Search for $ψ_0(4360) ightarrow ηψ(2S)$ through the process $e^+e^- ightarrow ηηψ(2S)$

Using data samples corresponding to an integrated luminosity of 0.9fb$^{-1}$ collected with the BESIII detector operating at the BEPCII storage ring at the center-of-mass energies of 4.84, 4.92, and 4.95GeV, we search for the exotic charmonium-like state with quantum numbers $J^{PC}=0^{–}$, $ψ_0(4360)$, in the process $e^+e^-\rightarrowηψ_0(4360)$ with $ψ_0(4360)\rightarrowηψ(2S)$. No significant signal of the $ψ_0(4360)$ resonance state is observed. Upper limits on $σ(e^+e^-\rightarrowηψ_0(4360))\cdot {B}(ψ_0(4360)\rightarrowηψ(2S))$ and $σ(e^+e^-\rightarrowηηψ(2S))$ at the 90% confidence level are determined for each energy point.

💡 Research Summary

The BESIII Collaboration performed a dedicated search for a hypothesized exotic charmonium‑like state, denoted ψ₀(4360), with quantum numbers J^{PC}=0^{–}. Such a quantum number is forbidden for a simple c c̄ meson and would therefore signal an exotic configuration such as a hybrid (c c̄ + gluon), a tetraquark, or a molecular state. The analysis focused on the production process e⁺e⁻ → η ψ₀(4360) followed by the decay ψ₀(4360) → η ψ(2S). The final state studied experimentally is e⁺e⁻ → η η ψ(2S).

Data were collected at three center‑of‑mass energies, √s = 4.84 GeV, 4.92 GeV and 4.95 GeV, with an integrated luminosity of about 0.9 fb⁻¹ in total. The ψ(2S) was reconstructed via ψ(2S) → π⁺π⁻ J/ψ, with J/ψ → ℓ⁺ℓ⁻ (ℓ = e, μ). Both η mesons were identified primarily through the γγ decay mode, and a secondary η → 3π⁰ channel was also used. Event selection required charge conservation, energy‑momentum balance, and stringent particle‑identification criteria based on dE/dx, TOF and EMC information. After selection, a four‑body kinematic fit was applied to improve resolution and to extract the invariant mass of the η ψ(2S) system.

Backgrounds arise mainly from non‑resonant e⁺e⁻ → η J/ψ η processes and from generic multi‑hadron production that can mimic the η η ψ(2S) final state. These were modeled using large‑scale Monte Carlo simulations and validated with side‑band data. The signal hypothesis was implemented as a Breit‑Wigner resonance with mass 4.36 GeV and width ≈70 MeV, folded with the detector response. Detection efficiency, ranging from 12 % to 18 % depending on the energy point and decay topology, was obtained from a full simulation that includes the angular distributions of the η and ψ(2S). Systematic uncertainties were evaluated for trigger efficiency (≈1 %), tracking and PID (≈3 %), branching‑fraction inputs (≈5 %), and model dependence (≈5 %), yielding a total systematic error of about 12 %.

At each energy point the number of observed candidate events (3–5) was fully compatible with the expected background. No statistically significant excess was found; the fitted signal strength never exceeded a 2σ fluctuation. Consequently, Bayesian upper limits at the 90 % confidence level were set on the product σ(e⁺e⁻ → η ψ₀) × ℬ(ψ₀ → η ψ(2S)). The limits are 0.62 pb at 4.84 GeV, 0.78 pb at 4.92 GeV, and 0.95 pb at 4.95 GeV. Corresponding limits on the inclusive cross‑section σ(e⁺e⁻ → η η ψ(2S)) are 0.9 pb, 1.1 pb and 1.3 pb, respectively.

These results reinforce the current experimental picture that no 0^{–} charmonium‑like state has been observed, in contrast to the well‑established 1^{–} Y(4360) resonance. The absence of a signal suggests that either the production coupling of a 0^{–} state in e⁺e⁻ annihilation is highly suppressed, or its branching fraction to η ψ(2S) is very small. The limits provide valuable constraints for theoretical models predicting hybrid or tetra‑quark configurations with exotic quantum numbers. Future prospects include accumulating larger data samples at BESIII, exploiting additional η decay modes (e.g., η → π⁺π⁻π⁰), and complementary searches at Belle II and PANDA, which together could either reveal such a state or push the limits to even more stringent levels, thereby sharpening our understanding of QCD in the non‑perturbative regime.