Revisiting the Vector Dominance Model in Radiative Vector-Meson Decays

The application of the vector dominance model (VDM) to the Dalitz decay ω→μ⁺μ^- π⁰ underestimates the experimental spectra, especially when approaching the kinematic limit for the dimuon invariant mass. Recently, the discrepancy became more apparent as the NA60 experiment at the CERN-SPS re-measured the ω form factor with better precision. In the present work, we augment the baseline VDM by simulating the finite size of the ωρπ-vertex through a hadronic form factor, which was introduced 14 years ago in a different context. The additional momentum dependence predicted by the form factor improves the description of the NA60 data noticeably. In addition, we have improved the intermediate ρ propagator by replacing its schematic width with a microscopic model for its vacuum self-energy. This leads to a further, albeit smaller, improvement in the description of the data. As another test of the form factor, we have checked the decay width of the ρ-meson into a gamma ray and a pion, which turns out to agree with the experimental value. We briefly look at the ρ→ηγ and ω→ηγ decay widths with the same approach and used our results from these vertices to calculate the partial widths for the η→γγ and η→π⁺π^-γ decays as well as the energy distribution for the η→π⁺π^-γ decay. Our results thus support the use of hadronic form factors to simulate finite-size effects in hadronic interactions and improve an apparent shortcoming of the VDM.