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

TL;DR

This paper calculates comprehensive radiative corrections to $ ext{eta}^{( ext{prime})}$ Dalitz decays, covering the entire Dalitz plot without approximations, and incorporates recent form factor models and mixing effects.

Contribution

It provides the first complete set of radiative corrections beyond the soft-photon approximation for these decays, including form factor dependencies and mixing effects.

Findings

Corrections depend on transition form factors.

Uses dispersive calculations for singly virtual form factors.

Employs vector-meson-dominance model for doubly virtual form factors.

Abstract

We provide 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 $\eta^{(\prime)}\to\gamma^*\gamma^{(*)}$ 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.