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| CMS-BPH-24-003 ; CERN-EP-2025-248 | ||
| Observation of a family of all-charm tetraquarks | ||
| CMS Collaboration | ||
| 2 Febraury 2026 | ||
| Submitted to Science Advances | ||
| Abstract: Three structures, $\mathrm{X} (6600)$, $\mathrm{X} (6600)$ and $\mathrm{X} (7100)$, have emerged from the $ \mathrm{J}/\psi \mathrm{J}/\psi $ ($ \mathrm{J}/\psi \to \mu^{+}\mu^{-} $) mass spectrum. These are candidates of all-charm tetraquarks, an exotic form of hadronic matter. A clearer picture of these states is obtained using proton-proton collision data collected by the CMS detector that corresponds to 315 fb$ ^{-1} $, which yields 3.6 times more $ \mathrm{J}/\psi \mathrm{J}/\psi $ 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 $ \mathrm{J}/\psi \psi(\mathrm{2S}) \to \mu^{+}\mu^{-}\mu^{+}\mu^{-} $ decay mode is also explored and the $\mathrm{X} (6900)$ and $\mathrm{X} (7100)$ states are found with significances exceeding 8 and 4 standard deviations, respectively. | ||
| Links: e-print arXiv:2602.02252 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; CADI line (restricted) ; | ||
| Figures | |
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Figure 1:
Idealized models of all-charm structures. Far left: conventional charmonium state. Center: various tetraquark configurations, i.e.,, [$ \mathrm{c}\overline{\mathrm{c}} $][$ \mathrm{c}\overline{\mathrm{c}} $] molecule, [$ \mathrm{c}\mathrm{c} $][$ \overline{\mathrm{c}}\overline{\mathrm{c}} $] diquarks, compact tetraquark with amorphous substructure, and hybrid $ \mathrm{c}\mathrm{c}\overline{\mathrm{c}}\overline{\mathrm{c}}\mathrm{g} $ state. Far right: example of a nonresonant threshold effect, a ``triangle singularity'', where virtual scattering of $ \mathrm{J}/\psi $ and $\psi(3770)$ mesons is enhanced through a triangular loop exchanging $ \mathrm{D} $ mesons, potentially leading to a peak-like structure in the $ \mathrm{J}/\psi \mathrm{J}/\psi $ mass spectrum around 6900 MeV [34]. |
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Figure 2:
The 2D event distributions in the $ m(\mu_1^{+},\mu_2^{-}) $ vs. $m(\mu_3^{+},\mu_4^{-}) $ plane. The two opposite-sign muon pairs, $ (\mu_1^{+}\mu_2^{-}) $ and $ (\mu_3^{+}\mu_4^{-}) $, are ordered by the dimuon transverse momenta in $ \mathrm{J}/\psi \mathrm{J}/\psi $ events, and by the dimuon mass in $ \mathrm{J}/\psi \psi(2S) $ events. The $ \mathrm{J}/\psi \mathrm{J}/\psi $ (left) and $ \mathrm{J}/\psi \psi(2S) $ (right) events with four-muon invariant masses below 15 GeV for Run 2+3 data are shown. |
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Figure 3:
The $ \mathrm{J}/\psi \mathrm{J}/\psi $ invariant-mass spectrum up to 9 GeV. The data is fit (up to 15 GeV, see text) with a three-way interference model using an unbinned likelihood, with the spectrum binned here for display. The model consists of three signal functions $ [ $$\mathrm{X} (6600)$, $\mathrm{X} (6900)$, and $ \mathrm{X} (7100)$ $]$, and background components (NRSPS, DPS, combinatorial, a background threshold $ \mathrm{BW}_0 $, and $ \mathrm{X} (6900) \to \mathrm{J}/\psi \psi(2S) $ feed-down). The cumulative squared signal amplitude (proportional to $ |\mathcal{M}|^{2} $) is also shown (``Interfering Xs''). The lower panel shows the difference between the data and the fitted model, in units of standard deviations. |
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Figure 4:
The $ \mathrm{J}/\psi \psi(2S) $ invariant-mass spectrum up to 9 GeV. The data is fit (up to 15 GeV, see text) with a two-way interference model, consisting of two signal functions [$\mathrm{X} (6900)$ and $\mathrm{X} (7100)$], and background components (NRSPS, DPS, and combinatorial). The cumulative squared signal amplitude is also shown (``Interfering Xs''). The lower panel shows the difference between the data and the fitted model, in units of standard deviations. |
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Figure 5:
Squared masses of $\mathrm{X} (6900)$, $\mathrm{X} (6600)$, $\mathrm{X} (7100)$ (statistical uncertainties only), and Upsilon ($ \Upsilon $, masses from Ref. [39], denoted as ``PDG''), families versus radial indices $ n= $ 2, 3, 4.} The solid lines are linear fits for the $ \mathrm{X} $ and $ \Upsilon $ families (see text), with dashed extrapolations to projected $ n= $ 1 states. Regge trajectories calculated for $ 0^{++} $ (spin-0 diquarks) and $ 2^{++} $ (spin-1 diquarks) tetraquarks are also shown. Bands correspond to $ \pm $1$ \sigma $ statistical uncertainties for data (pink band) and the fully correlated $ \pm $1$ \sigma $ uncertainty from the strong coupling constant $ \alpha_s $ for theory (green and blue bands) [21]. The lower panel shows the deviations of the measured $ \mathrm{X} $ masses from their fitted trajectory with error bars showing the statistical and total uncertainties. |
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Figure 6:
The widths of the $ \mathrm{X} $ states as a function of the radial quantum number (statistical uncertainties only). For comparison, the total widths and the three-gluon (3 $ \mathrm{g} $) partial widths of the $ \Upsilon{\textrm{(1S)}} $, $ \Upsilon{\textrm{(2S)}} $, and $ \Upsilon{\textrm{(3S)}} $ states are also displayed [39], denoted as ``PDG''. The lines are fits to exponential functions. |
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Figure 7:
Projections of the 2D fit of $ \mathrm{J}/\psi \psi(2S) $ (Fig. 2) of selected pairs with 4 $ \mu $ masses below 15 GeV. The $ \mathrm{J}/\psi $ and \PGyP2S mass requirements and the mass constraints have been removed. The breakdown of the signal and different background components is shown. Left: Projection onto the \PGyP2S mass reconstructed from $ \mu_1^{+}\mu_2^{-} $. Right: Projection onto the $ \mathrm{J}/\psi $ mass reconstructed from $ \mu_3^{+}\mu_4^{-} $. |
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Figure 7-a:
Projections of the 2D fit of $ \mathrm{J}/\psi \psi(2S) $ (Fig. 2) of selected pairs with 4 $ \mu $ masses below 15 GeV. The $ \mathrm{J}/\psi $ and \PGyP2S mass requirements and the mass constraints have been removed. The breakdown of the signal and different background components is shown. Left: Projection onto the \PGyP2S mass reconstructed from $ \mu_1^{+}\mu_2^{-} $. Right: Projection onto the $ \mathrm{J}/\psi $ mass reconstructed from $ \mu_3^{+}\mu_4^{-} $. |
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Figure 7-b:
Projections of the 2D fit of $ \mathrm{J}/\psi \psi(2S) $ (Fig. 2) of selected pairs with 4 $ \mu $ masses below 15 GeV. The $ \mathrm{J}/\psi $ and \PGyP2S mass requirements and the mass constraints have been removed. The breakdown of the signal and different background components is shown. Left: Projection onto the \PGyP2S mass reconstructed from $ \mu_1^{+}\mu_2^{-} $. Right: Projection onto the $ \mathrm{J}/\psi $ mass reconstructed from $ \mu_3^{+}\mu_4^{-} $. |
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Figure 8:
$ \mathrm{J}/\psi \mathrm{J}/\psi $ invariant-mass spectrum for the interference fit. The spectrum is shown up to 9 GeV (top) and over the full fit range (bottom). Three interfering BW signals are included, and the total contribution from all interfering amplitudes (including cross terms) is plotted as the curve labeled ``Interfering Xs''. The background components---NRSPS, DPS, combinatorial, feed-down, and threshold $ \mathrm{BW}_0 $---are shown separately. The lower panels give the number of standard deviations (statistical uncertainties only) that the binned data deviates from the fits. |
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Figure 8-a:
$ \mathrm{J}/\psi \mathrm{J}/\psi $ invariant-mass spectrum for the interference fit. The spectrum is shown up to 9 GeV (top) and over the full fit range (bottom). Three interfering BW signals are included, and the total contribution from all interfering amplitudes (including cross terms) is plotted as the curve labeled ``Interfering Xs''. The background components---NRSPS, DPS, combinatorial, feed-down, and threshold $ \mathrm{BW}_0 $---are shown separately. The lower panels give the number of standard deviations (statistical uncertainties only) that the binned data deviates from the fits. |
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Figure 8-b:
$ \mathrm{J}/\psi \mathrm{J}/\psi $ invariant-mass spectrum for the interference fit. The spectrum is shown up to 9 GeV (top) and over the full fit range (bottom). Three interfering BW signals are included, and the total contribution from all interfering amplitudes (including cross terms) is plotted as the curve labeled ``Interfering Xs''. The background components---NRSPS, DPS, combinatorial, feed-down, and threshold $ \mathrm{BW}_0 $---are shown separately. The lower panels give the number of standard deviations (statistical uncertainties only) that the binned data deviates from the fits. |
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Figure 9:
$ \mathrm{J}/\psi \psi(2S) $ invariant-mass spectrum for the interference fit. The spectrum is shown up to 9 GeV (top) and over the full fit range (bottom). Three interfering BW signals are included, and the total contribution from all interfering amplitudes (including cross terms) is plotted as the curve labeled ``Interfering Xs''. The background components are shown separately. The lower panel also displays the number of standard deviations (statistical uncertainties only) that the binned data deviates from the fits. |
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Figure 9-a:
$ \mathrm{J}/\psi \psi(2S) $ invariant-mass spectrum for the interference fit. The spectrum is shown up to 9 GeV (top) and over the full fit range (bottom). Three interfering BW signals are included, and the total contribution from all interfering amplitudes (including cross terms) is plotted as the curve labeled ``Interfering Xs''. The background components are shown separately. The lower panel also displays the number of standard deviations (statistical uncertainties only) that the binned data deviates from the fits. |
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Figure 9-b:
$ \mathrm{J}/\psi \psi(2S) $ invariant-mass spectrum for the interference fit. The spectrum is shown up to 9 GeV (top) and over the full fit range (bottom). Three interfering BW signals are included, and the total contribution from all interfering amplitudes (including cross terms) is plotted as the curve labeled ``Interfering Xs''. The background components are shown separately. The lower panel also displays the number of standard deviations (statistical uncertainties only) that the binned data deviates from the fits. |
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Figure 10:
The noninterference fit result of the $ \mathrm{J}/\psi \mathrm{J}/\psi $ invariant-mass spectrum up to 9 GeV. The lower panel shows the deviation of the data from the fit, in units of standard deviations. |
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Figure 11:
Comparison of the measured $ \mathrm{X} $ Regge trajectory to theoretical calculations of trajectories for various $ J^{PC} $ quantum numbers corresponding to $ L= $ 0 states [21,70,55,69]. Dashed lines show Regge trajectories fitted to the calculated squared masses, with the $ \mathrm{X} $ trajectory (solid line) overlaid for comparison (for visual clarity, no uncertainty bands are shown). The spin-0 and spin-1 labels correspond to scalar and axial-vector diquark configurations, respectively. $ L_{[\mathrm{c}\mathrm{c}][\overline{\mathrm{c}}\overline{\mathrm{c}}]} $ is the orbital angular momentum between the diquark and antidiquark, and $ S_{[\mathrm{c}\mathrm{c}][\overline{\mathrm{c}}\overline{\mathrm{c}}]} $ is the total spin of the diquark-antidiquark system. |
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Figure 11-a:
Comparison of the measured $ \mathrm{X} $ Regge trajectory to theoretical calculations of trajectories for various $ J^{PC} $ quantum numbers corresponding to $ L= $ 0 states [21,70,55,69]. Dashed lines show Regge trajectories fitted to the calculated squared masses, with the $ \mathrm{X} $ trajectory (solid line) overlaid for comparison (for visual clarity, no uncertainty bands are shown). The spin-0 and spin-1 labels correspond to scalar and axial-vector diquark configurations, respectively. $ L_{[\mathrm{c}\mathrm{c}][\overline{\mathrm{c}}\overline{\mathrm{c}}]} $ is the orbital angular momentum between the diquark and antidiquark, and $ S_{[\mathrm{c}\mathrm{c}][\overline{\mathrm{c}}\overline{\mathrm{c}}]} $ is the total spin of the diquark-antidiquark system. |
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Figure 11-b:
Comparison of the measured $ \mathrm{X} $ Regge trajectory to theoretical calculations of trajectories for various $ J^{PC} $ quantum numbers corresponding to $ L= $ 0 states [21,70,55,69]. Dashed lines show Regge trajectories fitted to the calculated squared masses, with the $ \mathrm{X} $ trajectory (solid line) overlaid for comparison (for visual clarity, no uncertainty bands are shown). The spin-0 and spin-1 labels correspond to scalar and axial-vector diquark configurations, respectively. $ L_{[\mathrm{c}\mathrm{c}][\overline{\mathrm{c}}\overline{\mathrm{c}}]} $ is the orbital angular momentum between the diquark and antidiquark, and $ S_{[\mathrm{c}\mathrm{c}][\overline{\mathrm{c}}\overline{\mathrm{c}}]} $ is the total spin of the diquark-antidiquark system. |
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Figure 11-c:
Comparison of the measured $ \mathrm{X} $ Regge trajectory to theoretical calculations of trajectories for various $ J^{PC} $ quantum numbers corresponding to $ L= $ 0 states [21,70,55,69]. Dashed lines show Regge trajectories fitted to the calculated squared masses, with the $ \mathrm{X} $ trajectory (solid line) overlaid for comparison (for visual clarity, no uncertainty bands are shown). The spin-0 and spin-1 labels correspond to scalar and axial-vector diquark configurations, respectively. $ L_{[\mathrm{c}\mathrm{c}][\overline{\mathrm{c}}\overline{\mathrm{c}}]} $ is the orbital angular momentum between the diquark and antidiquark, and $ S_{[\mathrm{c}\mathrm{c}][\overline{\mathrm{c}}\overline{\mathrm{c}}]} $ is the total spin of the diquark-antidiquark system. |
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Figure 12:
Comparison of the measured $ \mathrm{X} $ Regge trajectory to theoretical calculations of trajectories for various $ J^{PC} $ quantum numbers corresponding to $ L= $ 1 states [69,71,18]. Dashed lines show Regge trajectories fitted to the calculated squared masses, with the $ \mathrm{X} $ trajectory (solid line) overlaid for comparison (for visual clarity, no uncertainty bands are shown). The diquarks are in an axial-vector configuration. $ L_{[\mathrm{c}\mathrm{c}][\overline{\mathrm{c}}\overline{\mathrm{c}}]} $ is the orbital angular momentum between the diquark and antidiquark, and $ S_{[\mathrm{c}\mathrm{c}][\overline{\mathrm{c}}\overline{\mathrm{c}}]} $ is the total spin of the diquark-antidiquark system. |
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Figure 12-a:
Comparison of the measured $ \mathrm{X} $ Regge trajectory to theoretical calculations of trajectories for various $ J^{PC} $ quantum numbers corresponding to $ L= $ 1 states [69,71,18]. Dashed lines show Regge trajectories fitted to the calculated squared masses, with the $ \mathrm{X} $ trajectory (solid line) overlaid for comparison (for visual clarity, no uncertainty bands are shown). The diquarks are in an axial-vector configuration. $ L_{[\mathrm{c}\mathrm{c}][\overline{\mathrm{c}}\overline{\mathrm{c}}]} $ is the orbital angular momentum between the diquark and antidiquark, and $ S_{[\mathrm{c}\mathrm{c}][\overline{\mathrm{c}}\overline{\mathrm{c}}]} $ is the total spin of the diquark-antidiquark system. |
png pdf |
Figure 12-b:
Comparison of the measured $ \mathrm{X} $ Regge trajectory to theoretical calculations of trajectories for various $ J^{PC} $ quantum numbers corresponding to $ L= $ 1 states [69,71,18]. Dashed lines show Regge trajectories fitted to the calculated squared masses, with the $ \mathrm{X} $ trajectory (solid line) overlaid for comparison (for visual clarity, no uncertainty bands are shown). The diquarks are in an axial-vector configuration. $ L_{[\mathrm{c}\mathrm{c}][\overline{\mathrm{c}}\overline{\mathrm{c}}]} $ is the orbital angular momentum between the diquark and antidiquark, and $ S_{[\mathrm{c}\mathrm{c}][\overline{\mathrm{c}}\overline{\mathrm{c}}]} $ is the total spin of the diquark-antidiquark system. |
png pdf |
Figure 12-c:
Comparison of the measured $ \mathrm{X} $ Regge trajectory to theoretical calculations of trajectories for various $ J^{PC} $ quantum numbers corresponding to $ L= $ 1 states [69,71,18]. Dashed lines show Regge trajectories fitted to the calculated squared masses, with the $ \mathrm{X} $ trajectory (solid line) overlaid for comparison (for visual clarity, no uncertainty bands are shown). The diquarks are in an axial-vector configuration. $ L_{[\mathrm{c}\mathrm{c}][\overline{\mathrm{c}}\overline{\mathrm{c}}]} $ is the orbital angular momentum between the diquark and antidiquark, and $ S_{[\mathrm{c}\mathrm{c}][\overline{\mathrm{c}}\overline{\mathrm{c}}]} $ is the total spin of the diquark-antidiquark system. |
png pdf |
Figure 13:
Comparison of the measured $ \mathrm{X} $ Regge trajectory to theoretical calculations of trajectories for various $ J^{PC} $ quantum numbers corresponding to $ L= $ 2 states [69]. Dashed lines show Regge trajectories fitted to the calculated squared masses, with the $ \mathrm{X} $ trajectory (solid line) overlaid for comparison (for visual clarity, no uncertainty bands are shown). The spin-0 and spin-1 labels correspond to scalar and axial-vector diquark configurations, respectively. $ L_{[\mathrm{c}\mathrm{c}][\overline{\mathrm{c}}\overline{\mathrm{c}}]} $ is the orbital angular momentum between the diquark and antidiquark, and $ S_{[\mathrm{c}\mathrm{c}][\overline{\mathrm{c}}\overline{\mathrm{c}}]} $ is the total spin of the diquark-antidiquark system. |
| Tables | |
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Table 1:
Measured masses and widths of the three $ \mathrm{X} $ states from the fits to the $ \mathrm{J}/\psi \mathrm{J}/\psi $ and $ \mathrm{J}/\psi \psi(2S) $ mass spectra from the Run 2+3 data set. The two uncertainties are statistical (first) and systematic (second). For comparison, the results from Run 2 [15] are also shown. The values are in MeVns. |
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Table 2:
The principal contributions to the systematic uncertainties for $\mathrm{X} (6600)$, $\mathrm{X} (6900)$, and $\mathrm{X} (7100)$ from the $ \mathrm{J}/\psi \mathrm{J}/\psi $ interference fit. The values are in MeVns. |
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Table 3:
The principal contributions to the systematic uncertainties for $\mathrm{X} (6900)$ and $\mathrm{X} (7100)$ from the $ \mathrm{J}/\psi \psi(2S) $ interference fit. The values are in MeVns. |
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Table 4:
Fit results of the Run 2+3 $ \mathrm{J}/\psi \mathrm{J}/\psi $ mass spectra with the baseline interference model (reproduced from main text), and a noninterference model. Masses and widths are in MeVns (double uncertainties are statistical followed by systematic; single uncertainties are statistical only). |
| Summary |
| With almost four times more $ \mathrm{J}/\psi \mathrm{J}/\psi $ pairs than previously available [15], the data are well described by mutually interfering $\mathrm{X} (6600)$, $\mathrm{X} (6900)$, and $\mathrm{X} (7100)$ states. The statistical uncertainties in the masses and widths are reduced by a factor of three, benefiting not only from the increased number of events, but also from the improved fit model, and all three structures are established with significances well above 5$\sigma$ for the first time. In the $\mathrm{J}/\psi \psi(\mathrm{2S}) \to \mu^{+}\mu^{-}\mu^{+}\mu^{-} $ events, the $\mathrm{X} (6900)$ and $\mathrm{X} (7100)$ structures are seen with significances exceeding $8\sigma$ and $4\sigma$, respectively. In the $ \mathrm{J}/\psi \mathrm{J}/\psi $ events, interference among all three states is statistically compelling $({>}5\sigma)$. The $\mathrm{J}/\psi \psi(\mathrm{2S})$ result corroborates interference between $\mathrm{X} (6900)$ and $\mathrm{X} (7100)$ at the $2.5\sigma$ significance level. Interference implies common $J^{PC}$ quantum numbers for the three states. This is further supported and clarified by the $\mathrm{X}$ masses displaying radial Regge behavior, suggesting that the triplet represents a family of radial excitations of a common underlying configuration. An interpretation of the triplet of $\mathrm{X}$ states based on a configuration of [$\mathrm{c}\mathrm{c}$][$\mathrm{\bar{c}}\mathrm{\bar{c}}$] diquarks seems to account for the pattern of masses, consistent with a Regge trajectory, and with the decreasing natural widths, consistent with decays that are dominated by annihilation or rearrangement processes. In contrast, these features are problematic for molecular or threshold interpretations. In either of these cases, $ \mathrm{J}/\psi \mathrm{J}/\psi $ structures would be governed by the underlying charmonium pairs generating the structure [e.g., $\mathrm{J}/\psi \psi(\mathrm{3770})$ for the $\mathrm{X} (6900)$]. There are numerous charmonia pairings possible in the region of the triplet, but charmonia are generally irregularly spaced, so that the linear Regge behavior is not expected. Similarly, systematic trends among widths, let alone an exponentially decreasing one, are uncharacteristic of these interpretations, because different pairings are not expected to have simple correlations among their widths. However, this does not necessarily preclude the presence of molecular [50,51], or a resonant interplay with threshold effects [31]. Diquark and molecular models are idealized extremes of a continuum of possible internal configurations of four-quark systems. Another theoretical configuration is a four-body system with no systematic quark clustering. Expectations of any mass or width trends of such ``amorphous'' systems require detailed calculations and, without theoretical guidance, the possibility of an amorphous structure for the $\mathrm{X}$ triplet cannot be excluded. While hybrid models have predicted low-lying $\mathrm{c}\mathrm{c}\mathrm{\bar{c}}\mathrm{\bar{c}}\mathrm{g}$ states in the vicinity of the $\mathrm{X} (6900)$ (for $0^{++}$) and $\mathrm{X} (7100)$ (for $0^{-+}$), the different quantum numbers for the states cannot explain the observed interference and there is no associated $\mathrm{X} (6600)$ state [26,27]. The Regge trajectory of the $\mathrm{X}$ states is found to match the predictions for a pair of spin-1 diquarks with $\mathrm{X}$ $J^{PC}$ quantum numbers of $0^{++}$ or $2^{++}$. A recent CMS angular analysis of $\mathrm{X} \to \mathrm{J}/\psi \mathrm{J}/\psi $ decays, assuming the same $J^{PC}$ for the three states, strongly favors $J^{PC} = 2^{++}$ over other potential quantum numbers [52]. In addition, production of a $0^{++}$ state is predicted to be suppressed compared to a $2^{++}$ state [21,53,54]. Combining this information leads to a consistent picture of a system of aligned spin-1 diquarks with no orbital angular momentum ($L_{[\mathrm{c}\mathrm{c}][\mathrm{\bar{c}}\mathrm{\bar{c}}]}=0$). The observed structures would therefore be denoted as a triplet of $\mathrm{T}_{\mathrm{c}\mathrm{c}\mathrm{\bar{c}}\mathrm{\bar{c}}}$ states. In the $n\, ^{2S+1}L_J$ spectroscopic notation, the simplest scenario is that they are radially excited $n\, ^5 S_2$ states (``S'' indicating $L=0$) where, because our data does not discriminate between them, $n=1, 2, 3$ or $2, 3, 4$. Other configurations with $L_{[\mathrm{c}\mathrm{c}][\mathrm{\bar{c}}\mathrm{\bar{c}}]}\geq 2$ are possible, but high orbital excitations are more difficult to produce, and thus less likely. Although the hypothesis of a triplet of $2^{++}$ states made up of spin-1 diquarks describes our data well, the picture is potentially more complicated because other tetraquark states may contribute to the $ \mathrm{J}/\psi \mathrm{J}/\psi $ spectrum (e.g., $0^{++}$ [21,53,54]); or members of the triplet may consist of mixtures of different internal configurations with the same $J^{PC}$, such as pairs of spin-0 and anti-aligned spin-1 diquarks [22], or include a molecular subcomponent [50,51]. Further exploration, experimental and theoretical, of all-heavy tetraquarks is required to resolve these more subtle issues. |
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