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.

arXiv comment19 pages, added the refs [15], [16], [19]; sec.3 a bit extended

References in corpus (17)

• The Uses of Conformal Symmetry in QCD
• Adler Function, Bjorken Sum Rule, and the Crewther Relation to Order alpha_s^4 in a General Gauge Theory
• Connections between Deep-Inelastic and Annihilation Processes at Next-to-Next-to-Leading Order and Beyond
• Corrections of order ${\alpha }_s^3$ to $R_{had}$ in pQCD with light gluinos
• Adler Function, Sum Rules and Crewther Relation of Order O(alpha_s^4): the Singlet Case
• Generalization of the BLM procedure and its scales in any order of pQCD
• Generalization of the Brodsky-Lepage-Mackenzie optimization within the $\{\beta \}$-expansion and the Principle of Maximal Conformality
• Relating inclusive e+e- annihilation to electroproduction sum rules in Quantum Chromodynamics
• New perturbation theory representation of the conformal symmetry breaking effects in gauge quantum field theory models
• Gluino Contribution to the 3-loop QCD beta function in the Minimal Supersymmetric Standard Model
• Four-loop QCD $\beta$-function with different fermion representations of the gauge group
• Setting the Renormalization Scale in pQCD: Comparisons of the Principle of Maximum Conformality with the Sequential Extended Brodsky-Lepage-Mackenzie Approach
• Adler function and Bjorken polarized sum rule: Perturbation expansions in powers of $SU(N_c)$ conformal anomaly and studies of the conformal symmetry limit
• 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
• Four-loop renormalization of QCD with a reducible fermion representation of the gauge group: anomalous dimensions and renormalization constants
• On a realization of $\{\beta \}$-expansion in QCD

Cited by in corpus (4)

• Renormalization group summation and analytic continuation from spacelike to timeline regions
• Adler function, Bjorken polarized sum rule: confirmation of elements of the $\{\beta \}$-expansion and the diagrams
• The decomposed photon anomalous dimension in QCD and the $\{\beta \}$-expanded representations for the Adler function
• Scale-invariant total decay width $\Gamma (H\to b\bar{b})$ using the novel method of characteristic operator