Heavy hadronic molecules with pion exchange and quark core couplings: a guide for practitioners

Abstract

We discuss selected and important features of hadronic molecules as one of promising forms of exotic hadrons near thresholds. Using examples of $D{\bar{D}}^{\ast }$ systems such as $X(3872)$ and $Z_c$, emphasis is put on the roles of the one pion exchange interaction between them and their coupling to intrinsic quark states. Thus hadronic molecules emerge as admixtures of the dominant long-range hadron structure and short-range quark structure. For the pion exchange interaction, properties of the tensor force are analyzed in detail. More coupled channels supply more attractions, and heavier constituents suppress kinetic energies, providing more chances to form hadronic molecules of heavy hadrons. Throughout this article, we show details of basic ideas and methods.

75 pages, 21 figures, minor revisions, version published in J. Phys. G: Nucl. Part. Phys

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• Observation of a new charged charmoniumlike state in B -> J/psi K pi decays
• Observation of a Near-threshold $D^0{\bar{D}}^0{\pi }^0$ Enhancement in $B\to D^0{\bar{D}}^0{\pi }^{0}K$ Decay
• Analysis of the X(3872), Z_c(3900) and Z_c(3885) as axial-vector tetraquark states with QCD sum rules
• Suppressed decay into open charm for the Y(4260) being an hybrid
• Study of $P_c(4457)$, $P_c(4440)$, and $P_c(4312)$ in a quasipotential Bethe-Salpeter equation approach
• Heavy quark spin symmetric molecular states from ${\bar{D}}^{(\ast )}{\Sigma }_c^{(\ast )}$ and other coupled channels in the light of the recent LHCb pentaquarks
• Observation of X(3872) production in pp collisions at sqrt(s)= 7 TeV
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• Evidence for exotic hadron contributions to ${\Lambda }_b^0\to J/\psi p{\pi }^{-}$ decays
• Estimate for the X(3872) to gamma J/psi decay width
• Study of Resonances in Exclusive B Decays to Dbar(*)D(*)K
• Measurement of the X(3872) production cross section via decays to J/psi pi pi in pp collisions at sqrt(s) = 7 TeV
• Observation of $X(3872)\to J/\psi \gamma$ and search for $X(3872)\to {\psi }^{\prime }\gamma$ in B decays
• Evidence for X(3872) from DD* scattering on the lattice
• Dalitz analysis of B --> K pi psi' decays and the Z(4430)+
• Possible assignments of the $X(3872)$, $Z_c(3900)$ and $Z_b(10610)$ as axial-vector molecular states
• Line Shapes of the X(3872)
• Production of the X(3872) in charmonia radiative decays
• $Z_b$ and $Z_c$ Exotic States as Coupled Channel Cusps
• Search for B+ --> X(3872) K+, X(3872) --> J/psi gamma
• A J^PG=1++ Charged Resonance in the Y(4260) to pi+pi- J/psi Decay?
• Regularization, renormalization and "peratization" in effective field theory for two nucleons
• Interpretation of the X(3872) as a charmonium state plus an extra component due to the coupling to the meson-meson continuum
• Observation of $Z_c(3900{)}^0$ in $e^{+}{e}^{-}\to {\pi }^0{\pi }^{0}J/\psi$
• Searching for observable effects induced by anomalous triangle singularities
• Fate of the Tetraquark Candidate Zc(3900) from Lattice QCD
• Could the near-threshold $XYZ$ states be simply kinematic effects?
• Comprehensive analysis of the wave function of a hadronic resonance and its compositeness
• Study of the $B\to X(3872)(\to D^{\ast 0}{\bar{D}}^0)K$ decay
• Prediction of an $I=1$ $D{\bar{D}}^{\ast }$ state and relationship to the claimed $Z_c(3900)$, $Z_c(3885)$
• How the Z_c(3900) Reveals the Spectra of Quarkonium Hybrid and Tetraquark Mesons
• X(3872) as a molecular DD* state in a potential model
• QCD Sum Rules for the X(3872) as a mixed molecule-charmoniun state
• Z_c(3900) - what is inside?
• Quantum numbers of the $X(3872)$ state and orbital angular momentum in its ${\rho }^{0}J\psi$ decay
• The $Z_b(10610)$ and $Z_b(10650)$ as axial-vector tetraquark states in the QCD sum rules
• A study of B->X(3872) K, with X(3872)->J/Psi pi+ pi-
• Reproducing the $Z_c(3900)$ structure through the initial-single-pion-emission mechanism
• Tetraquark Interpretation of the Charged Bottomonium-like states Z_b^+-(10610) and Z_b^+-(10650) and Implications
• Precision Measurement of the X(3872) Mass in J/psi pi+ pi- Decays
• Is Z^+(4430) a loosely bound molecular state?
• X(3872) and Y(4140) using diquark-antidiquark operators with lattice QCD
• Exploring the threshold behavior and implications on the nature of Y(4260) and $Z_c(3900)$
• Hadronic Decays of the X(3872) to chi_{cJ} in Effective Field Theory
• Determination of spin and parity of the $Z_c(3900)$
• Confirming the molecular nature of the $Z_b(10610)$ and the $Z_b(10650)$
• Quark structure of the $X(3872)$ and ${\chi }_b(3P)$ resonances
• Dynamical origin and the pole structure of X(3872)
• Search for a Charged Partner of the X(3872) in the B Meson Decay B --> X- K, X- --> J/psi pi- pi0
• Roles of the tensor and pairing correlations on the halo formation in 11Li
• $Z_c(3900)$: what has been really seen?
• Isospin breaking, coupled-channel effects, and X(3872)
• A New Hadron Spectroscopy
• Study of the $Z_c^{+}$ channel using lattice QCD
• Exotic mesons with double charm and bottom flavor
• Study of $e^{+}{e}^{-}\to \gamma \omega J/\psi$ and Observation of $X(3872)\to \omega J/\psi$
• Strong decays of molecular states Zc(+) and Zc'(+)
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• Different pole structures in line shapes of the $X(3872)$
• Improved QCD sum rule study of $Z_c(3900)$ as a $\bar{D}{D}^{\ast }$ molecular state
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• Employing spin symmetry to disentangle different models for the XYZ states
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• Exotic baryons from a heavy meson and a nucleon -- Negative parity states --
• Structure of charmed baryons studied by pionic decays
• Exclusive Production of the X(3872) in B Meson Decay
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• Are two nucleons bound in lattice QCD for heavy quark masses? -- Consistency check with Lüscher's finite volume formula --
• Amplitude analysis of e+e- => Y(nS)pi+pi- at sqrt(s)=10.865 GeV
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• Strong $Z_c^{+}(3900)\to J/\psi {\pi }^{+};{\eta }_c{\rho }^{+}$ decays in QCD
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• $Z_c(3900)$ as a resonance from the $D{\bar{D}}^{\ast }$ interaction
• The Effects of Charged Charm Mesons on the Line Shapes of the X(3872)
• QCD sum rules study of the meson Z^+(4430)
• Quark model description of the tetraquark state X(3872) in a relativistic constituent quark model with infrared confinement
• Dynamics of Hadronic Molecule in One-Boson Exchange Approach and Possible Heavy Flavor Molecules
• Ambiversion of X(3872)
• Interpreting $Z_c(3900)$ and $Z_c(4025)/Z_c(4020)$ as charged tetraquark states
• Exotic mesons with hidden bottom near thresholds
• Search for Z_c^+(3900) in the 1^+- channel on the lattice
• First Observation of the Zb0(10610) in a Dalitz Analysis of Y(5S) -> Y(nS) pi0 pi0
• Spectroscopy of the hidden-charm $[qc][\bar{q}\bar{c}]$ and $[sc][\bar{s}\bar{c}]$ tetraquarks
• Decays of Zb(+) and Zb'(+) as hadronic molecules
• Search for tetraquark candidate Z(4430) in meson photoproduction
• Hidden-charm and bottom meson-baryon molecules coupled with five-quark states
• Pentaquark states in a chiral potential
• Low-energy Scattering of $(D{\bar{D}}^{\ast }{)}^{\pm }$ System And the Resonance-like Structure $Z_c(3900)$
• Electromagnetic Structure of the Z_c(3900)
• Study of the $B{\bar{B}}^{\ast }/D{\bar{D}}^{\ast }$ bound states in a Bethe-Salpeter approach
• The line shapes of the $Z_b(10610)$ and $Z_b(10650)$ in the elastic and inelastic channels revisited
• $X(3872)\to J/\psi {\pi }^{+}{\pi }^{-}$ and $X(3872)\to J/\psi {\pi }^{+}{\pi }^{-}{\pi }^0$ decay widths from QCD sum rules
• Heavy molecules and one-$\sigma /\omega$-exchange model
• On $X(3872)$ production in high energy heavy ion collisions
• X(3872) and its production at hadron colliders
• Study of $B{\bar{B}}^{\ast }$ and $B^{\ast }{\bar{B}}^{\ast }$ interactions in $I=1$ and relationship to the $Z_b(10610)$, $Z_b(10650)$ states
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• X(3872) is not a true molecule
• The Spin-orbit force, recoil corrections and possible $B{\bar{B}}^{\ast }$ and $D{\bar{D}}^{\ast }$ molecular states
• Treating $Z_c(3900)$ and $Z(4430)$ as the ground-state and first radially excited tetraquarks
• Hadronic effects on the X(3872) meson abundance in heavy ion collisions
• X(3872) as a hybrid state of the charmonium and the hadronic molecule
• General considerations on the nature of $Z_b(10610)$ and $Z_b(10650)$ from their pole positions
• Pionic transitions from X(3872) to chi_{cJ}
• $Z_b/Z_b^{\prime }\to {\rm Y}\pi$ and $h_b\pi$ decays in intermediate meson loops model
• Detecting the long-distance structure of the X(3872)
• Radiative Decays X(3872) -> psi(2S)+gamma and psi(4040) -> X(3872)+gamma in Effective Field Theory
• Zc(4200)+ decay width as a charmonium-like tetraquark state
• QCD Sum-Rule Interpretation of X(3872) with $J^{PC}=1^{++}$ Mixtures of Hybrid Charmonium and $\bar{D}{D}^{\ast }$ Molecular Currents
• Systematic studies of charmonium-, bottomonium-, and $B_c$-like tetraquark states
• Radiative E1 decays of X(3872)
• Energy scan of the $e^{+}{e}^{-}\to h_b(nP){\pi }^{+}{\pi }^{-}$ $(n=1,2)$ cross sections and evidence for ${\rm Y}(11020)$ decays into charged bottomonium-like states
• Remarks on the study of the X(3872) from Effective Field Theory with Pion-Exchange Interaction
• Quark mass dependence of the X(3872) binding energy
• Four-quark structure of Zc(3900), Z(4430) and Xb(5568) states
• Charged charmonium-like Z+(4430) from rescattering in conventional B decays
• Using Line Shapes to Discriminate between Binding Mechanisms for the X(3872)
• Hidden-Charm Tetraquarks and Charged Zc States
• The decay width of the $Z_c(3900)$ as an axialvector tetraquark state in solid quark-hadron duality
• Observation of the decay $X(3872)\to {\pi }^0{\chi }_{c1}(1P)$
• The meson $Z^{+}(4430)$ as a tetraquark state
• Galilean-Invariant XEFT
• Could $Z_c(3900)$ be a $I^G{J}^P=1^{+}{1}^{+}$ $D^{\ast }\bar{D}$ molecular state?
• Hadronic Loops versus Factorization in EFT calculations of $X(3872)\to {\chi }_{cJ}{\pi }^0$
• Note on X(3872) production at hadron colliders and its molecular structure
• The ratio of decay widths of X(3872) to ${\psi }^{\prime }\gamma$ and $J/\psi \gamma$ as a test of the X(3872) dynamical structure
• Exotic baryons from a heavy meson and a nucleon - Positive parity states -
• Radiative decays of the neutral $Z_c(3900)$
• A Refined Analysis on the $X(3872)$ Resonance
• Selected strong decay modes of Y(4260)
• Threshold corrections of ${\chi }_{\mathrm{c}}(2P)$ and ${\chi }_{\mathrm{b}}(3P)$ states and $J/\psi \rho$ and $J/\psi \omega$ transitions of the $X(3872)$ in a coupled-channel model
• Hidden-charm and radiative decays of the Z(4430) as a hadronic D_1 \bar{D^\ast} bound state
• Spin partners of the $Z_b(10610)$ and $Z_b(10650)$ revisited
• Consistency between Lüscher's finite volume method and HAL QCD method for two-baryon systems in lattice QCD
• Delicate interplay between the D0-D*0, rho0-J/psi, and omega-J/psi channels in the X(3872) resonance
• Low-energy $D^{\ast +}{D}_1^0$ Scattering and the Resonance-like Structure $Z^{+}(4430)$
• Lattice study on ${\eta }_{c2}$ and X(3872)
• Isospin properties of the X state near the D {\bar D}^{*} threshold
• The Tetraquark Candidate Zc(3900) from Dynamical Lattice QCD Simulations
• The decay of the X(3872) into χ_{cJ} and the Operator Product Expansion in XEFT
• $Z_c(3900)$ as a $D{\bar{D}}^{\ast }$ molecule from the pole counting rule
• $X(3872)\to D\bar{D}\gamma$ decays and the structure of X(3872)
• Radiative decay of the X(3872) as a mixed molecule-charmonium state in QCD Sum Rules
• $Z_c(3900)/Z_c(3885)$ as a virtual state from $\pi J/\psi -{\bar{D}}^{\ast }D$ interaction
• X(3872), I^G(J^{PC})=0^+(1^{++}), as the χ_{1c}(2P) charmonium
• A new tetra-quark interpretation of X(3872)
• Model-independent observation of exotic contributions to $B^0\to J/\psi K^{+}{\pi }^{-}$ decays
• Light quark mass dependence of the X(3872) in XEFT
• Magnetic and quadrupole moments of the $Z_c(3900)$
• Systematic study of $Z_c^{+}$ family from quark model's perspective
• Radiative and dilepton decays of the hadronic molecule Zc(3900)+
• What do the radiative decays of X(3872) tell us
• Resolving the puzzling decay patterns of charged $Z_c$ and $Z_b$ states
• ${\mathrm{Z}}^{+}(4430)$ and Analogous Heavy Flavor States
• Decays and productions via bottomonium for Z_b resonances and other B anti-B molecules
• Line Shapes of the Z(4430)
• $Z_c(3900)$: Confronting theory and lattice simulations
• Hidden charmed states and multibody color flux-tube dynamics
• QCD Sum Rules for the production of the X(3872) as a mixed molecule-charmonium state in B meson decay
• The strong decay patterns of $Z_c$ and $Z_b$ states in the relativized quark model
• Direct X(3872) production in e+e- collisions
• Light Quark Spin Symmetry in $Z_b$ Resonances?
• $Z_b(10610)$ and $Z_b^{\prime }(10650)$ decays in a covariant quark model
• Z_b(10610) and Z_b(10650) decays to bottomonium plus pion
• Systematic Power Counting in Cutoff Effective Field Theories for Nucleon-Nucleon Interactions and the Equivalence With PDS
• Enhanced mixing of partial waves near threshold for heavy meson pairs and properties of $Z_b(10610)$ and $Z_b(10650)$ resonances
• omega-rho^0 mixing as a possible origin of the hypothetical isospin non-conservation in the X(3872) --> pi^+ pi^- J/psi decay
• Unquenched quark-model calculation of X(3872) electromagnetic decays
• Comment on `Note on X(3872) production at hadron colliders and its molecular structure'
• Photoproduction of the charged charmoniumlike $Z_c^{+}(4200)$
• Novel charged charmoniumlike structures in the hidden-charm dipion decays of Y(4360)
• Exotic dibaryons with a heavy antiquark
• Using the decay ψ(4160) -> X(3872) γ to probe the molecular content of the X(3872)
• The magnetic moment of the $Z_c(3900)$ as an axialvector tetraquark state with QCD sum rules
• Elementarity of composite systems
• Comprehending Isospin breaking effects of $X(3872)$ in a Friedrichs-model-like scheme
• Hadronic molecules for charmed and bottom baryons near thresholds
• Decay of Theta+ in a quark model
• Threshold Effects and the Line Shape of the X(3872) in Effective Field Theory
• Spectroscopic parameters and decays of the resonance $Z_b(10610)$
• Testing the tetraquark structure for the $X$ resonances in low-lying region
• $Z_c(4430)$ and $Z_c(4200)$ as triangle singularities
• $Z_c(4100)$ and $Z_c(4200)$ as hadrocharmonium
• Decipher the short-distance component of $X(3872)$ in $B_c$ decays
• Triangle singularities in ${\bar{B}}^0\to {\chi }_{c1}{K}^{-}{\pi }^{+}$ relevant to $Z_1(4050)$ and $Z_2(4250)$
• Strategies for an accurate determination of the X(3872) energy from QCD lattice simulations
• Precision Measurement of the Mass of the $D^{\ast 0}$ Meson and the Binding Energy of the $X(3872)$ Meson as a $D^0\overline{D^{\ast 0}}$ Molecule
• An explanation why the Theta+ is seen in some experiments and not in others
• A possible explanation why the Theta+ is seen in some experiments and not in others
• The $c\bar{c}$ interaction above threshold and the radiative decay $X(3872)\to J/\psi \gamma$
• The two-body open charm decays of $Z^{+}(4430)$
• Distinguishing cusp effects and near-threshold-pole effects
• Is the Z^+(4430) a radially excited state of D_s?
• Production of $Z_c(3900$) and $Z_c(4020)$ in $B_c$ decay
• The nature of $Z_b$ states from a combined analysis of ${\rm Y}(5S)\to h_b(mP){\pi }^{+}{\pi }^{-}$ and ${\rm Y}(5S)\to B^{(\ast )}{\bar{B}}^{(\ast )}\pi$
• Radiative and $\rho$ transitions between heavy quarkonium and isovector four-quark states
• X(3872) as a molecular $D{\bar{D}}^{\ast }$ state in the Bethe-Salpeter equation approach
• Strong and radiative decays of X(3872) as a hadronic molecule with a negative parity
• Lambda(1405) as a Resonance in the Baryon-Meson Scattering Coupled to the q^3 State in a Quark Model
• Determination of the structure of the $X(3872)$ in $\bar{p}A$ collisions
• Kaon-Nucleon systems and their interactions in the Skyrme model
• Composite and elementary nature of a resonance in the sigma model
• Radially excited axial mesons and the enigmatic $Z_c$ and $Z_b$ in a coupled-channel model
• Kaon-Nucleon scattering states and potentials in the Skyrme model
• Pion-induced production of the $Z_c(3900)$ off a nuclear target
• A mixing model for bottomoniumlike $Z_b$ resonances
• Isospin analysis of $B\to D^{\ast }\bar{D}K$ and the absence of the $Z_c(3900)$ in $B$ decays
• Radiative Decays of the $X(3872)$ in the Charmonium-Molecule Hybrid Picture
• Are there near-threshold Coulomb-like Baryonia?

Cited by in corpus (59)

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• Chiral perturbation theory for heavy hadrons and chiral effective field theory for heavy hadronic molecules
• Coupled-channel approach to $T_{cc}^{+}$ including three-body effects
• Doubly Charmed Tetraquark $T_{cc}^{+}$ from Lattice QCD near Physical Point
• Selected Science Opportunities for the EicC
• Stable double-heavy tetraquarks: spectrum and structure
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• Coupled-channel effects of the ${\Sigma }_c^{(\ast )}{\bar{D}}^{(\ast )}$-${\Lambda }_c(2595)\bar{D}$ system and molecular nature of the $P_c$ pentaquark states from one-boson exchange model
• The production of doubly charmed exotic hadrons in heavy ion collisions
• Solving the left-hand cut problem in lattice QCD: $T_{cc}(3875{)}^{+}$ from finite volume energy levels
• Towards the quark mass dependence of $T_{cc}^{+}$ from lattice QCD
• X(3872) Production in Relativistic Heavy-Ion Collisions
• Doubly Heavy Tetraquark Resonant States
• Relativistic corrections to decays of heavy baryons in the quark model
• Exploring the electromagnetic properties of the ${\Xi }_c^{(\prime ,\ast )}{\bar{D}}_s^{\ast }$ and ${\Omega }_c^{(\ast )}{\bar{D}}_s^{\ast }$ molecular states
• The lineshape of the compact fully heavy tetraquark
• Productions of $X(3872)$, $Z_c(3900)$, $X_2(4013)$, and $Z_c(4020)$ in $B_{(s)}$ decays offer strong clues on their molecular nature
• Classifying Pole of Amplitude Using Deep Neural Network
• New insight into the exotic states strongly coupled with the $D{\bar{D}}^{\ast }$ from the $T_{cc}^{+}$
• Anticharmed strange pentaquarks from the one-boson-exchange model
• Observation of $e^{+}{e}^{-}\to \omega {\chi }_{bJ}(1P)$ and search for $X_b\to \omega {\rm Y}(1S)$ at $\sqrt{s}$ near 10.75 GeV
• Analysis of $T_{cc}$ and $T_{bb}$ based on the hadronic molecular model and their spin multiplets
• Radiative decays and magnetic moments of the predicted $B_c$-like molecules
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• On nuclear coalescence in small interacting systems
• Classifying near-threshold enhancement using deep neural network
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• $\sigma$ exchange in the one-boson exchange model involving the ground state octet baryons
• On the structure in the $\Lambda N$ cross section at the $\Sigma N$ threshold
• Heavy baryons in holographic QCD with higher dimensional degrees of freedom
• Study of exotic hadrons with machine learning
• Binding of the three-hadron $D{D}^{\ast }K$ system from the lattice effective field theory
• Open charm and bottom meson-nucleon potentials à la nuclear force
• Discover the GellMann-Okubo formula with machine learning
• Probing exotic $J^{PC}$ resonances from deeply bound charmoniumlike molecules: Insights for identifying exotic hadrons
• Investigating the Isospin Property of $T_{cc}^{+}$ from its Dalitz Plot Distribution
• Molecular states in $D_s^{(\ast )+}{\Xi }_c^{{(}^{\prime },\ast )}$ systems
• Tetraquarks in the Born-Oppenheimer approximation
• Hunting for $X_b$ via hidden bottomonium decays $X_b\to \pi \pi {\chi }_{bJ}$
• Interpretation of near-threshold peaks using the method of independent S-matrix poles
• ${\bar{B}}^0\to {\bar{K}}^{(\ast )0}X$, $B^{-}\to K^{(\ast )-}X$, ${\bar{B}}_s^0\to \eta ({\eta }^{\prime },\varphi )X$ from the $X(3872)$ molecular perspective
• Determination of the spectroscopic parameters of beauty-partners of $T_{cc}$ from QCD
• Probing the structure of ${\chi }_{c1}(3872)$ with photon transition form factors
• Mass and decay width of $T_{ccs}$ from symmetries
• Towards modeling the short-range interactions of hidden/open charm pentaquark molecular states
• Role of the short-range dynamics in the formation of $D^{(\ast )}{\bar{D}}^{(\ast )}/B^{(\ast )}{\bar{B}}^{(\ast )}$ hadronic molecules
• Hidden-Charm Tetraquarks in a Mixture Model: Coupled-Channel Analysis with $c\bar{c}$ and Hadronic Molecular Components
• X(3872) revisited: the roles of OPEP and the quark degrees of freedom
• $Z_c(3900)$ in a hadronic molecule and a triangle singularity approach at finite temperature
• Hints of the $J^{PC}=0^{--}$ and $1^{--}$ $K^{\ast }{\bar{K}}_1(1270)$ Molecules in the $J/\psi \to \varphi \eta {\eta }^{\prime }$ Decay
• Implementation of chiral two-nucleon forces to nuclear many-body methods with Gaussian-wave packets
• $D{\bar{D}}^{\ast }$-$\pi J/\psi$ scatterings of coupled channels for $Z_c(3900)$ channel
• First measurement of the Q^2 distribution of X(3915) single-tag two-photon production
• Exotic hadrons associated with $b$-quark
• The impact of quark many-body effects on exotic hadrons
• Role of the short-range dynamics in simultaneous interpretation of $P_{cs}$ pentaqurks via ${\Xi }_c^{(\prime ,\ast )}{\bar{D}}^{(\ast )}$ molecules
• P-wave $c\bar{c}$ meson contributions in exotic hadrons
• The possible $K{\bar{K}}^{\ast }$ and $D{\bar{D}}^{\ast }$ bound and resonance states by solving Schrodinger equation