The role of chiral loops in $η\toπ^0π^0γγ$

We consider the rare decay $\eta\to\pi^0\pi^0\gamma\gamma$ and calculate the non-resonant contribution to the amplitude to one loop in Chiral Perturbation Theory. We display our result as both a diphoton energy spectrum and a partial decay rate as a function of the photon energy cut. It turns out that the one-loop correction can be numerically very important and could be detected, at sufficiently large center-of-mass photon energies, from a measurement of the partial decay width.