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

摘要

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.