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We consider a new form of analytical perturbation theory expansion in themassless $SU(N_c)$ theory, for the non-singlet part of the$e^+e^-$-annihilation to hadrons Adler function $D^{ns}$ and of the Bjorken sumrule 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 atwo-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$\bar{\rm MS}$ scheme, for both considered physical quqantities. Comparisons ofthe terms in the $\{\beta\}$-expanded coefficients are made with thecorresponding terms obtained by using extra gluino degrees of freedom, orskeleton-motivated expansion, or $R_{\delta}$-scheme motivated expansion in thePrinciple of Maximal Conformality. Relations between terms of the$\{\beta\}$-expansion for the $D^{ns}$- and $C_{ns}^{Bjp}$-functions, whichfollow from the conformal symmetry limit and its violation, are presnted. Therelevance to the possible new analysis of the experimental data for the Adlerfunction and Bjorken sum rule is discussed.

physical review. d/physical review. d.

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