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

Abstract

We evaluate the $\pi^0\gamma^* \to \gamma$ transition form factor and $\gamma\gamma$ decay widths for $\pi^0, \eta_c$ and $\eta_b$ 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 $\eta_c$ and possibly $\eta_b$.