The Role of Chiral Loops in η->π^0π^0γγ

We consider the rare decay η->π^0π^0γγ 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 centre-of-mass photon energies, from a measurement of the partial decay width.