Two-loop electroweak corrections to the A0γγ and A0gg couplings of the CP-odd Higgs boson

Using the asymptotic-expansion technique, we compute the dominant two-loop electroweak corrections, of O(GFmt2), to production and decay via a pair of photons or gluons of the CP-odd Higgs boson A0 in a two-Higgs-doublet model with low to intermediate values of the Higgs-boson masses and ratio tanβ=v2/v1 of the vacuum expectation values. We also study the influence of a sequential heavy-fermion generation. The appearance of three γ5 matrices in closed fermion loops requires special care in the dimensional regularisation of ultraviolet divergences. The finite renormalisation constant for the pseudoscalar current effectively restoring the anticommutativity of the γ5 matrix, familiar from perturbative quantum chromodynamics, is found not to receive a correction in this order. We also revisit the dominant two-loop electroweak correction to the H→γγ decay width in the Standard Model with a fourth fermion generation.