QCD corrections to semi-inclusive hadron production in electron–positron annihilation at two loops

We report on the analytic calculation of the second-order QCD corrections to semi-inclusive hadron production in electron–positron annihilation. The calculation of the single-particle inclusive cross-section in time-like kinematics is performed in Mellin N  -space and uses an algorithmic evaluation of inclusive phase-space integrals, based on the unitarity cutting rules and integration-by-parts. We obtain splitting functions and coefficient functions up to second order in the strong coupling αsαs. Our results are in agreement with earlier calculations in the literature by Rijken and van Neerven.