Radiative corrections to the $η^{(\prime)}$ Dalitz decays

Abstract

We provide 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.