Review
Pentaquark and Tetraquark States

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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 Ref. [1]. 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 Pc 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 QQQ̄Q̄ and doubly heavy tetraquark states QQq̄q̄, where Q is a heavy quark. The QQQ̄Q̄ states may be produced at LHC while the QQq̄q̄ system may be searched for at BelleII and LHCb. Moreover, we shall pay special attention to various theoretical schemes such as the chromomagnetic interaction (CMI), constituent quark model, meson exchange model, heavy quark and heavy diquark symmetry, QCD sum rules, Faddeev equation for the three body systems, Skyrme model and the chiral quark-soliton model, and the lattice QCD simulations. We shall emphasize the model-independent predictions of various models which are truly/closely related to Quantum Chromodynamics (QCD). For example, the chromomagnetic interaction arises from the gluon exchange which is fundamental and universal in QCD and responsible for the mixing and mass splitting of the conventional mesons and baryons within the same multiplet. The same CMI mechanism shall also be responsible for the mixing of the different color configurations and mass splittings within the multiplets in the multiquark sector. 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 Pc 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.

Introduction

In the past decades, hadron physicists show great interest in hunting for evidences of the multiquark states. As a new form of matter beyond conventional mesons (q̄q) and baryons (qqq), multiquark states containing more than three quarks are of special importance in the hadron family. Especially, with the observations of various charmonium-like XYZ states, the study of multiquark states has entered upon a new era.

In this article, we will give a concise review on the research progress of the tetraquark (q̄q̄qq) and pentaquark (q̄qqqq) states, which are typical multiquark matters. Before doing that, let us first look back on the history of particle/hadron physics. It is well known that the development of quantum mechanics is closely related to the study of atomic spectroscopy, which reveals the mysterious veil of the atom’s microstructure. Here, we find a similar situation that the study of hadron spectroscopy is bringing us new insights into the internal structure and dynamics of hadrons.

In the early 1960s, many strongly interacting particles were observed in particle/nucleon experiments, which were named as “hadron” by L. B. Okun later [2]. Based on these observations, M. Gell-Mann and G. Zweig independently developed the classification scheme for hadrons—the quark model [3], [4], [5]. Especially, the name “quark” was given by M. Gell-Mann to denote the substructure of hadrons. The quark model achieves a great success, and it is a milestone in the development of particle physics. A well-known example is the prediction of the baryon with three strange quarks, that is the Ω. It was discovered in 1964 [6] after its existence, mass, and decay products had been predicted in 1961 independently by M. Gell-Mann [7] and Y. Ne’eman [8].

Then we would like to mention the establishment of the Cornell model. In 1974, as the first state in the charmonium family, the Jψ was discovered by the E598 Collaboration [9] and the SLAC-SP-017 Collaboration [10], which confirmed the existence of the charm quark [11]. After that, a series of charmonia were discovered, such as the ψ(3686) [12], ψ(3770) [13], ψ(4040) [14], ψ(4160) [15], and ψ(4415) [16], etc. Based on these experimental observations, the Cornell model was proposed [17], [18], which uses the Cornell potential V(r)=kr+ra2 [19] to depict the interaction between the charm and anti-charm quarks. This potential consists of both the Coulomb-type and linear potentials, which can well reproduce masses of the above observed charmonia at that time. Inspired by the Cornell model, various potential models were developed [20], [21], [22], [23], [24], [25], [26], [27], [28], [29], [30], [31], [32], [33], among which the Godfrey–Isgur model [33] is quite popular. This model contains the semi-relativistic kinetic and potential energy terms, which can be applied to quantitatively describe not only meson spectra [33] but also baryon spectra [34]. These phenomenological models, inspired by the charmonium family, greatly improve our understanding of the internal structure and dynamics of conventional mesons and baryons.

Nowadays several hundreds of hadrons have been observed in particle experiments, most of which can be categorized into two families: baryons made of three quarks and mesons made of one quark and one antiquark [35]. They are formed by the up, down, strange, charm, and bottom quarks/antiquarks (the top quark has a very short lifetime and therefore does not form hadrons), which are governed by the strong interaction. Although the mechanism of the color confinement remains one of the most difficult problems in particle physics, various phenomenological models were proposed to quantitatively describe the hadron spectroscopy. Due to the joint efforts from the particle/hadron theorists and experimentalists, the meson and baryon families have been nearly complete, and almost all the ground-state hadrons have been discovered. Especially, the doubly charmed baryon Ξcc++(3621) was recently discovered by LHCb Collaboration [36].

Other than hundreds of conventional mesons and baryons, there were only tens of multiquark candidates observed in particle experiments, although the concept of the multiquark states appeared together with the birth of the quark model. For example, M. Gell-Mann indicated [3]:“Baryons can now be constructed from quarks by using the combinations (qqq), (qqqqq̄), etc., while mesons are made out of (qq̄), (qqq̄q̄), etc”, and G. Zweig [5] also wrote: “In general, we would expect that baryons are built not only from the product of these aces, AAA, but also from ĀAAAA, ĀĀAAAAA, etc., where Ā denotes an anti-ace. Similarly, mesons could be formed from ĀA, ĀĀAA, etc”. Due to the constraint of reliable experimental and theoretical techniques, the study of the multiquark states was far from satisfactory before 2003. At that time, theorists mainly focused on (a) the light scalar mesons σ, κ, a0(980), and f0(980), (b) the scalar mesons f0(1370), f0(1500), and f0(1710), and (c) the Λ(1405), and discussed their possible interpretations as multiquark states and glueballs (see review articles [37], [38] for details).

2003 is an important year in the history of the multiquark states. Since 2003, there has been continuous progress in this field. With the accumulation of experimental data, a series of charmonium-like XYZ states were reported (see Fig. 1), which stimulated us to reveal their exotic inner structures. We shall try our best to convey the progress and excitement to the readers in the present review. Here are several typical examples:

  • The BES and BESIII Collaborations reported a series of light-flavor multiquark candidates, including the X(1860) observed in the Jψγpp̄ decay [39], the X(1835) in Jψγηπ+π [40], [41], the X(1812) in Jψγωϕ [42], the Y(2175) in Jψηϕf0(980) [43], [44], and so on. These observations inspired extensive discussions, and various exotic interpretations such as multiquark states were proposed. Since the present review mainly focuses on the heavy-flavor multiquark states, interested readers may consult Ref. [38] for more information.

  • In 1997, Diakonov et al. predicted the existence of a light-flavor pentaquark with the chiral soliton model [45], which has a mass around 1530 MeV, spin 12, isospin 0 and strangeness +1. In 2003, LEPS Collaboration claimed that a narrow Θ+(1540) particle consistent with the above prediction was observed in the γnK+Kn reaction [46]. Very quickly, the Θ+(1540), as a pentaquark candidate, became a super star at that time [47]. Unfortunately, it was not confirmed by the subsequent series of high precise experiments [48]. The Θ+(1540) is probably not a genuine resonance [49]. The rise and fall of the Θ+(1540) unveiled our ignorance on the non-perturbative behavior of quantum chromodynamics. The lessons and experience with the Θ+(1540) have been helpful in the search of the pentaquark and tetraquark states.

  • In 2003, BaBar Collaboration observed a narrow heavy-light state Ds0(2317) in the Ds+π0 invariant mass spectrum [50]. Since the mass of the Ds0(2317) is about 100MeV lower than the quark model prediction of the P-wave charmed-strange meson with JP=0+ [33], its tetraquark explanation was proposed in Refs. [51], [52], [53]. A similar situation happened to the Ds1(2460) observed by CLEO Collaboration [54]. The strong channel coupling between the S-wave DK(K) scattering states and bare quark model cs̄ states plays a pivotal role in lowering the masses of the Ds0(2317) and Ds1(2460) [55], [56].

  • Still in 2003, X(3872), as the first particle in charmonium-like XYZ family, was discovered by Belle Collaboration [57]. Since the mass of the X(3872) is close to the threshold of the DD̄ pair, its assignment as the DD̄ molecular state is very popular. We note that its nature is still under heated debates today. Similar to the Ds0(2317) and Ds1(2460), there also exists a low mass puzzle related to the X(3872). Its mass is much lower than the quark model prediction of the charmonium χc1(2P) state [33]. Again, the coupled channel effect may mediate this difference [58].

In the past 17 years, more and more candidates of the exotic hadrons were observed in the Belle, BaBar, BESIII, D0, CDF, CMS, and LHCb experiments, such as (a) the charmonium-like XYZ states Y(4260), Zc(4430), and Zc(3900), (b) the bottomonium-like states Zb(10610) and Zb(10650), and (c) the hidden-charm pentaquark states Pc(4380) and Pc(4450), etc. In Figs. 2–3, we summarize these observations concisely. An extensive review of the states observed before 2016 can be found in Ref. [1]. Here we briefly introduce the experimental observations after 2016:

  • In the Jψϕ invariant mass spectrum of the BKJψϕ decay, LHCb established the existence of the Y(4274) structure with 6σ significance [61], [62]. This state has a mass M=4273.3±8.33.6+17.2MeV, width Γ=56.2±10.911.1+8.4MeV, and quantum numbers JPC=1++. Before this observation, CDF and CMS had reported an evidence of a structure around 4274 MeV in the Jψϕ invariant mass spectrum [63], [64]. Besides the Y(4274) structure, two extra structures with higher masses were found in the Jψϕ invariant mass spectrum, which are the X(4500) and X(4700) with JP=0+. Their resonance parameters in units of MeV are [61], [62] MX(4500)=4506±1115+12,ΓX(4500)=92±2120+21,MX(4700)=4704±1024+14,ΓX(4700)=120±3133+42.

  • In 2017, BESIII Collaboration presented more precise measurements of the e+eπ+πJψ cross section at the center-of-mass energy from 3.77 to 4.60 GeV [65] and the e+eπ+πhc cross section at the center-of-mass energy from 3.896 to 4.600 GeV [66]. Three vector structures Y(4220), Y(4320) and Y(4390) were reported with the resonance parameters in units of MeV: In fact this updated analysis of the e+eπ+πJψ cross section [66] shows that the Y(4260) contains two substructures, the Y(4220) and Y(4320).

  • The Belle Collaboration carried out an analysis of the e+eJψDD̄ cross section, and concluded that a broad structure X(3860) exists in the DD̄ invariant mass spectrum, which has a mass M=38623213+26+40MeV and width 2016782+154+88MeV [67]. Their result shows that JPC=0++ is favored over JPC=2++ at the level of 2.5σ [67].

  • A new charged structure Zc(4032) was reported by BESIII Collaboration in the ψ(3860)π+ invariant mass spectrum of the e+eY(4260)ψ(3860)π+π process [68]. BESIII confirmed the vector charmonium-like structure Y(4220) in the ψ(3860)π+π invariant mass spectrum.

  • In 2018, LHCb found the evidence of a structure in the ηc(1S)π invariant mass spectrum of the B0ηc(1S)K+π decay, which was named as the X(4100) with a mass M=4096±2022+18MeV and width Γ=152±5835+60MeV [69]. The LHCb measurement also indicated that the X(4100) structure may be described under the spin–parity JP=0+ or JP=1+ assignments [69].

  • Very recently, the LHCb Collaboration announced the observation of three new pentaquarks [59], [60] at the Rencontres de Moriond QCD conference, as shown in Fig. 4. In the measured Jψp invariant mass spectrum, a new pentaquark Pc(4312) was discovered with a 7.3σ significance. The new LHCb analysis further found that the Pc(4450) is composed of two substructures Pc(4440) and Pc(4457) with 5.4σ significance. Their resonance parameters are collected as following Pc(4312)+:m=4311.9±0.70.6+6.8MeV,Γ=9.8±2.74.5+3.7MeV,Pc(4440)+:m=4440.3±1.34.7+4.1MeV,Γ=20.6±4.910.1+8.7MeV,Pc(4457)+:m=4457.3±1.34.1+0.6MeV,Γ=6.4±2.01.9+5.7MeV. The isospin of Pc(4312), Pc(4440) and Pc(4457) is I=12 since these three pentaquarks were discovered in the Jψp channel. The Pc(4312)+ lies below the Σc+D̄0 threshold, while the masses of the Pc(4440)+ and Pc(4457)+ are slightly lower than the Σc+D̄0 threshold. The observation of Pc(4312), Pc(4440) and Pc(4457) clearly confirms the hidden-charm molecular pentaquarks.

The present situation of the charmonium-like XYZ and Pc states is a bit similar to (a) that of the ground-state mesons and baryons in 1960s, and (b) that of the charmonia in 1980s. With such abundant novel phenomenon, the most important task is to identify the genuine tetraquark and pentaquark signals. There have accumulated hundreds of investigations of the tetraquark and pentaquark systems with various phenomenological models. In this review, we will introduce several typical phenomenological methods/models and their applications to multiquark states.

Our previous review focused on the hidden-charm and hidden-bottom multiquark systems [1]. In the present article, we will summarize the experimental and theoretical progress on the hidden-charm tetraquark and pentaquark states in the past three years. Besides the hidden heavy flavor systems, we shall discuss more interesting tetraquark and pentaquark systems either with open heavy flavor or with three/four heavy quarks. These new states include the exotic tetraquarks QQQ̄Q̄ and QQq̄q̄ systems where Q is a heavy quark. The QQQ̄Q̄ states may be produced at LHC while the QQq̄q̄ system may be searched for at BelleII. Moreover, we will summarize theoretical predictions of the multiquark states from various formalisms such as the chromomagnetic interaction (CMI), constituent quark model, meson exchange model, heavy quark and heavy diquark symmetry, QCD sum rules, Faddeev equation for the three body systems, Skyrme model and the chiral quark-soliton model, and the lattice QCD simulations. We shall pay special attention to those theoretical schemes which are not covered or not addressed in depth in our previous review  [1], such as the chromomagnetic interaction, heavy quark symmetry etc. We shall emphasize the model-independent predictions of these models which are truly/closely related to Quantum Chromodynamics (QCD).

Besides the present article and our previous review  [1], there exist many nice reviews of the XYZ states in literature [70], [71], [72], [73], [74], [75], [76], [77]. Interested readers are encouraged to consult them for a glimpse of this extremely active and vast field.

Section snippets

SU(6) symmetry and chromomagnetic interaction (CMI)

The hyperfine structure for atoms is induced by the spin-related interaction between electrons and nuclei. In a similar situation, the hyperfine structure in hadron spectroscopy is from the spin-related interaction between quarks or between quarks and antiquarks. In the Hamiltonian or Lagrangian formalism, such a term contains a color factor since quarks interact in the color space. The simple color-magnetic interaction arises from the one-gluon-exchange potential and causes the mass splittings

Constituent quark models

Various versions of nonrelativistic and relativistic constituent quark models can be found in the literature, which were proposed to understand hadron properties. Almost all of them incorporate both the short-range one-gluon-exchange (OGE) force and the term representing the color confinement, in either the coordinate or momentum space. Some of them include the additional flavor-dependent Goldstone–boson-exchange (GBE) force from the spontaneously broken chiral symmetry and/or the screening

Meson exchange and scattering methods

In the study of the hadronic molecules, almost all the meson-exchange models are constructed at the hadron level. One first derives the effective boson-exchange potentials in coordinate or momentum space, and then solves the bound state problem or scattering problem of two hadrons. From the obtained binding energy or scattering phase shifts, one extracts the resonance information. Such a formalism is a straightforward extension of the traditional meson exchange models in nuclear force.

There are

Heavy quark symmetry and multiquark states

QCD exhibits the chiral symmetry in the limit when quarks are massless, and the heavy quark symmetry [393] in the limit when quarks have infinitely large masses, both of which play important roles in understanding properties of hadrons and their interactions. The latter symmetry indicates both the heavy quark flavor symmetry (HQSS) which means that the dynamics is not affected by the exchange of heavy quark flavors, and the heavy quark spin symmetry (HQSS) which means that the dynamics is

QCD sum rules

The formalism of QCD sum rules is a powerful and successful non-perturbative method [412], [413], which has been widely applied to study the mass spectra and decay properties of various exotic hadrons. Since we have thoroughly reviewed its applications to the hidden-charm pentaquark and tetraquark states in Ref. [1] and its applications to the open-charm tetraquark states in Ref. [414], we shall only briefly introduce the recent progress of this method in the present view, and we refer

Three-body system

There are various two-body interpretations of the exotic hadrons, as we have reviewed in previous sections. There are also some three-body interpretations for exotic hadrons. For example, combining the Faddeev equations with the chiral unitary model [534], [535], the authors interpreted the Y(2175) as a dynamically generated state in the ϕKK̄ system. In this section, we review some of these studies. We note that the three-body system have also been extensively studied within the chiral

The Skyrme model and the chiral quark-soliton model

The Skyrme model was proposed by T. H. R. Skyrme in 1961 by introducing the Skyrme term to the nonlinear sigma model [588]. Within this model the baryons appear as collective excitations of the meson fields. In fact, the non-trivial topological field configuration, which is called as soliton, is identified with the baryon. Later in 1979, E. Witten developed this model by arguing that baryons indeed emerge as solitons in the large NC generalization of QCD [589]. He also studied static properties

Progresses from lattice QCD

Lattice QCD is the unique non-perturbative theoretical framework to study the hadron spectroscopy starting from the first principle QCD Lagrangian. In a lattice QCD simulation, the hadron mass En can be extracted from the N×N time-dependence correlation function Cij(t)=Ω|Oi(t)Oj(0)|Ω=n=1NeEntΩ|Oi|nn|Oj(0)|Ω, where the interpolating operator Oj(0)(j=1,2,,N) creates the state of interest from the vacuum |Ω at time t=0 and Oi(t) annihilates the state at a later Euclidean time t. En is

Production and decay properties

In this subsection, we shall discuss recent theoretical progress on the productions and decay properties of the multiquark states, which are crucial to understand the nature of exotic states. In particular, the non-resonant explanations for some XYZ states depend on their production processes.

The production of the multiquark systems at the quark level remains very challenging since nonperturbative effects are usually involved. One has to turn to effective formalisms such as the nonrelativistic

Summary and perspective

At the end of this review, we would give a brief summary and perspective for the progress on the multiquark physics. It is useful and instructive to recall the establishment of the quark model before we discuss the multiquark systems. The quark model was first proposed in 1964 to deal with the classification of hadrons. In 1974, the discovery of the Jψ meson gave the direct evidence for the existence of the charm quark, which was known as “November Revolution”. Actually, the existence of the

Acknowledgments

We would like to express our gratitude to all the collaborators and colleagues who contributed to the investigations presented here, in particular to Dian-Yong Chen, Rui Chen, Xiao-Lin Chen, Er-Liang Cui, Wei-Zhen Deng, Jun He, Ning Li, Shi-Yuan Li, Xiao-Hai Liu, Yu-Nan Liu, Zhi-Gang Luo, Li Ma, Takayuki Matsuki, Zong-Guo Si, T. G. Steele, Zhi-Feng Sun, Guan-Juan Wang, Jing Wu, Lu Zhao, Zhi-Yong Zhou. We thank Er-Liang Cui for helping prepare some relevant documents. This project is supported

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