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

TL;DR

This paper confirms elements of the $eta$-expansion in QCD for the Adler function and Bjorken sum rule up to N$^4$LO, using independent methods and diagram-based estimates to validate previous results.

Contribution

It provides independent confirmation of the $eta$-expansion elements in QCD for specific sum rules and introduces a diagram-based approach to estimate high-order calculations.

Findings

Confirmation of $eta$-expansion elements up to N$^4$LO

Development of a diagram-based estimation method

Validation of previous theoretical results

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.