Two-photon processes of pseudoscalar mesons in a Bethe-Salpeter approach

Abstract

We evaluate the $π^0γ^* \to γ$ transition form factor and $γγ$ decay widths for $π^0, η_c$ and $η_b$ treated as $q\bar{q}$ bound states in the Bethe-Salpeter formalism, incorporating the dynamical chiral symmetry breaking and the Goldstone nature of the pion. In the chiral limit, the Abelian axial anomaly is incorporated analytically in our coupled Schwinger-Dyson and Bethe-Salpeter approach, which is also capable of quantitatively describing systems of heavy quarks, concretely $η_c$ and possibly $η_b$.