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Inspired by the observation of charmoniumlike $Z(4200)$, we explore thediscovery potential of the neutral $Z^{0}(4200)$ production byantiproton-proton annihilation with an effective Lagrangian approach. Byinvestigating the $\bar{p}p\rightarrow J/\psi \pi ^{0}$ process including the$Z^{0}(4200)$ signal and background contributions, it is found that the centerof mass energy $E_{c.m.}\simeq 4.0-4.5$ GeV is the best energy window forsearching the neutral $Z^{0}(4200)$, where the signal can be clearlydistinguished from background. The relevant calculations is not only helpful tosearch for the neutral $Z^{0}(4200)$ in the future experiment, but also willpromote the understanding the nature and production mechanism of neutral$Z^{0}(4200)$ better.

Discovery potential for the neutral charmoniumlike $Z^{0}(4200)$ by $\bar{p}p$ annihilation