The generalized BLM approach to fix scale-dependence in QCD: the current status of investigations

Understand

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.