方法被证明是能够描述最近更新的ALEPH和OPAL实验数据包含τ轻子强子衰变的矢量和轴向矢量通道。在这两个通道中获得的QCD尺度参数的值附近证明了所开发的方法以自洽的方式描述上述数据的潜在能力。
Infrared freezing of Euclidean observables and analyticity in perturbative QCD
由于运行耦合的朗道极点，QCD观测量的重整化群改进的有限阶展开式在欧几里德区域具有非物理奇异性。最近有人声称，通过使用修改的Borel表示，在欧几里德QCD观测量的骨架展开中，领先的单链项是有限的，并且在朗道极点上是连续的，然后表现出红外冻结行为，在$Q^2=0$处消失。在本文中，我们表明，使用说明的阿德勒- ${\cal D}$功能，上述博雷尔处方违反了因果关系的性质表示的能量平面解析：功能${\cal D}(Q^2)$因此定义是一个分段解析函数在复平面上的边界值，而不是一个标准的解析函数。因此，欧几里得QCD观测量的红外冻结所付出的代价是局域量子场论的一个基本性质的丧失。
A method of evaluation of spacelike QCD observables ${\cal D}(Q^2)$ is developed, motivated by the renormalon structure of these quantities. A related auxiliary quantity ${\widetilde {\cal D}}(Q^2)$ is introduced, which is renomalization scale independent only at the one-loop level, and a large-$β_0$-type renormalon motivated ansatz is made for the Borel transform of this quantity. This leads to a `dressed' Borel transform of the considered observable ${\cal D}(Q^2)$. From there, a Neubert-type distribution is obtained for the observable. The described method is then applied to the massless Ad…
Renormalon Singularities of the QCD Vacuum Polarization Function to Leading Order in $1/N_{f}$
我们明确地确定了QCD真空极化函数（Adler D-函数）的Borel平面中所有紫外（UV）和红外（IR）重正化子极点的留数和阶数，以夸克味数$N_{f}$的展开为主导阶数。奇点结构正是根据一般理由所预期的那样。特别地，不存在主导IR重正子，这与算子乘积展开思想一致。有一个奇怪的和无法解释的对称性之间的第三和更高的UV和IR renormalon残基。我们能够分别总结UV和IR的贡献，以获得封闭形式的结果，涉及$ζ$ -功能。我们认为，领先的UV renormalon应该有一个更复杂的结构比传统的假设。IR重正性子在味饱和SU（$N$）QCD中的消失被证明发生在$N=3,6$或9。
$π^0$ to two-photon decay in lattice QCD
我们计算了格点量子色动力学中中性π介子（$π^0$）到离壳双光子（$γ^*γ^*$）跃迁的形状因子。跃迁形状因子可以从形式为（轴向-矢量）-（矢量）-（矢量）的三点函数中提取，作为离壳双光子动量的函数。由于轴反常在$π^0\toγγ$衰变过程中起着重要的作用，我们采用了重叠费米子，它保持了晶格上精确的手征对称性。利用基于矢量介子占优（VMD）模型的拟合函数外推到手征和消失光子动量极限后，我们发现Adler-Bell-Jackiw反常被正确地再现。
We discuss the method of conformal mappings applied to perturbative QCD. The approach is based on the Borel-Laplace integral regulated with the principal value prescription and the expansion of the Borel transform in powers of the variable which performs the conformal mapping of the cut Borel plane onto the unit disk. We write down the expression of the conformal mapping for the most general location of the singularities of the Borel transform and review the properties of the corresponding expansions of the correlators. Unlike the standard perturbative expansions, which are divergent, the modi…
In this work we consider the possibility of representing the perturbative series for renormalization group invariant quantities in QCD in the form of their decomposition in powers of the conformal anomaly $β(α_s)/α_s$ in the ${\rm{\overline{MS}}}$-scheme. We remind that such expansion is possible for the Adler function of the process of $e^+e^-$ annihilation into hadrons and the coefficient function of the Bjorken polarized sum rule for the deep-inelastic electron-nucleon scattering, which are both related by the Crewther-Broadhurst-Kataev relation. In addition, we study the discussed decompos…
All-Orders Renormalon Resummations for some QCD Observables
对于含$N_{f}$夸克味的SU（$N$）QCD，我们利用QCD Adler $D$ -函数和深度非弹性散射求和规则的精确大$N_{f}$结果，将包含$b$ = $\frac{1}{6}(11N$ -- $2N_{f})$的最高幂的QCD微扰系数部分求和到所有阶.这些条款对应于在Borel平面的重正马龙奇点，并预计渐近占主导地位的系数的所有订单中的$1/N_{f}$展开。值得注意的是，我们注意到，这已经是显而易见的，在与精确的次领先阶（NLO）和次领先阶（NNLO）微扰系数的比较。在Borel变换的紫外（$UV$）和红外（$IR$）renormalon奇异隔离和Borel和（主值调节$IR$）进行。恢复的结果也得到了与$D$ -函数，$e^{+}e^{-}$ $R$ -比和类似的$τ$ -轻子衰变比，$R_τ$有关的闵可夫斯基量.讨论了这些部分重正化方案的依赖性，并与其他群的结果[1- 3]和NNLO下的精确定阶微扰理论的结果进行了比较。通过包括更精确的细节的博雷尔变换的改进recrmation的前景被认为是。
We propose a method to help control cutoff effects in the short-distance contribution to integrated correlation functions, such as the hadronic vacuum polarization (HVP), using the corresponding screening correlators computed at finite temperature. The strategy is investigated with Wilson fermions at leading order, which reveals a logarithmically-enhanced lattice artifact in the short-distance contribution, whose coefficient is determined at this order. We then perform a numerical study with $N_\mathrm{f}=2$ O($a$)-improved Wilson fermions and a temperature $T\approx250~\mathrm{MeV}$, with lat…
The scalar gluonium correlator: large-beta_0 and beyond
标量胶子关联函数的研究是有趣的，因为它携带真空的量子数，相关的强子流与手征极限下QCD能量动量张量的反常迹有关。在回顾了次次领先阶的纯微扰修正后，利用大β_0近似研究了所有阶的关联函数的行为。与QCD Adler函数类似，高阶行为由领先的紫外重正子极点控制。红外重整化极的结构，被有关的运营算子乘积展开，以及低能量定理的关联函数，提供了一个关系到重整化群不变的胶子凝聚，和真空矩阵元的轨迹的QCD能量动量张量。
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