Production of the charmoniumlike state $Y(4220)$ through the $p\bar{p}\to Y(4220){\pi }^0$ reaction

The $Y(4220)$ production in the process of $p\bar{p}\to Y(4220){\pi }^0$ is studied within the effective Lagrangian approach. We first study the $e^+e^-\to Y(4220) \to p\bar{p}\pi^0$reactionatcenter-of-massenergy$4.258$ GeV with the assumption that the $Y(4220)$ is a $\psi (4S)$ state. We show that the inclusion of nucleon and nucleon resonance leads to a quite good description of the experimental data of ${\pi }^{0}p$ and ${\pi }^0\bar{p}$ invariant mass distributions. Then, the total and angular distributions of the $p\bar{p} \to Y(4220)\pi^0$ reaction are investigated. It is shown that the nucleon pole is dominant but the contributions from excited nucleon resonances are non-negligible. The $p\bar{p}\to Y(4220){\pi }^0$ reaction is useful for studying the property of $Y(4220)$ and our calculated results may be tested at the forthcoming $\bar{P}$ANDA experiments.