Electromagnetic decays of the neutral pion investigated in the Dyson-Schwinger formalism

We summarize recent work in determining the transition form factor (TFF) of the neutral pion (${\pi }^0\to {\gamma }^{\ast }{\gamma }^{\ast }$), by solving the non-perturbative Dyson-Schwinger and Bethe-Salpeter equations. We first study the transition form factor, followed by the rare decay ${\pi }^0\to e^{+}{e}^{-}$, which requires the TFF as input. In addition to the aspects of truncation required to compute the solution, we discuss unexpected behavior in the large $Q^2$ regime (with $Q^2$ the photon virtuality), and also touch on a path deformation in the complex plane to access the total decay rate for the rare decay.