$O({\alpha }_s^2)$ Contributions to the asymmetric fragmentation function in $e^{+}{e}^{-}$ annihilation

Abstract

The order \alpha_s^2 contributions to the coefficient functions corresponding to the asymmetric fragmentation function $F_A(x,Q^2)$ in $e^{+}{e}^{-}$ annihilation are calculated. From this calculation we infer that the order $({\alpha }_s/4\pi {)}^2$ correction to the flavour asymmetry sum rule is non vanishing and amounts to $-12{\beta }_0{C}_F\zeta (3)$. We also study the effect of the higher order QCD corrections on $F_A(x,Q^2)$ and compare them with the OPAL data. The latter put a strong constraint on the valence part of the fragmentation densities $D_q^H(x,{\mu }^2)$.

Comments: 15 pages, latex2e, uses mcite, amsfonts. PostScript version also available at http://rulgm4.leidenuniv.nl/preprints/asymmfrag.ps