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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 $p\bar{p}\to π^0 Ψ$ with and without form factor (FF) indicate that the FF contribution in the calculation cannot be ignored. The obtained cross section of $p\bar{p}\to π^0 J/ψ$ with FF can fit the E760 data well. We also predict the total cross sections and the center-of-mass frame angular distributions of $p\bar{p}\to ωΨ$, which show that these physical quantities are dependent on Pauli ($g_ω$) and Dirac ($κ_ω$) coupling constants of the $ppω$ interaction. Thus, $p\bar{p}\to ωΨ$ can be as the ideal channel to test the different theoretical values of $g_ω$ and $κ_ω$. Applying the formulae of $p\bar{p}\to π^0 Ψ$ and $p\bar{p}\to ωΨ$, we predict the total cross sections of the $p\bar{p}\to ηΨ$ and $p\bar{p}\to ρΨ$ 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 $η_c$ production is the largest one among all discussed processes. The above observations can be directly tested at the forthcoming $\bar{P}$ANDA experiment.