{β}-expansion in QCD, its conformal symmetry limit: theory + applications

The basis of the {β}-expansion for the perturbative series evaluated in the scheme for the renormalization group invariant quantities is summarized. Comparison with a similar representation, used within the BLM-motivated Principle of Maximal Conformality, is discussed.We stress that the original {β}-expansion contains a completed list of terms rather than its PMC analog. The arguments in favour of the complete {β}-expansion are presented. They are based on the relations which follow from the power β-function generalization of the Crewther relation for the nonsinglet contributions to the Adler DNS-function and to the Bjorken sum rule of the polarized lepton-nucleon scattering. The terms of the complete {β}-expansion at the level for DNS and These perturbative results are expressed in the PMC-type form. The problem of applications of these expressions for phenomenological applications is summarized.