Hadronic Molecules Research Articles

Pc states in the mixture of molecular and pentaquark pictures

We systematically study hidden charm pentaquark states in the constituent quark model with a general Hamiltonian for multiquark systems, considering the coupling between the Σc(*)D¯(*) molecular states and the q3cc¯ compact pentaquark states by the one-gluon exchange hyperfine interaction. The ground state hidden-charm pentaquark mass spectra and the strong decay widths are calculated. This work suggests that Pc(4312), Pc(4457), and Pc(4380) resonances might be mainly ΣcD¯, ΣcD¯*, and Σc*D¯ hadronic molecules respectively, and Pc(4440) might include sizable pentaquark components. Published by the American Physical Society 2024

Productions of X(3872), Zc(3900)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Z_c(3900)$$\\end{document}, X2(4013)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$X_2(4013)$$\\end{document}, and Zc(4020)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Z_c(4020)$$\\end{document} in B(s)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$B_{(s)}$$\\end{document} decays offer strong clues on their molecular nature

The exotic states X(3872) and Zc(3900)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Z_c(3900)$$\\end{document} have long been conjectured as isoscalar and isovector D¯∗D\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\bar{D}}^*D$$\\end{document} molecules. In this work, we first propose the triangle diagram mechanism to investigate their productions in B decays as well as their heavy quark spin symmetry partners, X2(4013)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$X_2(4013)$$\\end{document} and Zc(4020)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Z_c(4020)$$\\end{document}. We show that the large isospin breaking of the ratio B[B+→X(3872)K+]/B[B0→X(3872)K0]\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathcal {B}}[B^+ \\rightarrow X(3872) K^+]/{\\mathcal {B}}[B^0 \\rightarrow X(3872) K^0] $$\\end{document} can be attributed to the isospin breaking of the neutral and charged D¯∗D\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\bar{D}}^*D$$\\end{document} components in their wave functions. For the same reason, the branching fractions of Zc(3900)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Z_c(3900)$$\\end{document} in B decays are smaller than the corresponding ones of X(3872) by at least one order of magnitude, which naturally explains its non-observation. A hierarchy for the production fractions of X(3872), Zc(3900)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Z_c(3900)$$\\end{document}, X2(4013)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$X_2(4013)$$\\end{document}, and Zc(4020)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Z_c(4020)$$\\end{document} in B decays, consistent with all existing data, is predicted. Furthermore, with the factorization ansatz we extract the decay constants of X(3872), Zc(3900)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Z_c(3900)$$\\end{document}, and Zc(4020)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Z_c(4020)$$\\end{document} as D¯∗D(∗)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\bar{D}}^*D^{(*)}$$\\end{document} molecules via the B decays, and then calculate their branching fractions in the relevant B(s)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$B_{(s)}$$\\end{document} decays, which turn out to agree with all existing experimental data. The mechanism we proposed is useful to elucidate the internal structure of the many exotic hadrons discovered so far and to extract the decay constants of hadronic molecules, which can be used to predict their production in related processes.

Hadronic Molecules with Heavy Quarks

We discuss how to decipher the nature of near-threshold exotic states from ex perimental line shapes and lattice QCD simulations. A brief overview of the effective-field-theory approach for analyzing such states is presented, highlight ing the special role played by the longest-range pion exchange interaction. The method is exemplified through an analysis of the recently discovered doubly-charm state Tcc(3875)+.

Double strangeness molecular-type pentaquarks from coupled channel dynamics

Abstract. The existence of the nucleonic pentaquark resonances Pc (4312), Pc(4380), Pc(4440) and Pc(4457), established by the LHCb collaboration, has been one of the major discoveries in hadron physics in the latest years. This has been followed by the discovery of pentaquarks with one unit of strangeness, Pcs(4338) and Pcs(4457). Most of these states can be understood as hadronic molecules, namely bound states of a sufficiently attractive meson-baryon interaction. A widely used model, based on unitarized meson-baryon amplitudes obtained from vector meson exchange interactions derived from the hidden gauge formalism, which predicted these states prior to their discovery, is also predicting the existence of pentaquarks with double strangeness content, at around 4500 MeV and 4600 MeV [1]. Our model also suggest that one of these double strangeness pentaquarks can be seen in the weak decay of the Eb baryon into J/ΨϕΞ. A detailed study of this reaction is still under investigation, but in these proceedings we shall show some preliminary results, which confirm the possibility of observing traces of S=-2 pentaquark in invariant mass spectra of J/ΨΞ pairs produced in the decays Ξb → J/ΨϕΞ.

The Y(4230) as a D1D molecule

Abstract. We show that the currently available data are consistent with Y(4230) being a D1D¯ hadronic molecule. By a simultaneous fit to data from e+e− → D0D*−π+, J/ψπ+π−, J/ψK+ K−, hcπ+π−, J/ψη, χc0ω, χc1(3872)γ and µ+µ−, we demonstrate that this single state can explain the experimental signals in the mass range from 4.2 to 4.35 GeV.

Resonance X(7300): excited 2S tetraquark or hadronic molecule χc1χc1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\chi _{c1}\\chi _{c1}$$\\end{document}?

We explore the first radial excitation X4c∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$X_{\ extrm{4c}}^{*}$$\\end{document} of the fully charmed diquark-antidiquark state X4c=ccc¯c¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$X_{\ extrm{4c}}=cc{\\overline{c}}{\\overline{c}} $$\\end{document} built of axial-vector components, and the hadronic molecule M=χc1χc1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathcal {M}} =\\chi _{c1}\\chi _{c1}$$\\end{document}. The masses and current couplings of these scalar states are calculated in the context of the QCD two-point sum rule approach. The full widths of X4c∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$X_{\ extrm{4c}}^{*}$$\\end{document} and M\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathcal {M}}$$\\end{document} are evaluated by taking into account their kinematically allowed decay channels. We find partial widths of these processes using the strong couplings gi∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$g_i^{*}$$\\end{document} and Gi(∗)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$G_i^{(*)}$$\\end{document} at the X4c∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$X_{\ extrm{4c}}^{*}$$\\end{document}(M\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathcal {M}}$$\\end{document} )-conventional mesons vertices computed by means of the QCD three-point sum rule method. The predictions obtained for the parameters m=(7235±75)MeV\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$m=(7235 \\pm 75)~ \ extrm{MeV}$$\\end{document}, Γ=(144±18)MeV\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Gamma =(144 \\pm 18)~\ extrm{MeV}$$\\end{document} and m~=(7180±120)MeV\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\widetilde{m}}=(7180 \\pm 120)~\ extrm{MeV}$$\\end{document}, Γ~=(169±21)MeV\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\widetilde{\\Gamma }}=(169 \\pm 21)~\ extrm{MeV}$$\\end{document} of these structures, are compared with the experimental data of the CMS and ATLAS Collaborations. In accordance to these results, within existing errors of measurements and uncertainties of the theoretical calculations, both the excited tetraquark and hadronic molecule may be considered as candidates to the resonance X(7300). Detailed analysis, however, demonstrates that the preferable model for X(7300) is an admixture of the molecule M\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathcal {M}}$$\\end{document} and sizeable part of X4c∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$X_{\ extrm{4c}}^{*}$$\\end{document}.

Molecular states in systems* *Supported by the Doctoral Program of Tian Chi Foundation of Xinjiang Uyghur Autonomous Region of China (51052300506), the NSFC and the Deutsche Forschungsgemeinschaftn(DFG, German Research Foundation) through the funds provided to the Sino-German Collaborative Research Center TRR110 “Symmetries and the Emergence of Structure in QCD” (NSFC 12070131001, DFG Project-ID 196253076 - TRR 110), the NSFC (11835015,

The possible hadronic molecules in systems with , and are investigated with interactions described by light meson exchanges. By varying the cutoff in a phenomenologically reasonable range of GeV, we find ten near-threshold (bound or virtual) states in the single-channel case. After introducing the coupled-channel dynamics of ----- systems, these states, except those below the lowest channels in each sector, move into the complex energy plane and become resonances in the mass range GeV. Their spin-parities and nearby thresholds are , , , , , , , , , and . The impact of the -term in the one-boson-exchange model on these states is presented. Setting GeV as an illustrative value, it is found that is a stable bound state (becoming unstable if the coupling to lower channels is turned on), and are physical resonances in cases where the -term is included or excluded, and the other seven states are physical resonances or "virtual-state-like" poles near thresholds, depending on whether the -term is included. In addition, the partial decay widths of the physical resonances are provided. These double-charm hidden-strangeness pentaquark states, as the partners of the experimentally observed and states, can be searched for in the final states in the future.

Search for a three-proton resonance state in d+12C, α+12C and 12C+12C collisions at 3.37AGeV

The new experimental results on the search and study of formation of a possible three-proton resonance state in a target fragmentation region in the total ensemble of collisions of deuterons (2H), [Formula: see text]-particles (4He), and carbon-12 nuclei with target carbon-12 nuclei at incident kinetic energy 3.37[Formula: see text]GeV per nucleon are presented. The narrow peak structure of a possible three-proton resonance state was observed with a four-sigma statistical significance in the spectrum of invariant masses of three protons in the analyzed ensemble of collisions in the collision events with four protons in the final state. The peak structure was not visible in the other channels with the number of protons equal 3, 5, and [Formula: see text]. The mass and width of this possible three-proton resonance state were estimated to be [Formula: see text][Formula: see text]MeV/[Formula: see text] and [Formula: see text][Formula: see text]MeV/[Formula: see text]. The inclusive cross-section of formation of this possible resonance state was estimated to be [Formula: see text][Formula: see text]mb. It was deduced that the three-proton resonances could possibly be formed as a result of capture by a two-proton resonance (with mass [Formula: see text][Formula: see text]MeV/[Formula: see text]) of one more proton with a close velocity. The observed three-proton as well as two-proton resonances are likely to be the hadronic molecules. Taking into account an alpha cluster structure of carbon-12 nuclei, one of the possible mechanisms of formation of three-proton resonances could be the effective fusing of pair of protons with opposite spins, from one fragmenting alpha cluster, with a proton, originating from the second fragmenting alpha cluster.

Charmoniumlike tetraquarks in a chiral quark model

The lowest-lying charmonium-like tetraquarks c{bar{c}}q{bar{q}}(q=u,,d) and c{bar{c}}s{bar{s}}, with spin-parity J^P=0^+, 1^+ and 2^+, and isospin I=0 and 1, are systematically investigated within the theoretical framework of complex-scaling range for a chiral quark model that has already been successfully applied in former studies of various tetra- and penta-quark systems. A four-body S-wave configuration which includes meson–meson, diquark–antidiquark and K-type arrangements of quarks, along with all possible color wave functions, is comprehensively considered. Several narrow resonances are obtained in each tetraquark channel when a fully coupled-channel computation is performed. We tentatively assign theoretical states to experimentally reported charmonium-like signals such as X(3872), Z_c(3900), X(3960), X(4350), X(4685) and X(4700). They can be well identified as hadronic molecules; however, other exotic components which involve, for instance, hidden-color channels or diquark–antidiquark structures play a considerable role. Meanwhile, two resonances are obtained at 4.04 GeV and 4.14 GeV which may be compatible with experimental data in the energy interval 4.0–4.2 GeV. Furthermore, the X(3940) and X(4630) may be identified as color compact tetraquark resonances. Finally, we also find few resonance states in the energy interval from 4.5 to 5.0 GeV, which would be awaiting for discovery in future experiments.

Revealing the inner structure of the newly observed η 1(1855) via photoproduction

Very recently, a new hadronic exotic state η 1(1855) at the invariant mass spectrum of was observed by the BESIII Collaboration. According to its properties, such as the mass and decay width, the η 1(1855) have been suggested to be a compact multi-quark state, a hadron molecule, or a hybrid meson. In order to distinguish the various interpretations of the η 1(1855), a Reggeized model combined with the vector dominance model for η 1(1855) photoproduction on the proton target is presented. The η 1(1855) photoproduction is dominated by the t-channel vector mesons ρ, ω, and ϕ exchange. If the η 1(1855) is a hybrid meson, the Primakoff effect also should be included. Our calculations show that the total cross section of the η 1(1855) production via γ p reaction can reach up to 0.276 pb for θ = 15° or 0.119 pb for θ = 0°, about 0.0297% or 0.0128% of the total cross section obtained by considering the η 1(1855) as an S-wave molecule. We also find their line shapes are sizably different. If the η 1(1855) is a molecular state, the photoproduction of η 1(1855) near the threshold offers a nice place to test its molecular nature. However, it should be better to take high energy, at least above E γ = 16.97 GeV, to observe the production of η 1(1855) if η 1(1855) is a hybrid meson. These results can be measured in the GlueX experiment or electron-ion collider in China to test the nature of the η 1(1855).

Charmed-strange tetraquarks and their decays in the potential quark model

In the framework of a nonrelativistic potential quark model, we investigate the mass spectrum of the $1S$-wave charmed-strange tetraquark states of $cn\overline{s}\overline{n}$ and $cs\overline{n}\overline{n}$ ($n=u$ or $d$) systems. The tetraquark system is solved by a correlated Gaussian method. With the same parameters fixed by the meson spectra, we obtained the mass spectra for the $1S$-wave tetraquark states. Furthermore, based on the predicted tetraquark spectra we estimate their rearrangement decays in a quark-exchange model. We find that the rearrangement decays of the tetraquarks may be mainly driven by the spin-spin interactions. The resonances ${X}_{0}(2900{)}^{0}$ and ${T}_{c\overline{s}0}^{a}(2900{)}^{++/0}$ reported from LHCb may be assigned to be the lowest $1S$-wave tetraquark states ${\overline{T}}_{cs0}^{f}(2818)$ and ${T}_{c\overline{s}0}^{a}(2828)$ classified in the quark model, respectively. It also allows us to extract the couplings for the initial tetraquark states to their nearby $S$-wave interaction channels. We find that some of these couplings turn out to be sizeable. Following the picture of the wave function renormalization for the near-threshold strong $S$-wave interactions, the sizeable coupling strengths can be regarded as an indication of their dynamic origins as candidates for hadronic molecules. Furthermore, our predictions suggest that signals for the $1S$-wave charmed-strange tetraquark states can also be searched in the other channels, such as ${D}^{0}{K}^{+}$, ${D}^{+}{K}^{+}$, ${D}^{*+}{K}^{\ensuremath{-}}$, ${D}^{*+}{K}^{+}$, ${D}^{*0}{K}^{+}$, ${D}^{0}{\overline{K}}^{*0}$, ${D}_{s}^{+}{\ensuremath{\rho}}^{0}$, etc.

Near-threshold structures in the Ds+Ds− mass distribution of the decay B+→Ds+Ds−K+

Two near-threshold peaking structures with spin-parities $J^{\mathrm{PC} }=0^{++}$ were recently discovered by the LHCb Collaboration in the $ D_{s}^{+}D_{s}^{-}$ invariant mass distribution of the decay $ B^{+}\rightarrow D_{s}^{+}D_{s}^{-}K^{+}$. The first of them is the resonance $X(3960)$, whereas the second one, $X_0(4140)$, is a structure with the mass around $4140~\mathrm{MeV}$. To explore their natures and model them, we study the hadronic molecule $\mathcal{M}=D_s^{+}D_s^{-}$ and calculate its mass, current coupling, and width. The mass and current coupling of the molecule are extracted from the QCD two-point sum rule analyses by taking into account vacuum condensates up to dimension $10$. To evaluate its full width, we consider the processes $\mathcal{M} \to D_{s}^{+}D_{s}^{-}$, $\mathcal{M} \to\eta_{c}\eta^{(\prime)}$, and $\mathcal{ M} \to J/\psi\phi$. Partial widths of these decays are determined by the strong couplings $g_i, \ i=1,2,3,4 $ at vertices $\mathcal{M} D_{s}^{+}D_{s}^{-}$, $\mathcal{M}\eta_{c} \eta^{(\prime)}$, and $\mathcal{M} J/\psi\phi$. They are computed by means of the three-point sum rule method. Predictions for the mass $m=(4117 \pm 85)~\mathrm{MeV}$ and width $\Gamma_{ \mathcal{M}}=(62 \pm 12)~\mathrm{MeV}$ of the molecule $\mathcal{M}$ are compared with the corresponding LHCb data, and also with our results for the diquark-antidiquark state $X=[cs][\overline{c}\overline{s}]$. We argue that the structure $X_0(4140)$ may be interpreted as the hadronic molecule $ D_s^{+}D_s^{-}$, whereas the resonance $X(3960)$ can be identified with the tetraquark $X$.

Modeling the resonance Tcs0a(2900)++ as a hadronic molecule D*+K*+

The doubly charged scalar resonance $T_{cs0}^{a}(2900)^{++}$ is studied in the context of the hadronic molecule model. We consider $ T_{cs0}^{a}(2900)^{++}$ as a molecule $M=D^{\ast +}K^{\ast +}$ composed of vector mesons, and calculate its mass, current coupling and full width. The spectroscopic parameters of $M$, i.e., its mass and current coupling, are found by means of the QCD two-point sum rule method by taking into account vacuum expectation values of quark, gluon and mixed operators up to dimension $10$. The width of the molecule $M$ is evaluated through the calculations of the partial widths of the decay channels $M \to D_{s}^{+}\pi^{+}$, $M \to D_{s}^{\ast +}\rho^{+}$, and $M \to D^{\ast +}K^{\ast +}$. Partial widths of these processes are determined by strong couplings $g_1$, $g_2$, and $g_3$ of particles at vertices $ MD_{s}^{+}\pi^{+} $, $MD_{s}^{\ast +}\rho^{+}$, and $M D^{\ast +}K^{\ast +}$ , respectively. We calculate the couplings $g_i$ by employing the QCD light-cone sum rule approach and technical tools of the soft-meson approximation. Predictions obtained for the mass $m=(2924 \pm 107)~\mathrm{ MeV}$ and width $\Gamma=(123 \pm 25)~\mathrm{MeV}$ of the hadronic molecule $ M$ allow us to consider it as a possible candidate of the resonance $ T_{cs0}^{a}(2900)^{++}$.

Isospin-conserving hadronic decay of the D s1(2460) into D s π + π −

The internal structure of the charm-strange mesons and D s1(2460) are the subject of intensive studies. Their widths are small because they decay dominantly through isospin-breaking hadronic channels and . The D s1(2460) can also decay into the hadronic final states , conserving isospin. In that case there is, however, a strong suppression from phase space. We study the transition in the scenario that the D s1(2460) is a D * K hadronic molecule. The π π final state interaction is taken into account through dispersion relations. We find that the ratio of the partial widths of the obtained in the molecular picture is consistent with the existing experimental measurement. More interestingly, we demonstrate that the π + π − invariant mass distribution shows a double bump structure, which can be used to disentangle the hadronic molecular picture from the compact state picture for the D s1(2460)+. Predictions on the are also made.

Double-Strangeness Molecular-Type Pentaquarks from Coupled-Channel Dynamics.

The existence of pentaquarks with strangeness content zero and one are major discoveries of the latest years in hadron physics. Most of these states can be understood as hadronic molecules and were predicted prior to their discovery within a model based on unitarized meson-baryon amplitudes obtained from vector-meson exchange interactions. Contrary to earlier statements, we show this model to also predict the existence of pentaquarks with double strangeness, at about 4500 and 4600MeV, which are generated in a very specific and unique mechanism, via an attraction induced by a strong coupling between the two heaviest meson-baryon states.

Understanding the [formula omitted] and [formula omitted] charmonium(-like) states near 3.9 GeV

We propose that the X(3915) observed in the J/ψω channel is the same state as the χc2(3930), and the X(3960), observed in the Ds+Ds- channel, is an S-wave Ds+Ds- hadronic molecule. In addition, the JPC=0++ component in the B+→D+D-K+ assigned to the X(3915) in the current Review of Particle Physics has the same origin as the X(3960), which has a mass around 3.94 GeV. To check the proposal, the available data in the DD¯ and Ds+Ds- channels from both B decays and γγ fusion reaction are analyzed considering both the DD¯-DsD¯s-D*D¯*-Ds*D¯s* coupled channels with 0++ and a 2++ state introduced additionally. It is found that all the data in different processes can be simultaneously well reproduced, and the coupled-channel dynamics produce four hidden-charm scalar molecular states with masses around 3.73, 3.94, 3.99 and 4.23 GeV, respectively. The results may deepen our understanding of the spectrum of charmonia as well as of the interactions between charmed hadrons.

Identifying hadronic molecular states with a neural network

Neural networks are trained to judge whether or not an exotic state is a hadronic molecule of a given channel according its line-shapes. This method performs well in both trainings and validation tests. As applications, it is applied to study X(3872), X(4260) and Z_c(3900). The results show that Z_c(3900) should be regarded as a {bar{D}}^* D molecular state but X(3872) not. As for X(4260), it can not be a molecular state of chi _{c0}omega . Some discussions on X_1(2900) are also provided.

Charmonium, Bc and X(3872) Transport at the LHC

We deploy a kinetic-rate equation to evaluate the transport of J/ψ, ψ(2S), Bc and X (3872) in ultrarelativistic heavy-ion collisions and compare their production yields to experimental data from the Large Hadron Collider. The rate equation has two main transport parameters: the equilibrium limit and reaction rate for each state. The temperature-dependent equilibrium limits include charm- and bottom-quark fugacities based on their initial production. The reaction rates for charmonia, bottomonia and Bc rely on charm- and bottomquark masses and binding energies from a thermodynamic T-matrix approach. For the X (3872) particle, internal structure information is encoded in reaction rates and initial conditions in the hadronic phase via two different scenarios: a loosely bound hadronic molecule vs. a compact tetraquark.

Semi-inclusive electroproduction of hidden-charm and double-charm hadronic molecules

The semi-inclusive electroproduction of exotic hadrons, including the $T_{cc}$, $P_{cs}$, and hidden-charm baryon-antibaryon states, is explored under the assumption that they are $S$-wave hadronic molecules of a pair of charmed hadrons. We employ the Monte Carlo event generator Pythia to produce the hadron pairs and then bind them together to form hadronic molecules. With the use of such a production mechanism, the semi-inclusive electroproduction rates are estimated at the order-of-magnitude level. Our results indicate that a larger number of $P_{cs}$ states and $\Lambda_c\bar{\Lambda}_c$ molecules can be produced at the proposed electron-ion colliders in China (EicC) and in the US (EIC). The results also suggest that the $T_{cc}$ states and other hidden-charm baryon-antibaryon states can be searched for at EIC. Besides, the potential 24-GeV upgrade of the Continuous Beam Accelerator Facility at the Thomas Jefferson National Accelerator Facility can play an important role in the search for the hidden-charm tetraquark and pentaquark states due to its high luminosity.

Molecular interpretation of X(3960) as D_s^+ D_s^- state

We study D_s^+ D_s^- and D bar{D} states assuming that they are hadronic molecules with J^{PC}=0^{++} quantum number. We use two-point QCD sum rule formalism and extract the mass and decay constant values of these states. We take into account contributions of various quark, gluon, and mixed vacuum condensates up to dimension eight. The extracted mass and decay constant values of D bar{D} and D_s^+ D_s^- states read as M_{D bar{D}} = 3795^{+85}_{-82}~{textrm{MeV}} , f_{D bar{D}} = 1.70^{+0.33}_{-0.29} times 10^{-2} ~{textrm{GeV}}^5, and M_{D_s^+ D_s^-} = 3983^{+93}_{-88} ~{textrm{MeV}}, f_{D_s^+ D_s^-} = 2.52^{+0.64}_{-0.54} times 10^{-2} ~{textrm{GeV}}^5, respectively. The predicted mass of D_s^+ D_s^- state is in good agreement with the recent LHCb observation and supports quantum number and molecular picture assignments. A possible observation of D bar{D} state would help for establishing the lowest four-quark state in charmonium sector.