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 $R=\Gamma ({\pi }^0\to e^{+}{e}^{-}\gamma (\gamma ))/\Gamma ({\pi }^0\to \gamma \gamma )=11.978(6)\times 10^{-3}$, 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 ${\eta }^{(\prime )}\to {\gamma }^{\ast }{\gamma }^{(\ast )}$ 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.

Comments: 4 pages, 3 figures; contribution to the proceedings of the following conferences: 22nd High-Energy Physics International Conference in Quantum Chromodynamics (QCD 19) and XVIII International Conference on Hadron Spectroscopy and Structure (HADRON2019). arXiv admin note: text overlap with arXiv:1811.12350