Abstract

In this work we consider the possibility of representing the perturbative series for renormalization group invariant quantities in QCD in the form of their decomposition in powers of the conformal anomaly \({{\beta ({{\alpha }_{s}})} \mathord{\left/ {\vphantom {{\beta ({{\alpha }_{s}})} {{{\alpha }_{s}}}}} \right. \kern-0em} {{{\alpha }_{s}}}}\) in the \(\overline {{\text{MS}}} \)-scheme. We remind that such expansion is possible for the Adler function of the process of \({{e}^{ + }}{{e}^{ - }}\) annihilation into hadrons and the coefficient function of the Bjorken polarized sum rule for the deep-inelastic electron-nucleon scattering, which are both related by the CBK relation. In addition, we study the discussed decomposition for the static quark-antiquark Coulomb-like potential, its relation with the quantity defined by the cusp anomalous dimension and the coefficient function of the Bjorken unpolarized sum rule of neutrino-nucleon scattering. In conclusion we also present the formal results of applying this approach to the non-renormalization invariant ratio between the pole and \(\overline {{\text{MS}}} \)-scheme running mass of heavy quark in QCD and compare them with those already known in the literature. The arguments in favor of the validity of the considered representation in powers of \({{\beta ({{\alpha }_{s}})} \mathord{\left/ {\vphantom {{\beta ({{\alpha }_{s}})} {{{\alpha }_{s}}}}} \right. \kern-0em} {{{\alpha }_{s}}}}\) for all mentioned renorm-invariant perturbative quantities are discussed.

中文翻译：

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通过共形反常的幂表示微扰 QCD 中的 RG 不变量

摘要

在这项工作中，我们考虑以共角异常幂的分解形式表示 QCD 中重正化群不变量的微扰级数的可能性\({{\beta ({{\alpha }_{s}})} \mathord{\left/ {\vphantom {{\beta ({{\alpha }_{s}})} {{{\alpha }_{s}}}}} \right.\kern-0em} {{ {\alpha }_{s}}}}\)在\(\overline {{\text{MS}}} \)方案中。我们提醒一下，这种展开对于过程\({{e}^{ + }}{{e}^{ - }}\) 的Adler 函数是可能的强子湮没和深部非弹性电子-核子散射的 Bjorken 极化和规则的系数函数，两者都通过 CBK 关系相关。此外，我们还研究了所讨论的静态类夸克-反夸克库仑势的分解，其与尖点反常维数定义的量以及中微子-核散射的Bjorken非极化和规则的系数函数的关系。总之，我们还提出了将该方法应用于QCD 中重夸克的极点和\(\overline {{\text{MS}}} \)方案运行质量之间的非重正化不变比的正式结果，并进行了比较与文献中已知的那些。支持所考虑的权力代表有效性的论据\({{\beta ({{\alpha }_{s}})} \mathord{\left/ {\vphantom {{\beta ({{\alpha }_{s}})} {{{\alpha讨论了所有提到的重范不变微扰量的}_{s}}}}} \right. \kern-0em} {{{\alpha }_{s}}}}\)。