Towards the NNLO evolution of polarised parton distributions

We report on the first calculation of the structure function g1 in polarised deep-inelastic scattering to the third order in massless perturbative QCD. The calculation follows the dispersive approach already used for the corresponding unpolarised cases of F2,L, but additionally involves higher tensor integrals and the Dirac matrix γ5 in D≠4 dimensions. Our results confirm all known two-loop expressions including the coefficient functions of Zijlstra and van Neerven not independently verified before. At three loops we extract the helicity-difference next-to-next-to-leading order (NNLO) quark-quark and gluon-quark splitting functions ΔPqq and ΔPqg. The results exhibit interesting features concerning sum rules and the momentum-fraction limits x→1 and x→0.