The μ(x, β, α) function and its role in the analysis of the QCD-SVZ sum rules

Abstract
The μ(x, β, α) function and related quantities required by QCD-SVZ sum rules are constructed as FORTRAN functions. A careful study of the behaviour of its asymptotic expansions is performed. It is stated that it does not go at the same pace of the physical expansion for renormalization group dependent quantities, such as α_s , in QCD.

Title of program: MUNU
Catalogue Id: ACHH_v1_0

Nature of problem
The careful treatment of the QCD-SVZ sum rules requires an asymptotic analysis of those mu-functions. In study of any n-point function in QCD one expands alpha s(x) in the (1/log(x)) expansion due to their renormalization group equations to the corresponding level of perturbation theory. The improvement of that n-point function via Borel sum rules result to be linear combinations of the mu(x,beta,alpha) function (and the related nu(x,alpha)) for different values of the alpha and beta parameters. ...

Versions of this program held in the CPC repository in Mendeley Data
ACHH_v1_0; MUNU; 10.1016/0010-4655(92)90202-A

This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2019)

摘要
已将QCD-SVZ求和规则（QCD-SVZ Sum Rules）所需的μ(x, β, α)函数及相关物理量构造为FORTRAN函数。本文对其渐近展开的行为开展了严谨的研究，文中指出：在量子色动力学（Quantum Chromodynamics, QCD）中，对于依赖于重整化群的物理量（如强耦合常数α_s），该展开的进度与物理展开并不同步。

程序名称：MUNU
目录编号：ACHH_v1_0

问题本质
对QCD-SVZ求和规则的严谨处理，需要对这类μ函数进行渐近分析。在量子色动力学中研究任意n点函数时，由于其重整化群方程，需将α_s(x)按(1/log(x))展开至对应阶的微扰论水平。通过Borel求和规则（Borel Sum Rules）对该n点函数进行优化后，其结果可表示为不同α与β参数取值下的μ(x,β,α)函数（及相关ν(x,α)函数）的线性组合……

Mendeley数据的CPC库中收录的本程序版本：
ACHH_v1_0; MUNU; 10.1016/0010-4655(92)90202-A

本程序源自贝尔法斯特女王大学维护的CPC程序库（1969-2019）