Adler function, Bjorken polarized sum rule: confirmation of elements of the $\{\beta \}$-expansion and the diagrams

Abstract

Different ways exist to obtain the elements of the $\{\beta \}$-expansion for renormgroup invariant quantities. Here we consider independent confirmation within the standard QCD of a number of our results [1] for the values of elements of this expansion for the nonsinglet Adler $D_A$-function, Bjorken polarized sum rules $S^{Bjp}$ up to the order N${}^4$LO. We suggest an approach to estimate the results of high order QCD calculations using a smaller number of diagrams of the specific type. This type is based on a proposed generalization of Naive NonAbelianization.

In version 3:minor corrections to version 2, corresponds to journal publication JHEP10(2024)166. 14 pages,3 figures

References in corpus (5)

• Adler Function, Bjorken Sum Rule, and the Crewther Relation to Order alpha_s^4 in a General Gauge Theory
• Higher-order QCD perturbation theory in different schemes: From FOPT to CIPT to FAPT
• Generalization of the Brodsky-Lepage-Mackenzie optimization within the $\{\beta \}$-expansion and the Principle of Maximal Conformality
• The $\overline{\mathrm{MS}}$-scheme ${\alpha }_s^5$ QCD contributions to the Adler function and Bjorken polarized sum rule in the Crewther-type two-fold $\{\beta \}$-expanded representation
• The $\{\beta \}$-expansion for Adler function, Bjorken Sum Rule, and the Crewther-Broadhurst-Kataev relation at order $O({\alpha }_s^4)$

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