Abstract
We summarize recent work in determining the transition form factor (TFF) of the neutral pion , by solving the non-perturbative Dyson-Schwinger and Bethe-Salpeter equations. We first study the transition form factor, followed by the rare decay , 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 Q2 regime (with Q2 the photon virtuality), and also touch on a path deformation in the complex plane to access the total decay rate for the rare decay.
Highlights
Meson transition form factors are intermediate states of many decay and collision processes
We summarize the calculations described in Refs. [1, 2]. These two publications are concerned with the calculation of the pion transition form factor π0 → γ∗γ∗ and further leptonic decays of the pion, such as the rare decay π0 → e+e−, which poses an interesting case due to a discrepancy between theoretical and experimental data
Transition form factor π0 → γγ The π → γ∗γ∗ transition matrix element is given by the tensor
Summary
Meson transition form factors are intermediate states of many decay and collision processes. These two publications are concerned with the calculation of the pion transition form factor π0 → γ∗γ∗ and further leptonic decays of the pion, such as the rare decay π0 → e+e−, which poses an interesting case due to a discrepancy between theoretical and experimental data. Besides the on-shell point the form factor is evaluated in different kinematic regions, see Fig 1 (b).
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