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

Inspired by the BESIII newest observation of an axial-vector particle $X(2300)$ in the $\psi(3686)\rightarrow \phi\eta \eta'$ process, we simulate its production in $e^+e^-$ 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 hadronic state (FHS) are simulated and recorded sequentially. We propose, for the first time, that $X(2300)$ could be a $q\bar{q}s\bar{s}$ ($q=u/d$) state or a hadro-strangeonium state, i.e., a bound system of a strangeonium and a light hadron. The excited strangeonium candidate is formed by coalescing an $s\bar{s}$ quark pair in the FPS with the quantum statistical mechanics inspired dynamically constrained phase-space coalescence model. The tetraquark candidates of $q\bar{q}s\bar{s}$ and $ss\bar{s}\bar{s}$ are similarly produced by coalescing four constituent quarks in the FPS. In contrast, a hadro-strangeonium candidate emerges from the recombination of the constituent $\phi$ and $\eta/\eta$ in the FHS. 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 $J^{PC}=1^{+-}$, $X(2300)$ is identified as a $P$-wave $s\bar{s}$, an $S$-wave $q\bar{q}s\bar{s}/ss\bar{s}\bar{s}$ or $S$-wave $\phi\eta'/\phi \eta$ candidate. For the first time, we estimate the production rates for these configurations. The $P$-wave $s\bar{s}$ and $S$-wave $q\bar{q}s\bar{s}$ states are produced at rates on the order of $10^{-5}$, whereas the $S$-wave $ss\bar{s}\bar{s}$ and $\phi\eta'/\phi \eta$ states appear at rates on the order of $10^{-6}$. Moreover, significant discrepancies are observed in the rapidity and transverse momentum distributions among different candidates. These discrepancies could be served as valuable criteria for deciphering the nature of $X(2300)$.