γ★γ→ π0 transition and asymptotics of γ★γ and γ★γ★ transitions of unflavored pseudoscalar mesons

Abstract

For the spacelike momenta k of the virtual photon γ ★, the π 0( p) γ ★( k) γ( k ′) transition form factor is considered in the coupled Schwinger–Dyson and Bethe-Salpeter approach in conjunction with the generalized impulse approximation using the dressed quark–photon–quark vertices of the Ball–Chiu and Curtis-Pennington type. These form factors are compared with the ones predicted by the vector meson dominance, operator product expansion, QCD sum rules, and the perturbative QCD for the large spacelike transferred momenta k. The most important qualitative feature of the asymptotic behavior, namely the 1/ k 2 dependence, is in our approach obtained in the model-independent way. Again model-independently, our approach reproduces also the Adler–Bell–Jackiw anomaly result for the limit of both photons being real. For the case of one highly virtual photon, we find in the closed form the asymptotic expression which is then easily generalized both to the case of other unflavored pseudoscalar mesons P 0= π 0, η 8, η 0, η c , η b , and to the case of arbitrary virtuality of the other photon.