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

Abstract

We summarize recent work in determining the transition form factor (TFF) of the neutral pion ($π^0 \to γ^*γ^*$), by solving the non-perturbative Dyson-Schwinger and Bethe-Salpeter equations. We first study the transition form factor, followed by the rare decay $π^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.

Contribution to the Proceedings of the Workshop FAIRNESS 2017. 5 pages, 3 figures