Towards the NNLO evolution of polarised parton distributions

Understand

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.