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arXiv 1607.08698hep-thhep-ph
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微扰QCD中的$\{β\}$ -展开形式及其推广

The $\{β\}$-expansion formalism in perturbative QCD and its extension

A. L. Kataev, S. V. Mikhailov

备注：
16 pages, 3 figures, a few editorial corrections for JHEP version
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摘要：

我们讨论了重整化群不变量的$\{ β\}$ -展开，并将这种展开追踪到相应的不完全BPHZ $R$ -运算的不同压缩.所有的耦合重整化，这遵循这些收缩，应该考虑到$\{ β\}$ -扩展。我们说明了这一特点考虑非单态阿德勒函数$D^\text{NS}$在第三阶扰动。我们提出了重整化群协变量的$\{ β\}$ -展开式的一个推广--$\{ β,γ\}$ -展开式.

英文摘要：

We discuss the $\{ β\}$-expansion for renormalization group invariant quantities tracing this expansion to the different contractions of the corresponding incomplete BPHZ $R$-operation. All of the coupling renormalizations, which follow from these contractions, should be taken into account for the $\{ β\}$-expansion. We illustrate this feature considering the nonsinglet Adler function $D^\text{NS}$ in the third order of perturbation. We propose a generalization of the $\{ β\}$-expansion for the renormalization group covariant quantities -- the $\{ β,γ\}$-expansion.

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