The hidden-charm pentaquark and tetraquark states

10.2 MB·

by  Hua-Xing Chen

The hidden-charm pentaquark and tetraquark states
Hua-XingChen1a,b,WeiChen1c,XiangLiud,e,∗,Shi-LinZhua,f,g,∗∗
aSchoolofPhysicsandStateKeyLaboratoryofNuclearPhysicsandTechnology,PekingUniversity,Beijing100871,China
bSchoolofPhysicsandNuclearEnergyEngineering,BeihangUniversity,Beijing100191,China
cDepartmentofPhysicsandEngineeringPhysics,UniversityofSaskatchewan,Saskatoon,SaskatchewanS7N5E2,Canada
dSchoolofPhysicalScienceandTechnology,LanzhouUniversity,Lanzhou730000,China
eResearchCenterforHadronandCSRPhysics,LanzhouUniversityandInstituteofModernPhysicsofCAS,Lanzhou730000,China
fCollaborativeInnovationCenterofQuantumMatter,Beijing100871,China
gCenterofHighEnergyPhysics,PekingUniversity,Beijing100871,China
6
1
0 Abstract
2
Inthepastdecademanycharmonium-likestateswereobservedexperimentally.Especiallythosechargedcharmonium-
y
likeZ statesandbottomonium-likeZ statescannotbeaccommodatedwithinthenaivequarkmodel. Thesecharged
a c b
M Zcstatesaregoodcandidatesofeitherthehidden-charmtetraquarkstatesormoleculescomposedofapairofcharmed
mesons. Recently, the LHCb Collaboration discovered two hidden-charm pentaquark states, which are also beyond

2 thequarkmodel. Inthiswork,wereviewthecurrentexperimentalprogressandinvestigatevarioustheoreticalinter-
2 pretationsofthesecandidatesofthemultiquarkstates. Welistthepuzzlesandtheoreticalchallengesofthesemodels

when confronted with the experimental data. We also discuss possible future measurements which may distinguish
]
h thetheoreticalschemesontheunderlyingstructuresofthehidden-charmmultiquarkstates.
p
- Keywords: Hidden-charmpentaquark,Hidden-charmtetraquark,Charmonium-likestate,Charmonium,Exoticstate,
p
Phenomenologicalmodels
e
PACS:21.10.-k,21.10.Pc,21.60.Jz,11.30.Pb,03.65.Pm
h
[

3
v
Contents
2
9
0 1 Introduction 3
2 1.1 Quarkmodelandthemultiquarkstates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
0 1.1.1 Quarkmodel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
.
1 1.1.2 Exoticstatesandmultiquarkstates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
0 1.1.3 ComparisonofQEDandQCDandtheirspectrum . . . . . . . . . . . . . . . . . . . . . . . 6
6 1.2 Generalstatusofhadronspectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1
:
v 2 Experimentalprogressonthehidden-charmmultiquarkstates 7
i 2.1 TheCharmonium-likeXYZstates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
X
2.1.1 XYZstatesproducedthroughBmesondecays . . . . . . . . . . . . . . . . . . . . . . . . . . 8
ar 2.1.2 Y statesproducedthroughthee+e−annihilation . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.1.3 Xstatesproducedthroughdoublecharmoniumproduction . . . . . . . . . . . . . . . . . . . 29
2.1.4 TheXYZstatesfromγγfusionprocesses . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.1.5 Chargedcharmonium-likeZ states . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
c
2.2 Chargedbottomonium-likestatesZ (10610)andZ (10650) . . . . . . . . . . . . . . . . . . . . . . . 38
b b
2.3 Thehidden-charmpentaquarkstatesobservedbyLHCb . . . . . . . . . . . . . . . . . . . . . . . . . 40
1Theseauthorsequallycontributetothiswork.
∗Correspondingauthor
∗∗Correspondingauthor
Emailaddresses:[email protected](Hua-XingChen),[email protected](WeiChen),[email protected](XiangLiu),
[email protected](Shi-LinZhu)
PreprintsubmittedtoPhysicsReports May24,2016
3 Theoreticalinterpretationsofthehidden-charmpentaquarkstates 41
3.1 Themolecularscheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
3.1.1 Thedeuteronasahadronicmolecule. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
3.1.2 Themesonexchangemodel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
3.1.3 Predictionsforthehidden-charmpentaquarksbeforeLHCb’sdiscovery . . . . . . . . . . . . 44
3.1.4 MolecularassignmentsafterLHCb’sdiscovery . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.1.5 Configurationmixing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
3.1.6 OrbitalexcitationsandtheP parity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
c
3.2 Dynamicallygeneratedresonance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
3.3 QCDsumrules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
3.3.1 AshortintroductiontothemethodofQCDsumrule . . . . . . . . . . . . . . . . . . . . . . 52
3.3.2 Pentaquarkcurrents. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
3.3.3 OperatorProductExpansion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
3.3.4 ParityofPentaquarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
3.3.5 Numericalresultsanddiscussions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
3.4 Tightlyboundpentaquarkstateinthequarkmodel . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
3.4.1 Chiralquarkmodel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
3.4.2 Thediquark/triquarkmodel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
3.5 Kinematicaleffect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
3.6 Othertheoreticalschemes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
3.7 Productionanddecaypatterns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
3.7.1 ProductionoftheP viaweakdecays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
c
3.7.2 Photo-productionoftheP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
c
3.7.3 StrongdecaypatternsoftheP states . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
c
3.8 Thehidden-bottomanddoublyheavypentaquarkstates . . . . . . . . . . . . . . . . . . . . . . . . . 63
3.9 Theoreticalandexperimentalchallenges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
4 TheoreticalinterpretationsoftheXYZstates 66
4.1 Z (10610)andZ (10650) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
b b
4.1.1 Molecularscheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
4.1.2 Thetetraquarkassignment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
4.1.3 Kinematicaleffect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
4.1.4 Productionanddecaypatterns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
4.1.5 Ashortsummary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
4.2 Z (3900),Z (4020)andZ (4025) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
c c c
4.2.1 Molecularscheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
4.2.2 Tetraquarkstateassignment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
4.2.3 Kinematicaleffect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
4.2.4 Productionanddecaypatterns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
4.2.5 Ashortsummary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
4.3 Z+(4430) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
4.3.1 Molecularstatescheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
4.3.2 Thetetraquarkassignment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
4.3.3 Cuspeffect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
4.3.4 Production,decaypatterns,andothertheoreticalschemes. . . . . . . . . . . . . . . . . . . . 83
4.3.5 Ashortsummary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
4.4 Otherchargedstates: Z+(4051),Z+(4248)andZ+(4200) . . . . . . . . . . . . . . . . . . . . . . . . 84
4.4.1 Molecularstatescheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
4.4.2 Tetraquarkstateassignment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
4.4.3 Productionanddecaypatterns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
4.4.4 Ashortsummary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
4.5 X(3872) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
2
4.5.1 Molecularscheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
4.5.2 Theaxialvectortetraquarkstate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
4.5.3 Radialexcitationoftheaxialvectorcharmonium . . . . . . . . . . . . . . . . . . . . . . . . 93
4.5.4 LatticeQCD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
4.5.5 Othertheoreticalschemes,productionanddecaypatterns . . . . . . . . . . . . . . . . . . . . 95
4.5.6 Ashortsummary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
4.6 Y(4260) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
4.6.1 IsY(4260)ahighercharmonium? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
4.6.2 Thehybridcharmonium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
4.6.3 Thevectortetraquarkstate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
4.6.4 Themolecularstate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
4.6.5 Non-resonantexplanations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
4.6.6 Othertheoreticalschemes,productionanddecaypatterns . . . . . . . . . . . . . . . . . . . . 105
4.6.7 Ashortsummary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
4.7 Y(3940),Y(4140)andY(4274) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
4.7.1 Molecularstatescheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
4.7.2 Othertheoreticalschemes,productionanddecaypatterns . . . . . . . . . . . . . . . . . . . . 108
4.7.3 Ashortsummary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
4.8 Othercharmonium-likestates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
4.8.1 Y(4008)andY(4360) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
4.8.2 Y(4660)andY(4630) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
4.8.3 X(3915),X(4350)andZ(3930) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
4.8.4 X(3940)andX(4160) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
4.8.5 Narrowenhancementstructuresaround4.2GeVinthehidden-charmchannels . . . . . . . . 114
4.8.6 X(3823) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
4.8.7 Ashortsummary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
5 Outlookandsummary 118
5.1 Currentstatusandfutureconfirmationofthehidden-charmmultiquarkstates . . . . . . . . . . . . . 118
5.2 Non-resonantschemes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
5.3 Partnerstates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
5.4 ConnectionsbetweendifferentXYZstates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
5.5 Open-charm,pionicandradiativedecays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
5.6 Hidden-charmbaryoniumordibaryonswithtwocharmquarks . . . . . . . . . . . . . . . . . . . . . 121
5.7 Futurefacilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
5.8 Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
1. Introduction
1.1. Quarkmodelandthemultiquarkstates
QuantumChromodynamics(QCD)istheunderlyingtheoryofstronginteraction. AccordingtoQCD,quarksand
anti-quarksareinthefundamentalrepresentationofthenon-AbelianSU(3)colorgaugegroupwhilegluonsbelongto
theadjointrepresentation. TheQCDLagrangianreads
(cid:16) (cid:17) 1
L = ψ¯ iγµ(D ) −mδ ψ − Ga Gµν, (1)
i µ ij ij j 4 µν a
wherethecovariantderivativeisdefinedas
(D ) = ∂ δ −igAaTa. (2)
µ ij µ ij µ ij
In Eq. (1), ψ(x) is the quark field, and Aa is the gluon field, both of which carry the color charge. γ is the Dirac
i µ µ
matrixandTa =λa/2isthegeneratoroftheSU(3)gaugegroup.
ij ij
3
QCD has three important properties: asymptotic freedom, confinement, approximate chiral symmetry and its
spontaneous breaking. Quarks and gluons are confined within the mesons and baryons. Their color interactions
increase as the involved energy scale decreases. At the hadronic scale, QCD is highly non-perturbative due to the
complicatedinfraredbehaviorofthenon-AbelianSU(3)gaugegroup.
AtpresentitisstillimpossibleforustoderivethehadronspectrumanalyticallyfromtheQCDLagrangian.Lattice
QCDwasinventedtosolveQCDnumericallythroughsimulationsonthelattice,whichhasprovenverypowerfulin
thecalculationofthehadronspectrumandhadronicmatrixelements. BesideslatticeQCD,manyphenomenological
models with some kind of QCD spirit were proposed. Among them, the quark model may be the most successful
one, whichcategorizeshadronsintotwofamilies: mesonsandbaryons. Theformeraremadeofonequarkandone
antiquark,andthelatteraremadeofthreequarks.
Withtheexperimentalprogressinthepastdecade,dozensofcharmonium-likeXYZstateshavebeenreported[1].
Theyprovidegoodopportunitiestoidentifytetraquarkstates,whicharemadeoftwoquarksandtwoantiquarks.More-
over, the LHCb Collaboration recently observed two hidden-charm pentaquark resonances, P (4380) and P (4450),
c c
in the J/ψp invariant mass spectrum [2]. They are good candidates of pentaquark states, which are made of four
quarks and one antiquark. We shall briefly review the experimental progress on these charmonium-like states and
hidden-charmpentaquarkresonancesinSec.2.
To study these tetraquark and pentaquark candidates, the traditional quark model as well as its updated version
seems to be incapable any more. Various theoretical frameworks were proposed to interpret these new multiquark
systems, such as the one-boson-exchange (OBE) model, the one-pion-exchange (OPE) model, the chiral unitary
model,theQCDsumrule,thechiralquarkmodel,thediquark-antidiquarkmodeletc. Weshallbrieflyintroducethese
modelsandreviewtheirapplicationsonthehidden-charmpentaquarkresonancesinSec.3,andreviewtheapplications
ofmoretheoreticalframeworksonthecharmonium-likestatesinSec.4.Anoutlookandabriefsummarywillbegiven
inSec.5.
1.1.1. Quarkmodel
Accordingtothetraditionalquarkmodel,amesoniscomposedofapairofquarkandantiquarkandabaryonis
composedofthreequarks. Bothmesonsandbaryonsarecolorsinglets. Thequarkinthequarkmodelissometimes
denotedastheconstituentquark,whichisdifferentfromthecurrentquarkintheQCDLagrangian. Forexample,the
constituentup/downquarkmassisaboutonethirdofthenucleonmassoronehalfoftheρmesonmass. Attheenergy
scalearound2GeV,theup/downcurrentquarkmassisaroundseveralMeV.
(cid:112)
Within the quark model, each quark carries the energy m2+p2, where m is the constituent quark mass and p
denotesitsmomentum. Inthenon-relativisticlimit,theenergytermisexpandedasthesumofthemassandkinetic
energy. The inter-quark interactions include the linear confinement force and the one gluon exchange force. There
alsoexistvarioushyperfineinteractionssuchasthespin-spininteraction,thecolor-magneticinteraction,thespin-orbit
interaction, and the tensor force etc. Up to now, nearly all the mesons and baryons can be classified within such a
simplequarkmodelpicture.
ThediscoveryofJ/ψ[3,4]in1974inspiredtheoriststoproposepotentialmodels[5,6].Themassspectrumofthe
charmonium family was obtained by solving the Schro¨dinger equation. The hadron spectroscopy was reconsidered
intheframeworkofquarkmodel[7,8,9,10,11,12,13,14,15,16,17]. Inthefollowing, wetakethewell-known
Godfrey-Isgur(GI)quarkmodelasanexampleandintroduceitbriefly[17].
IntheGImodel[17],theinteractionbetweenthequarkandantiquarkisdescribedbytheHamiltonian
(cid:113) (cid:113)
H = m21+p2+ m22+p2+Veff(p,r) , (3)
where the subscripts 1 and 2 denote the quark and the antiquark, respectively. Veff(p,r) is the effective potential of
theqq¯ system,andcontainstheshort-distanceone-gluon-exchangeinteractionandthelong-distancelinearconfining
interaction. ThelatterwasatfirstemployedbytheCornellgroupandlaterconfirmedbythelatticeQCDsimulations.
Veff(p,r) is obtained from the on-shell qq¯ scattering amplitudes in the center-of-mass (CM) frame [17]. In the
non-relativisticlimit,Veff(p,r)istransformedintothestandardnon-relativisticpotentialVeff(r):
Veff(r)= Hconf +Hhyp+HSO. (4)
4
ThefirsttermHconf includesthespin-independentlinearconfinementandCoulomb-typeinteractions
(cid:34) (cid:35)
3 3 α (r)
Hconf =− c+ br− s F ·F , (5)
4 4 r 1 2
thesecondtermHhypisthecolor-hyperfineinteraction
(cid:34) (cid:35)
α (r) 8π 1(cid:16)3S ·rS ·r (cid:17)
Hhyp = − s S ·S δ3(r)+ 1 2 −S ·S F ·F , (6)
m m 3 1 2 r3 r2 1 2 1 2
1 2
andthethirdtermHSOisthespin-orbitinteraction
HSO = HSO(cm)+HSO(tp), (7)
whereHSO(cm)isthecolor-magnetictermandHSO(tp)istheThomas-precessionterm,i.e.,
(cid:32) (cid:33)(cid:32) (cid:33)
α (r) 1 1 S S
HSO(cm) = − s + 1 + 2 ·L F ·F , (8)
r3 m m m m 1 2
1 2 1 2
(cid:32) (cid:33)
−1∂Hconf S S
HSO(tp) = 1 + 2 ·L. (9)
2r ∂r m2 m2
1 2
Intheaboveexpressions,S /S denotesthespinofthequark/antiquarkand Listheorbitalmomentumbetweenthe
1 2
quark and the antiquark. F is related to the Gell-Mann matrix, F = λ /2 and F = −λ∗/2. Especially, we have
1 1 2 2
(cid:104)F ·F (cid:105)=−4/3forthemesons.
1 2
TherelativisticeffectswerealsotakenintoaccountintheGImodel. MoredetailsoftheGImodelcanbefound
in Appendices of Ref. [17]. The GI quark model was very successful in the description of the spectrum and static
propertiesofthemesonsandbaryons.
1.1.2. Exoticstatesandmultiquarkstates
According to the quark model, the parity for a meson is P = (−)L+1 and theC-parity for a neutral mesonC =
(−)L+S, where L and S are the orbital and spin angular momentum, respectively. The allowed JPC reads: 0−+, 0++,
1−−, 1+−, 1++, ···. In contrast, a conventional qq¯ meson in the quark model can not carry the following quantum
numbers: 0−−,0+−,1−+,2+−,···. Stateswiththese JPC quantumnumbersarebeyondthenaivequarkmodel,which
are sometimes denoted as exotic or non-conventional states. Different from the meson case, the qqq baryon in the
quarkmodelcanexhaustalltheJPquantumnumbers,i.e.,JP = 1±,3±,5±,···.
2 2 2
However,theconstituentquarkmodelcannotbederivedrigorouslyfromQCD.Thequarkmodelspectrumisnot
necessarilythesameastheQCDhadronspectrum. QCDmayallowamuchricherhadronspectrum.
Infact,atthebirthofthequarkmodel[18,19],Gell-MannandZweigproposednotonlytheexistenceoftheqq¯
mesonsandqqqbaryonsbutalsothepossibleexistenceoftheqq¯qq¯ tetraquarksandqqqqq¯ pentaquarks. Theconcept
ofthemultiquarkswasproposedevenbeforetheadventofquantumchromodynamics(QCD)!
In Ref. [18], M. Gell-Mann wrote: “Baryons can now be constructed from quarks by using the combinations
(qqq),(qqqqq¯),etc.,whilemesonsaremadeoutof(qq¯),(qqq¯q¯),etc.”
InRef.[19],G.Zweigalsowrote: “Ingeneral,wewouldexpectthatbaryonsarebuiltnotonlyfromtheproduct
oftheseaces,AAA,butalsofromA¯AAAA,A¯A¯AAAAA,etc.,whereA¯denotesananti-ace. Similarly,mesonscouldbe
formedfromA¯A,A¯A¯AA,etc.”
The multiquarks can be further classified into tetraquarks (qqq¯q¯), pentaquarks (qqqqq¯), dibaryon (qqqqqq) and
baryonium(qqqq¯q¯q¯)etc. JaffestudiedthetetraquarkstateswithintheframeworkoftheMITbagmodelin1976[20,
21]. This subject was later studied by Chan and Hogaasen [22], and many other theorists. The tetraquark states
containing heavy quarks were investigated by Chao in 1979 [23, 24]. The pentaquarks (qqqqq¯) composed of light
quarkswereinvestigatedbyHogaasenandSorba[25]in1978andStrotmannin1979[26]. Thename“pentaquark”
wasfirstproposedbyLipkinin1987[27]. Twogroupsstudiedpossiblepentaquarkscontainingonecharmquarkin
1987[28,27].
5
In 2003, the LEPS Collaboration announced the observation of the Θ pentaquark which is composed of uudds¯
[29]. However,thisstatewasnotconfirmedbythesubsequentmoreadvancedexperiments[30].
Jaffe also discussed the H-dibaryon, where six light quarks uuddss are confined within one MIT bag [31]. In
nature there exists the deuteron which is also composed of six light quarks (see discussions in Refs. [32, 33]). The
difference between the dibaryon and deuteron lies in their color configurations. Within the deuteron, there are two
quarkclusters,bothofwhicharecolorsinglets. Forthedibaryon,oneexpectssixquarkswithinonecluster.
In QCD, the gluons not only mediate the strong interaction between quarks but also interact among themselves
since they carry color charges. Two or more gluons may form the color singlet, which is called the glueball. One
or more gluons may interact with a pair of quark and antiquark to form the hybrid meson. The hybrid mesons or
tetraquarkstatesortheglueballscancarryalltheso-calledexotic JPC quantumnumbersinthequarkmodel. Strictly
speaking, there does not exist any exotic quantum number from the viewpoint of QCD. One can construct color-
singlet local operators to verify that these quantum numbers are allowed in QCD. We shall illustrate this point in
thefollowingsections. Throughoutthisreview,eithertheword“exotic”or“non-conventional”shouldbeunderstood
withinthecontextofthequarkmodel.
1.1.3. ComparisonofQEDandQCDandtheirspectrum
Quantum Electrodynamics (QED) is very different from QCD. The gauge group of QED is U(1). The photon
mediatestheelectromagneticinteractionsbetweencharges. However,thephotonisneutralanddoesnotcarrycharge.
There does not exist the photon self-interaction. We do not have the analogue of the glueball and hybrid meson in
QED.Insteadtherearefreeelectronsandphotonswhileallquarksandgluonsareconfinedwithinthehadrons.
Excepttheabovebigdifference,it’sintriguingtonoticethesimilaritybetweenQEDandQCD.Inthefollowing,
we compare the well-known bound states in QED and possible hadrons in QCD. In QED we have the bound states
composed of e+e−, µ+µ−, µ+e−. In QCD we have the light mesons composed of qq¯, ss¯, sq¯, where q = u,d is the
up/downquark,andsisthestrangequark. ForthehydrogenatominQED,theelectroncirclesaroundtheproton. For
theheavy-flavoredmeson/baryoninQCD,thelightquarkscirclearoundtheheavycharmorbottomquark.
In QED there exist the bound states composed of e+e−e+e− and e+e−µ+µ− [34, 35]. In QCD some of the scalar
mesons below 1 GeV may have the flavor configurations qq¯qq¯ and qq¯ss¯. In QED we have the hydrogen molecule
wheretwoelectronsaresharedbythetwoprotonsandthevalencebondbindsthissystemtightly. InQCDwemay
expecttheqQ¯qQ¯ andq¯QqQ¯ tetraquarkstateswithinoneMITbag,wherethetwolightquarksaresharedbythetwo
heavyquarks.
InQEDthereexistmanymoleculeswhicharelooselyboundbythevanderVaalsforce. ThevanderVaalsforce
isnothingbuttheresidualelectromagneticforcearisingfromthetwo-photonexchangeprocessinQED.InQCDwe
have the deuteron which is the hadronic molecular state bound by the meson exchange force. At the quark-gluon
level, the meson exchange force is the residual strong interaction force arising from the gluon and quark exchange
process. In QCD we may also expect other loosely bound deuteron-like molecular states composed of two heavy
flavoredhadrons.
1.2. Generalstatusofhadronspectroscopy
Althoughmostoftheobservedhadronscanbeclassifiedastheordinaryqq¯ mesonsandqqqbaryons,therehave
beenhugetheoreticalandexperimentaleffortstosearchforthecandidatesoftheexotichadrons. Theseexoticstates
encodeimportantinformationofQCD.Forexample,theidentificationoftheglueballsandhybridmesonswillestab-
lishthedirectevidenceofthedynamicalroleofthegluonsinthelowenergysector.
The exotic JPC quantum numbers provide a convenient handle in the search of the nonconventional states. If a
resonancedecaysintothefinalstatewithJPC =1−+,theparentresonanceisagoodcandidateofthehybridmeson.
On the other hand, the exotic flavor quantum number is also a valuable asset in the experimental search of the
exotic states. If the resonance carries the isospin I = 2 or a meson has an isospin I = 3/2, it may be a multiquark
candidate. For the Θ resonance, its baryon number is 1 and strangeness S = +1. Hence, it must be a candidate of
pentaquarks.
Some hadrons do not have exotic JPC or flavor quantum numbers. But they may have exotic color or flavor
orspatialconfigurations. Thesestatescanbesearchedforthroughtheoverpopulationofthequarkmodelspectrum.
Sometimesthedeviationfromthequarkmodelpredictionsoftheirmasses,decaywidths,variousreactions,production
anddecaybehaviorsmayalsoprovideinsightfulcluesinthesearchoftheexoticstates.
6
Let’s take the JPC = 0++ scalar isoscalar mesons as an example. Below 2 GeV, we have σ, f (980), f (1370),
0 0
f (1500), f (1710), f (1790), f (1810) [1]. Within the quark model, there are only four scalar isoscalar mesons
0 0 0 0
withinthismassrangeevenifweconsidertheradialexcitations. Clearlythereisseriousoverpopulationofthescalar
spectrum. The quark content of some of the above states can not be qq¯. Overpopulation of the spectrum provides
anotherusefulwindowintheexperimentalsearchofthenon-conventionalstates.
Let’smoveontotheninescalarmesonsbelow1GeV,whichplayafundamentalroleinthespontaneousbreaking
of the chiral symmetry in QCD. The scalar meson carries one orbital excitation. Hence, its mass is expected to be
several hundred MeV higher than the ρ meson mass in the quark model. Either lattice QCD simulation or other
theoreticalapproachesindicatesthe L = 1qq¯ stateliesaround1.2GeV.Withinthequarkmodel,the f (980)meson
0
withthequarkcontent ss¯shouldbe200 ∼ 300MeVheavierthanthea (980)withthequarkcontentqq¯. However,
0
theyarealmostdegenerateinreality. Theunusuallowmassofthescalarnonetandtheabnormalmassorderingofthe
f (980)anda (980)aretwopuzzlesinthequarkmodel. Incontrast,bothpuzzlescanbesolvedverynaturallyifthe
0 0
scalarmesonsbelongtothetetraquarknonet[21,36]. Thechiralunitaryapproachfortheinteractionofpseudoscalar
mesonsmayalsogiverisetothesestructures[37,38,39].
Since2003,manycharmonium-likestateshavebeenobservedthroughBmesondecays,theinitialstateradiation
(ISR),double charmoniumproduction, two photonfusion, and excitedcharmoniumor bottomoniumdecays. Some
of them do not fit into the quark model spectrum easily and are proposed as the candidates of the hidden-charm
exotic mesons, including the di-meson molecular states, tetraquarks, hybrid charmonium states and conventional
charmoniumstatesdistortedbythecoupled-channeleffects,etc. Molecularstatesarelooselyboundstatescomposed
ofapairofheavymesons. Theyareprobablyboundbythelong-rangecolor-singletpionexchange. Tetraquarksare
boundstatesoftwoquarksandtwoantiquarks,whichareboundbythecoloredforcebetweenquarksandantiquarks.
There are many states within the same tetraquark multiplet. Some members are charged or even carry strangeness.
Hybridcharmoniaareboundstatescomposedofacharmquark-antiquarkpairandoneexcitedgluon.
In this review, we focus on the recent experimental and theoretical progress on the hidden-charm multiquark
systems such as hybrid charmonia, hidden-charm tetraquarks, hidden-charm pentaquarks, and hadronic molecules
composedofapairofheavy-flavoredhadrons. InterestedreadersmayalsoconsultreviewsinRefs. [40,41,42,43,
44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,39].
2. Experimentalprogressonthehidden-charmmultiquarkstates
2.1. TheCharmonium-likeXYZstates
Withtheexperimentalprogress,thefamilyofthecharmonium-likestateshasbecomemoreandmoreabundant.To
date,dozensofcharmonium-likestateshavebeenobservedbyseveralmajorparticlephysicsexperimentalcollabora-
tionssuchasCLEO-c,BaBar,Belle,BESIII,CDF,DØ,LHCb,CMSandsoon.Since2003,thesecollaborationshave
beencontinuingtosurpriseuswithnoveldiscoveries,whichhaveinspiredtheorists’extensiveinterestsinexploring
theunderlyingmechanismbehindthoseexoticphenomena. Asoneofthemostimportantissuesinhadronphysics,
the study of the charmonium-like states provides us a good chance to deepen our understanding of the complicated
non-perturbative behavior of QCD in the low energy regime. Especially, investigations of the underlying structures
of the charmonium-like states may help us to understand the mechanism of the confinement and chiral symmetry
breakingbetter.
All the above major particle physics experimental collaborations have contributed to the observations of the
charmonium-like states. Before reviewing the experimental status of the charmonium-like states, we would like
tointroducethecollaborationsbriefly:
1. CLEO-c: CLEO-c was the experiment at the Cornell Electron Storage Ring (CESR) located at Wilson Lab-
oratory of Cornell University. As the upgrade of CLEO, the CLEO-c experiment ran at lower energies and
carried out the study of charmonia and charmed mesons due to the competition from two B factories BaBar
andBelle. TheCLEO-cexperimentconfirmedtheobservationoftheY(4260)[60]. AlthoughCLEO-cfinished
data-collectingon3March2008,theaccumulatedCLEO-cdatawasappliedtoconfirmtheobservationofthe
chargedcharmonium-likestructureZ (3900)[61].
c
2. BaBar:AsoneofthetwoBfactories,theBaBarexperimentwasdesignedtostudyCPviolationintheBmeson
system. ItsdetectorwaslocatedatSLACNationalAcceleratorLaboratory,whichceasedoperationon7April
7
2008. However, itsdataanalysisisstillongoing. DuetothedevelopmentoftheInitialStateRadiation(ISR)
technique, the BaBar experiment also focused on the study of charmonia and charmonium-like states. In the
pastdecade,BaBarhasplayedacrucialroleinthediscoveriesofmanycharmonium-likestates. Forexample,
BaBarfirstobservedthefamousY(4260)inthee+e− → J/ψπ+π−process[62].
3. Belle: As the other B factory, the Belle experiment was located at the High Energy Accelerator Research
Organization(KEK),whichwasalsosetuptostudyCPviolationinthe Bmesonsystem. Asabyproduct,the
BelleCollaborationdiscoveredmanycharmonium-likestates. Forexample, Bellereportedtheobservationof
theX(3872)in2003[63],whichisthefirstmemberinthefamilyofthecharmonium-likestates.AlthoughBelle
finisheditsdata-takingon30June2010,itsdataanalysisisgoingon.
4. BESIII: BESIII is the experiment at Beijing Electron-Positron Collider II (BEPC II), located at Institute of
HighEnergyPhysics(IHEP).Sinceitscenterofmassenergycangoupto4.6GeV,theBESIIIexperimenthas
becomeanidealplatformtoexplorethecharmonium-likestates. In2013,BESIIIannouncedtheobservationof
thechargedcharmonium-likestructureZ (3900)[64].
c
5. CDF and DØ: CDF and DØ were the two particle experiments located at the Tevatron at Fermilab. They
discoveredthetopquarkin1995[65,66]. TheCDFandDØexperimentsbothconfirmedtheX(3872)[67,68].
TheCDFCollaborationalsoreportedthecharmonium-likestateY(4140)[69].
6. LHCb: AsoneofsevenparticlephysicsexperimentsattheLargeHadronCollider(LHC)atCERN,theLHCb
experimentfocusesonB-physics. LHCbalsostudiestheproductionsofthecharmonium-likestatesthroughthe
direct ppcollisionsandthe Bmesondecays. Forexample, theLHCbCollaborationmeasuredthespin-parity
quantumnumberoftheX(3872)[70].
7. CMS:CMSisanotherimportantexperimentatLHCatCERN.TheCMSandATLAScollaborationsdiscovered
theHiggsBosoninJuly2012[71,72]. Inrecentyears,CMSalsocontributedtothesearchofthecharmonium-
likestatessuchastheX(3872)[73]andtheY(4140)[74].
Figure1:(Coloronline)Thelogosoftheexperimentalcollaborationswhichcontributedtotheobservationofthecharmonium-likestates.
InFig. 1,wecollectLogosoftheseexperimentalcollaborationswhichhavecontributedtotheobservationsofthe
charmonium-likestates.
Accordingtothedifferentproductionmechanisms,alltheobservedcharmonium-likestatescanbecategorizedinto
fivegroupsasshowninFig. 2. Thestatescollectedinthefirst,second,third,andfourthcolumnsareproducedviathe
Bmesondecays, initialstateradiationtechnique(ISR)inthee+e− annihilation, thedoublecharmoniumproduction
processes, and two photon fusion processes, respectively. The Z (3900)/Z (4025)/Z (3885)/Z (4200) listed in the
c c c c
fifthcolumnareproducedfromthehadronicdecaysoftheY(4260).
2.1.1. XYZstatesproducedthroughBmesondecays
2.1.1.1. X(3872). The X(3872) resonance was first observed by the Belle Collaboration in 2003 [63]. Since its
discovery,itsexistencewasconfirmedbymanysubsequentexperiments[75,76,77,78,79,80,67,81,82,83,68,84,
85,86,87,88,89,90,91,70,92,73,93]asshowninFig. 3. Despitethehugeexperimentalefforts,westilldonot
fullyunderstanditsnature.
8
s
c e− γ c e− c γ c π∓
γ* γ* c Y(4260)
b c
Z±
c c
q q e+ c e+ J/ψ γ
X(3872) Y(4260) X(3940) X(3915) Z (3900)
c
Y(3940) Y(4008) X(4160) X(4350) Z (4025)
c
Z+(4430) Y(4360) Z(3930) Z (4020)
c
Z+(4051) Y(4630) Z (3885)
c
Z+(4248) Y(4660)
Y(4140)
Y(4274)
Z +(4200)
c
Z+(4240)
X(3823)
Figure2:(Coloronline)Fivegroupsofthecharmonium-likestatescorrespondingtofiveproductionmechanisms.
45
GeV )40 a) GeV )35 b) GeV )25 c)
Events / ( 0.005 3305 Events / ( 0.005 2350 Events / ( 0.015 20
25 20 15
20
15
10
15
10
10
5
5 5
0 0 0
5.2 5.215.225.235.245.255.265.275.285.29 5.3 3.82 3.84 3.86 3.88 3.9 3.92 -0.1 -0.05 0 0.05 0.1 0.15 0.2
Mbc (GeV) M(J/ψπ π) (GeV) ∆E (GeV)
(cid:113)
Figure3: (Coloronline)Thebeam-energyconstrainedmass Mbc = (EbCeMam)2−(pCBM)2 (left),theπ+π−J/ψinvariantmass(middle),andthe
energydifference∆E=ECM−ECM (right)fortheX(3872)→π+π−J/ψsignalregion,fromBelle[63].
B beam
9
n 107
bi LHCb
s /
nt 106
e
m Simulated JPC=2-+ Simulated JPC=1++
peri 105
x
e
of
er 104
b t
m
u data
N 103
102
-200 -100 0 100 200
t = -2 ln[ L(2-+)/L(1++) ]
Figure4:(Coloronline)DistributionoftheteststatistictforthesimulatedexperimentswithJPC =2−+and1++,fromLHCb[70],withtdatathe
valueoftheteststatisticforthedata.
ThemassandwidthoftheX(3872)fromdifferentexperimentsaresummarizedinTable1.Afittotheseparameters
yields an average mass (3871.69±0.17) MeV [1] and a width < 1.2 MeV at 90% C.L. [80]. Its mass is extremely
closetotheD0D¯∗0massthreshold,(3871.81±0.09)MeV.WealsocollectitsproductionsanddecaymodesinTable1.
The X(3872) was mostly observed in the B meson decay process B±,0 → K±,0X(3872) with the X(3872) decaying
(S)
into π+π−J/ψ. The X(3872) was also produced in pp¯ annihilations, pp collisions, and e+e− annihilations (possibly
throughtheY(4260),seeSec.2.1.2.1)anddecaysintoD∗0D¯0, D0D¯0π0,γJ/ψ,γψ(3686),andωJ/ψwithωdecaying
intoπ+π−π0. ItsquantumnumbershavebeenstudiedbyBelle,BaBarandCDF,anddeterminedtobeIGJPC =0+1++
bytherecentLHCbexperiment[70],asshowninFig.4.
BesidestheresonanceparameterslistedinTable1,theseexperimentsprovidedmanybranchingfractions.Theyare
alsousefulexperimentalinformation,andwesummarizesomeoftheminTable2. Particularly,welistthefollowing
isospin-violatingbranchingfractions
Γ(X →π+π−π0J/ψ)
= 1.0±0.4±0.3, (10)
Γ(X →π+π−J/ψ)

Γ(X →ωJ/ψ) =  0.7±0.3 for B+ events , (11)
Γ(X →π+π−J/ψ)  1.7±1.3 for B0 events
whichwereobservedbyBelle[75]andBaBar[90],respectively.
The difference between B0 → K0X and B± → K±X also attracted much experimental interest. The Belle Col-
laboration measured the ratio of branching fractions Γ(B0 → K0X)/Γ(B+ → K+X) to be (0.82±0.22±0.05) [77],
(1.26±0.65±0.06)[78]and(0.50±0.14±0.04)[80],andthemassdifferencebetweentheX(3872)statesproducedinB+
andB0decaytobeδM = M(B+→K+X)−M(B0→K0X) =(0.18±0.89±0.26)MeV[77]and(−0.69±0.97±0.19)MeV[80],
whiletheBaBarCollaborationmeasuredthisratiotobe(0.50±0.30±0.05)[85],and(0.41±0.24±0.05)[88],andthis
massdifferencetobe(2.7±1.3±0.2)MeV[85]and(2.7±1.6±0.4)MeV[88],wherewehaveassumedexperimental
resultsfromB+andB−arethesame.
Besidestheaboveobservations,theX(3872)resonancewasnotseen(allvaluesaregivenat90%confidencelevel
(C.L.).):
1. intheγχ decaymodeinBelle[63],andtheupperlimitwasmeasuredtobe
c1
Γ(X(3872)→γχ )
c1 <0.89. (12)
Γ(X(3872)→π+π−J/ψ)
10