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We briefly summarize current experimental and theoretical results on the$\pi^0$ Dalitz decay, including the new value for the ratio $R={\Gamma(\pi^0\toe^+e^-\gamma(\gamma))}/{\Gamma(\pi^0\to\gamma\gamma)}=11.978(6)\times10^{-3}$,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, wepresent (inclusive) radiative corrections for the $\Sigma^0\to\Lambda e^+e^-$decay, evaluated as well beyond the soft-photon approximation, i.e., over thewhole range of the Dalitz plot and with no restrictions on the energy of theradiative photon. Here, we also calculate explicitly the 1$\gamma$IRcontribution and the correction to the $\Sigma^0\Lambda\gamma$ vertex andconfirm that these can be neglected.

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