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.
#5
Intesar
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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?