  I present a brief review of the generalized Brodsky-Lepage-McKenzie (BLM)
approaches to fix the scale-dependence of the renormalization group (RG)
invariant quantities in QCD. At first, these approaches are based on the
expansions of the coefficients of the perturbative series for the RG-invariant
quantities in the products of the coefficients $\beta_i$ of the QCD
$\beta$-function, which are evaluated in the MS-like schemes. As a next step
all $\beta_i$-dependent terms are absorbed into the BLM-type scale(s) of the
powers of the QCD couplings. The difference between two existing formulations
of the above mentioned generalizations based on the seBLM approach and the
Principle of Maximal Conformality (PMC) are clarified in the case of the
Bjorken polarized deep-inelastic scattering sum rule. Using the conformal
symmetry-based relations for the non-singlet coefficient functions of the Adler
D-function and of Bjorken polarized deep-inelastic scattering sum rules $C^{\rm
Bjp}_{\rm NS}(a_s)$ the $\beta_i$-dependent structure of the NNLO approximation
for $C^{\rm Bjp}_{\rm NS}(a_s)$ is predicted in QCD with $n_{gl}$-multiplet of
gluino degrees of freedom, which appear in SUSY extension of QCD. The
importance of performing the analytical calculation of the N$^3$LO additional
contributions of $n_{gl}$ gluino multiplet to $C^{\rm Bjp}_{\rm NS}(a_s)$ for
checking the presented in the report NNLO prediction and for the studies of the
possibility to determine the discussed $\{\beta\}$-expansion pattern of this
sum rule at the $O(a_s^4)$-level is emphasised.

High Energy Physics - Phenomenology;High Energy Physics - Experiment