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Recent advancements in charmoniumlike state have significantly enriched thediscovery of new hadronic states, providing exciting opportunities for furtherinvestigations into the fascinating realm of charmonium physics. In thisletter, we focus on the vector charmonium family and perform a detailedanalysis of the recently observed $e^+e^-\to \pi^+ D^0 D^{*-}$ process. Ourfindings demonstrate a striking agreement between the observed peak structuresand the predicted characterized energy level structure of higher vectorcharmonia including the $\psi(4220)$, $\psi(4380)$, $\psi(4415)$, and$\psi(4500)$, which are derived from an unquenched potential model. Thisdiscovery challenges conventional understanding of higher charmonia above 4 GeVand offers fresh insights into the dynamics of charm and anti-charm quarks inthe formation of these states. Furthermore, the identification of these highercharmonia in the precisely measured $\pi^+ D^0D^{*-}$ open-charm decay channelwould serve as compelling evidence supporting the unquenched scenario andcontribute to a deeper understanding of the nonperturbative aspects of thestrong interaction.

Identifying a characterized energy level structure of higher charmonium well matched to the peak structures in $e^+e^-\to \pi^+ D^0 D^{*-}$