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arXiv 1611.01367hep-thhep-ph
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关于2点和3点函数的重正化群

On Finiteness of 2- and 3-point Functions and the Renormalisation Group

Vladimir Prochazka, Roman Zwicky

备注：
12 pages plus refs, open access version - identical to version in PRD
发表信息：
Phys. Rev. D 95, 065027 (2017)
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摘要：

本文分析了复合算子的二点函数和三点函数关于（数学上）发散接触项的情况。使用重正化组的尺寸正则化，它是由异常尺寸的运营商和领先的UV行为的$1/ε$ -系数的分歧。给出了类QCD理论中能量动量张量的$<G^2G^2>$ -、$<ΘΘ>$ -迹和$<\bar q q \bar q q>$ -迹的明确例子。前两个收敛时，所有的订单都考虑到，但发散的每一个订单微扰理论意味着后者和$ε\to 0$限制一般不交换。有限的关联函数服从未减色散关系，当它们与物理可观测量直接相关时，这是很重要的。作为副产品，使用最近的$<G^2G^2>$ -计算将$R^2$ -异常扩展为NNLO（$O(α^5)$）。

英文摘要：

Two and three point functions of composite operators are analysed with regard to (logarithmically) divergent contact terms. Using the renormalisation group of dimensional regularisation it is established that the divergences are governed by the anomalous dimensions of the operators and the leading UV-behaviour of the $1/ε$-coefficient. Explicit examples are given by the $<G^2G^2>$-, $<ΘΘ>$-trace of the energy momentum tensor) and $<\bar q q \bar q q>$- correlators in QCD-like theories. The former two are convergent when all orders are taken into account but divergent at each order in perturbation theory implying that the latter and the the $ε\to 0$ limit do not generally commute. Finite correlation functions obey unsubtracted dispersion relations which is of importance when they are directly related to physical observables. As a byproduct the $R^2$-anomaly is extended to NNLO ($O(α^5)$) using a recent $<G^2G^2>$-computation.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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