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

TL;DR

This paper uses Dyson-Schwinger equations to study the neutral pion's electromagnetic transition form factor and rare decay, revealing unexpected high-energy behavior and methods to compute decay rates.

Contribution

It presents a non-perturbative calculation of the pion's transition form factor and decay rate using Dyson-Schwinger formalism, including novel insights into large $Q^2$ behavior.

Findings

Unexpected behavior in the large $Q^2$ regime of the TFF

Successful computation of the $ ext{π}^0 o e^+ e^-$ decay rate

Method development for complex plane path deformation

Abstract

We summarize recent work in determining the transition form factor (TFF) of the neutral pion ($\pi^0 \to \gamma^*\gamma^*$), 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.