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arXiv 1405.3196hep-phhep-th
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重整化群不变性与最优QCD重正化标度设置

Renormalization Group Invariance and Optimal QCD Renormalization Scale-Setting

Xing-Gang Wu, Yang Ma, Sheng-Quan Wang, Hai-Bing Fu, Hong-Hao Ma, Stanley J. Brodsky, Matin Mojaza

备注：
20 pages, 5 figures. References updated and discussions improved. To be published in Reports on Progress in Physics as a Review Article
发表信息：
Reports on Progress in Physics 78, 126201 (2015)
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摘要：

从量子场论对物理观测值的有效预测应该与重整化方案的选择无关--这是重整化群不变性（RGI）的基本要求。满足格式不变性是微扰QCD（pQCD）的一个具有挑战性的问题，因为截断的微扰序列不能自动满足重整化群的要求.文献中提出了满足RGI原则的两种不同方法。一个是“最大保形性原理”（PMC），其中与$β$ -函数相关的项被吸收到每个微扰阶的运行耦合的尺度中;其预测在每个有限阶都是方案和尺度独立的。另一种方法是“最小灵敏度原理”（PMS），它基于局部RGI; PMS方法通过要求可观测量的近似斜率为零来确定最佳重整化尺度。本文通过分析pQCD中四圈量级的两个物理观测量$R_{e+e-}$和$Γ(H\to b\bar{b})$，详细比较了PMC和PMS方法。在四个回路的水平，PMC和PMS的预测，这两个可观的同意在小的误差与传统的尺度设置假设一个物理动机的规模，每个预测显示小规模的依赖性。然而，高阶pQCD级数的收敛性表现得完全不同：PMC显示出最好的pQCD收敛性，因为它消除了发散的重整化项;相反，PMS预测的收敛性是有问题的，往往比基于重整化标度的任意猜测的传统预测更差。......

英文摘要：

A valid prediction for a physical observable from quantum field theory should be independent of the choice of renormalization scheme -- this is the primary requirement of renormalization group invariance (RGI). Satisfying scheme invariance is a challenging problem for perturbative QCD (pQCD), since a truncated perturbation series does not automatically satisfy the requirements of the renormalization group. Two distinct approaches for satisfying the RGI principle have been suggested in the literature. One is the "Principle of Maximum Conformality" (PMC) in which the terms associated with the $β$-function are absorbed into the scale of the running coupling at each perturbative order; its predictions are scheme and scale independent at every finite order. The other approach is the "Principle of Minimum Sensitivity" (PMS), which is based on local RGI; the PMS approach determines the optimal renormalization scale by requiring the slope of the approximant of an observable to vanish. In this paper, we present a detailed comparison of the PMC and PMS procedures by analyzing two physical observables $R_{e+e-}$ and $Γ(H\to b\bar{b})$ up to four-loop order in pQCD. At the four-loop level, the PMC and PMS predictions for both observables agree within small errors with those of conventional scale setting assuming a physically-motivated scale, and each prediction shows small scale dependences. However, the convergence of the pQCD series at high orders, behaves quite differently: The PMC displays the best pQCD convergence since it eliminates divergent renormalon terms; in contrast, the convergence of the PMS prediction is questionable, often even worse than the conventional prediction based on an arbitrary guess for the renormalization scale. ......

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