Dispersive analysis of the $J/\psi\to\pi^0 \gamma^\ast$ transition form factor with $\rho$-$\omega$ mixing effects

Motivated by the discrepancies noted recently between the theoretical predictions of the electromagnetic $J/\psi \to \pi^0 \gamma^*$ 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 $\rho$-$\omega$ 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 2.8GeV. We demonstrate that the $\rho\pi^0$ decay mode of the $J/\psi$ is dominated by strong interaction, while the $\omega\pi^0$ 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 $J/\psi$ as $(62 \pm 21)^{\circ}$. This could provide useful information in understanding the long-standing $\rho \pi$ puzzle in $J/\psi$ decays.