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 $ψ(3686)\rightarrow ϕηη’$ 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 $ϕ$ and $η/η$ 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 $ϕη’/ϕη$ 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 $ϕη’/ϕη$ 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 $X(2300)$.

💡 Research Summary

The paper investigates the nature of the newly observed axial‑vector resonance X(2300) reported by the BESIII Collaboration in the decay ψ(3686)→ϕηη′. Using the parton‑and‑hadron cascade model PACIAE 4.0, the authors simulate e⁺e⁻ annihilation at √s = 4.95 GeV, generate the final partonic state (FPS) and the final hadronic state (FHS), and then apply a dynamically constrained phase‑space coalescence (DCPC) algorithm, inspired by quantum‑statistical mechanics, to form possible X(2300) configurations. Three distinct structural hypotheses are examined: (i) an excited s s̄ strangeonium (P‑wave), (ii) a tetra‑quark with light‑light‑strange‑strange content (q q̄ s s̄) or a fully strange tetra‑quark (s s s̄ s̄) (both S‑wave), and (iii) a hadro‑strangeonium, i.e. a bound state of a strangeonium (ϕ) and a light pseudoscalar meson (η or η′) (S‑wave). The DCPC model imposes spatial and invariant‑mass constraints (Δm≈½ ΓX, R0≈1–2 fm) to select clusters that satisfy the quantum‑number requirements. The orbital angular momentum L of each candidate is extracted from the vector sum of constituent r×p in the X rest frame, quantised via L(L+1)≈l*²/ℏ², and combined with spin S to obtain the total J. For JPC=1⁺⁻, the allowed assignments are: P‑wave s s̄, S‑wave q q̄ s s̄, S‑wave s s s̄ s̄, or S‑wave ϕη(′). The authors compute event‑averaged yields, rapidity (y) and transverse‑momentum (pT) spectra for each configuration. The production rates are: (s s̄)P‑wave ≈4.05×10⁻⁵, (q q̄ s s̄)S‑wave ≈8.43×10⁻⁵, (s s s̄ s̄)S‑wave ≈6.50×10⁻⁶, (ϕη′)S‑wave ≈6.97×10⁻⁶, (ϕη)S‑wave ≈6.06×10⁻⁶. The yields of the P‑wave strangeonium and the q q̄ s s̄ tetra‑quark are of order 10⁻⁵, while the fully‑strange tetra‑quark and the hadro‑strangeonium are an order of magnitude smaller (10⁻⁶). Rapidity distributions show that the strangeonium candidate is more central (|y|<1) than the tetra‑quark and hadro‑strangeonium, which are broader. The pT spectra reveal a harder tail for the q q̄ s s̄ state (average ⟨pT⟩≈0.9 GeV) compared with the s s̄ (⟨pT⟩≈0.6 GeV) and the hadro‑strangeonium (⟨pT⟩≈0.5 GeV). These characteristic differences are proposed as experimental discriminants. The paper also discusses the compatibility of the X(2300) mass (≈2316 MeV) with a 3¹P₁ s s̄ assignment, noting that it lies above the φ(2170) (identified as a 2³D₁ or 3³S₁ s s̄ state) and below the predicted mass of a D‑wave s s̄ tetra‑quark (≈2600 MeV). The authors conclude that the PACIAE‑DCPC framework provides the first quantitative estimates of production rates for the various exotic configurations and that future measurements of rapidity and pT spectra at BESIII or Belle II could decisively identify whether X(2300) is an excited strangeonium, a light‑strange tetra‑quark, a fully‑strange tetra‑quark, or a hadro‑strangeonium bound state.