Analytic Calculation of Two Loop Corrections to Heavy Quark Pair Production Vertices Induced by Light Quarks

Non-singlet $\mathcal{O}({\alpha }_s^2)$ corrections from light quarks are calculated analytically for the massive quark-antiquark pair production rates through the vector, axial-vector, scalar and pseudoscalar currents for all energies above the threshold. The results are presented in terms of the moments of the absorptive part of the vacuum polarization function of the light quarks which allows for an immediate determination of $\mathcal{O}({\alpha }_s^2)$ corrections coming from other types of light particles. The kinematic regime close to the threshold is examined.