This paper (https://arxiv.org/pdf/1506.05669.pdf) is using ##H\to \gamma\gamma## to study the spin-2 hypothesis (but they also use other channels), but it does not seem to be sensitive to the pseudo-scalar hypothesis.
Do we expect that parity and spin are conserved in this particular decay? If so can we use the spin and parity of the two photons to predict those for the H boson?