Radiative corrections to the Dalitz decay $\pi^0\to e^+e^-\gamma$ revisited

TL;DR

This paper recalculates the radiative corrections to the Dalitz decay of the neutral pion, including higher-order terms and contributions, providing more accurate results applicable to heavier particles.

Contribution

It extends previous calculations by including higher-order mass terms, one-photon-irreducible, and muon loop contributions, improving accuracy across the entire Dalitz plot.

Findings

Recalculated radiative corrections beyond soft-photon approximation.

Included higher-order mass terms and loop contributions.

Results applicable to heavier particles in decay processes.

Abstract

We have recalculated the Mikaelian and Smith radiative corrections to the Dalitz decay $\pi^0\to e^+e^-\gamma$ beyond the soft-photon approximation, i.e. over the whole range of the Dalitz plot and with no restrictions on the radiative photon. In contrast to the previous calculations, we did not neglect the terms of order higher than $\mathcal{O}(m^2)$ and also included the one-photon-irreducible contribution at one-loop level and the virtual muon loop contribution. The results can then be used also for heavier particles in the final state.