论文标题

QCD [Ph.D.的重新归一化量表设置问题论文]

The Renormalization Scale Setting Problem in QCD [Ph.D. Thesis]

论文作者

Di Giustino, Leonardo

论文摘要

在扰动QCD中做出精确预测的关键问题是设定重新归一化量表的不确定性。如果原则上,整个扰动系列没有这个问题,则实际上已经知道扰动校正的准确性和规模不变性顺序仅近似近似导致所谓的方案和规模的歧义。根据常规规模设置(CSS),无法避免此问题,并将重新归一化量表设置为流程$ Q $的典型比例,并且通过在两个$ [q/2; 2q] $的范围内改变量表来估算错误。该方法并非没有歧义,而导致受大理论错误影响的预测。优化截短扩展的其他策略,例如最低敏感性(PMS)的原理和最快的明显收敛性(FAC)标准,具有相同的CSS困难,并带来不正确和非物理结果。通常,如果规模设定程序保留了重要的自洽要求,例如所有重新归一化组属性,则认为它是可靠的。通过已知的测试理论,该系列的收敛行为或现象学结果和方案独立性提出了其他要求。可以立即满足可靠规模设定过程的所有理论要求,从而通过使用最大保密性原理(PMC),从而导致准确的结果。该方法将Brodsky-Lepage-Mackenzie(BLM)方法概括为所有订单和所有可观察到的方法,并从统一所有互动的理论的角度来看,例如,统一的统一理论(GUT),PMC提供了在理论的所有领域中应用相同方法的可能性,从最初的原理开始,消除了肾上腺的增长和范围,并逐渐启用了计划,并实现了培训的态度和范围,并取得了态度,并取消了计划的态度和规模,并将其态度逐渐增长,并逐渐逐渐增长。 $ N_C \至0 $限制中的Gell-Mann-low方案。

A key issue in making precise predictions in perturbative QCD is the uncertainty in setting the renormalization scale. If in principle, the entire perturbative series is void of this issue, in practice the perturbative corrections are known up to a certain order of accuracy and scale invariance is only approximated leading to the so-called scheme and scale ambiguities. According to the conventional scale setting (CSS) this problem cannot be avoided and the renormalization scale is set to the typical scale of a process $Q$, and errors are estimated by varying the scale over a range of two $[Q/2;2Q]$. This method is not void of ambiguities and leads to predictions affected by large theoretical errors. Other strategies for the optimization of the truncated expansion, such as the Principle of Minimal Sensitivity (PMS) and the Fastest Apparent Convergence (FAC) criterion, have the same difficulties of CSS and lead to incorrect and unphysical results. In general a scale-setting procedure is considered reliable if it preserves important self-consistency requirements such as all the renormalization group properties. Other requirements are suggested by known tested theories, by the convergence behavior of the series or by phenomenological results and scheme independence. All theoretical requirements for a reliable scale-setting procedure can be satisfied at once, leading to accurate results by using the Principle of Maximum Conformality (PMC). This method generalizes the Brodsky-Lepage-Mackenzie (BLM) method to all orders and to all observables and in the perspective of a theory unifying all interactions, such as the grand unified theory (GUT), the PMC offers the possibility to apply the same method in all sectors of a theory, starting from first principles, eliminating the renormalon growth, the scheme and scale ambiguities, and satisfying the QED Gell-Mann-Low scheme in the $N_c\to 0$ limit.

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