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

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 ${\eta }^{(\mathrm{\prime })}\to {\mathrm{\ell }}^{+}{\mathrm{\ell }}^{-}\gamma$ beyond the soft-photon approximation. The corrections inevitably depend on the ${\eta }^{(\mathrm{\prime })}\to {\gamma }^{\ast }{\gamma }^{(\ast )}$ transition form factors. Finally, we present (inclusive) radiative corrections for the ${\mathrm{\Sigma }}^0\to \mathrm{\Lambda }{e}^{+}{e}^{-}$ 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 ${\mathrm{\Sigma }}^0\mathrm{\Lambda }\gamma$ vertex and confirm that these can be neglected.