Hadronic Molecules Research Articles

Analysis of DD* and D¯(*)Ξcc(*) molecule by one boson exchange model based on heavy quark symmetry

Numerous exotic hadrons with heavy quarks have been reported in the experiments. In such states, symmetries of heavy quarks are considered to play a significant role. In particular, the superflavor symmetry, or also called the heavy quark antidiquark symmetry is one of the interesting symmetries, which links a quark Q to an antidiquark Q¯Q¯ having the same color representation as Q. In this paper, we study a D¯Ξcc molecular state as a superflavor partner of the doubly charmed tetraquark Tcc reported by LHCb recently. Tcc locating slightly below the DD* threshold is a candidate of the hadronic molecule. Thus by replacing the singly charmed meson D(*) with the doubly charmed baryon Ξcc(*), superflavor symmetry predicts the existence of the D¯(*)Ξcc(*) bound state. We employ the one boson exchange model respecting with the heavy quark spin symmetry where the parameter is obtained to reproduce the Tcc binding energy. We apply this model with superflavor symmetry to the D¯(*)Ξcc(*) molecule and predict a bound state with I(JP)=0(12−). If the pentaquark state corresponding to D¯(*)Ξcc(*) molecular state is observed in future experiments as predicted in this work, it is more likely that Tcc is a DD* molecular state. Published by the American Physical Society 2024

Heavy exotic hadrons near thresholds: [formula omitted] and its partners

Recent accelerator experiments have reported unexpected states known as exotic hadrons, whose properties cannot be explained by the conventional picture. In 2022, the LHCb collaboration reported the doubly charmed tetraquark Tcc+ which is a genuine exotic states whose minimal quark content is ccūd̄. We consider the Tcc state as a DD∗ hadronic molecule. The one meson exchange potentials are employed as for the hadron interactions, and a bound state properties is investigated. Furthermore, the superflavor symmetry predicts a new pentaquark state D̄Ξcc from Tcc, which is obtained by replacing a D(∗) meson with a Ξcc(∗) baryon. We also study a possible existence of the D̄Ξcc bound state, and its properties.

Zb states as the mixture of the molecular and diquark-anti-diquark components within the effective field theory

In this study, we reconsider the states Zb(10610) and Zb(10650) by investigating the presence of diquark-anti-diquark components as well as the hadronic molecule components in the framework of effective field theory. The different masses of pseudoscalar mesons such as π0, η8, and η0, as well as vector mesons like ρ0 and ω violate the Okubo-Zweig-Iizuka (OZI) rule that is well depicted under the [U(3)L⊗U(3)R]global⊗[U(3)V]local symmetry. To account for the contribution of intermediate bosons of heavy masses within the one-boson-exchange model, we introduce an exponential form factor instead of the commonly used monopole form factor in the past. By solving the coupled-channel Schrödinger equation with the Gaussian expansion method, our numerical results indicate that the Zb(10610) and Zb(10650) states can be explained as hadronic molecules slightly mixing with diquark-anti-diquark states. Published by the American Physical Society 2024

Predicting isovector charmonium-like states from X(3872) properties

Using chiral effective field theory, we predict that there must be isovector charmonium-like DD¯∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ D{\\overline{D}}^{\\ast } $$\\end{document} hadronic molecules with JPC = 1++ denoted as Wc1. The inputs are the properties of the X(3872), including its mass and the ratio of its branching fractions of decays into J/ψρ0 and J/ψω. The predicted states are virtual state poles of the scattering matrix, pointing at a molecular nature of the X(3872) as well as its spin partners. They should show up as either a mild cusp or dip at the DD¯∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ D{\\overline{D}}^{\\ast } $$\\end{document} thresholds, explaining why they are elusive in experiments. The so far negative observation also indicates that the X(3872) is either a bound state with non-vanishing binding energy or a virtual state, only in these cases the X(3872) signal dominates over that from the Wc10\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {W}_{c1}^0 $$\\end{document}. The pole positions are 3881.2−0.0+0.8\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {3881.2}_{-0.0}^{+0.8} $$\\end{document}−i1.6−0.9+0.7\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ i{1.6}_{-0.9}^{+0.7} $$\\end{document} MeV for Wc10\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {W}_{c1}^0 $$\\end{document} on the fourth Riemann sheet of the D0D¯∗0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {D}^0{\\overline{D}}^{\\ast 0} $$\\end{document}-D+D∗− coupled-channel system, and 3866.9−7.7+4.6\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {3866.9}_{-7.7}^{+4.6} $$\\end{document}− i(0.07 ± 0.01) MeV for Wc1±\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {W}_{c1}^{\\pm } $$\\end{document} on the second Riemann sheet of the DD¯∗±\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\left(D{\\overline{D}}^{\\ast}\\right)}^{\\pm } $$\\end{document} single-channel system. The findings imply that the peak in the J/ψπ+π− invariant mass distribution is not purely from the X(3872) but contains contributions from Wc10\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {W}_{c1}^0 $$\\end{document} predicted here. The states should have isovector heavy quark spin partners with JPC = 0++, 2++ and 1+−, with the last one corresponding to Zc. We suggest to search for the charged 0++, 1++ and 2++ states in J/ψπ±π0.

Revealing the mystery of the double charm tetraquark in pp collision

A novel approach is proposed to probe the nature of the double charm tetraquark through the prompt production asymmetry between Tc¯c¯-\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T_{\\bar{c}\\bar{c}}^-$$\\end{document} and Tcc+\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T_{cc}^+$$\\end{document} in pp collisions. When comparing two theoretical pictures, i.e. the compact tetraquark and hadronic molecular pictures, we find that the former one exhibits a significantly larger production asymmetry, enabling the unambiguous determination of the tetraquark’s internal structure. Additionally, distinctive differences in the transverse momentum and rapidity distributions of Tc¯c¯-\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T_{\\bar{c}\\bar{c}}^-$$\\end{document} and Tcc+\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T_{cc}^+$$\\end{document} cross sections emerge, particularly at pT≈2GeV\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$p_\ extrm{T}\\approx 2~\ extrm{GeV}$$\\end{document} and y≈±6\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$y\\approx \\pm 6$$\\end{document} at a center-of-mass energy of 14TeV\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$~\ extrm{TeV}$$\\end{document}. The insignificant asymmetry in hadronic molecular picture is because that hadronic molecules are produced in hadronic phase, where the phase space of their constituents needs to be taken into account rigorously. Our work can be extended to the exploration of other double heavy tetraquark candidates, offering a versatile approach to advance our understanding of exotic hadrons.

Role of hidden-color components in the tetraquark mixing model

Multiquarks can have two-hadron components and hidden-color components in their wave functions. The presence of two-hadron components in multiquarks introduces a potential source of confusion, particularly with respect to their resemblance to hadronic molecules. On the other hand, hidden-color components are essential for distinguishing between multiquarks and hadronic molecules. In this work, we study the hidden-color components in the wave functions of the tetraquark mixing model, a model that has been proposed as a suitable framework for describing the properties of two nonets in the JP=0+\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$J^{P}=0^{+}$$\\end{document} channel: the light nonet [a0(980)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$a_{0} (980)$$\\end{document}, K0∗(700)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$K_{0}^{*} (700)$$\\end{document}, f0(500)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f_{0} (500)$$\\end{document}, f0(980)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f_{0} (980)$$\\end{document}] and the heavy nonet [a0(1450)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$a_{0} (1450)$$\\end{document}, K0∗(1430)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$K_{0}^* (1430)$$\\end{document}, f0(1370)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f_{0} (1370)$$\\end{document}, f0(1500)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f_{0} (1500)$$\\end{document}]. Our analysis reveals a substantial presence of hidden-color components within the tetraquark wave functions. To elucidate the impact of hidden-color components on physical quantities, we conduct computations of the hyperfine masses, ⟨VCS⟩\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\langle V_{CS}\\rangle $$\\end{document}, for the two nonets, considering scenarios involving only the two-meson components and those incorporating the hidden-color components. We demonstrate that the hidden-color components constitute an important part of the hyperfine masses, such that the mass difference formula, ΔM≈Δ⟨VCS⟩\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Delta M\\approx \\Delta \\langle V_{CS}\\rangle $$\\end{document}, which has been successful for the two nonets, cannot be achieved without the hidden-color contributions. This can provide another evidence supporting the tetraquark nature of the two nonets.

Production of hidden-heavy and double-heavy hadronic molecules at the Z factory of CEPC

With a clean environment and high collision energy, the Circular Electron Positron Collider (CEPC) would be an excellent facility for heavy flavor physics. Using the Monte Carlo event generator ythia, we simulate the production of the charmed (bottom) hadron pairs in the electron-positron collisions at the Z factory of CEPC, and the inclusive production rates for typical candidates of the hidden/double-charm and hidden/double-bottom S-wave hadronic molecules are estimated at an order-of-magnitude level with the final state interactions after the hadron pair production. The predicted cross sections for the hidden-charm meson-meson molecules X(3872) and Zc(3900) are at pb level, which are about two to three orders of magnitude larger than the production cross sections for the double-charm meson-meson molecules Tcc and Tcc*, as the double-charmed ones require the production of two pairs of cc¯ from the Z boson decay. The production cross sections for the hidden-charm pentaquark states Pc and Pcs as meson-baryon molecules are a few to tens of fb, which are about one magnitude larger than those of the possible hidden-charm baryon-antibaryon and double-charm meson-baryon molecules. In the bottom sector, the production cross sections for the Zb states as B(*)B¯* molecules are about tens to hundreds of fb, indicating 106–107 events from a two-year operation of CEPC, and the expected events from the double-bottom molecules are about 2–5 orders of magnitude smaller than the Zb states. Our results shows great prospects of probing heavy exotic hadrons at CEPC. Published by the American Physical Society 2024

Production of singly charm pentaquarks from meson-baryon interactions in B -meson decay

In the paper, we discuss the possible interpretation of the JP=1/2− singly charm pentaquark as hadronic molecules. With the effective Lagrangian method, we further analyze the production properties of singly charm pentaquark from decays of B meson, including strong coupling constants and production branching ratios of the charm pentaquark. Our numerical results show that the branching ratio of production of pentaquark from B meson can reach to order of 10−6. Published by the American Physical Society 2024

Doubly heavy dibaryons as seen by string theory

We propose the stringy description of the system consisting of two heavy and four light quarks in the case of two light flavors of equal mass. As an application, we consider the three low-lying Born-Oppenheimer potentials as a function of the heavy quark separation. Our analysis shows that the ground state potential is described in terms of both hadroquarkonia and hadronic molecules. A connected string configuration makes the dominant contribution to the potential of an excited state at small separations, and for separations larger than 0.1 fm, it exhibits the diquark-diquark-diquark structure [Qq][Qq][qq]. For better understanding the quark organization inside the system, we introduce several critical separations related to the processes of string reconnection, breaking and junction annihilation. We also discuss the simplest string configurations including the five-string junctions and their implications for the system, in particular the emergence of composite quark objects different from diquarks and the process of junction fusion. Published by the American Physical Society 2024

Spectrum of the molecular pentaquarks

We investigate the mass spectrum of the molecular pentaquarks composed of a baryon and a meson. We establish the underlying relations among the near-threshold interactions of the molecular tetraquark and pentaquark systems. We find the existence of the molecule candidates in the ΣcD¯(*), DD*, and DD¯* systems indicates a substantial presence of the hadronic molecules in the heavy baryon plus heavy meson systems ( refers to the hadrons with the c and/or s quarks). We make an exhaustive prediction of the possible bound/virtual molecular states in the systems: Σc(*)D¯(*), Σc(*)D(*), Ξc(′,*)D¯(*), Ξc(′,*)D(*), Σc(*)K*, Σc(*)K¯*, Ξc(′,*)K*, Ξc(′,*)K¯*, Ξcc(*)D¯(*), Ξcc(*)D(*), Ξcc(*)K*, Ξcc(*)K¯*, Σ(*)D¯(*), Σ(*)D(*), Ξ(*)D¯(*), Ξ(*)D(*), Σ(*)K*, Σ(*)K¯*, Ξ(*)K*, Ξ(*)K¯*. Hunting for the predicted states in experiments will significantly deepen our understanding of the formation mechanism of the hadronic molecules, and shed light on the manifestation of flavor symmetry in the low-energy residual strong interactions. Published by the American Physical Society 2024

The effect of cutoff dependence on heavy quark spin symmetry partners

Hadron spectroscopy is revealed by observing heavy resonances. Among various explanations of the internal structure of these hadronic states, hadronic molecules play a unique role. For hadronic molecules, which are associated with meson–meson or meson–baryon interactions, the [Formula: see text] cutoff is a significant factor in determining the composite states’ binding energies and overall properties. The cutoff becomes important when it comes to the location of hadronic molecules’ masses because it influences the predictions. From this perspective, in the light of cutoff dependency, heavy quark spin partners of near-threshold the [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text] resonances, which are considered as hadronic molecules, are examined.

Hints of the JPC = 0−− and 1−−[formula omitted] molecules in the J/ψ → ϕηη′ decay

The primary objective of this study is to investigate hadronic molecules of K⁎K¯1(1270) using a one-boson-exchange model, which incorporates exchanges of vector and pseudoscalar mesons in the t-channel, as well as the pion exchange in the u-channel. Additionally, careful consideration is given to the three-body effects resulting from the on-shell pion originating from K1(1270)→K⁎π. Then the BESIII data of the J/ψ→ϕηη′ process is fitted using the K⁎K¯1(1270) scattering amplitude with JPC=0−− or 1−−. The analysis reveals that both the JPC=0−− and 1−− assumptions for K⁎K¯1(1270) scattering provide good descriptions of the data, with similar fit qualities. Notably, the parameters obtained from the best fits indicate the existence of K⁎K¯1(1270) bound states, denoted by ϕ(2100) and ϕ0(2100) for the 1−− and 0−− states, respectively. The current experimental data, including the η polar angular distribution, cannot distinguish which K⁎K¯1(1270) bound state contributes to the J/ψ→ϕηη′ process, or if both are involved. Therefore, we propose further explorations of this process, as well as other processes, in upcoming experiments with many more J/ψ events to disentangle the different possibilities.

Coupled-channel description of charmed heavy hadronic molecules within the meson-exchange model and its implication

Coupled-channel description of charmed heavy hadronic molecules within the meson-exchange model and its implication

Production of the X(4014) as the Spin-2 Partner of X(3872) in e + e − Collisions

In 2021, the Belle collaboration reported the first observation of a new structure in the ψ(2S)γ final state produced in the two-photon fusion process. In the hadronic molecule picture, this new structure can be associated with the shallow isoscalar D*D¯* bound state and as such is an excellent candidate for the spin-2 partner of the X(3872) with the quantum numbers J PC = 2++ conventionally named X 2. In this work we evaluate the electronic width of this new state and argue that its nature is sensitive to its total width, the experimental measurement currently available being unable to distinguish between different options. Our estimates demonstrate that the planned Super τ-Charm Facility offers a promising opportunity to search for and study this new state in the invariant mass distributions for the final states J/ψγ and ψ(2S)γ.

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.