Double bubble corrections to heavy quark production

Abstract Second order O (α 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 self-energy insertion and a certain class of O (α s 3 ) and O (α s 4 ) corrections are determined. For the special choice of the gauge parameter, ξ = 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.