  We compute the radiative corrections to the four-point amplitude $g+g
\rightarrow A+A$ in massless Quantum Chromodynamics (QCD) up to order $a_s^4$
in perturbation theory. We used the effective field theory that describes the
coupling of pseudo-scalars to gluons and quarks directly, in the large top
quark mass limit. Due to the CP odd nature of the pseudo-scalar Higgs boson,
the computation involves careful treatment of chiral quantities in dimensional
regularisation. The ultraviolet finite results are shown to be consistent with
the universal infrared structure of QCD amplitudes. The infrared finite part of
these amplitudes constitutes the important component of any next to next to
leading order corrections to observables involving pair of pseudo-scalars at
the Large Hadron Collider.
