Radiative corrections in Dalitz decays of ${\pi }^0$, $\eta$ and ${\eta }^{\prime }$ mesons

Abstract

We briefly summarize current experimental and theoretical results on the two important processes of the low-energy hadron physics involving neutral pions, the rare decay ${\pi }^0\to e^{+}{e}^{-}$ and the Dalitz decay of ${\pi }^0$, and provide a 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. This value is obtained using the complete set of the next-to-leading-order radiative corrections in the QED sector, and incorporates up-to-date values of the ${\pi }^0$-transition-form-factor slope. The ratio $R$ translates into the branching ratios of the two main ${\pi }^0$ decay modes: $\mathcal{B}({\pi }^0\to \gamma \gamma )=98.8131(6)\%$ and $\mathcal{B}({\pi }^0\to e^{+}{e}^{-}\gamma (\gamma ))=1.1836(6)\%$. Furthermore, we present the complete set of radiative corrections to the Dalitz decays ${\eta }^{(\prime )}\to {\ell }^{+}{\ell }^{-}\gamma$ beyond the soft-photon approximation, i.e. over the whole range of the Dalitz plot and with no restrictions on the energy of a radiative photon. The corrections inevitably depend on the ${\eta }^{(\prime )}\to {\gamma }^{\ast }{\gamma }^{(\ast )}$ transition form factors. For the singly-virtual transition form factor appearing e.g. in the bremsstrahlung correction, recent dispersive calculations are used. For the one-photon-irreducible contribution at the one-loop level (for the doubly-virtual form factor), we use a vector-meson-dominance-inspired model while taking into account the $\eta$-${\eta }^{\prime }$ mixing.

Comments: 9 pages, 3 figures; contribution to the proceedings of the following conferences: XIIIth Quark Confinement and the Hadron Spectrum, 15th International Workshop on Meson Physics and 9th International Workshop on Chiral Dynamics