O(αs2) contributions to the asymmetric fragmentation function in e+e− annihilation

The order αs2 contributions to the coefficient functions corresponding to the asymmetric fragmentation function FA(x,Q2) in e+e− annihilation are calculated. From this calculation we infer that the order (αs4π)2 correction to the flavour asymmetry sum rule is non-vanishing and amounts to −12β0CFζ(3). We also study the effect of the higher order QCD corrections on FA(x,Q2) and compare them with the OPAL data. The latter put a strong constraint on the valence part of the fragmentation densities DqH(x,μ2).