Observation of a family of all-charm tetraquarks

Three structures, X(6600), X(6900), and X(7100), have emerged from the J$/ψ,$J$/ψ$ (J$/ψ$ $\to$ $μ^+μ^-$) mass spectrum. These are candidates of all-charm tetraquarks, an exotic form of hadronic matter. A clearer picture of these states is obtained using proton-proton collision data collected by the CMS detector that corresponds to 315 fb$^{-1}$, which yields 3.6 times more J$/ψ,$J$/ψ$ pairs than previous studies by CMS. All three structures, and their mutual interference, have statistical significances above five standard deviations. The presence of interference implies that the structures have common quantum numbers. Their squared masses align linearly with a resonance index and have natural widths that systematically decrease as the index increases. These features are consistent with radial excitations of tetraquarks composed of two aligned spin-1 diquarks without orbital excitation, and disfavor other interpretations. The J$/ψ,$$ψ$(2S) $\to$ $μ^+μ^-μ^+μ^-$ decay mode is also explored and the X(6900) and X(7100) states are found with significances exceeding 8 and 4 standard deviations, respectively.

💡 Research Summary

The CMS Collaboration presents a comprehensive study of all‑charm tetraquark candidates using the full Run 2 and Run 3 proton‑proton data collected at the LHC, corresponding to an integrated luminosity of 315 fb⁻¹. The analysis focuses on two four‑muon final states: J/ψ J/ψ (with each J/ψ → μ⁺μ⁻) and J/ψ ψ(2S) (ψ(2S) → μ⁺μ⁻). By applying the same selection criteria as in the previous CMS study and adding a re‑optimized selection for the ψ(2S) channel, the authors obtain 44 424 J/ψ J/ψ candidates and 386 J/ψ ψ(2S) candidates, a factor of 3.6 increase in the J/ψ J/ψ sample relative to the earlier analysis.

The invariant‑mass spectra are modeled with a sophisticated unbinned maximum‑likelihood fit. Three resonant structures—named X(6600), X(6900), and X(7100)—are described by relativistic S‑wave Breit‑Wigner functions. Crucially, the three amplitudes are allowed to interfere, leading to a total signal amplitude |M|² = |r₁e^{iφ₁}BW₆₆₀₀ + BW₆₉₀₀ + r₃e^{iφ₃}BW₇₁₀₀|². This interference term is essential: it improves the fit quality, yields a coherent picture of the three peaks, and implies that the three states share the same quantum numbers (most plausibly J^{PC}=0^{++} or 2^{++}). Background contributions are modeled in detail: a near‑threshold enhancement (BW₀), non‑resonant single‑parton scattering (NRSPS) derived from Monte‑Carlo simulation, double‑parton scattering (DPS) obtained via event mixing, feed‑down from X → J/ψ ψ(2S) decays, and combinatorial background estimated with the “nine‑tile” sideband method. Systematic uncertainties from detector resolution, efficiency variations, and background modeling are incorporated as nuisance parameters.

The fit results for the J/ψ J/ψ channel are:

• X(6600): M = 6593 ± 15 (stat) ± 25 (syst) MeV, Γ = 446 + 66₋₅₄ ± 87 MeV.
• X(6900): M = 6847 ± 10 ± 15 MeV, Γ = 135 ± 16 ± 14 MeV.
• X(7100): M = 7173 + 9₋₁₀ ± 13 MeV, Γ = 73 + 18₋₁₅ ± 10 MeV.

All three structures exceed a statistical significance of 5σ; X(7100) reaches 7.7σ, establishing it as a newly observed state. Alternative fit configurations that omit interference or modify background components never reduce the significance below the observation threshold, confirming the robustness of the result.

In the J/ψ ψ(2S) channel, only X(6900) and X(7100) are kinematically accessible. The same interference framework (now a two‑way interference) yields masses consistent with the J/ψ J/ψ results (M≈6876 MeV for X(6900) and M≈7169 MeV for X(7100)) and widths of 253 MeV and 154 MeV, respectively, albeit with larger uncertainties due to the smaller sample. The significances are >8σ for X(6900) and >4σ for X(7100).

A striking phenomenological pattern emerges: the squared masses of the three states lie on a straight line when plotted versus an integer “radial index”, and the natural widths decrease monotonically with increasing index. This behavior matches the expectations for a family of radial excitations of a compact tetraquark composed of two aligned spin‑1 diquarks (