The {β}-expansion for Adler function, Bjorken Sum Rule, and the Crewther-Broadhurst-Kataev relation at order O($$ {\alpha}_s^4 $$)

Abstract

Abstract We derive explicit expressions for the elements of the {β}-expansion for the nonsinglet Adler DA-function and Bjorken polarized sum rules SBjp in the N4LO using recent results by Chetyrkin for these quantities computed within extended QCD including any number of fermion representations. We discuss the properties of the {β}-expansion for DA and SBjp at higher orders which follow from the Crewther [1] and the Broadhurst-Kataev [2] relation.