  A precision determination of the neutral-pion width would improve
determinations of the splitting between the up- and down-quark masses, and
matrix elements for the decay of neutral mesons into two photons could play a
role in the attempt to probe beyond-the-Standard Model physics in muon $g-2$
experiments. The theoretical error is dominated by hadronic light-by-light
diagrams, and since direct measurements are extremely difficult, model
calculations factorize it into two-photon diagrams connected by the lightest
hadrons. We employ perturbative techniques to express the photon as a
superposition of QCD eigenstates accessible in lattice-QCD calculations and
found that vector-meson dominance is a poor description of the two-photon decay
process when both photons are off shell.
