New perturbation theory representation of the conformal symmetry breaking effects in gauge quantum field theory models

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We propose a hypothesis on the detailed structure for the representation of the conformal symmetry breaking term in the basic Crewther relation generalized in the perturbation theory framework in QCD renormalized in the MS scheme. We establish the validity of this representation in the O(αₛ⁴) approximation. Using the variant of the generalized Crewther relation formulated here allows finding relations between specific contributions to the QCD perturbation series coefficients for the flavor nonsinglet part of the Adler function Dnsₐ for the electron-positron annihilation in hadrons and to the perturbation series coefficients for the Bjorken sum rule SBjp for the polarized deep-inelastic lepton-nucleon scattering. We find new relations between the αₛ⁴ coefficients of Dnsₐ and SBjp. Satisfaction of one of them serves as an additional theoretical verification of the recent computer analytic calculations of the terms of order αₛ⁴ in the expressions for these two quantities.