arXiv2025
Inspired by the BESIII observation of exotic hadron $G$(3900) in $e^+e^-\rightarrow D\bar D$ process [PRL 133(2024)081901], we use the parton and hadron cascade model PACIAE to simulate the productions of charmonium-like exotic hadrons including $X(3872)$, $Z_{c}(3900)^0$ and $G(3900)$ in the $e^+e^-$ annihilations at $\sqrt s$=4.95 GeV. The charmonium-like candidates are recombined by Dynamically Constrained Phase-space Coalescence model using component mesons $D\bar D$ (for $G(3900)$) or $D\bar D^*/\bar DD^*$ (for $X(3872)$, $Z_{c}(3900)^0$ and $G(3900)$) in the PACIAE simulated final hadronic state. We then calculate, for the first time, the charmonium-like candidate's orbital angular momentum quantum number in its rest frame and perform the spectral classification for each of the above candidates. For $G(3900)$, as its $J^{PC}$ is $1^{--}$, it is identified as the $P$-wave $D\bar D$ or $D\bar D^*/\bar DD^*$ state. Meanwhile, for $X(3872)$ and $Z_{c}(3900)^0$, as their $J^{PC}$s are, respectively, $1^{++}$ and $1^{+-}$, they are identified as the $S$-wave $D\bar D^*/\bar DD^*$ candidates. It is observed that the yield of the $P$-wave $G(3900)$ composed of $D\bar D^*/\bar DD^*$ is significantly larger than that composed of $D\bar D$. Moreover, in the $D\bar D^*/\bar DD^*$ channel, the yield of the $P$-wave $G(3900)$ is around three times as large as the yield of the $S$-wave $Z_{c}(3900)^0$, and it is around two orders of magnitude as large as the yield of the $S$-wave $X(3872)$. Finally, significant discrepancies are observed in the transverse momentum spectra and the rapidity distributions among the $X(3872)$, $Z_{c}(3900)^0$ and $G(3900)$ states. These discrepancies are proposed as valuable criteria for identifying the different charmonium-like exotic hadrons from each other.