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 A FB H and the shape constant a H 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 A FB H 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