Adler function and Bjorken polarized sum rule: Perturbation expansions in powers of $SU(N_c)$ conformal anomaly and studies of the conformal symmetry limit

Abstract

We consider a new form of analytical perturbation theory expansion in the massless $SU(N_c)$ theory, for the non-singlet part of the $e^{+}{e}^{-}$-annihilation to hadrons Adler function $D^{ns}$ and of the Bjorken sum rule of the polarized lepton-hadron deep-inelastic scattering $C_{ns}^{Bjp}$, and demonstrate its validity at the $O({\alpha }_s^4)$-level at least. It is a two-fold series in terms of powers of the conformal anomaly and of $SU(N_c)$ coupling ${\alpha }_s$. Explicit expressions are obtained for the $\{\beta \}$-expanded perturbation coefficients at $O({\alpha }_s^4)$ level in $\overline{\mathrm{MS}}$ scheme, for both considered physical quqantities. Comparisons of the terms in the $\{\beta \}$-expanded coefficients are made with the corresponding terms obtained by using extra gluino degrees of freedom, or skeleton-motivated expansion, or $R_{\delta }$-scheme motivated expansion in the Principle of Maximal Conformality. Relations between terms of the $\{\beta \}$-expansion for the $D^{ns}$- and $C_{ns}^{Bjp}$-functions, which follow from the conformal symmetry limit and its violation, are presnted. The relevance to the possible new analysis of the experimental data for the Adler function and Bjorken sum rule is discussed.

arXiv comment7 pages, Extra clarifications added, 1 reference added, prepared following the version accepted for publication to Phys.Rev.D Rapid Communications section

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Cited by in corpus (15)

• Polarized electron-deuteron deep-inelastic scattering with spectator nucleon tagging
• Renormalization scheme and gauge (in)dependence of the generalized Crewther relation: what are the real grounds of the $\beta$-factorization property?
• The three-loop Adler $D$-function for $\mathcal{N}=1$ SQCD regularized by dimensional reduction
• The Generalized Scheme-Independent Crewther Relation in QCD
• Optimized determination of the polarized Bjorken sum rule in pQCD
• Ambiguities of the principle of maximum conformality procedure for hadron collider processes
• 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 $O({\alpha }_s^4)$
• Generalized Crewther relation and a novel demonstration of the scheme independence of commensurate scale relations up to all orders
• On a realization of $\{\beta \}$-expansion in QCD
• Adler function, Bjorken polarized sum rule: confirmation of elements of the $\{\beta \}$-expansion and the diagrams
• Holographic CBK Relation
• The decomposed photon anomalous dimension in QCD and the $\{\beta \}$-expanded representations for the Adler function
• Riemann $\zeta (4)$ function contributions to $O\left({{\alpha }_s}^5\right)$ terms of Adler D-function and Bjorken polarized sum rule in $SU\left(N_c\right)$ QCD: results and consequences
• Deviation pattern approach for optimizing perturbative terms of QCD renormalization group invariant observables