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

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.

19 pages, added the refs [15], [16], [19]; sec.3 a bit extended

References in corpus (5)

• Adler Function, Bjorken Sum Rule, and the Crewther Relation to Order alpha_s^4 in a General Gauge Theory
• Generalization of the Brodsky-Lepage-Mackenzie optimization within the $\{\beta \}$-expansion and the Principle of Maximal Conformality
• Setting the Renormalization Scale in pQCD: Comparisons of the Principle of Maximum Conformality with the Sequential Extended Brodsky-Lepage-Mackenzie Approach
• The $\{\beta \}$-expansion formalism in perturbative QCD and its extension
• 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

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• Scale-invariant total decay width $\Gamma (H\to b\bar{b})$ using the novel method of characteristic operator