A calculation of the three-loop helicity-dependent splitting functions in QCD

Abstract

We have calculated the complete matrix of three-loop helicity-difference (`polarized') splitting functions Delta P_ik^(2), i,k = q,g, in massless perturbative QCD. In this note we briefly discuss some properties of the polarized splitting functions and our non-standard determination of the hitherto missing lower-row quantities Delta P_gq^(2) and Delta P_gg^(2). The resulting next-to-next-to-leading order (NNLO) corrections to the evolution of polarized parton distributions are illustrated and found to be small even at rather large values of the strong coupling constant alpha_s.