On a realization of {\u03b2}-expansion in QCD

Abstract

We suggest a simple algebraic approach to fix the elements of the {β}-expansion for renormalization group invariant quantities, which uses additional degrees of freedom. The approach is discussed in detail for N2LO calculations in QCD with the MSSM gluino — an additional degree of freedom. We derive the formulae of the {β}-expansion for the nonsinglet Adler D-function and Bjorken polarized sum rules in the actual N3LO within this quantum field theory scheme with the MSSM gluino and the scheme with the second additional degree of freedom. We discuss the properties of the {β}-expansion for higher orders considering the N4LO as an example.