Pentaquark and Tetraquark states

Abstract

The past seventeen years have witnessed tremendous progress on the experimental and theoretical explorations of the multiquark states. The hidden-charm and hidden-bottom multiquark systems were reviewed extensively in [Phys. Rept. 639 (2016) 1-121]. In this article, we shall update the experimental and theoretical efforts on the hidden heavy flavor multiquark systems in the past three years. Especially the LHCb collaboration not only confirmed the existence of the hidden-charm pentaquarks but also provided strong evidence of the molecular picture. Besides the well-known $XYZ$ and $P_c$ states, we shall discuss more interesting tetraquark and pentaquark systems either with one, two, three or even four heavy quarks. Some very intriguing states include the fully heavy exotic tetraquark states $QQ\bar{Q}\bar{Q}$ and doubly heavy tetraquark states $QQ\bar{q}\bar{q}$, where $Q$ is a heavy quark. The $QQ\bar{Q}\bar{Q}$ states may be produced at LHC while the $QQ\bar{q}\bar{q}$ system may be searched for at BelleII and LHCb. Moreover, we shall pay special attention to various theoretical schemes. We shall emphasize the model-independent predictions of various models which are truly/closely related to Quantum Chromodynamics (QCD). There have also accumulated many lattice QCD simulations through multiple channel scattering on the lattice in recent years, which provide deep insights into the underlying structure/dynamics of the $XYZ$ states. In terms of the recent $P_c$ states, the lattice simulations of the charmed baryon and anti-charmed meson scattering are badly needed. We shall also discuss some important states which may be searched for at BESIII, BelleII and LHCb in the coming years.

Long review invited by Progress in Particle and Nuclear Physics, 153 pages. References added, comments and suggestions welcome

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• QCD Sum Rule Study of the Masses of Light Tetraquark Scalar Mesons
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• Quantum chromodynamics quark benzene
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• Investigation of $cs\bar{c}\bar{s}$ tetraquark in the chiral quark model
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• Static-light meson-meson potentials
• The Strong Decays of X(3940) and X(4160)
• Predicting the existence of a 2.9 GeV $D{f}_0(980)$ molecular state
• Branching fractions of $B_{(c)}$ decays involving $J/\psi$ and $X(3872)$
• Light vector meson and heavy baryon strong interaction
• Exotic hadron production in quark combination model
• Radiative and pionic transitions $Z_c(4020{)}^0\to X(3872)\gamma$ and $Z_c(4020{)}^{\pm }\to X(3872){\pi }^{\pm }$
• Hidden charm pentaquark and $\Lambda (1405)$ in the ${\Lambda }_b^0\to {\eta }_c{K}^{-}p(\pi \Sigma )$ reaction
• $Qq\bar{Q}{\bar{q}}^{\prime }$ States in Chiral SU(3) Quark Model
• Spectroscopy and production of doubly charmed tetraquarks
• Decays of Pentaquarks in Hadrocharmonium and Molecular Pictures
• Bi-local baryon interpolating fields with two flavours
• $J/\psi N$ interactions revisited and ${\Lambda }_b^0\to J/\psi K^{-}({\pi }^{-})p$ decays
• The "Closed" Chiral Symmetry and Its Application to Tetraquark
• The possible candidates of tetraquark : $Z_b(10610)$ and $Z_b(10650)$
• A lattice study of interaction mechanisms in a heavy-light meson-meson system
• Production of the charmoniumlike state $Y(4220)$ through the $p\bar{p}\to Y(4220){\pi }^0$ reaction
• Baryon Tri-local Interpolating Fields
• A mixing model for bottomoniumlike $Z_b$ resonances
• Chiral partner structure of heavy baryons from the bound state approach with hidden local symmetry
• The production of neutral $N^{\ast }(11052)$ resonance with hidden beauty from ${\pi }^{-}p$ scattering
• Faddeev fixed center approximation to $\pi \bar{K}{K}^{\ast }$ system and the ${\pi }_1(1600)$
• Hidden-charm pentaquark formation in antiproton - deuterium collisions
• Isospin analysis of $B\to D^{\ast }\bar{D}K$ and the absence of the $Z_c(3900)$ in $B$ decays
• Spin-1 charmonium-like states in QCD sum rule
• Pentaquarks in semileptonic ${\Lambda }_b$ decays
• An Estimate of the Inclusive Branching Ratio to ${\bar{B}}_c$ in ${\Xi }_{bbq}$ Decay
• Scalar Tetraquark Currents With Application to the QCD Sum Rule
• The Possible Heavy Tetraquarks $qQ\bar{q}\bar{Q}$, $qq\bar{Q}\bar{Q}$ and $qQ\bar{Q}\bar{Q}$
• A study of meson-meson potential in the chiral quark model
• The axial charges of the hidden-charm pentaquark states
• Dynamical study of $S$-wave $\bar{Q}Q\bar{q}q$ system
• Unquenching the quark model in a non-perturbative scheme
• Light Scalar Mesons in the QCD Sum Rule

Cited by in corpus (189)

• A survey of heavy-heavy hadronic molecules
• Interpretation of the LHCb $P_c$ States as Hadronic Molecules and Hints of a Narrow $P_c(4380)$
• Anatomy of the newly observed hidden-charm pentaquark states: $P_c(4312)$, $P_c(4440)$ and $P_c(4457)$
• Explaining the Many Threshold Structures in the Heavy-Quark Hadron Spectrum
• Spectrum of the strange hidden charm molecular pentaquarks in chiral effective field theory
• Heavy tetraquarks in the relativistic quark model
• Probing the long-range structure of the $T_{cc}^{+}$ with the strong and electromagnetic decays
• Hidden-charm and hidden-bottom molecular pentaquarks in chiral perturbation theory
• Masses of doubly heavy tetraquarks $T_{Q{Q}^{\prime }}$ in a relativized quark model
• $Z_{cs}(3985{)}^{-}$ as the $U$-spin partner of $Z_c(3900{)}^{-}$ and implication of other states in the ${\text{SU(3)}}_F$ symmetry and heavy quark symmetry
• Can the newly $P_{cs}(4459)$ be a strange hidden-charm ${\Xi }_c{\bar{D}}^{\ast }$ molecular pentaquarks?
• Can discovery of hidden charm strange pentaquark states help determine the spins of $P_c(4440)$ and $P_c(4457)$?
• Magnetic dipole moments of the hidden-charm pentaquark states: $P_c(4440)$, $P_c(4457)$ and $P_{cs}(4459)$
• Study of the $DK$ interaction with femtoscopic correlation functions
• Structure and decays of hidden heavy pentaquarks
• Magnetic moments and transition magnetic moments of $P_c$ and $P_{cs}$ states
• Spectrum of the Hidden-Bottom and the Hidden-Charm/Strange Exotics in the Dynamical Diquark Model
• Hidden charm tetraquark states in a diquark model
• Masses and radiative decay widths of S- and P-wave singly-, doubly- and triply-heavy charm and bottom baryons
• What can we learn from the electromagnetic properties of hidden-charm molecular pentaquarks with single strangeness?
• Strong decays of the newly $P_{cs}(4459)$ as a strange hidden-charm ${\Xi }_c{\bar{D}}^{\ast }$ molecule
• Decoding the nature of $Z_{cs}(3985)$ and establishing the spectrum of charged heavy quarkoniumlike states in chiral effective field theory
• Emergence of molecular-type characteristic spectrum of hidden-charm pentaquark with strangeness embodied in the $P_{\psi s}^{\Lambda }(4338)$ and $P_{cs}(4459)$
• Prediction of hidden-charm pentaquarks with double strangeness
• $S$-wave fully charmed tetraquark resonant states
• Fully heavy pentaquarks
• Perfect $D{D}^{\ast }$ molecular prediction matching the $T_{cc}$ observation at LHCb
• How to reveal the nature of three or more pentaquark states?
• Hidden-charm pentaquarks with triple strangeness due to the ${\Omega }_c^{(\ast )}{\bar{D}}_s^{(\ast )}$ interactions
• Fully-heavy tetraquark production by $\gamma \gamma$ interactions in hadronic collisions at the LHC
• Hidden charm pentaquark states in a diquark model
• Benchmark calculations of fully heavy compact and molecular tetraquark states
• One Born$-$Oppenheimer Effective Theory to rule them all: hybrids, tetraquarks, pentaquarks, doubly heavy baryons and quarkonium
• Are the $Y$ states around 4.6 GeV from $e^{+}{e}^{-}$ annihilation higher charmonia?
• A combined analysis of the $Z_c(3900)$ and the $Z_{cs}(3985)$ exotic states
• Mass behavior of hidden-charm pentaquarks with open-strange inspired by these established $P_c$ molecular states
• Excited $K$ meson, $K_c(4180)$, with hidden charm as a $D\bar{D}K$ bound state
• All-charm tetraquark in front form dynamics
• $QQ\bar{s}\bar{s}$ tetraquarks in the chiral quark model
• The Spectrum of $P$-Wave Hidden-Charm Exotic Mesons in the Diquark Model
• Spectrum of $cc\bar{b}\bar{b}$, $bc\bar{c}\bar{c}$, and $bc\bar{b}\bar{b}$ Tetraquark States in the Dynamical Diquark Model
• Photoproduction of strange hidden-charm and hidden-bottom states
• Searching for a $D\bar{D}$ bound state with the $\psi (3770)\to \gamma D^0{\bar{D}}^0$ decay
• Fully-heavy structures in the invariant mass spectrum of $J/\psi \psi (3686)$, $J/\psi \psi (3770)$, $\psi (3686)\psi (3686)$, and $J/\psi {\rm Y}(1S)$ at hadron colliders
• Spectroscopic survey of higher-lying states of $B_c$ meson family
• Heavy baryon spectrum with chiral multiplets of scalar and vector diquarks
• The resonances $X(4140)$, $X(4160)$, and $P_{cs}(4459)$ in the decay of ${\Lambda }_b\to J/\psi \Lambda \varphi$
• Decay behaviors of the fully-bottom and fully-charm tetraquark states
• Where are $3P$ and higher $P-$wave states in the charmonium family?
• Magnetic moments of the doubly charged axial-vector $T_{cc}^{++}$ states
• Probing the electromagnetic properties of the ${\Sigma }_c^{(\ast )}{D}^{(\ast )}$-type doubly charmed molecular pentaquarks
• Heavy flavor pentaquarks with four heavy quarks
• Can $\Omega (2012)$ be explained as a molecular state?
• Triply-heavy tetraquarks in an extended relativized quark model
• Radiative decays and magnetic moments of the predicted $B_c$-like molecules
• Radiative decays of the spin-$2$ partner of $X(3872)$
• Exploring the magnetic dipole moments of $T_{QQ\bar{q}\bar{s}}$ and $T_{QQ\bar{s}\bar{s}}$ states in the framework of QCD light-cone sum rules
• Doubly heavy tetraquark bound and resonant states
• Possibility of $T_{c\bar{s}}(2900)$ as the resonance-like structure induced by threshold effects
• Improved understanding of the peaking phenomenon existing in the new di-$J/\psi$ invariant mass spectrum from the CMS Collaboration
• Insights into $Z_b(10610)$ and $Z_b(10650)$ from dipion transitions from ${\rm Y}(10860)$
• New type of doubly charmed molecular pentaquarks containing most strange quarks: Mass spectra, radiative decays, and magnetic moments
• Bottomoniumlike states in proton collisions: Fragmentation and resummation
• The possibility of $X(4014)$ as a $D^{\ast }{\bar{D}}^{\ast }$ molecular state
• The interplay between compact and molecular structures in tetraquarks
• The structure of the X(3872) as explained by a Diffusion Monte Carlo calculation
• Semi-inclusive lepto-production of hidden-charm exotic hadrons
• Photo- and electro-production of narrow exotic states: from light quarks to charm and up to bottom
• Fully strange tetraquark resonant states as the cousins of $X(6900)$
• Searching for doubly charmed tetraquark candidates $T_{cc}$ and $T_{cc\bar{s}}$ in $B_c$ decays
• Identify the hidden charm pentaquark signal from non-resonant background in electron-proton scattering
• Looking for the exotic $X_0(2866)$ and its $J^P=1^{+}$ partner in the ${\bar{B}}^0\to D^{(\ast )+}{K}^{-}{K}^{(\ast )0}$ reactions
• One way to verify the molecular picture of exotic hadrons --from $DK$ to $DDK/D{\bar{D}}^{(\ast )}K$
• Fully heavy tetraquark resonant states with different flavors
• Charmed baryon$-$nucleon interaction
• Fragmentation functions for axial-vector heavy tetraquarks: A TQ4Q1.1 update
• Flavor Physics at the CEPC: a General Perspective
• Diabatic description of charmoniumlike mesons II: mass corrections and strong decay widths
• Mass spectra for the $cc\bar{b}\bar{b}$/$bb\bar{c}\bar{c}$ tetraquark states
• Reconciling the X(2240) with the Y(2175)
• $P$-wave charmonium contribution to hidden-charm states from reanalysis of lattice QCD data
• Method to observe the $J^P=2^{+}$ partner of the $X_0(2866)$ in the $B^{+}\to D^{+}{D}^{-}{K}^{+}$ reaction
• Colloquium: Hadron Production in Open-charm Meson Pair at $e^{+}{e}^{-}$ Collider
• Regge trajectories for the heavy-light diquarks
• Fragmentation of fully heavy tetraquarks: The TQ4Q1.1 functions as a case study
• Spectrum of the molecular hexaquarks
• Probing hidden-bottom pentaquarks in fixed-target collisions at the LHC
• The role of the $\omega (4S)$ and $\omega (3D)$ states in mediating the $e^{+}{e}^{-}\to \omega \eta$ and $\omega {\pi }^0{\pi }^0$ processes
• Towards a precision determination of the $X(6200)$ parameters from data
• Investigating the M1 radiative decay behaviors and the magnetic moments of the predicted triple-charm molecular-type pentaquarks
• P-wave fully charm and fully bottom tetraquark states
• The role of electromagnetic interaction in the $X(3872)$ and its analogs
• Spectrum of two-flavored spin-zero heavy dibaryons in lattice QCD
• Exploring the mass spectrum and the electromagnetic properties of the possible ${\Xi }_{cc}{K}^{(\ast )}$ and ${\Xi }_{cc}{\bar{K}}^{(\ast )}$ molecules
• Is two-poles' $\Lambda (1405)$ one state or two?
• Study of exotic hadrons with machine learning
• Doubly charmed hexaquarks in the diquark picture
• Double pole structures of $X_1(2900)$ as the $P$-wave ${\bar{D}}^{\ast }{K}^{\ast }$ resonances
• Triply heavy baryon spectroscopy revisited
• Discover the GellMann-Okubo formula with machine learning
• Production of $X_b$ via ${\rm Y}(5S,6S)$ radiative decays
• Models and Potentials in Hadron Spectroscopy
• Two-pion exchange for coupled-channel scattering of two heavy mesons
• Study of the hidden charm $D{\bar{D}}^{\ast }$ interactions in chiral effective field theory
• Searching for fully-heavy tetraquark states in QCD moment sum rules
• Probing the hidden-bottom pentaquark resonances in photonuclear bottomonium production near threshold: differential observables
• Triply heavy tetraquark states in a mass-splitting model
• Trilepton and tetralepton bound and resonant states: the QED counterpart of multiquark states
• Observation of the open-charm tetraquark candidate $T_{cs0}^{\ast }(2870{)}^0$ in the $B^{-}\to D^{-}{D}^0{K}_{\mathrm{S}}^0$ decay
• Spectroscopic Properties of Double-Strangeness Molecular Tetraquarks
• Production of pentaquarks with hidden charm and double strangeness in ${\Xi }_b$ and ${\Omega }_b$ decays
• $P_c(4457)$ interpreted as a $J^P=1/2^{+}$ state by ${\bar{D}}^0{\Lambda }_c^{+}(2595)$-${\pi }^0{P}_c(4312)$ interaction
• 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
• Structure of open-flavour four-quark states in the charm and bottom region
• Investigation of ${\Delta }^0{\Delta }^0$ dibaryon in QCD
• Fully charmed P-wave tetraquark resonant states in the quark model
• Constraining the $DD{D}^{\ast }$ three-body bound state via the $Z_c(3900)$ pole
• Tetraquark-Jet Systems at the High-Luminosity LHC
• $J/\psi$ decay to $\varphi ,\omega ,K^{\ast 0}$ plus $f_0(1370)$, $f_0(1710)$, $K_0^{\ast }(1430)$, $f_2(1270)$, $f_2^{\prime }(1525)$ and $K_2^{\ast }(1430)$: role of the $D$-wave for tensor production
• Probing the structure of $X(3872)$ in photoproduction
• Mixing angle of $K_1(1270/1400)$ and the $K{\bar{K}}_1(1400)$ molecular interpretation of ${\eta }_1(1855)$
• Quark structure of the $X(4500)$, $X(4700)$ and ${\chi }_{\mathrm{c}}(4P,5P)$ states
• DeepQuark: A Deep-Neural-Network Approach to Multiquark Bound States
• The Pentaquark Spectrum from Fermi Statistics
• The $\varphi NN,J/\psi NN,{\eta }_{c}NN$ systems based on HAL QCD interactions
• $\lambda$ and $\rho$ Regge trajectories for hidden bottom and charm tetraquarks $(Qq)(\bar{Q}{\bar{q}}^{\prime })$
• The ground states of hidden-charm tetraquarks and their radial excitations
• Study of the hidden charm pentaquarks ${\Lambda }_{c\bar{c}}$ above $4$ GeV
• The ground states and first radial excitations of the vector tetraquark states with explicit P-waves via the QCD sum rules
• Production potential of hidden-strange molecular pentaquarks through the ${\pi }^{-}p\to K^{\ast }\Sigma$ process
• Regge trajectories for the triply heavy triquarks
• Hidden and open heavy-flavor hadronic states
• Production of $1^{-+}$ exotic charmonium-like states in electron-positron collisions
• Radiative decays of the neutral $Z_c(3900)$ and $Z_c(4020)$
• Possible molecules of triple-heavy pentaquarks within the extended local hidden gauge formalism
• Electromagnetic properties of possible triple-charm molecular hexaquarks
• Electromagnetic characteristics as probes into the inner structures of the predicted ${\Xi }_c^{{(}^{\prime },\ast )}{D}_s^{(\ast )}$ molecular states
• Pole analysis for the $D^{\ast }\bar{K}$-$D\overline{K^{\ast }}$ coupled-channel system
• Finding Interaction Mechanism between Exotic Molecule and Conventional Hadron
• Is the $3S$-$2D$ mixing strong for the charmonia $\psi (4040)$ and $\psi (4160)$?
• Electromagnetic properties of the $D{\bar{D}}^{\ast }K$ molecular hexaquark state
• Proper constituent gluon mass as the final piece to construct hybrid mesons
• Discovering an Unquenched Dynamics Mechanism for Charmonium Scattering
• A coupled-channel perspective analysis on bottom-strange molecular pentaquarks
• Exotic Heavy Hadrons
• All-charm tetraquarks at hadron colliders: A high-precision fragmentation perspective
• Unraveling $K(1690)$ as a pseudoscalar $ud\bar{d}\bar{s}$ tetraquark state
• 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
• Possible ${\Sigma }_c^{\ast }\bar{\Sigma }$ molecular states
• $\lambda$ and $\rho$ Regge trajectories for the pentaquark $P_{cc\bar{c}bb}$ in the diquark-triquark picture
• Photon-induced production of the exotic charged charmonium-like state $Z_c(3900)$ off nuclear targets and its internal structure
• Spectroscopic properties of $1F$-wave singly bottom baryons
• Doubly-charmed pentaquark states in a mass splitting model
• $Z_c(3900)$ in a hadronic molecule and a triangle singularity approach at finite temperature
• Coupled-channel study of $4S$-$3D$ mixing dynamics in $\psi (4220)$ and $\psi (4380)$
• Investigating the two-pion exchange of the double charm $D{D}^{\ast }$ chiral interactions and $T_{cc}$
• Spectrum of Hidden-Charm, Open-Strange Exotics in the Dynamical Diquark Model
• Analysis of the hadronic molecules $DK$, $D^{\ast }K$, $D{K}^{\ast }$ and their bottom analogs with QCD sum rules
• Non-$D\bar{D}$ Decays into Light Meson Pairs of the $D$-Wave Charmonium ${\psi }_3(3842)$
• Five-flavor molecular pentaquarks in the ${\Xi }_b^{(\prime ,\ast )}{\bar{D}}^{(\ast )}$ and ${\Xi }_c^{(\prime ,\ast )}{B}^{(\ast )}$ systems
• Is ${\chi }_{c1}(3872)$ generated from string breaking?
• Revisit the $Z_c(4025)$ structure observed by BESIII in the $e^{+}{e}^{-}\to (D^{\ast }{\bar{D}}^{\ast }{)}^{\pm ,0}{\pi }^{\mp ,0}$ reactions at $\sqrt{s}=4.26$ GeV
• Possible bound states in the triple-${\eta }_c$ and triple-$J/\psi$ systems
• The $B^{-}\to J/\psi {\eta }^{\prime }{K}^{-}$ reaction and the $Y(4710)$ and $K_0^{\ast }(1430)$ contributions
• Dalitz-plot decomposition for the $e^{+}{e}^{-}\to J/\psi \pi \pi (K\bar{K})$ and $e^{+}{e}^{-}\to h_c\pi \pi$ processes
• Observation and investigation of the $T_{c\bar{c}1}(4430{)}^{+}$ structure in $B^{+}\to \psi (2S)K_{\text{S}}^0{\pi }^{+}$ decays
• Searching for a $P_{cs}(4200)$ state in the ${\Lambda }_b\to \varphi {\eta }_c\Lambda$ reaction
• Meson scattering and tetraquarks in two-dimensional QCD
• Assessing the validity of the Born-Oppenheimer approximation in potential models for doubly heavy hadrons
• Coupled-channel meson-meson scattering in the diabatic framework
• Structural dissection of hadronic molecules: The $D^{(\ast )}{\bar{K}}^{(\ast )}$ family under QCD light-cone sum rules
• Exotic hadrons associated with $b$-quark
• Systematic exploration of triply heavy tetraquarks: spectroscopic and decay characteristics
• Dispersive Analysis of $D$- and $B$-Meson Form Factors with Chiral and Heavy-Quark Constraints
• Proposed mixing between $2P$ and $1F$ wave charmonia
• Role of $a_0(1710)$ in the $J/\psi \to {\rho }^{+}{\rho }^{-}\omega$ and $J/\psi \to \gamma {\rho }^0\omega$ reactions
• Two-body strong decays of the pseudoscalar hidden-charm tetraquark states via the QCD sum rules
• Analytic electromagnetic signatures of compact pentaquark structure: A multi-current QCD light-cone sum rules analysis of the $P_{\psi s}^{\Lambda }$ states
• Charting doubly strange hidden-charm pentaquarks: An electromagnetic mapping of spin-$\frac{1}{2}$ and $\frac{3}{2}$ states
• The dynamically generated $h_1$ state by the $K^{\ast }{\bar{K}}^{\ast }$ interaction and its $K_1(1270)\bar{K}$ and $b_1(1235)\pi$ decays
• An analysis on doubly bottom molecular tetraquarks composed of $H_{(s)}$ and $T_{(s)}$ doublets
• Insights into the exotic charged states $Z_b(10610)$ and $Z_b(10650)$ from their photoproduction off nuclei
• Role of the short-range dynamics in simultaneous interpretation of $P_{cs}$ pentaqurks via ${\Xi }_c^{(\prime ,\ast )}{\bar{D}}^{(\ast )}$ molecules
• Electromagnetic probes revealing the inner structure of the ${\Lambda }_c(2940)$
• New Types of Hydrogenlike matter Composed of Electron(s) and Meson(s)
• Unified coupled-channel description for the five near-threshold structures $\psi (3770)$, $G(3900)$, $R(3760)$, $R(3780)$ and $R(3810)$ from $e^{+}{e}^{-}$ annihilation
• Prospects for compact hexaquarks under the limitation imposed by quark confinement
• Predicting charmed-strange molecular tetraquarks with $K^{(\ast )}$ and $T$-doublet charmed or anticharmed meson