Dispersive analysis of the J / ψ → π 0 γ * transition form factor with ρ – ω mixing effects

Motivated by the discrepancies noted recently between the theoretical predictions of the electromagnetic J / ψ → π 0 γ * transition form factor and the BESIII data, we reanalyze this transition form factor using the dispersive Khuri-Treiman equations, with final-state interactions in both the direct channel and the crossed channels properly considered. This improved framework incorporates ρ – ω mixing effects. The effect of four-pion states is evaluated through a dispersively improved vector-meson-dominance model. From this information, we propose a two-parameter fit that provides an excellent description of the BESIII data over the broad energy range from 0 to 2.8 GeV. We demonstrate that the ρ π 0 decay mode of the J / ψ is dominated by strong interaction, while the ω π 0 mode is dominated by one-photon exchange. From this, we extract the relative phase between the strong and the one-virtual-photon (electromagnetic) modes in hadronic decays of J / ψ as ( 62 ± 21 ) ° . This could provide useful information in understanding the long-standing ρ π puzzle in J / ψ decays.