CMS-PAS-BPH-24-003

CMS-PAS-BPH-24-003
Observation of a family of all-charm tetraquark candidates at the LHC
CMS Collaboration
7 April 2025

Abstract: Three structures, $\mathrm{X(6600)}$ , $\mathrm{X(6900)}$ , and $\mathrm{X(7100)}$ , have been reported in the $\mathrm{J}/\psi \, \mathrm{J}/\psi$ channel. These are prime candidates for all-charm tetraquarks. We extend our earlier study of these structures in proton-proton collisions using the CMS detector at the LHC, with 3.6 times more $\mathrm{J}/\psi \, \mathrm{J}/\psi$ pairs (315 fb $^{-1}$ of total integrated luminosity). The statistical uncertainties on the masses and widths are reduced by about a factor of three, and the systematic uncertainties are also substantially reduced. For the first time all three structures are established with a significance well above five standard deviations (5 $\sigma$ ). Good descriptions of the $\mathrm{J}/\psi \, \mathrm{J}/\psi$ spectrum were based on quantum interference among structures, which is now validated with significances of more than 5 $\sigma$ relative to the fit with no interference---implying all structures have the same $J^{PC}$ quantum numbers, and suggests a family of states.
Links: CDS record (PDF) ; CADI line (restricted) ;

Figures & Tables	Summary	References	CMS Publications

Figures
png pdf	Figure 1: Idealized models of potential quark configurations for all-charm mesons. Far left: a conventional charmonium state, which is not a viable option for the very massive $\mathrm{J}/\psi\mathrm{J}/\psi$ states. Center: various possibilities for tetraquarks---weakly bound molecule, $\mathrm{c}\mathrm{c}-\overline{\mathrm{c}}\overline{\mathrm{c}}$ diquark, and a compact tetraquark with amorphous substructure, and hybrid state of $\mathrm{c}\mathrm{c}\overline{\mathrm{c}}\overline{\mathrm{c}}$ plus valence gluon (g). Far right: one example of the class of non-resonant threshold effects, a triangle singularity, where, in this case, the scattering of $\mathrm{J}/\psi$ and $\psi(3770)$ mesons in production is enhanced through a triangular loop exchanging $\mathrm{D}$ mesons (the $\psi(3770)$ is an excited state of the $\mathrm{J}/\psi$ ), and this could potentially lead to a peak-like structure in the $\mathrm{J}/\psi\mathrm{J}/\psi$ mass around 6900 MeV [15].
png pdf	Figure 2: The two dimensional distribution of the double-dimuon masses for the final selection of $\mathrm{J}/\psi\mathrm{J}/\psi$ events in the 6--15 GeV four-muon mass range for the Run 2+3 data. The two $\mu^{+}\mu^{-}$ pairs are ordered by their total transverse momentum ( $p_T$ ).
png pdf	Figure 3: The selected $\mathrm{J}/\psi\mathrm{J}/\psi$ invariant-mass spectrum up to 9 GeV. The data is fit (up to 15 GeV, see text) with the 3-way interference model, consisting of three signal functions ( $\mathrm{BW}_1$ , $\mathrm{BW}_2$ , and $\mathrm{BW}_3$ ), a background threshold $\mathrm{BW}_0$ , and background components (NRSPS, DPS, combinatoric, and $\mathrm{X(6900)}{\to} \mathrm{J}/\psi\psi(2\text{S})$ feeddown). The cumulative squared amplitude of the interfering signals is also shown. The lower panel shows the deviations of the data points from the fitted curve in standard deviations.
png pdf	Figure 4: The $\mathrm{J}/\psi\mathrm{J}/\psi$ invariant mass spectrum for the no-interference in the 6--9 GeV four-muon mass range (upper) and the interference fit for the full fit range (lower) (see text in the main paper for model details). The curve labeled "Interfering BWs" represents the total contribution from all interference amplitudes and their cross terms. The lower panels of the plots display the number of standard deviations (considering only statistical uncertainties) by which the binned data deviate from the fit.
png pdf	Figure 4-a: The $\mathrm{J}/\psi\mathrm{J}/\psi$ invariant mass spectrum for the no-interference in the 6--9 GeV four-muon mass range (upper) and the interference fit for the full fit range (lower) (see text in the main paper for model details). The curve labeled "Interfering BWs" represents the total contribution from all interference amplitudes and their cross terms. The lower panels of the plots display the number of standard deviations (considering only statistical uncertainties) by which the binned data deviate from the fit.
png pdf	Figure 4-b: The $\mathrm{J}/\psi\mathrm{J}/\psi$ invariant mass spectrum for the no-interference in the 6--9 GeV four-muon mass range (upper) and the interference fit for the full fit range (lower) (see text in the main paper for model details). The curve labeled "Interfering BWs" represents the total contribution from all interference amplitudes and their cross terms. The lower panels of the plots display the number of standard deviations (considering only statistical uncertainties) by which the binned data deviate from the fit.
png pdf	Figure 5: The $\mathrm{X}$ widths as a function of radial index for both interference and no-interference fits. An exponential function is fit to the points. Uncertainties are only statistical.
png pdf	Figure 6: The $\mathrm{J}/\psi\mathrm{J}/\psi$ invariant mass spectrum for the individual Run 2 and Run 3 datasets (upper), and for Run 2 compared with the combined Run 2 $+$ 3 dataset (lower).
png pdf	Figure 6-a: The $\mathrm{J}/\psi\mathrm{J}/\psi$ invariant mass spectrum for the individual Run 2 and Run 3 datasets (upper), and for Run 2 compared with the combined Run 2 $+$ 3 dataset (lower).
png pdf	Figure 6-b: The $\mathrm{J}/\psi\mathrm{J}/\psi$ invariant mass spectrum for the individual Run 2 and Run 3 datasets (upper), and for Run 2 compared with the combined Run 2 $+$ 3 dataset (lower).
png pdf	Figure 7: The $\mathrm{J}/\psi\mathrm{J}/\psi$ invariant mass spectrum for the interference fit for the 6--9 GeV range (upper) and the full fit range (lower) with the Run 3 data. The curve labeled "Interfering BWs" represents the total contribution from all interference amplitudes and their cross terms. The lower panels of the plots display the number of standard deviations (considering only statistical uncertainties) by which the binned data deviate from the fit.
png pdf	Figure 7-a: The $\mathrm{J}/\psi\mathrm{J}/\psi$ invariant mass spectrum for the interference fit for the 6--9 GeV range (upper) and the full fit range (lower) with the Run 3 data. The curve labeled "Interfering BWs" represents the total contribution from all interference amplitudes and their cross terms. The lower panels of the plots display the number of standard deviations (considering only statistical uncertainties) by which the binned data deviate from the fit.
png pdf	Figure 7-b: The $\mathrm{J}/\psi\mathrm{J}/\psi$ invariant mass spectrum for the interference fit for the 6--9 GeV range (upper) and the full fit range (lower) with the Run 3 data. The curve labeled "Interfering BWs" represents the total contribution from all interference amplitudes and their cross terms. The lower panels of the plots display the number of standard deviations (considering only statistical uncertainties) by which the binned data deviate from the fit.

Tables
png pdf	Table 1: Fit results of the $\mathrm{J}/\psi \, \mathrm{J}/\psi$ mass spectra for various data sets with interference in MeV (uncertainties are statistical followed by systematic). The ``Run 2'' result is a copy of Ref. [12] for comparison.
png pdf	Table 2: The dominant contributions to the systematic uncertainties, in MeV, for the triplet for our main fit.
png pdf	Table 3: Fit results of the $\mathrm{J}/\psi \, \mathrm{J}/\psi$ mass spectra for various data sets in MeV (dual uncertainties are statistical followed by systematic, single uncertainties are statistical only). Our baseline fit is Run 2 $+$ Run 3 data with interference (reproduced from main text).

Summary

We have extended our study of the

$\mathrm{J}/\psi\mathrm{J}/\psi$ mass spectrum with 3.6 times more

$\mathrm{J}/\psi\mathrm{J}/\psi$ pairs. The spectrum is well described by mutually interfering

$\mathrm{X(6600)}$ ,

$\mathrm{X(6900)}$ , and

$\mathrm{X(7100)}$ structures. The statistical uncertainties on their masses and widths are reduced by a factor of three over our previous results [12]. For the first time, all three structures are established with a significance well above five standard deviations (5

$\sigma$ ). Similarly, interference among the three structures is now statistically compelling. Interference implies that the structures have common

$J^{PC}$ quantum numbers---suggesting a family of states. Recently CMS reported an angular analysis of the

$\mathrm{X} {\to} \mathrm{J}/\psi\mathrm{J}/\psi$ decay characteristics and found the

$J^{PC}$ quantum numbers of the

$\mathrm{X}$ family is most likely

$2^{++}$ [35].

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