The hidden-charm multiquark states

0.08 MB·

by  Hua-Xing Chen

The hidden-charm multiquark states
7 Hua-XingChen
1
SchoolofPhysicsandBeijingKeyLaboratoryofAdvancedNuclearMaterialsandPhysics,
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2 BeihangUniversity,Beijing100191,China

n
WeiChen
a
J
DepartmentofPhysicsandEngineeringPhysics,UniversityofSaskatchewan,Canada
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Jun He
]
h
p NuclearTheoryGroup,InstituteofModernPhysicsofCAS,Lanzhou730000,China
-
p XiangLiu
e
h SchoolofPhysicalScienceandTechnology,LanzhouUniversity,Lanzhou730000,China
[
Shi-Lin Zhu∗†
1
v DepartmentofPhysicsandStateKeyLaboratoryofNuclearPhysicsandTechnology
1 andCollaborativeInnovationCenterofQuantumMatter,
5
PekingUniversity,Beijing100871,China
5
1 E-mail: [email protected]
0
.
1 Since2003manycharmonium-likestateswereobservedexperimentally.Especiallythosecharged
0
charmonium-likeZ states andbottomonium-likeZ states cannotbe accommodatedwithin the
7 c b
1 naive quark model, which are good candidates of either the hidden-charm tetraquark states or
:
v moleculescomposedofapairofcharmedmesons. In2015,theLHCbCollaborationdiscovered
i
X twohidden-charmpentaquarkstates,whicharealsobeyondthequarkmodel. Inthistalk,were-
r viewthecurrentexperimentalprogressandinvestigatevarioustheoreticalinterpretationsofthese
a
candidatesofthemultiquarkstates. Welistthepuzzlesandtheoreticalchallengesofthesemod-
elswhenconfrontedwith theexperimentaldata. We also discusspossiblefuturemeasurements
whichmaydistinguishthetheoreticalschemesontheunderlyingstructuresofthehidden-charm
multiquarkstates.
The26thInternationalNuclearPhysicsConference
11-16September,2016
Adelaide,Australia
∗
Speaker.
†Plenarytalk.
(cid:13)c Copyrightownedbytheauthor(s)underthetermsoftheCreativeCommons
Attribution-NonCommercial-NoDerivatives4.0InternationalLicense(CCBY-NC-ND4.0). http://pos.sissa.it/
Shi-LinZhu
1. Motivation
We all know the motion and interaction of hadrons differ from those of nuclei and quark or
gluons. Hadron physics is the bridge between nuclear physics and particle physics. The famous
Higgsmechanismcontributesaround20MeVtothenucleonmassthroughthecurrentquarkmass.
Nearlyallthemassofthenucleon andvisiblematterinouruniversecomesfromthenonperturba-
tive QCD interaction. The study of hadron spectrum explores the mechanism of confinement and
chiralsymmetrybreaking(c SB).
According to the number (N) of the valence quarks, we have the glueballs (N=0), mesons
(N=2), baryons (N=3), tetraquarks (N=4), pentaquarks (N=5), deuteron (N=6), nuclei, neutron
stars. Atpresent, thetetraquarks andpentaquarks arestillmissing.
It’sinteresting tocompareQCDandQED.Infact,theQEDanalogues ofthebaryon,glueball
andhybridmesondoNOTexist. However,therearecommonfeaturesbetweentheQEDandQCD
spectrum. Forthepositronium,wehavethepionwhichiscomposedofqq¯. Forthehydrogenatom,
wehavetheheavymesonandbaryonwherethelightquarkscirclearoundtheheavyquark. Forthe
positronium molecule,onemayexpectthelightscalartetraquarkcandidates suchasthesigmaand
kappa mesons. For the hydrogen molecule, one may expect the hidden-charm tetraquark states.
For the polarized atoms or molecules, we have the deuteron. We may also expect other hadronic
molecules composedofheavyhadrons.
The organizers of the conference asked me to tell the audience why the XYZ states are in-
teresting to nuclear physicists. First of all, some XYZ state may be shallow deuteron-like states.
The chiral dynamics (or the pion-exchange force) and coupled channel effects are important. We
can use the same nuclear physics techniques to study some of the XYZ states. In my talk I will
mainly focus on the XYZ states which the audience may have interest in. Interested readers may
alsoconsulttheextensivereviewonthehidden-charm multiquarkstates[1].
2. Experimental status
Since 2003, many charmonium-like states were observed. Their production mechanisms in-
cludetheinitialstateradiation,doublecharmoniumproduction,two-photonfusion,Bmesondecay
and excited charmonium decays etc. Their discovery modes include both the hidden-charm and
open-charm modes.
Up to now, the lattice QCD simulation reproduces the charmonium spectrum below the DD¯
threshold verywell. Ontheother hand, manynewstates abovetheDD¯ threshold werediscovered
experimentallysince2003. Someareevencharged. Theyaregoodcandidatesoftheexoticmesons.
In the very beginning, I want to emphasize that many XYZ states lie very close to the open-
charm threshold. It’s quite possible that some states are not real resonances. They could be fake
signals arisingfrom
• -Kinematical effect
• -Openingofnewthreshold
• -Cuspeffect
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• -Finalstateinteraction
• -Interference betweencontinuum andwell-knowncharmonium states
• -Trianglesingularity duetothespecialkinematics
• -···
3. Theory
Many XYZstates do not fitinto quark model spectrum easily. There are some popular theo-
reticalspeculations.
• Hadronic molecules are loosely bound states composed of a pair of heavy hadrons. The
long-range pion exchange force may play an important role in the formation of the loosely
bound hadronic molecules. The molecular states may be quite sensitive to the isospin con-
figurations.
• Tetraquarks are speculated to be tightly bound objects of four quarks. They are bound by
thecolored-force betweenquarks. Theymaydecaythrough rearrangement. Sincethedomi-
nant partofthecolorconfining forceareflavorindependent, thetetraquarks shall alwaysbe
accompanied by partner states. In general, there are many states within the same multiplet.
Some are even charged or carry strangeness, which provides a powerful handle in the ex-
perimental searchofthesestates. Thecolor-magnetic interaction isresponsible forthemass
splitting between these states. If one member of the multiplet exists, all the other members
should alsoexist.
• Hybridcharmonium areboundstatescomposed ofapairofquarksandoneormoregluons.
• Last but not the least, these XYZ states could also be the conventional charmonium. One
should be very cautious that the quark model spectrum could be distorted by the coupled-
channel effects.
4. Selected examples: P,X(3872),Z /Z ,Y(4260)
c b c
The multiquark states were first proposed by Gell-Mann in 1964 in his pioneering paper [2].
However,noconvincing stateswerediscovered inthepastseveraldecades. In2003, LEPScollab-
oration reportedtheQ pentaquark [3]. Nowthissignaldisappeared.
4.1 P states
c
In 2015, the LHCb collaboration reported two hidden-charm pentaquark states [4]. In the
decay process L →J/y PK, LHCb observed two resonances in the J/y P final state. The lower
b
state is broad. Its mass is 4380 MeV and width is around 205 MeV. The higher state lies around
4450 MeV. It’s quite narrow. From the best fit, their spin-parity quantum numbers are 3− and 5+
2 2
respectively.
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According to the color configurations, there are two possible binding mechanisms: tightly
bound or weakly bound. The idea of the loosely bound molecular states is not new in nuclear
physics sinceYukawaproposed thepion in1935. Thedeuteron isaveryloosely bound molecular
statecomposedofaprotonandneutronarisingfromthecolor-singlet mesonexchange.
Weadoptedthesameone-meson-exchange formalismtodiscussthepossiblemolecularstates
composed of apair ofheavy hadrons. The charmed meson and baryon are the same as the proton
and neutron inthe formation ofthe loosely bound molecular states. Severalyears ago, westudied
the hidden-charm molecular baryons composed of anti-charmed meson and charmed baryon [5].
ThelowerstateP(4380)couldbeexplainedtheD¯(∗)S (∗) molecule[5,6].
c c
Through the S-wave charmed meson and baryon scattering, the hidden-charm baryons with
negative parity can also be generated dynamically [7]. The total widths of the hidden-charm
baryons were less than 60 MeV, quite narrow. The charm-less decay modes are important within
thisformalism.
The two P states were also explained as the tightly bound states [8, 9]. For example, the
c
authors of Ref. [8] assumed quarks and diquarks are fundamental building blocks in the diquark
model. ThemassdifferencebetweenP(4380)andP(4450)isabout70MeV,whichis-partlydue
c c
to theorbital excitation around 280 MeVandpartly duetothe massdifference between thescalar
andaxial-vector diquarks around200MeV.
Theotherpossible interpretations oftheseP statescanbefoundinthereview[1].
c
4.2 X(3872)
In 2003, Belle collaboration observed X(3872) in the J/ypp mode [10], which was the first
XYZ state. The JPC quantum numbers of X(3872) are 1++. Its production rate at the hadron
colliders (TetraronandLHC)issimilartothatofy ′. Thequarkmodelprediction forthe c ′ mass
c1
isroughly100MeVhigher, wherethe c ′ istheradialexcitation oftheaxialvectorcharmonium.
c1
X(3872) lies very close to the D¯D∗ threshold with a mass difference less than 0.2 MeV.
This state is very narrow. Its total width is less than 1 MeV. The discovery mode X(3872) →
J/yr →J/ypp violates isospin symmetry, but itsdecay widthis comparable to thedecay width
of X(3872) → J/yw → J/yppp decay mode. One may wonder whether X(3872) is an axial-
vectorcharmonium ormolecularstate.
Within the meson exchange model, we considered (1) the S-D wave mixing which plays an
important roleinforming theloosely bound deuteron; (2)the massdifference between theneutral
and charged D/D∗ mesons, and (3) the coupling ofD¯D∗ toD¯∗D∗ channel [11,12, 13]. Wenotice
that X(3872) is a good candidate of the loosely bound molecular state. In fact, if we replace the
protonandneutroninsidethedeuteronbytheD¯ andD∗mesons,wereproducetheX(3872). Within
themolecular scheme,thelargeisospin violation canbeexplained naturally [11].
However, the E1 decay pattern suggests that X(3872) is a good candidate of the axial vector
charmonium [14,15]. IfX(3872)isaradialexcitationofc ,boththeradialwavefunctionsofc ′
c1 c1
and y (2S) contain one node. Their overlapping is large. c ′ will decay into y (2S)g more easily.
c1
In fact, the experimental E1 decay rate of X(3872) is consistent with the quark model prediction
forthe c ′ .
c1
Based on the measurement of the E1 decay ratio, LHCb concludes: "The measured value
agreeswithexpectationsforapurecharmoniuminterpretationofX(3872)andamolecular-charmonium
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mixtureinterpretations"[15]. Moreover,thelargeproductioncrosssectionofX(3872)atLHCwith
verylargeP iscomparablewiththatofy (2S),whichrequiresasignificantcc¯component. Onthe
T
other hand, the isospin violating dipion decay ofX(3872) requires the molecular component. The
current experimental information strongly suggests that X(3872) should probably be a mixture of
c ′ andD¯D∗ molecule[16].
c1
The recent dynamical lattice QCD simulation used many operators including cc¯, two-meson
anddiquark-antidiquark ones[17]. TheyfoundalatticecandidatefortheX(3872)withJPC=1++
and I = 0 only if both the cc¯ and D¯D∗ operators are included. This candidate cannot be found
withoutthecc¯component. ThislatticeQCDsimulation strongly supports X(3872)asamixtureof
cc¯andmolecule.
It’s interesting to compare three candidates of the exotic states: L (1405), D (2317) and
sj
X(3872). L (1405) is lower than the quark model prediction for the P-wave uds state and lies
veryclosetotheK¯N threshold. D (2317)islowerthanthequarkmodelpredictionfortheP-wave
sj
charm strange meson and lies very close to the DK threshold. X(3872) is lower than the quark
modelprediction fortheP-wavecc¯state c ′ andliesveryclosetotheD¯D∗ threshold.
c1
In the above three cases, we observe the common feature: the couple channel effects play
a very important role and lower the bare quark model level significantly. The S-wave continuum
couplestothebarequarkmodelstatestrongly. Thequarkmodelspectrumisdistorteddramatically.
For comparison, the bottomonium analogue X was not found since c ′ is not close to the B¯B∗
b b1
threshold.
4.3 ThechargedZ andZ states
b c
Let’s move on to the charged states. In 2011, Belle collaboration observed two charged Z
b
states [18]. They are very close to the B¯B∗ and B¯∗B∗ threshold with JP =1+. Their open-bottom
decay modes are dominant. Later, BESIII [19] and Belle [20] collaborations observed a similar
state Z (3900) in the J/yp mode, which is close to the D¯D∗ threshold with JP =1+. This state
c
was also observed inthe D¯D∗ mode. Compared with thetraditional charmonium, the open-charm
decaymodeofZ (3900)isstrongly suppressed. Thedecaydynamicsmightbedifferent. TheseZ
c b
andZ statesareverysimilar.
c
OnemaywonderwhetherZ andZ aretetraquarkstates. Iftheyaretetraquarks,theyshallfall
b c
apart into the open-charm modes easily. The s-wave D¯D∗ mode should dominate the D¯∗D∗ mode
for thehigher state Z (4025) because ofthe huge phase space difference. However, BESIIIdidn’t
c
observeD¯D∗ modeforZ (4025)uptonowwhileBelledidn’tobserveB¯B∗ modeforthehigherZ
c b
state.
Let’s turn back to the above dynamical lattice QCD simulation, which used many operators.
They didn’t find any exotic candidates in the isovector channel. This lattice QCD simulation
strongly disfavors either the diquark-antidiquark or tetraquark interpretations of the X(3872) and
Z (3900)[17].
c
IftheZ states arerealresonances, theycould bethe S-waveB¯(∗)B∗ molecular states [21, 12,
b
13]. Infact,withinthemesonexchangemodel,bothZ statescanbeexplainedastheB¯B∗andB¯∗B∗
b
molecules. BesidestheisovectorZ states,therearealsoseverallooselyboundisoscalarmolecular
b
states. However, within the same model, the Z states seem unbound with a "reasonable" cutoff
c
parameter [22, 23]. The potential is roughly the same for the Z and Z systems. But the kinetic
b c
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energy oftheZ systems islarger since theDmeson massissmaller than the Bmeson mass. The
c
hidden-charm/bottom moleculeswerediscussed extensively inliterature [22,23,24,25,26].
The Z states lie above the open-charm thresholds. Their measured mass and width seem
c
channel dependent. Could they be non-resonant signals arising from open-charm/bottom thresh-
olds, final state interactions such as D¯D∗ rescattering or triangle singularity etc? Some of these
non-resonant mechanismscouldexplainthecurrentexperimental data.
4.4 Y(4260)
In PDG, there are three well-established vector charmonium above 4 GeV: 3S/y (4040),
2D/y (4160),4S/y (4415). Inthequarkmodel,oneexpectsatmostfivevectorcharmoniumstates
between 4 and 4.7 GeV: 3S/y (4040), 2D/y (4160), 4S/y (4415), 3D, 5S. But seven states were
observed experimentally: y (4008), y (4040), y (4160), y (4260), y (4360), y (4415), y (4660).
Whataretheseadditional Ystates? Thesituation isveryconfusing now.
Y(4260)wasfirstdiscovered intheJ/ypp modewiththeISRtechnique byBabarcollabora-
tion [27]whileY(4360) wasobserved inthey (2S)pp channel withthesametechnique [28]. But
these two states were not observed in the R-value scan and open-charm process. In the R-value
scan,allthewell-establishedvectorcharmoniumappearasapeak. ButY(4260)andY(4360)show
upasadip.
Y(4260) may be accommodated as the y (4S) charmonium state with the screened linear po-
tential[29]. Y(4260)alsoseemsaverygoodcandidateofthecharmoniumhybrid[30,31,32]. Ac-
cordingtolatticeQCDsimulation[33,34],thevectorhybridcharmoniumliearound4.26GeV.Be-
−−
causeofthegluon,the1 hybridcharmoniumdoesnotcoupletothevirtualphotonverystrongly,
which explains the dip in the R-value scan. One of the favorable decay mode of hybrid states is
the p-wave + s-wave meson pair, which explains the non-observation in the D(∗)D¯(∗) modes. The
cc¯pair withinthevector charmonium isaspin-singlet whilethegluon iscolor-magnetic, which is
favorable tothespin-singlet hidden-charm decaymode.
5. Summary
Now let me summarize. The excited Upsilon states act as a molecule factory. Because
M[¡ (5S)]=10.860GeV,M[BB∗+p ]=10.604+0.140=10.744GeV,andM[B∗B∗+p ]=10.650+
0.140=10.790 GeV, the phase space of the decay ¡ (5S)→B¯(∗)B∗p is tiny. The relative motion
between the B¯(∗)B∗ pair is very slow, which is favorable to the formation of the B¯(∗)B∗ molec-
ular states. ¡ (5S) or ¡ (6S) is the ideal place to study either the molecular states or the B¯(∗)B∗
interaction. Similarsignalswillbeproduced abundantly atBelle2inthecomingyears!
Thevectorcharmonium spectrum isverypuzzling atpresent. Theexcited charmonium decay
isidealinthesearchoftheZ signals. Theg ,1p ,2p ,3p andotherlightdegreeoffreedomwillact
c
asaquantum numberfilterofthese states. X(3872), c ′ ,and Y(4260) arethekeystates inreveal-
c1
ing the underlying structure of the charmonium-like XYZ states. Through the decay pattern and
possible partner states, wecantestthe various theoretical picture. Theexperimental measurement
ofthevariouspionicandelectromagnetic transitions arecrucial.
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Shi-LinZhu
Acknowledgments
The authors are grateful to X.L.Chen, M.L.Du, W.Z.Deng, N. Li, X.H.Liu, Y.R. Liu, Z.G.
Luo, L. Ma, T.G. Steele, Z.F. Sun, and L. Zhao for fruitful collaborations. This project was
supported by the 973 program and National Natural Science Foundation of China under Grants
11575008 and11621131001.
References
[1] H.X.Chen,W.Chen,X.Liu,andShi-LinZhu,Phys.Rept.639(2016)1-121.
[2] M.Gell-Mann,Phys.Lett.8(1964)214.
[3] T.Nakano,etal.,[LEPSCollaboration],Phys.Rev.Lett.91(2003)012002.
[4] R.Aaij,etal.,[LHCbCollaboration],Phys.Rev.Lett.115(2015)072001.
[5] Z.-C.Yang,Z.-F.Sun,J.He,X.Liu,S.-L.Zhu,Chin.Phys.C36(2012)6.
[6] R.Chen,X.Liu,X.-Q.Li,S.-L.Zhu,Phys.Rev.Lett.115(2015)132002.
[7] J.-J.Wu,R.Molina,E.Oset,B.S.Zou,Phys.Rev.Lett.105(2010)232001.
[8] L.Maiani,A.D.Polosa,V.Riquer,Phys.Lett.B749(2015)289.
[9] H.-X.Chen,W.Chen,X.Liu,T.G.Steele,S.-L.Zhu,Phys.Rev.Lett.115(2015)172001.
[10] S.K.Choi,etal.,[BelleCollaboration],Phys.Rev.Lett.91(2003)262001.
[11] N.Li,Shi-LinZhu,Phys.Rev.D86(2012)074022.
[12] X.Liu,Z.G.Luo,Y.R.Liu,Shi-LinZhu,Eur.Phys.J.C61(2009)411.
[13] Y.R.Liu,X.Liu,W.Z.Deng,Shi-LinZhu,Eur.Phys.J.C56(2008)63.
[14] B.Aubert,etal.,[BaBarCollaboration],Phys.Rev.Lett.102(2009)132001.
[15] R.Aaij,etal.,[LHCbCollaboration],Nucl.Phys.B886(2014)665.
[16] C.Meng,Y.-J.Gao,K.-T.Chao,Phys.Rev.D87(2013)074035.arXiv:hep-ph/0506222.
[17] M.Padmanath,C.B.Lang,S.Prelovsek,Phys.Rev.D92(2015)034501.
[18] A.Bondaretal.(BelleCollaboration),Phys.Rev.Lett.108(2012)122001.
[19] M.Ablikimetal.(BESIIICollaboration),Phys.Rev.Lett.110(2013)252001.
[20] Z.Q.Liuetal.(BelleCollaboration),Phys.Rev.Lett.110(2013)252002.
[21] Z.F.Sun,J.He,X.Liu,Z.G.Luo,Shi-LinZhu,Phys.Rev.D84(2011)054002.
[22] J.He,X.Liu,Z.F.Sun,Shi-LinZhu,Eur.Phys.J.C73(2013)2635.
[23] Z.F.Sun,Z.G.Luo,J.He,X.Liu,Shi-LinZhu,Chin.Phys.C36(2012)194.
[24] A.E.Bondar,A.Garmash,A.I.Milstein,R.Mizuk,M.B.Voloshin,Phys.Rev.D84(2011)054010.
[25] M.B.Voloshin,Phys.Rev.D84(2011)031502.
[26] S.Ohkoda,Y.Yamaguchi,S.Yasui,K.Sudoh,A.Hosaka,Phys.Rev.D86(2012)014004.
[27] B.Aubert,etal.,[BaBarCollaboration],Phys.Rev.Lett.95(2005)142001.
6
Shi-LinZhu
[28] B.Aubert,etal.,[BaBarCollaboration],Phys.Rev.Lett.98(2007)212001.
[29] B.Q.LiandK.T.Chao,Phys.Rev.D79(2009)094004.
[30] Shi-LinZhu,Phys.Lett.B625(2005)212.
[31] E.Kou,O.Pene,Phys.Lett.B631(2005)164.
[32] F.E.Close,P.R.Page,Phys.Lett.B628(2005)215.
[33] HadronSpectrumCollaboration(L.Liuetal.),JHEP1207(2012)126.
[34] Y.Chen,W.F.Chiu,M.Gong,L.C.Gui,Z.Liu,Chin.Phys.C40(2016)081002.
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