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arXiv 1302.0599hep-phhep-th
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QCD中的重整化标度设置问题

The Renormalization Scale-Setting Problem in QCD

Xing-Gang Wu, Stanley J. Brodsky, Matin Mojaza

备注：
75 pages, 19 figures. Review article to be published in Prog. Part. Nucl. Phys
发表信息：
Prog. Part. Nucl. Phys. 72 (2013) 44
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摘要：

在进行精确的微扰QCD预言时，一个关键的问题是设置合适的运行耦合的重整化标度。传统的标度设置过程为固定阶pQCD预测分配任意范围和任意系统误差。事实上，这个{ \it ad hoc}过程给出的结果依赖于重整化方案的选择，并且它与QED中使用的标准标度设置过程相冲突。物理结果的预测应该独立于方案的选择或其他理论约定。我们回顾了当前关于如何处理重整化标度模糊性的想法和观点，并展示了如何获得重整化方案和标度独立的估计。我们首先介绍了重整化群（RG）方程和一个扩展的版本，它表示下的重整化方案和标度参数变换的物理观测量的不变性。RG方程为估计物理过程的方案和尺度依赖性提供了一种方便的方法.然后，我们讨论的RG方程的自洽要求，如自反性，对称性和传递性，这必须满足的尺度设置方法。文献中提出了四种典型的标度设置方法，{ \it，}介绍了最快表观收敛（FAC）准则、最小灵敏度原理（PMS）、Brodsky-Lepage-Mackenzie方法（BLM）和最大保形原理（PMC）。讨论了它们的基本性质及其应用。我们特别注意PMC，它满足RG不变性的所有要求。[full摘要在论文中）。

英文摘要：

A key problem in making precise perturbative QCD predictions is to set the proper renormalization scale of the running coupling. The conventional scale-setting procedure assigns an arbitrary range and an arbitrary systematic error to fixed-order pQCD predictions. In fact, this {\it ad hoc} procedure gives results which depend on the choice of the renormalization scheme, and it is in conflict with the standard scale-setting procedure used in QED. Predictions for physical results should be independent of the choice of scheme or other theoretical conventions. We review current ideas and points of view on how to deal with the renormalization scale ambiguity and show how to obtain renormalization scheme- and scale- independent estimates. We begin by introducing the renormalization group (RG) equation and an extended version, which expresses the invariance of physical observables under both the renormalization scheme and scale-parameter transformations. The RG equation provides a convenient way for estimating the scheme- and scale- dependence of a physical process. We then discuss self-consistency requirements of the RG equations, such as reflexivity, symmetry, and transitivity, which must be satisfied by a scale-setting method. Four typical scale setting methods suggested in the literature, {\it i.e.,} the Fastest Apparent Convergence (FAC) criterion, the Principle of Minimum Sensitivity (PMS), the Brodsky-Lepage-Mackenzie method (BLM), and the Principle of Maximum Conformality (PMC), are introduced. Basic properties and their applications are discussed. We pay particular attention to the PMC, which satisfies all of the requirements of RG invariance...... [full Abstract is in the paper].

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