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We propose a hypothesis on the detailed structure for the representation ofthe conformal symmetry breaking term in the basic Crewther relation generalizedin the perturbation theory framework in QCD renormalized in the ${\rm\bar{MS}}$ scheme. We establish the validity of this representation in the$O(\alpha_s^4)$ approximation. Using the variant of the generalized Crewtherrelation formulated here allows finding relations between specificcontributions to the QCD perturbation series coefficients for the flavornonsinglet part of the Adler function $D^{ns}_A$ for the electron-positronannihilation in hadrons and to the perturbation series coefficients for theBjorken sum rule $S_\text{Bjp}$ for the polarized deep-inelastic lepton-nucleonscattering. We find new relations between the $\alpha_s^4$ coefficients of$D^{ns}_A$ and $S_\text{Bjp}$. Satisfaction of one of them serves as anadditional theoretical verification of the recent computer analyticcalculations of the terms of order $\alpha_s^4$ in the expressions for thesetwo quantities.

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