In a recent paper [<a href="http://dx.doi.org/10.1103/PhysRevLett.126.132001">Phys. Rev. Lett. 126, 132001 (2021)</a>], the LHCb data on the di-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi></math> production in proton-proton collisions were analyzed in a coupled-channel framework based on double-vector-charmonium channels. This investigation identified a robust pole near the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi><mi>J</mi><mo>/</mo><mi>ψ</mi></math> threshold, tagged <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>X</mi><mo stretchy="false">(</mo><mn>6200</mn><mo stretchy="false">)</mo></math>, suggesting it as a new state. The present work extends that investigation by incorporating recent di-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi></math> production data from the CMS and ATLAS Collaborations and performing a combined analysis of all three datasets. This study confirms the existence of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>X</mi><mo stretchy="false">(</mo><mn>6200</mn><mo stretchy="false">)</mo></math>, and its pole position is now determined with a higher precision than in the previous study, where only a single dataset was employed. The pole corresponding to the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>X</mi><mo stretchy="false">(</mo><mn>6900</mn><mo stretchy="false">)</mo></math> is also extracted, though its actual position and residue depend on a particular coupled-channel model employed and deviate from values reported in the experimental investigations. Moreover, we demonstrate that the currently available data do not allow one to determine whether there is an additional pole in the studied mass range. The dielectron width of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>X</mi><mo stretchy="false">(</mo><mn>6200</mn><mo stretchy="false">)</mo></math> is estimated under different conjectures on its quantum numbers, and the number of such states that can be annually produced at the future Super <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>τ</mi></math>-Charm Facility is estimated. The line shape in the complimentary <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>J</mi><mo>/</mo><mi>ψ</mi><mi>ψ</mi><mo stretchy="false">(</mo><mn>2</mn><mi>S</mi><mo stretchy="false">)</mo></math> channel is discussed, and a good agreement with the ATLAS data is found.

China

Yi-Lin Song

Yu Zhang

Germany

Vadim Baru

Feng-Kun Guo

Christoph Hanhart

Portugal

Alexey Nefediev

Toward a precision determination of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>X</mi><mo stretchy="false">(</mo><mn>6200</mn><mo stretchy="false">)</mo></mrow></math> parameters from data

We demonstrate that the dip observed near the total energy of 3872 MeV in the recent cross section data from the BESIII Collaboration for <math><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup><mo>→</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup></math> admits a natural explanation as a coupled-channel effect: it is a consequence of unitarity and a strong <math><mi>S</mi></math>-wave <math><mi>D</mi><msup><mover><mi>D</mi><mo>¯</mo></mover><mo>*</mo></msup></math> attraction that generates the state <math><mi>X</mi><mo>(</mo><mn>3872</mn><mo>)</mo></math>. We anticipate the appearance of a similar dip in the <math><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup><mo>→</mo><mi>J</mi><mo>/</mo><mi>ψ</mi><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup><msup><mi>π</mi><mn>0</mn></msup></math> final state near the <math><msup><mi>D</mi><mo>*</mo></msup><msup><mover><mi>D</mi><mo>¯</mo></mover><mo>*</mo></msup></math> threshold driven by the same general mechanism, then to be interpreted as a signature of the predicted spin-2 partner of the <math><mi>X</mi><mo>(</mo><mn>3872</mn><mo>)</mo></math>.

Slovenia

How does the <math><mi>X</mi><mo>(</mo><mn>3872</mn><mo>)</mo></math> show up in <math><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup></math> collisions: Dip versus peak

The <math><mi>D</mi><msup><mi>D</mi><mo>*</mo></msup></math> scattering phase shifts in the <math><msubsup><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow><mo>+</mo></msubsup><mo>=</mo><mi>c</mi><mi>c</mi><mover><mi>u</mi><mo>¯</mo></mover><mover><mi>d</mi><mo>¯</mo></mover></math> channel are extracted from lattice QCD for five different charm quark masses and a fixed light-quark mass corresponding to <math><msub><mi>m</mi><mi>π</mi></msub><mo>≃</mo><mn>280</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math>. The phase shifts are analyzed employing two approaches: effective range expansion and Lippmann-Schwinger equation derived in the effective field theory. In the latter case, the results imply an attraction at short range parametrized by contact terms and a slight repulsion at long range mediated by one-pion exchange with <math><msub><mi>m</mi><mi>π</mi></msub><mo>&gt;</mo><msub><mi>m</mi><msup><mi>D</mi><mo>*</mo></msup></msub><mo>−</mo><msub><mi>m</mi><mi>D</mi></msub></math>. The poles in the amplitude across the complex energy plane are extracted and their trajectories are discussed as the charm quark mass is varied. Two complex conjugate poles corresponding to a resonance below threshold are found for <math><msub><mi>m</mi><mi>c</mi></msub></math> close to the physical value. They turn into a pair of virtual states at the largest <math><msub><mi>m</mi><mi>c</mi></msub></math> studied. With further increasing <math><msub><mi>m</mi><mi>c</mi></msub></math>, one virtual pole representing <math><msubsup><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow><mo>+</mo></msubsup></math> is expected to move towards the two-body threshold and turn into a bound state. The light-quark mass dependence of the <math><msubsup><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow><mo>+</mo></msubsup></math> pole is briefly discussed using the data on <math><mi>D</mi><msup><mi>D</mi><mo>*</mo></msup></math> scattering from other lattice collaborations.

Sara Collins

India

M. Padmanath

Sasa Prelovsek

Toward the quark mass dependence of <math><msubsup><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow><mo>+</mo></msubsup></math> from lattice QCD

Recent data for the masses of <math><mi>D</mi></math> and <math><msup><mi>D</mi><mo>*</mo></msup></math> mesons determined using methods of lattice QCD for several values of the charm quark mass different from its physical mass are analyzed in heavy quark effective theory. Nonperturbative parameters are extracted that arise at order <math><mi>O</mi><mo>(</mo><mn>1</mn><mo>/</mo><msub><mi>m</mi><mi>c</mi></msub><mo>)</mo></math> in the heavy quark mass expansion of a heavy-light meson mass. The determined parameters are used to establish the charm quark masses corresponding to the employed lattice sets.

Extraction of nonperturbative parameters for <math><msup><mi>D</mi><mrow><mo>(</mo><mo>*</mo><mo>)</mo></mrow></msup></math> mesons from lattice data

We discuss recent lattice data for the <math><msub><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow></msub><mo>(</mo><mn>3875</mn><msup><mo>)</mo><mo>+</mo></msup></math> state to stress, for the first time, a potentially strong impact of left-hand cuts from the one-pion exchange on the pole extraction for near-threshold exotic states. In particular, if the left-hand cut is located close to the two-particle threshold, which happens naturally in the <math><mi>D</mi><msup><mi>D</mi><mo>*</mo></msup></math> system for the pion mass exceeding its physical value, the effective-range expansion is valid only in a very limited energy range up to the cut and as such is of little use to reliably extract the poles. Then, an accurate extraction of the pole locations requires the one-pion exchange to be implemented explicitly into the scattering amplitudes. Our findings are general and potentially relevant for a wide class of hadronic near-threshold states.

Meng-Lin Du

Arseniy Filin

Xiang-Kun Dong

Evgeny Epelbaum

Spain

Juan Nieves

Qian Wang

Role of Left-Hand Cut Contributions on Pole Extractions from Lattice Data: Case Study for <math><msub><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow></msub><mo>(</mo><mn>3875</mn><msup><mo>)</mo><mo>+</mo></msup></math>

We compute the chromopolarizabilities of the fully heavy baryons <math><mrow><msub><mrow><mi>Ω</mi></mrow><mrow><mi>Q</mi><mi>Q</mi><msup><mrow><mi>Q</mi></mrow><mrow><mo>′</mo></mrow></msup></mrow></msub></mrow></math> (<math><mi>Q</mi><mo>,</mo><msup><mi>Q</mi><mo>′</mo></msup><mo>=</mo><mi>b</mi></math>, <math><mrow><mi>c</mi></mrow></math>) in the framework of potential nonrelativistic quantum chromodynamics. At leading order, the fully heavy hadrons are considered as ground chromo-Coulombic bound states. We find that the chromopolarizability <math><msub><mi>β</mi><mi>Ω</mi></msub></math> of a fully heavy baryon <math><mi>Q</mi><mi>Q</mi><mi>Q</mi></math> is 2.6 times the chromopolarizability <math><msub><mi>β</mi><mi>ψ</mi></msub></math> of the quarkonium <math><mover><mi>Q</mi><mo>¯</mo></mover><mi>Q</mi></math> with the same heavy quark flavor <math><mi>Q</mi></math>. This result is accurate up to the correction of the order 0.3 for <math><mi>Q</mi><mo>=</mo><mi>b</mi></math> and provides an order-of-magnitude estimate for <math><mi>Q</mi><mo>=</mo><mi>c</mi></math>. We discuss the dependence of the ratio <math><msub><mi>β</mi><mi>Ω</mi></msub><mo>/</mo><msub><mi>β</mi><mi>ψ</mi></msub></math> on the heavy quark mass <math><msub><mi>m</mi><mi>Q</mi></msub></math> and the strong coupling constant <math><msub><mi>α</mi><mi>s</mi></msub></math> as well as on the ratio of the masses <math><mrow><msub><mrow><mi>m</mi></mrow><mrow><msup><mrow><mi>Q</mi></mrow><mrow><mo>′</mo></mrow></msup></mrow></msub><mo>/</mo><msub><mrow><mi>m</mi></mrow><mrow><mi>Q</mi></mrow></msub></mrow></math>, in the case not all quarks in the baryon are identical. Since the chromopolarizability of heavy hadrons defines the strength of their interaction at low energies mediated by soft gluons, which at long range hadronize into pairs of pions and kaons, our findings argue in favor of the existence of near-threshold states composed of pairs of fully heavy baryons.

United States

Jaume Tarrús Castellà

Chromopolarizabilities of fully heavy baryons

The last two decades are marked by a renaissance in hadronic spectroscopy caused by the arrival of vast experimental information on exotic states in the spectrum of charmonium and bottomonium. Most of such states have properties at odds with the predictions of the quark model and reside very close to strong hadronic thresholds. Prominent examples are provided by the glorious <math><mi>X</mi><mo>(</mo><mn>3872</mn><mo>)</mo></math> charmoniumlike state and the doubly charmed tetraquark <math><msubsup><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow><mo>+</mo></msubsup></math> with the masses within less than 1 MeV from the <math><mi>D</mi><msup><mover><mi>D</mi><mo>¯</mo></mover><mo>*</mo></msup></math> and <math><mi>D</mi><msup><mi>D</mi><mo>*</mo></msup></math> open-charm thresholds, respectively. The universality of this feature hints towards the existence of a general pattern for such exotic states. In this work we discuss a possible generic mechanism for the formation of near-threshold molecular states as a result of the strong coupling of compact quark states with a hadronic continuum channel. The compact states that survive the strong coupling limit decouple from the continuum channel and therefore also from the formed hadronic molecule—if realized this scenario would provide a justification to treat hadronic molecules isolated, ignoring the possible influence from surrounding, compact quark-model states. We confront the phenomenology of the <math><msub><mi>D</mi><mrow><mi>s</mi><mn>1</mn></mrow></msub><mo>(</mo><mn>2460</mn><mo>)</mo></math> and <math><msub><mi>D</mi><mrow><mi>s</mi><mn>1</mn></mrow></msub><mo>(</mo><mn>2536</mn><mo>)</mo></math> with this picture and find consistency, although other explanations remain possible for those states.

Do near-threshold molecular states mix with neighboring <math><mover><mi>Q</mi><mo>¯</mo></mover><mi>Q</mi></math> states?

We discuss some general features of the effective range expansion, the content of its parameters with respect to the nature of the pertinent near-threshold states and the necessary modifications in the presence of coupled channels, isospin violations and unstable constituents. As illustrative examples, we analyse the properties of the <math><msub><mrow><mi>χ</mi></mrow><mrow><mi>c</mi><mn>1</mn></mrow></msub><mo>(</mo><mn>3872</mn><mo>)</mo></math> and <math><msubsup><mrow><mi>T</mi></mrow><mrow><mi>c</mi><mi>c</mi></mrow><mrow><mo>+</mo></mrow></msubsup></math> states supporting the claim that these exotic states have a predominantly molecular nature.

Effective range expansion for narrow near-threshold resonances

A coupled-channel approach is applied to the charged tetraquark state <math><msubsup><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow><mo>+</mo></msubsup></math> recently discovered by the LHCb Collaboration. The parameters of the interaction are fixed by a fit to the observed line shape in the three-body <math><msup><mi>D</mi><mn>0</mn></msup><msup><mi>D</mi><mn>0</mn></msup><msup><mi>π</mi><mo>+</mo></msup></math> channel. Special attention is paid to the three-body dynamics in the <math><msubsup><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow><mo>+</mo></msubsup></math> due to the finite life time of the <math><msup><mi>D</mi><mo>*</mo></msup></math>. An approach to the <math><msubsup><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow><mo>+</mo></msubsup></math> is argued to be self-consistent only if both manifestations of the three-body dynamics, the pion exchange between the <math><mi>D</mi></math> and <math><msup><mi>D</mi><mo>*</mo></msup></math> mesons and the finite <math><msup><mi>D</mi><mo>*</mo></msup></math> width, are taken into account simultaneously to ensure that three-body unitarity is preserved. This is especially important to precisely extract the pole position in the complex energy plane whose imaginary part is very sensitive to the details of the coupled-channel scheme employed. The <math><msup><mi>D</mi><mn>0</mn></msup><msup><mi>D</mi><mn>0</mn></msup></math> and <math><msup><mi>D</mi><mn>0</mn></msup><msup><mi>D</mi><mo>+</mo></msup></math> invariant mass distributions, predicted based on this analysis, are in good agreement with the LHCb data. The low-energy expansion of the <math><msup><mi>D</mi><mo>*</mo></msup><mi>D</mi></math> scattering amplitude is performed and the low-energy constants (the scattering length and effective range) are extracted. The compositeness parameter of the <math><msubsup><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow><mo>+</mo></msubsup></math> is found to be close to unity, which implies that the <math><msubsup><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow><mo>+</mo></msubsup></math> is a hadronic molecule generated by the interactions in the <math><msup><mi>D</mi><mrow><mo>*</mo><mo>+</mo></mrow></msup><msup><mi>D</mi><mn>0</mn></msup></math> and <math><msup><mi>D</mi><mrow><mo>*</mo><mn>0</mn></mrow></msup><msup><mi>D</mi><mo>+</mo></msup></math> channels. Employing heavy-quark spin symmetry, an isoscalar <math><msup><mi>D</mi><mo>*</mo></msup><msup><mi>D</mi><mo>*</mo></msup></math> molecular partner of the <math><msubsup><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow><mo>+</mo></msubsup></math> with <math><msup><mi>J</mi><mi>P</mi></msup><mo>=</mo><msup><mn>1</mn><mo>+</mo></msup></math> is predicted under the assumption that the <math><mrow><mi>D</mi><msup><mrow><mi>D</mi></mrow><mrow><mo>*</mo></mrow></msup><mtext>−</mtext><msup><mrow><mi>D</mi></mrow><mrow><mo>*</mo></mrow></msup><msup><mrow><mi>D</mi></mrow><mrow><mo>*</mo></mrow></msup></mrow></math> coupled-channel effects can be neglected.

Russia

Coupled-channel approach to <math><msubsup><mi>T</mi><mrow><mi>c</mi><mi>c</mi></mrow><mo>+</mo></msubsup></math> including three-body effects

Recently, the LHCb Collaboration reported pronounced structures in the invariant mass spectrum of <math><mi>J</mi><mo>/</mo><mi>ψ</mi></math> pairs produced in proton-proton collisions at the Large Hadron Collider. In this Letter, we argue that the data can be very well described within two variants of a coupled-channel approach employing <math><mi>T</mi></math> matrices consistent with unitarity: (i) with just two channels, <math><mi>J</mi><mo>/</mo><mi>ψ</mi><mi>J</mi><mo>/</mo><mi>ψ</mi></math> and <math><mi>ψ</mi><mo>(</mo><mn>2</mn><mi>S</mi><mo>)</mo><mi>J</mi><mo>/</mo><mi>ψ</mi></math>, as long as energy-dependent interactions in these channels are allowed, or (ii) with three channels <math><mi>J</mi><mo>/</mo><mi>ψ</mi><mi>J</mi><mo>/</mo><mi>ψ</mi></math>, <math><mi>ψ</mi><mo>(</mo><mn>2</mn><mi>S</mi><mo>)</mo><mi>J</mi><mo>/</mo><mi>ψ</mi></math>, and <math><mi>ψ</mi><mo>(</mo><mn>3770</mn><mo>)</mo><mi>J</mi><mo>/</mo><mi>ψ</mi></math> with just constant contact interactions. Both formulations hint at the existence of a near-threshold state in the <math><mi>J</mi><mo>/</mo><mi>ψ</mi><mi>J</mi><mo>/</mo><mi>ψ</mi></math> system with the quantum numbers <math><msup><mi>J</mi><mrow><mi>P</mi><mi>C</mi></mrow></msup><mo>=</mo><msup><mn>0</mn><mrow><mo>+</mo><mo>+</mo></mrow></msup></math> or <math><msup><mn>2</mn><mrow><mo>+</mo><mo>+</mo></mrow></msup></math>, which we refer to as <math><mi>X</mi><mo>(</mo><mn>6200</mn><mo>)</mo></math>. We suggest experimental tests to check the existence of this state and discuss what additional channels need to be studied experimentally to allow for distinctive tests between the two mechanisms proposed. If the molecular nature of <math><mi>X</mi><mo>(</mo><mn>6200</mn><mo>)</mo></math>, as hinted by the three-channel approach, is confirmed, many other double-quarkonium states should exist driven by the same binding mechanism. In particular, there should be an <math><msub><mi>η</mi><mi>c</mi></msub><msub><mi>η</mi><mi>c</mi></msub></math> molecule with a similar binding energy.

Coupled-Channel Interpretation of the LHCb Double-<math><mi>J</mi><mo>/</mo><mi>ψ</mi></math> Spectrum and Hints of a New State Near the <math><mi>J</mi><mo>/</mo><mi>ψ</mi><mi>J</mi><mo>/</mo><mi>ψ</mi></math> Threshold