Towards the NNLO evolution of polarised parton distributions

Abstract

We report on the first calculation of the structure function g_1 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 F_2,L, but additionally involves higher tensor integrals and the Dirac matrix gamma_5 in D unequal 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 Delta P_qq and Delta P_qg. The results exhibit interesting features concerning sum rules and the momentum-fraction limits x to 1 and x to 0.

Comments: 7 pages, LaTeX, 4 ps/eps-figures. Contribution to the proceedings of the workshops `Loops and Legs in Quantum Field Theory', April 2008, Sondershausen (Germany) and (shortened) DIS 2008, London, April 2008