  We present the first full analytic evaluation of the scattering amplitude for
the process $q {\bar q} \to Q {\bar Q}$ up-to two loops in Quantum
Chromodynamics, for a massless $(q)$ and a massive $(Q)$ quark flavour. The
interference terms of the one- and two-loop amplitudes with the Born amplitude,
decomposed in terms of gauge invariant form factors depending on the colour and
flavour structure, are analytically calculated by keeping complete dependence
on the squared center-of-mass energy, the squared momentum transfer, and the
heavy-quark mass. The results are expressed as Laurent series around four
space-time dimensions, with coefficients given in terms of generalised
polylogarithms and transcendental constants up-to weight four. Our results
validate the known, purely numerical calculations of the squared amplitude, and
extend the analytic knowledge, previously limited to a subset of form factors,
to their whole set, coming from both planar and non-planar diagrams, up-to the
second order corrections in the strong coupling constant.
