The $\{\beta\}$-expansion for Adler function, Bjorken Sum Rule, and the Crewther-Broadhurst-Kataev relation at order $O(\alpha_s^4)$

P. A. Baikov; S. V. Mikhailov

doi:10.1007/jhep09(2022)185

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arXiv · 2206.14063

The $\{\beta\}$-expansion for Adler function, Bjorken Sum Rule, and the Crewther-Broadhurst-Kataev relation at order $O(\alpha_s^4)$

P. A. Baikov·S. V. Mikhailov

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Abstract

We derive explicit expressions for the elements of the $\{ \beta \}$-expansion for the nonsinglet Adler $D_A$-function and Bjorken polarized sum rules $S^{Bjp}$ in the N$^4$LO using recent results by Chetyrkin for these quantities computed within extended QCD including any number of fermion representations. We discuss the properties of the $\{ \beta \}$-expansion for $D_A$ and $S^{Bjp}$ at higher orders which follow from the Crewther [1] and the Broadhurst-Kataev [2] relation.

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P. A. Baikov, S. V. Mikhailov. 2022-06-28. The $\{\beta\}$-expansion for Adler function, Bjorken Sum Rule, and the Crewther-Broadhurst-Kataev relation at order $O(\alpha_s^4)$. https://doi.org/10.1007/jhep09(2022)185

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