Second order QCD corrections to the forward-backward asymmetry in e+e−-collisions

We will present the result of an analytical calculation of the second order contribution to the forward-backward asymmetry AFBH and the shape constant aH for heavy flavour production in e+e−-collisions. The calculation has been carried out by assuming that the quark mass is equal to zero. This is a reasonable approximation for the exact second order correction for charm and bottom quark production at LEP energies but not for top production at future linear colliders. Our result for AFBH is a factor 2.6 (charm) and 4.7 (bottom) larger than obtained by a numerical calculation performed earlier in the literature. We study the effect of the second order corrections on the above parameters including their dependence on the renormalization scale. Further we make a comparison between the fixed pole mass and the running mass approach.