Lattice QCD and the two-photon decay of the neutral pion

Two-photon decays probe the structure of mesons and represent an important contribution to hadronic light-by-light scattering. For the neutral pion, the decay amplitude tests the effects of the chiral anomaly; for a heavy quarkonium state, it measures the magnitude of its wave function at the origin. We rederive the expression of the decay amplitude in terms of a Euclidean correlation function starting from the theory defined on the torus. The derivation shows that for timelike photons the approach to the infinite-volume decay amplitude is exponential in the periodic box size.