arXiv2018
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 $π^0\to e^+e^-$ and the Dalitz decay of $π^0$, and provide a new value for the ratio $R={Γ(π^0\to e^+e^-γ(γ))}/{Γ(π^0\toγγ)}=11.978(6)\times10^{-3}$, 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 $π^0$-transition-form-factor slope. The ratio $R$ translates into the branching ratios of the two main $π^0$ decay modes: $\mathcal{B}(π^0\toγγ)=98.8131(6)\,\%$ and $\mathcal{B}(π^0\to e^+e^-γ(γ))=1.1836(6)\,\%$. Furthermore, we present the complete set of radiative corrections to the Dalitz decays $η^{(\prime)}\to\ell^+\ell^-γ$ 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 $η^{(\prime)}\toγ^*γ^{(*)}$ 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 $η$-$η^{\prime}$ mixing.