Form factor π 0 → γ* + γ* at different photon virtualities

The π 0 γγ vertex for virtual photons of squared masses q 1 2 and q 2 2 plays a vital rôle in several physical processes; for example for q 1 2 < 0, q 2 2 < 0, in the two-photon physics reaction e + e − → e + e − π 0 , and for q 1 2 > 0, q 2 2 > 0, in the annihilation process e + e − → π 0 l + l − . It is also of interest because of its link to the axial anomaly. We suggest a new approach to this problem. We have obtained a closed analytic expression for the vertex in the limit in which at least one of ¦ q 1 2 ¦ and ¦ q 2 2 ¦ is large for arbitrary fixed values of the ratio q 1 2 / q 2 2 . We compare our results with those obtained previously by Brodsky and Lepage. It should be straightforward to test our predictions experimentally.