Deciphering the nature of $X(2300)$ with the PACIAE model

Abstract: Inspired by the BESIII newest observation of an axial-vector particle $X(2300)$ in the $\psi(3686)\rightarrow \phi\eta \eta&#39;$ process (Phys. Rev. Lett. {\bf134}, 191901 (2025)), we simulate its production in $e<sup>+e<sup>-$ collisions at $\sqrt{s}=4.95$ GeV using the parton and hadron cascade model PACIAE 4.0. In this model, the final partonic state (FPS) and the final hadronic state (FHS) are simulated and recorded sequentially. Besides the excited strangeonium and tetraquark interpretations, we propose for the first time that the $X(2300)$ could also be a hadro-strangeonium state, in which a strangeonium and a light hadron are bound together. The excited strangeonium and tetraquark states are, respectively, produced by coalescing with $s\bar{s}$ and $ss\bar{s}\bar{s}$ in the FPS with the quantum statistical mechanics inspired dynamically constrained phase-space coalescence (DCPC) model. The hadro-strangeonium state is generated by the recombination of $\phi\eta/\phi \eta&#39;$ in the FHS with DCPC. We then calculate the $X(2300)$'s orbital angular momentum quantum number in its rest frame and perform the spectral classification for each of the above candidates. Given its quantum numbers $J^{PC} = 1<sup>{+-}$, the $X(2300)$ is identified as a $P$-wave $s\bar{s}$, an $S$-wave $ss\bar{s}\bar{s}$ or an $S$-wave $\phi\eta/\phi \eta&#39;$ candidate. The production rates for the $X(2300)$ candidates with different configurations are estimated for the first time. Those for the excited strangeonium and tetraquark states are on the order of $10<sup>{-4}$, while the hadro-strangeonium state is produced at a rate on the order of $10<sup>{-6}$. Moreover, significant discrepancies are observed in the rapidity distributions and the transverse momentum spectra among the different configurations. These discrepancies could be served as valuable criteria for deciphering the nature of the $X(2300)$.