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In this work we consider the possibility of representing the perturbativeseries for renormalization group invariant quantities in QCD in the form oftheir decomposition in powers of the conformal anomaly$\beta(\alpha_s)/\alpha_s$ in the ${\rm{\overline{MS}}}$-scheme. We remind thatsuch expansion is possible for the Adler function of the process of $e^+e^-$annihilation into hadrons and the coefficient function of the Bjorken polarizedsum rule for the deep-inelastic electron-nucleon scattering, which are bothrelated by the Crewther-Broadhurst-Kataev relation. In addition, we study thediscussed decomposition for the static quark-antiquark Coulomb-like potential,its relation with the quantity defined by the cusp anomalous dimension and thecoefficient function of the Bjorken unpolarized sum rule of neutrino-nucleonscattering. In conclusion we also present the formal results of applying thisapproach to the non-renormalization invariant ratio between the pole and${\rm{\overline{MS}}}$-scheme running mass of heavy quark in QCD and comparethem with those already known in the literature. The arguments in favor of thevalidity of the considered representation in powers of$\beta(\alpha_s)/\alpha_s$ for all mentioned perturbative quantities arediscussed.

Representation of the RG-invariant quantities in perturbative QCD through powers of the conformal anomaly