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

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 ${\eta }^{(\prime )}\to {\gamma }^{\ast }{\gamma }^{(\ast )}$ 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: 30 pages, 8 figures, 12 tables; v2: hadronic vacuum polarization contribution, spectral function fit and ancillary files containing data points added, minor corrections; v3: accepted version for publication in Phys. Rev. D., extended results section and end of Section IV, corrected values in Tables III-VI, Figs. 5a and 5b and ancillary files updated, other minor corrections and improvemets