Probing exotic $J^{PC}$ resonances from deeply bound charmoniumlike molecules: Insights for identifying exotic hadrons

We investigate the resonance phenomenon in deeply bound charmoniumlike states. By interpreting the $Y(4220)$, $Y(4360)$, and $\psi(4415)$ states as deeply $S$-wave bound $D \bar D_1$, $D^* \bar D_1$, and $D^* \bar D_2^*$ molecules, respectively, we robustly predict the existence of $4$ $S$-wave deeply bound $C$-parity partner states and $13$ $P$-wave charmoniumlike molecular resonances. These states, formed by exchanging the light mesons and pinpointed through the complex scaling method, include $3$ $S$-wave bound states with exotic quantum numbers $I(J^{PC})$= $0(1^{-+})$ and $5$ $P$-wave resonances with exotic $0(0^{-+})$ and $0(2^{+-})$. We expect future experiments to search for such exotic molecular resonances, which will not only enrich the ongoing construction of ``Particle Zoo 2.0" but also help to scrutinize the hadronic molecular assignments of the $Y$-family particles including the $Y(4220)$, $Y(4360)$, and $\psi(4415)$ states.