Radiative corrections for Dalitz decays of $\pi^0$, $\eta^{(\prime)}$ and $\Sigma^0$

Abstract

We briefly summarize current experimental and theoretical results on the $\pi^0$ Dalitz decay, including the new value for the ratio $R={\Gamma(\pi^0\to e^+e^-\gamma(\gamma))}/{\Gamma(\pi^0\to\gamma\gamma)}=11.978(6)\times10^{-3}$, which is by two orders of magnitude more precise than the current PDG average. Furthermore, we discuss radiative corrections for the Dalitz decays $\eta^{(\prime)}\to\ell^+\ell^-\gamma$ beyond the soft-photon approximation. The corrections inevitably depend on the $\eta^{(\prime)}\to\gamma^*\gamma^{(*)}$ transition form factors. Finally, we present (inclusive) radiative corrections for the $\Sigma^0\to\Lambda e^+e^-$ decay, evaluated as well beyond the soft-photon approximation, i.e., over the whole range of the Dalitz plot and with no restrictions on the energy of the radiative photon. Here, we also calculate explicitly the 1$\gamma$IR contribution and the correction to the $\Sigma^0\Lambda\gamma$ vertex and confirm that these can be neglected.