79. Heavy Non-qq Mesons

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79. Heavy Non-qq Mesons
Revised March 2024 by T. Gutsche (Tübingen U.), C. Hanhart (FZ Jülich) and R.E. Mitchell(Indiana U.).
The constituent quark model describes the observed meson spectrum as bound qq states grouped
into SU(N) flavor multiplets (see the ‘Quark Model’ in this issue of the Review of Particle Physics).
However, the self coupling of gluons in QCD suggests that additional mesons made of bound gluons(glueballs), or qq-pairs with an excited gluon (hybrids), may exist. Furthermore, multiquark color
singlet states such as qqqq (tetraquarks as compact diquark-antidiquark systems and ‘molecular’
bound states of two mesons) or qqqqqq (six-quark, ‘baryonium’ or quasinuclear baryon-antibaryon
bound states) have also been predicted. The focus of this review is on the current understanding of
exotic states that apparently do not fit into the constituent quark model and contain at least one
heavy quark (charm or bottom — the lifetime of the top quark is too short to allow it to hadronise).
Light non-qq candidates (made of u, d and s quarks) are discussed in ‘Scalar Mesons below 1 GeV’and ‘Spectroscopy of Light Meson Resonances’ in this Review.
There are candidates for exotic states with both quantum numbers not allowed and quantum
number allowed for q̄q states. For the latter class it is up to now unclear to what extend a mixing
of conventional and unconventional states occurs. While Refs. [1–4] report a significant mixing,
Refs. [5, 6] describe a scenario where the mixing especially between molecular structures and q̄qstates is suppressed.
The review is split into 3 parts, discussing separately heavy–light systems, heavy–heavy systems, as well as systems with more than two heavy quarks. For a more detailed discussion of
the experimental and/or theoretical status on exotic meson candidates in the doubly heavy meson
sector we refer to Refs. [7–13]. Reviews with main focus on tetraquarks and molecular states arepresented in Ref. [14] and in Ref. [15], respectively.
The naming scheme for hadrons has been updated by the Particle Data Group in 2023, and now
covers the heavy “exotic” tetraquark (qq q̄ q̄) and pentaquark (qqqq q̄) candidates recently discovered.
We use the new naming scheme in the following. See “Naming Scheme for Hadrons” in this Review
for details and a table mapping old and new particle names.

79.1 Heavy-light systems
79.1.1 Positive parity open charm ground states∗ (2317)± and D (2460)± , were observed at B factories [16, 17].
Two very narrow states, Ds0
s1
They lie far below the predicted masses for the two expected broad P -wave cs mesons. However,strong cusp effects, due to the nearby DK (DK ∗ ) thresholds, could shift their masses downwards
and quench the observed widths, still allowing for a conventional explanation of these states [18].
Such an effect was also claimed for the a0 (980) and f0 (980) mesons, which lie just below the KK
threshold. In contrast to this picture, many authors favour exotic explanations for these lightest
positive parity charmed states, such as four-quark states [19–22] or DK (DK ∗ ) molecules [23–28].
Both states are isoscalars and thus strong isospin-violating decays are possible only to the isovector(∗)±
channels Ds π 0 , leading to very small widths. For compact structures the hadronic decay is drivenby η − π 0 mixing and one finds widths below 10 keV [18, 29]. In contrast to this a hadronic width
typically larger than 100 keV would be the unequivocal signature for a prominent molecular nature∗ (2317)± [25,27,28,30,31], since then meson loops generating enhanced isospin violation due toof Ds0the energy difference between the D∗0 K + and the D∗+ K 0 thresholds would contribute significantly.
The most refined analysis in the molecular scenario [30], where the parameters of the formalism areconstrained by a large bulk of lattice QCD data on singly charmed systems, reports a prediction
S. Navas et al. (Particle Data Group), Phys. Rev. D 110, 030001 (2024)
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79. Heavy Non-qq Mesons

for the width in the range (104–116) keV. The currently measured upper bound for the width is
3.8 MeV.
It should be stressed that – akin to qq mesons – multiquark states also appear in multiplets. An
important probe for the structure of hadrons is therefore the spectra, and in particular the SU(3)flavor multiplets within the different scenarios. For example the tetraquark model advocated in∗ (2317)± should be degenerate with its non-strange partner state
Refs. [22, 32] finds that the Ds0∗
D0 (2300) in line with the currently available experimental analyses. However, Ref. [33] showedthat the recent LHCb data for B → Dππ [34, 35] call for a significantly lighter lightest non-strange
scalar charmed meson as soon as constraints from the chiral symmetry of QCD are employed in theanalysis. This claim is in line with the recent lattice QCD study of Ref. [36]. In fact, experimental aswell as lattice data turn out to be consistent with the predictions from unitarised chiral perturbation
theory pioneered for these systems in Ref. [24]. For more recent calculations see Refs. [30, 37, 38].
Moreover, all these latter calculations predict that there should be in addition an about 300 MeV
heavier flavor exotic state, formally a member of a flavor sixtet and absent for cq̄ states, that indeed
shows up in the above mentioned LHCb data [38] — why this state was not reported in the lattice
study of Ref. [39] is explained in Ref. [40] by its being located on a hidden Rieman-sheet. Thus, inthis picture the structure that appears as D0∗ (2300) in the Listings originates from the interplay of
two poles, similar to the Λ(1405) in the baryon sector, see ‘Pole structure of the Λ(1405) region’ inthis Review. Two poles in the non-strange scalar sector are also generated in the tetraquark pictureof Ref. [22], but in this work the real parts of the poles are located at 2308 MeV and 2666 MeV,
in conflict with the data mentioned above. In the refined analysis of Ref. [32] it is shown, however,that the exact pole locations and even the ordering of the higher multiplets depend on the detailsof the model.
Lattice QCD allows for predictions of the flavor partner states in the B-sector. The most recent
analysis can be found in Ref. [41]. In this work also a comparison with theoretical predictions canbe found. Unfortunately an experimental confirmation for those states is difficult with existing
facilities. Radiative decays are predicted to be the most prominent decay channels [31], since theabove mentioned isospin violation from meson loops is suppressed in the B sector as a consequenceof the tiny B ± − B 0 mass difference.
∗ (2870) and T ∗ (2900)
79.1.2 The Tcs0
cs1

Manifestly exotic candidates around 2.9 GeV were reported in Refs. [42, 43] by LHCb in theD̄K system. Since the strong interaction preserves the quark flavor and the final state contains
an s̄ as well as a c̄, color neutrality calls for a minimum quark content of udc̄s̄. The explanation
for those states include compact tetraquarks [44–46], hadronic molecules with a prominent D∗ K̄ ∗component [47–51], or kinematic effects such as cusps or triangle singularities without nearby
poles [52, 53]. The different pictures are contrasted and observable differences between them are
discussed in Ref. [54].
∗ (2900)0 and T ∗ (2900)++
79.1.3 The Tcs̄0
cs̄0

There is a very recent report by LHCb [55] on the observation of a doubly charged open-charm
tetraquark candidate together with a neutral partner in the Ds π channel, with masses near 2.9 GeV.
The results imply two states with cs̄ūd or cs̄ud¯ flavor structures. Although masses and widths are
consistent with the Tcs states of Refs. [42, 43], the strangeness quantum numbers do not match.
The first explanation for those states in coupled-channel studies is based on a kinematic effect suchas a cusp [56], while a molecular structure with a dominant D∗ K ∗ component is claimed to be
excluded [57].
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79.2 Heavy-heavy systems
With the discovery of the χc1 (3872)1 in B ± → K ± X (X → J/ψ(1S) π + π − ) by Belle [58]in 2003, soon confirmed by BaBar [59], many searches for states beyond the standard q q̄ quark
model were initiated in the charm and bottom sectors. For an updated collection of the currently
available experimental information on multiquark states we refer to ‘Spectroscopy of mesons containing two heavy quarks’ in this Review, and in particular to Table 78.2. Moreover, in the decay
Λ0b → J/ψ(1S) K − p the LHCb collaboration has recently reported the observation of new baryons
decaying into J/ψ(1S) p, which are candidates for heavy pentaquark states [60, 61]. They are
discussed in some depth in ‘Pentaquarks’ in this Review.
When restricting ourselves to confirmed states we are faced with several states that do not seemto fit into the mass and quantum number schemes of q q̄ quark models. This is clear for the fiveestablished charged states (Tcc̄1 (3900)± , Tcc̄ (4020)± and Tcc̄1 (4430)± in the charmonium sector,
and Tbb̄1 (10610)± and Tbb̄1 (10650)± in the bottomonium sector). The neutral states (χc1 (3872),
ψ(4230), ψ(4360), and ψ(4660))2 also challenge the quark model since their masses and decay
properties are in conflict with expectations. Although so far seen just by a single experiment in asingle channel [62, 63], the Tcc (3875) should not remain unmentioned.
79.2.1 The χc1 (3872)
The quantum numbers of the χc1 (3872) have been determined by LHCb to be J P C = 1++ ,first by assuming zero angular momentum between the J/ψ(1S) and the dipion [64] and then byrelaxing this constraint [65]. The χc1 (3872) cannot be identified with the χc1 (23 P1 ) since the latteris predicted to lie about 100 MeV higher in mass [66]. Instead, the X(3940) reported by Bellein e+ e− → J/ψ(1S)X, decaying into D∗ D̄ but not into DD̄ [67] could be the χc1 (23 P1 ). The
χc2 (3930) 23 P2 tensor partner was reported by Belle at 3931 MeV in γγ interactions [68].
The χc1 (3872) lies within 200 keV of the D0 D̄∗0 threshold and its width is very small — recent
Breit-Wigner analyses by LHCb [69, 70] result in an average value of Γ = (1.19 ± 0.21) MeV as
indicated in the Listings; employing the Flatté formalism of Ref. [71] under the constraint that theD∗ D̄ decay channel dominates, results in Γ = 0.22+0.18−0.19 MeV, where the standard convention isapplied to use twice the imaginary part of the pole location as width. In the future those values
can be refined more by either a direct measurement of the width that should be possible at theplanned PANDA experiment [72, 73] or by exploiting the interplay of a triangle singularity andthe χc1 (3872) pole [74–76]. Therefore the most natural explanation for this state is a 1++ DD̄∗molecule [77], for which strong isospin breaking is predicted [77, 78], since the distance of the poleof the χc1 (3872) to the D0 D̄∗ 0 threshold is significantly smaller than to the D+ D∗− threshold.
Indeed, the comparable rates for ωJ/ψ(1S) and ρ0 J/ψ(1S) are consistent with an interpretationof χc1 (3872) as an isoscalar DD̄∗ molecule, when the different widths of the ρ and ω are taken
into account [79]. Similarly, a dominant molecular D0 D̄∗0 structure in the χc1 (3872) with further
subleading hadronic components is used to explain strong and radiative decays involving J/ψ(1S)and ψ(2S) in the final states [80, 81]. From an effective field theory point of view these radiativetransitions are not well suited to identify the molecular admixture in the χc1 (3872), since there
appears a counter term at leading order, diminishing the sensitivity to the long ranged molecularcomponent [82].
A four-quark state cqc̄q̄ 0 is another possible interpretation of the χc1 (3872) [21] but a charged
partner of the χc1 (3872) has not been observed (e.g. not in B − → K̄ 0 X − nor in B 0 → K + X − ,where X − → J/ψ(1S) π − π 0 [83] ) – see [84] for a possible explanation of this non-observation within
the tetraquark approach assuming specific diquark correlations and the more recent discussion in
1

The χc1 (3872) is also known as the X(3872). According to the PDG naming scheme, the primary name for ameson expresses its quantum numbers.
2
The ψ(4230), ψ(4360), and ψ(4660) are also known as the Y (4230), Y (4360), and Y (4660), respectively. Before
improved mass measurements, the ψ(4230) was originally called the ψ(4260) or Y (4260).
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Ref. [85]. The claim that χc1 (3872) must be a compact (tetraquark) state, since it is also produced
at very high pT in p̄p collisions [86] and in high multiplicity final states [87], was challenged in [88]and [89], respectively, which in particular stress the importance of rescattering, see also Refs. [90,91].
The high statistics measurement of the χc1 (3872) lineshape of Ref. [69] also allowed for an
extraction of the effective range for the D0 D̄∗0 interaction. At face value, the values provided
in this publication indicate a large and negative effective range [92], which could be interpreted
as a signature of a prominent compact component in the χc1 (3872) wave function — this follows
from the famous Weinberg compositeness criterion [93]. The effect of the one-pion exchange on theeffective range turns out to be small [94–97] and should therefore not invalidate the Weinberg-type
analysis. However, it was argued in Ref. [98] that once the effect of the large isospin violation as wellas the strong correlations between the effective parameters appearing in Ref. [71] are subtracted,
the effective range is consistent with a purely molecular χc1 (3872). There is no consensus yet how
to interpret the line shapes of χc1 (3872).
79.2.2 The ψ(4230) and ψ(4360)
A broad structure, originally called Y (4260), decaying into J/ψ(1S) π + π − was reported by
BaBar in initial state radiation e+ e− → (γISR )Y (4260) [99]. A subsequent measurement with significantly improved precision was reported by BESIII [100], and revealed that the original Y (4260)
cannot be described with a simple resonant lineshape. Fitting the BESIII data with two BreitWigner distributions leads to a narrower and lighter structure (referred to in the Listings as theψ(4230)), but also requires a second state at 4320 MeV. However, note that the D1 (2420)D̄ molecular model for the ψ(4230) can describe the same data with just one single pole [101]. How many
vector states are in the mass range between 4220 MeV and 4400 MeV is not yet settled, but knowing
this is crucial to allow for further progress.
There are no charmonium states expected in this mass region with quantum numbers 1−−
from quark models using the Cornell type of interaction, although this might not be true forsome screened versions thereof – for a recent discussion we refer to Ref. [102]. In addition, acharmonium state at this mass is expected to have significant couplings to one or more of theD̄(∗) D(∗) channels [103, 104], a feature that is not observed for the ψ(4230). This state could be a
hybrid charmonium with a spin-1 [105, 106] or a spin-0 [107, 108] c̄c core. However, provided thatthe observation of ψ(4230) decay into hc (1P )ππ by BESIII [109] is confirmed, the hybrid hypothesis
would be under pressure, since the spin of the heavy quarks (coupled to zero in the hc (1P )) should
be conserved in leading order in the expansion in (ΛQCD /mc ). (The individual conservation of
the heavy quark spin and the total angular momentum of the light quark cloud is a consequenceof the heavy-quark spin symmetry, see ‘Heavy-Quark and Soft-Collinear Effective Theory’ in thisissue of the Review.) The same criticism applies to the hadrocharmonium interpretation of theψ(4230), which describes this state as spin-1 quarkonium surrounded by a light quark cloud [110].
To circumvent the spin-symmetry argument, Ref. [111] argues that ψ(4230) and ψ(4360) could be
mixtures of two hadrocharmonia with spin-triplet and spin-singlet heavy quark pairs. The samekind of mixing could also be at work for hybrid structures. Hybrids can also treated employing theBorn-Oppenheimer EFT originally suggested in Ref. [112, 113]. Those studies revealed that whilethe ψ(4230) is in principle a good candidate for a hybrid state [114], its decays are incompatible
with this assignment [115].
A dominant D1 (2420)D̄ component in the ψ(4230) [116] explains naturally why the Tcc̄1 (3900)±(interpreted by the authors as a D̄D∗ bound state) is seen in ψ(4230) → π ∓ Tcc̄1 (3900)± . A
similar mechanism is also found in Ref. [117] linking in addition the J/ψ(1S)π + π − and ψ(2S)π + π −decays of the ψ(4230). Furthermore, a copious production of χc1 (3872) in ψ(4230) radiative decays
was predicted from the prominent D1 D̄ component of the ψ(4230) [118], which was confirmed by
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79. Heavy Non-qq Mesons

BESIII [119]. Possible charmonia components both in ψ(4230) and χc1 (3872) can influence theradiative transition but they are shown to be of subleading order [120]. It was proposed thatψ(4360) as a D1 D̄∗ bound state could be the spin partner of the ψ(4230) [121, 122]. In Ref. [123]a dynamical model is presented that identifies the vector states ψ(4230), ψ(4360) and ψ(4415) asDD̄1 , D∗ D̄1 and D∗ D̄2 molecular states, respectively. Moreover, an exotic 0−− state is predictedas D∗ D̄1 molecule with a mass of 4366 ± 18 MeV and a width of less than 10 MeV.
The tetraquark picture calls for four ground state vector states — once the parameters of themodel are fixed from some candidate states in the negative and positive parity sector, states withother quantum numbers can be predicted. Possible scenarios are for instance discussed in Ref.
[124] which builds on a tailor-made spin-spin interaction [125] to describe the χc1 (3872), bothTcc̄1 (3900)±,0 and Tcc̄ (4020)± and even the Tcc̄1 (4430)± confirmed by Belle [126] and LHCb [127].
This model also explains the copious production of χc1 (3872) in ψ(4230) radiative decays mentioned above [125, 128]. However, tetraquark models (in most cases based on diquark-antidiquark
configurations) tend to predict many additional charged and neutral states which have not yet been
discovered. In particular, as for the conventional q̄q structures one should expect nearly degenerateisoscalar and isovector states in analogy to the near degeneracy of ρ(770) and ω(782). The problem
and possible explanations are discussed in some detail in Refs. [84, 85].
Ref. [129] found a sizeable SU(3) flavor octet contribution when analysing the ππ final statefrom ψ(4230) → J/ψ(1S)π + π − , which is consistent with both a molecular and a tetraquark interpretation of ψ(4230), but at odds with a hybrid or a c̄c interpretation.
79.2.3 The ψ(4660)
In the mass range above 4600 MeV, the number of poles is also not yet settled. Experimental∗−
signals are seen in the ψ(2S)ππ, Λ+c Λ̄c , Ds D̄s1 , and Ds D̄s2 final states. In the Listings thesestructures go into one node, ψ(4660), due to their proximity in parameter values. Moreover,various theoretical works describe these states in a combined analysis [130–132]. The signal in thehidden strangeness mode around 4630 MeV still calls for confirmation and might be yet anotherrealisation of the same state, but there are already speculations about its nature. While Ref. [133](∗)(∗)
argues in favor of a Ds D̄s1 (2536) or Ds D̄s2 (2573) [134] molecular nature, Ref. [135] does notconfirm these claims. Ref. [136] identifies the structure as P -wave [cs][c̄s̄] tetraquark state. Other−
explanations of the ψ(4660) include a ψ(2S)f0 (980) molecule [137] and a Λ+c Λ̄c baryonium [130].
Also in this mass range studies of the partner states, driven either by spin or flavor symmetry will
be very valuable — see e.g. the predictions in Ref. [138].
79.2.4 The Tcc̄1 (3900), Tcc̄ (4020), Tbb̄1 (10610), and Tbb̄1 (10650)
The isovector states Tcc̄1 (3900) and Tcc̄ (4020), first observed by BESIII [139, 140], decay predominantly into D̄D∗ and D̄∗ D∗ , respectively, while the Tbb̄1 (10610) and Tbb̄1 (10650), first observedby Belle [141, 142], decay predominantly into B̄B ∗ and B̄ ∗ B ∗ [143], respectively, although all four
were discovered in the decay mode heavy quarkonium plus pion. This suggests that these states areclose relatives and their interactions are connected via heavy quark flavor symmetry. A molecularinterpretation for the bottomonium states was proposed shortly after the discovery of the two Tbb̄states [144] and also shortly after that of the Tcc̄1 (3900) [116]. This picture is confirmed within themeson exchange model of Ref. [145]. Decay patterns of Tcc̄1 (3900) and the two Tbb̄ were also shown
to be consistent with a molecular interpretation [146–148]. However, some of their properties also
appear to be consistent with tetraquark structures [149]. If the molecular picture were correct for
the Tbb̄ states, spin symmetry would lead to the existence of spin partner states [150–152], which
are still to be found. In Ref. [153] it was shown that the actual pole locations of these partner
states would be good probes of one-pion exchange in the molecular potential, which makes theexperimental search for those states even more interesting.
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79.2.5 The Tcc̄1 (4200) and Tcc̄1 (4430)
The heaviest confirmed charged state in the charmonium sector is the Tcc̄1 (4430)± observed byBelle [126]. It is interpreted as hadrocharmonium [110], D̄1 D∗ molecule [154], as well as tetraquark[125]. Alternatively, in [155,156] the Tcc̄1 (4430)± is explained as a cross-channel effect enhanced bya triangle singularity from open charm states. These works were criticised in Ref. [157] where analternative triangle consisting of a K ∗ , a π, and the ψ(4230), is proposed to generate the Tcc̄1 (4430).
The Argand diagram shows an anticlockwise circle, in line with the experimental analysis [127],
while the one of Ref. [156] shows a clockwise motion. By replacing the ψ(4230) with the ψ(3770),
and changing the K ∗ , one can also interpret the Tcc̄1 (4200) as a kinematic effect [157]. A possible
interpretation of Tcc̄1 (3900) and Tcc̄ (4020) as crossed channel effects is put forward in Ref. [158]. It
remains to be seen, however, if this kind of explanation is also capable of explaining the observationsof these lowest Tcc̄ states, also at other total energies.
79.2.6 The Tcc̄s̄1 (4000)
There is recent evidence for a charged charmonium-like state with strangeness, Tcc̄s̄1 (4000),from BESIII [159] and LHCb [160]. The possible existence of a strange partner to the Tcc̄ near theDs D̄∗ thresholds has been predicted in molecular models [161, 162], for tetraquarks [163, 164], forhadrocharmonium structures [164,165], and as a coupled-channel effect [166]. Later on this state isinterpreted in Refs. [167, 168] as a member of the same multiquark octet and in Refs. [169–171] asa member of the same molecular one as the Tcc̄1 (3900). Ref. [168] is also able to describe the recent
LHCb data in the J/ψ(1S)K − system [160], although the extracted total width for their lowest Tcc̄s̄
state is an order of magnitude larger than that found by BESIII. Refs. [172, 173] claim that boththe molecular components and the compact tetraquark core are relevant to describe the Tcc̄1 (3900)
and Tcc̄s̄1 (4000) resonances. Again, in [174] the Tcc̄s̄1 (4000) can be explained as a coupled-channel
effect producing the enhancement close to threshold.
Ref. [169] comes to the conclusion that an understanding of the experimental data for the
Tcc̄s̄1 (4000) calls for the inclusion of both triangle diagrams as well as a pole term. The authors
conclude from their calculations that Tcc̄s̄1 (4000) and Tcc̄1 (3900) are members of the same SU(3)multiplet. This conclusion was confirmed in Ref. [175] and the study extended to higher energies.
The fit of the experimental data allowed for two solutions, one where the Tcc̄ (4020) is a spin partnerof the mentioned isovector states and one where it is not. Data e.g. for e+ e− → K + D∗− D∗0 isclaimed to be decisive which scenario is indeed realised.
It should be stressed that the various scenarios, while describing much of the available data, also
make decisive predictions, e.g. yet unobserved quantum numbers [124, 176]. The forthcoming dataon heavy meson spectroscopy from various facilities should provide a much deeper understandingof how QCD forms matter out of quarks and gluons.
79.2.7 The Tcc (3875)
There is a recent report and follow-up by LHCb [62, 63] on the observation of a narrow peak in
the D0 D0 π + mass spectrum just below the D∗+ D0 threshold. The observed state is a candidate for+ tetraquark configuration with a quark content of ccūd.
¯ Unsuccessful
an isoscalar double-charm Tcc
+
0
+
+
+
searches in D D π and D D mass spectra disfavour the isovector assignment. The D0 π + mass
+ proceeds through the formation of a D ∗ in the intermediate
distribution indicates that the Tcc
state. The additional proximity to the D∗ D0 mass threshold favors the J P = 1+ assignment. The+ has a remarkable narrow width and lies very close to the D ∗+ D 0 threshold [63], comparable toTcc
the properties of the χc1 (3872) [177].
A first evaluation in the context of QCD sum rules [178] results in mass and width values+ . A poleconsistent with the assumption of a compact diquark-antidiquark structure of the Tcc
0
0
+
∗+
0
+ has its
analysis performed with D D π − D D coupled-channels [179] suggests that the Tcc
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79. Heavy Non-qq Mesons

origin in a D∗+ D0 virtual state resulting from the attraction in this channel and the coupling to+ as a D ∗ D molecular structure was pursued inD0 D0 π + . The interpretation of the observed Tcc
quark models [180–183] and the Bethe-Salpeter framework [184]. Predictions depend on fine model
details and are usually accompanied by additional partner states, like an isovector molecule or+higher radial excitations. In analogy to the case of the χc1 (3872) in Ref. [177] the production of Tcc
in high-energy proton-proton collisions at the LHC is studied. Effects of a charm-meson triangle+ from the rescattering of DD leads to a narrow peaksingularity on the inclusive production of Tcc+++ is predicted in Refs. [182,183],in the Tcc π invariant mass distribution. A spin 2 partner of the Tcc
who’s hadronic decays are studied in Ref. [185].
As for the χc1 (3872) one can employ the effective range deduced from experiment for theeffective range in the DD∗ -channel as a measure of the nature of the Tcc (3875). Also here isospin
violations are significant. It turns out that in a calculation where the one-pion exchange is kept
fully non-perturbative, its effect on the effective range is small and positive [183], while it is small
and negative when being treated perturbatively [97, 186].
First lattice studies are also available for the Tcc (3875) [187–189], all performed at pion masses
slightly larger than physical such that the D∗ and with this also the Tcc (3875) are stable. They allfind that at these pion masses the Tcc is a virtual state. In Ref. [190] it was stressed, however, that
all those analyses should be redone, since the proximity of a left-hand cut invalidates the methodused.

79.3 Systems containing four heavy quarks
79.3.1 The Tccc̄c̄ (6900)
LHCb reported the observation of pronounced structures in a double-J/ψ(1S) invariant mass
distribution [191] thus pointing at states with ccc̄c̄ quarks contents. First results on di-J/ψ(1S)and J/ψ(1S)ψ(2S) invariant mass distributions in proton-proton collision data by the CMS [192]and ATLAS [193] Collaborations confirm and extend the resonance structures seen by LHCb. Bellereported on a first search for a double-charmonium state with e+ e− → ηc J/ψ(1S) near threshold
via the ISR process. No significant signal of the double charmonium state is found in several binsof the invariant mass of ηc J/ψ(1S) [194]. Recently the COMPASS [195] Collaboration also studied
double J/ψ(1S) production in pion scattering off nuclear targets. No significant signatures that
could be associated with tetraquarks are found in the double J/ψ(1S) mass spectrum, although
the COMPASS data sample is limited.
From quark models the possible existence of bound states like this was discussed already long ago[196,197]. There are now also many model calculations available in the literature. For discussions of
those data from the compact tetraquark perspective see Refs. [198–204]. Most of these quark model
calculations assign the reported structure to a ccc̄c̄ state in the 2S multiplet with near-degenerate
J P = 0+ , 1+ and 2+ configurations. The dominance of a compact tetraquark component in theapparently exotic structure is also supported by the coupled multichannel study of Ref. [205]. The
full coupled-channel study of Ref. [206] leads to a rich spectrum of cc̄-cc̄ states where parts are
candidates for the observed double J/ψ(1S) structures. For direct analyses of the data within thetetraquark approach, see, e.g., Ref. [207]. Also QCD sum rule studies of the system were published,
but do not give consistent results: For example Ref. [208] interprets the structure at 6900 MeV asa hybrid state, Ref. [209] as a tetraquark, and Ref. [210] states that both molecular and tetraquarkinterpretations are possible. An alternative view on the LHCb double-J/ψ(1S) data is provided
in Refs. [211–213] where the analyses are performed using coupled channel T -matrices. In theseworks the structures in the data emerge from the interplay of thresholds and resonances with the
non-trivial prediction that there should exist, if this dynamical picture were correct, a state locatedvery near the double-J/ψ(1S) threshold which can be searched for experimentally. In Ref. [214]31st May, 2024

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79. Heavy Non-qq Mesons

it was shown that a J/ψ(1S)J/ψ(1S) scattering potential sufficiently strong to bind is in fact
consistent with our current understanding of πJ/ψ(1S) scattering as well as the strength of the ππinteractions.
In contrast, Ref. [215, 216] explains the double-J/ψ(1S) data as cusps without nearby poles.
This claim can be tested experimentally: if this explanation were correct, there should not be any
narrow near threshold structure in the channel that generates the cusp, for that would call for a
non-perturbative interaction in that channel, as pointed out in Ref. [217].
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31st May, 2024