Revisiting the production of charmonium plus a light meson at PANDA

In this work, we calculate the total cross sections and the center-of-mass frame angular distributions of the charmonium production plus a light meson by the low energy $p\bar{p}$ interaction. The results of $p\bar{p}\to \pi^0 \Psi$ with and without form factor (FF) indicate that the FF contribution in the calculation cannot be ignored. The obtained cross section of $p\bar{p}\to \pi^0 J/\psi$ with FF can fit the E760 data well. We also predict the total cross sections and the center-of-mass frame angular distributions of $p\bar{p}\to \omega \Psi$, which show that these physical quantities are dependent on Pauli ($g_\omega$) and Dirac ($\kappa_\omega$) coupling constants of the $pp\omega$ interaction. Thus, $p\bar{p}\to \omega \Psi$ can be as the ideal channel to test the different theoretical values of $g_\omega$ and $\kappa_\omega$. Applying the formulae of $p\bar{p}\to \pi^0 \Psi$ and $p\bar{p}\to \omega \Psi$, we predict the total cross sections of the $p\bar{p}\to \eta \Psi$ and $p\bar{p}\to \rho \Psi$ reactions. Our results show a common behavior of the charmonium production with a light meson by the $p\bar{p}$ interaction, where the total cross section of the $\eta_c$ production is the largest one among all discussed processes. The above observations can be directly tested at the forthcoming $\bar{P}$ANDA experiment.