Double Bubble Corrections to Heavy Quark Production
  Second order ${\cal O}(\alpha_s^2)$ corrections to the heavy quark production cross-section due to massless quarks and coloured scalars are calculated for all energies above threshold. Based on the method introduced in this letter also the gauge non-invariant second order corrections due to the pure gluonic selfenergy insertion and a certain class of ${\cal{O}}(\alpha_s^3)$ and ${\cal{O}}(\alpha_s^4)$ corrections are determined. For the special choice of the gauge parameter, $\xi=4$, the leading threshold and high energy behaviour of the pure second order gluonic corrections to the cross-section are governed by the gluonic self energy insertion. 
K.G. Chetyrkin (MPI f\"ur Physik, Munich, Germany), A.H. Hoang, J.H.   Kuehn, M. Steinhauser (Uni. Karlsruhe, Germany), T. T...