Hadron spectroscopy from strangeness to charm and beauty

0.24 MB·English

by  B. S. Zou

Nuclear
Physics A
NuclearPhysicsA00(2013)1–5
Hadron spectroscopy from strangeness to charm and beauty
B.S.Zou
3
1)StateKeyLaboratoryofTheoreticalPhysics,InstituteofTheoreticalPhysics,ChineseAcademyofSciences,Beijing100190,China
1
2)InstituteofHighEnergyPhysicsandTheoreticalPhysicsCenterforScienceFacilities,ChineseAcademyofSciences,Beijing100049,China
0
2

n
a
J

7
Abstract

] Quarksofdifferentflavorshavedifferentmasses,whichwillcausebreakingofflavorsymmetriesofQCD.Flavorsymmetriesand
h
theirbreakinginhadronspectroscopyplayimportantroleforunderstandingtheinternalstructuresofhadrons.Hadronspectroscopy
p
withstrangenessrevealstheimportanceofunquenched quarkdynamics. Systematicstudyofhadronspectroscopy withstrange,
-
p charmandbeautyquarkswouldbeveryrevealingandessentialforunderstandingtheinternalstructureofhadronsanditsunderlying
e quarkdynamics.
h
[
c 2012PublishedbyElsevierLtd.
(cid:13)
1
Keywords:
v
8
2
1. Hadronspectroscopywithstrangeness
1
1
Inclassicalconstituentquarkmodels,baryonsareascribedasthree-quark(qqq)statesandmesonsareascribedas
.
1 quark-anti-quark(qq¯)states. Thispictureisverysuccessfulinexplainingpropertiesofthespatialgroundstatesofthe
0
flavorSU(3)vectormesonnonet,baryonoctetanddecuplet.ItspredictedΩ(sss)baryonwithmassaround1670MeV
3
wasdiscoveredbylaterexperiments. Howeverevenforthelowestspatialexcitedstates, thispicturefailedbadlyin
1
: bothmesonandbaryonsectors.
v
Inthemesonsector,thelowestspatialexcitedSU(3)nonetisthescalarnonetcomposedof f (500),κ(600 800),
i 0 ∼
X a (980)and f (980). Intheclassicalconstituentquarkmodels,thesescalarsshouldbeqq¯ (L=1)stateswith f (500)
0 0 0
ar as(uu¯ +dd¯)/√2state, a00(980)as(uu¯ −dd¯)/√2stateand f0(980)asmainly ss¯state. Theninthispicture,itcannot
explainwhythemassofa (980)isdegeneratewith f (980)insteadofcloseto f (500)asintheρ-ωcaseinthevector
0 0 0
nonet. This made R.J.Jaffe [1] proposingthese scalars are q2q¯2 states instead of qq¯ states. In the new picture, the
f (500)isascribedas[ud][ud]state,a0(980)as([us][us] [ds][ds])/√2stateand f (980)as([us][us]+[ds][ds])/√2
0 0 − 0
state. Thisgivesanaturalexplanationofthedegeneracyofa (980)and f (980). Here[q q ]meansagooddiquark
0 0 1 2
withconfigurationofflavorrepresentation3¯, spin0andcolor3¯. Alternatively,thesescalarsarealsoproposedtobe
meson-mesondynamicallygeneratedstates[2,3].
In the baryon sector, the similar thing seems also happening [4]. In the classical quark models, the excited
baryonstatesaredescribedasexcitationofindividualconstituentquarks,similartothecasesforatomicandnuclear
excitations. The lowest spatial excited baryon is expected to be a (uud) N state with one quark in orbital angular
∗
momentumL = 1 state, andspin-parity1/2 . However,experimentally,the lowestnegativeparity N resonanceis
− ∗
foundtobe N (1535),whichisheavierthantwootherspatialexcitedbaryons: Λ (1405)and N (1440). Thisisthe
∗ ∗ ∗
long-standingmassreverseproblemforthelowestspatialexcitedbaryons.
1
B.S.Zou/NuclearPhysicsA00(2013)1–5 2
In the simple 3q constituent quark models, it is also difficult to understand the strange decay properties of the
N (1535),whichseemstocouplestronglytothefinalstateswithstrangeness.BesidesalargecouplingtoNη,alarge
∗
value of g is deduced [5, 6] by a simultaneousfit to BES data on J/ψ p¯pη, pK Λ¯ +c.c., and COSY
N (1535)KΛ −
∗ →
dataon pp pK+Λ. Thereisalsoevidenceforlargeg couplingfromγp pη reactionatCLAS[7]and
N (1535)Nη ′
→ ∗ ′ →
pp ppη reaction[8],andlargeg couplingfromπ p nφ,pp ppφandpn dφreactions[9,10,11].
′ N (1535)Nφ −
→ ∗ → → →
The third difficulty is the strange decay pattern of another member of the 1/2 -nonet, Λ (1670), which has its
− ∗
couplingtoΛηmuchlargerthanNK andΣπaccordingtoitsbranchingratioslistedinPDG[12].
Allthesedifficultiescanbeeasilyunderstoodbyconsideringlarge5-quarkcomponentsinthem[4,5,13,14].The
N (1535)couldbe the lowest L = 1 orbitalexcited uud > state with a largeadmixtureof [ud][us]s¯ > pentaquark
∗
| |
componenthaving[ud],[us]and s¯inthegroundstate. TheN (1440)couldbethelowestradialexcited uud >state
∗
withalargeadmixtureof [ud][ud]d¯>pentaquarkcomponenthavingtwo[ud]diquarksintherelativeP-w|ave.While
|
the lowest L = 1 orbitalexcited uud > state shouldhave a mass lower than the lowest radialexcited uud > state,
the [ud][us]s¯ > pentaquark com|ponent has a higher mass than [ud][ud]d¯ > pentaquark component.| The lighter
| |
Λ (1405)1/2 isalso understandableinthispicture. Itsmain5-quarkconfigurationis [ud][qs]q¯ > whichislighter
∗ −
|
thanthecorresponding5-quarkconfiguration [ud][us]s¯>intheN (1535)1/2 . Thelargemixtureofthe [ud][us]s¯>
∗ −
| |
pentaquark component in the N (1535) naturally results in its large couplings to the Nη, Nη, Nφ and KΛ. The
∗ ′
main5-quarkconfigurationfortheΛ (1670)is [us][ds]s¯>whichmakesitheavierthanother1/2 statesandlarger
∗ −
|
couplingtoΛη.
Besides the penta-quarkconfigurationswith the diquarkcorrelation, the penta-quarksystem may also be in the
formofmeson-baryonstates. TheN (1535),Λ (1405)andsomeotherbaryonresonancesareproposedtobemeson-
∗ ∗
baryondynamicallygeneratedstates[3,15,16,17,18,19,20].However,achallengeforthismeson-baryondynamical
pictureistoexplainthemassanddecaypatternoftheΛ (1670).
∗
Fromabovefactsanddiscussionforbothmesonandbaryonsectors,onecanseethatunlikeatomicandnuclear
excitationswherethenumberofconstituentparticlesarefixed,thefavorablehadronicexcitationmechanismforthe
lowestspatialexcitedstatesinlightquarksectorseemstobedraggingoutalightqq¯ pairfromgluonfieldratherthan
toexciteaconstituentquarktobeL=1state. Abreathingmodeofqqq qqqqq¯isproposed[21,22]forthelowest
↔
1/2 baryonnonet.Eachbaryonisamixtureofthethree-quarkandfive-quarkcomponents.
−
Whilethenewpicturegivesaniceaccountofpropertiesofscalarmesonnonetandwell-establishedmembersof
the lowest 1/2 baryonnonet, it is necessary to check its distinguishablepredictionsof other membersin the 1/2
− −
baryonnonet. While the classicalquenchedquarkmodels[23] predictthe1/2 Σ andΞ to be around1650MeV
− ∗ ∗
and1760MeV,respectively,theunquenchedquarkmodels[13,14,22]expectthemtobearound1400MeVand1550
MeV,respectively,andmeson-baryondynamicalmodels[24,25,26]predictthemtobearound1450MeVand1620
MeV,respectively.
For Σ resonance with JP = 1−, the PDG [12] lists a two-star Σ(1620) resonance, which seems to support the
2
quenched quark models. However, only four references listed in PDG show weak evidence for its existence. In
Ref. [27], the total cross sections for K p and K n are analyzed, which indicates some Σ resonance around 1600
− −
MeVwithoutJPquantumnumber.Refs.[28,29]arebasedonmultichannelanalysisoftheKNreactions.Bothclaim
evidenceforaΣ 1−resonancewithmassaround1620MeVbutgivecontradictedcouplingpropertiestoπΛandtoπΣ.
2
OtherlatermultichannelanalysesoftheKN reactionssupporttheexistenceofanΣ(1660)1+[12]. Ref.[30]analyzes
2
thereactionK−n→π−ΛandgivestwocomparablesolutionswithandwithoutΣ(1620)21−.
On the other hand, there are also some supportsof the unquenched5-quarkmodelswith Σ∗(21−) of muchlower
Σm(a1s3s8e5s.)3T+hpeeraek-a[n3a1l]y.sFisroomfoalndadnaatlaysoinsoKf−thpe→recΛenπt+LπE−PfiSnddasthaiodndeγnnΣ∗(12K−+)Σwit(h13m8a5s)s[3a2ro],utnhder1e3i8s0alMsoeaVpuonsdsiebriltihtye
2 → ∗−
fortheexistenceofsuchlowmassΣ∗(21−)[33]. AnanalysisofCEBAFdataonγp → K+πΣalsosuggestsapossible
Σ∗(21−)around1400MeV[34].
ToclarifythesituationforΣresonances,recently,acombinedfitforthenewCBdata[35]onK p π0Λtogether
−
→
withtheolddata[30]onK n π Λfortheenergiesfrom1569to1676MeVwasperformed[36]. TheKN πΛ
− −
→ →
reactionis the best channelavailable forthe study of the Σ resonancesbecause the πΛ is a pure isospin 1 channel.
The highprecisionCrystal Ball Λ polarizationdata [35] are crucialfordiscriminatingΣ(1620)1− from Σ(1635)1+.
2 2
Itshowsthat the Σ(1660)1+ is definitely needed,while Σ(1620)1− is notneededat all. AlthoughΣ(1380)1− is not
2 2 2
2
B.S.Zou/NuclearPhysicsA00(2013)1–5 3
demanded in this analysis, it cannot be excluded. Therefore, no evidence to support the classical quenched quark
modelsatallfromthe1/2−baryons.AdditionalΣ(1542)23−,Σ(1840)23+ andΣ(1610)21+ mayexist.
TheΣ(1542)3− isconsistentwith theresonancestructureΣ(1560)orΣ(1580)3− inPDG [12]andseemsa good
2 2
isospinpartnerofΛ(1520)3−.RecentlyaveryinterestingnarrowΛ(1670)3−withawidthabout1.5MeVwasclaimed
2 2
fromananalysisofK−p→ηΛdata[37]. TogetherwithN∗(1520)23−andeitherΞ(1620)orΞ(1690),theyfitinanice
3/2 baryonnonetwithlargepenta-quarkconfiguration,i.e.,N (1520)as [ud] uq q¯ >state,Λ(1520)as [ud] sq q¯ >
− ∗
| { } | { }
state,Λ(1670)as [ud] ss s¯>state,andΞ(16xx)as [ud] ss q¯ >state. Here q q meansadiquarkwithconfiguration
1 2
of flavor represen|tatio{n6}, spin 1 and color 3¯. The|Λ(1{670})as [ud] ss s¯ >{ stat}e givesa naturalexplanationfor its
| { }
dominantηΛdecaymodewithaverynarrowwidthduetoitsverysmallphasespacemeanwhileaD-wavedecay.
The available informationon the hadronspectroscopy with strangeness strongly indicates that qqqqq¯ in S-state
is more favorable than qqq state with L = 1 and q2q¯2 in S-state is more favorable than qq¯ state with L = 1. The
multi-quarkcomponentsareverysubstantialandimportantforhadronicexcitedstates. Evenq6q¯ configurationmay
playdominantroleforsomebaryonresonances[38,39].
Tofurtherestablishthemulti-quarkpictureforhadronicexcitedstates, itisveryimportanttocompletethelow-
lyinghyperonspectrum,especiallythe1/2 and3/2 Σ ,Ξ andΩ . HeretheΩ spectrumhasauniqueadvantage
− − ∗ ∗ ∗ ∗
thatthefavorableqq¯excitationsfromquarkseahavedifferentflavorfromthevalencestrangequarks[40].Kaonbeam
experimentat JPARC and hyperonproductionfromcharmoniumdecaysatBESIII may playveryimportantrolein
thisaspect. Itisalsoimportanttocheckthecaseswithsquarksreplacedbycorbquarks.
2. Fromstrangenesstocharmandbeauty
Variouspicturesanddynamicsforthespectroscopywithstrangenesscanbeextendedtoandcheckedbyitscharm
andbeautypartners.Forexample,if f (980)isaKK¯ moleculemainlyduetolightvectormesonexchangeforce[41],
0
thenwiththesamemechanismthereshouldalsoexistDK,BK¯,DD¯ andB¯Bmolecules[42,43].Thenewlyestablished
D (2317)isregardedasa DK moleculeortetra-quarkstatebymanypeople[44]. The f (1420)wasproposedtobe
∗s0 1
aK K¯ molecule[45];nowthenewlyestablishedX(3872)isregardedasitsD D¯ partner[46,47]. TheΛ (2595)1/2
∗ ∗ c −
wasproposed[48]tobeDN moleculeasthecharmpartnerofΛ(1405).
Although many hadron resonances were proposed to be hadron-hadrondynamically generated states or multi-
quarkstates,mostofthemcannotbeclearlydistinguishedfromclassicalquarkmodelstatesduetotunableingredients
andpossiblelargemixingof variousconfigurationsin these models. Evenin 2010,the PDG [49] still claimedthat
“ThecleanΛ spectrumhasinfactbeentakentosettlethedecades-longdiscussionaboutthenatureoftheΛ(1405)
c
– true 3-quarkstate or mere K¯N threshold effect? – unambiguouslyin favor of the first interpretation.”A possible
solution to this problem is to extend the penta-quark study to the hidden charm and hidden beauty sectors. If the
N (1535)istheK¯Σquasi-boundstatewithhiddenstrangeness,thennaturallybyreplacing ss¯bycc¯ orbb¯ onewould
∗
expectsuper-heavyN stateswithhiddencharmandhiddenbeautyjustbelowD¯Σ andBΣ thresholds,respectively.
∗ c b
FollowingtheValenciaapproachofRef.[50]andextendingittothehiddencharmsector,theinteractionbetween
variouscharmedmesonsandcharmedbaryonswerestudiedwiththelocalhiddengaugeformalisminRefs.[51,52].
Several meson-baryondynamically generated narrow N and Λ resonances with hidden charm are predicted with
∗ ∗
massaround4.3GeVandwidthsmallerthan100MeV.TheS-waveΣ D¯ andΛ D¯ stateswithisospinI=1/2andspin
c c
S=1/2werealsoinvestigatedbyvariousotherapproaches[53,54,55]. TheyconfirmthattheinteractionbetweenΣ
c
andD¯ isattractiveandresultsinaΣ D¯ boundstatenotfarbelowthreshold.Thelow-lyingenergyspectraoffivequark
c
systemsuudcc¯(I=1/2,S=0)andudscc¯(I=0,S= 1)arealsoinvestigatedwiththreekindsofschematicinteractions:
−
thechromomagneticinteraction,theflavor-spindependentinteractionandtheinstanton-inducedinteraction[56]. In
all the three models, the lowest five quark state (uudcc¯ or udscc¯) has an orbitalangular momentum L = 0 and the
spin-parity JP = 1/2 ; the mass of the lowest udscc¯ state is heavier than the lowestuudcc¯ state, whichis different
−
fromthepredictionofmeson-baryondynamicalmodel[51,52]. Thepredictednewresonancesdefinitelycannotbe
accommodatedbyquarkmodelswiththreeconstituentquarks.Becausethesepredictedstateshavemassesaboveη N
c
andη Λthresholds,theycanbelookedforattheforthcomingPANDA/FAIRandJLab12-GeVupgradeexperiments.
c
Thisisanadvantagefortheirexperimentalsearches,comparedwiththosebaryonswithhiddencharmsbelowtheη N
c
thresholdproposedbyotherearlierapproaches[57,58].
3
B.S.Zou/NuclearPhysicsA00(2013)1–5 4
Thesamemeson-baryoncoupledchannelunitaryapproachwiththelocalhiddengaugeformalismwasextendedto
thehiddenbeautysectorinRef.[59]. TwoN statesandfourΛ stateswerepredictedtobedynamicallygenerated.
b∗b¯ ∗bb¯
Becauseofthehiddenbb¯ componentsinvolvedinthesestates,themassesofthesestatesareallabove11GeVwhile
their widths are of only a few MeV, which should form part of the heaviest island for the quite stable N and Λ
∗ ∗
baryons. FortheValenciaapproach,thestaticlimitisassumedforthet-channelexchangeoflightvectormesonsby
neglectingmomentumdependentterms. In orderto investigatethe possible influence of the momentumdependent
terms, the conventional Schrodinger Equation approach was also used to study possible bound states for the BΣ
b
channel by keeping the momentum dependentterms in the t-channelmeson exchange potential. It was found that
within the reasonable model parameter range the two approachesgive consistent predictions about possible bound
states. ThisgivessomejustificationofthesimpleValenciaapproachalthoughtherecouldbeanuncertaintyof10-20
MeVforthebindingenergies.
ProductioncrosssectionsofthepredictedN resonancesinppandepcollisionswereestimatedasaguideforthe
b∗b¯
possibleexperimentalsearchatrelevantfacilitiesinthefuture. Forthe pp ppη reaction,thebestcenter-of-mass
b
→
energyforobservingthepredictedN is13 25GeV,wheretheproductioncrosssectionisabout0.01nb. Forthe
b∗b¯ ∼
e p e pΥreaction,whenthecenter-of-massenergyislargerthan14GeV,theproductioncrosssectionshouldbe
− −
→
largerthan0.1nb. Nowadays,theluminosityforpporepcollisionscanreach1033cm 2s 1, thiswillproducemore
− −
than 1000eventsper day for the N production. It is expectedthat futurefacilities, such as proposedelectron-ion
b∗b¯
collider(EIC),maydiscovertheseveryinterestingsuper-heavyN andΛ withhiddenbeauty.
∗ ∗
Very recently, the observationof the iso-vectormeson partnersof the predicted N , Z (10610)and Z (10650),
b∗b¯ b b
were reported by Belle Collaboration [60]. This gives us stronger confidence on the existence of the super-heavy
islandfortheN andΛ resonances.
b∗b¯ ∗bb¯
3. Conclusions
Available information on hadron spectroscopy with strangeness and charm reveals unquenched quark picture.
Draggingoutaqq¯ fromgluonfieldisaveryimportantexcitationmechanismforhadrons. Tocorrectlydescribethe
hadronspectrum,itisnecessarytogobeyondtheclassicalquenchedquarkmodelswhichassumingafixednumber
ofconstituentquarks. Distinguishablepredictionforhyperonspectroscopyfromthenewpictureisyellingforexper-
imentalconfirmation. KaonbeamexperimentsatJPARC andhyperonproductiondata fromcharmoniumdecaysat
BESIIIcanplayveryimportantrolehere.Super-heavynarrowN andΛ resonancesarepredictedbyvariousmodels
∗ ∗
to exist around 4.3 GeV and 11 GeV for hidden charm and beauty, respectively. Their iso-vector meson partners
Z (10610)andZ (10650)haverecentlybeenobserved. Experimentalconfirmationofthemwillunambiguouslyes-
b b
tablishmulti-quarkdynamics.TheycanbelookedforatCEBAF-12GeV-upgradeatJlabandPANDAatFAIR,maybe
alsoatJPARC,super-B,RHIC,EIC.
4. Acknowledgments
I thankC. S. An, P. Z. Gao, J. He, F. Huang, T. S. H. Lee, R. Molina, E. Oset, J. Shi, W. L. Wang, K. W. Wei,
J.J.Wu,H.S.Xu,S.G.Yuan,L.Zhao,Z.Y.Zhangforcollaborationworksreviewedhere. Thisworkissupported
bytheNationalNaturalScienceFoundationofChinaunderGrant11035006,11121092,11261130311(CRC110by
DFGandNSFC),theChineseAcademyofSciencesunderProjectNo.KJCX2-EW-N01andtheMinistryofScience
andTechnologyofChina(2009CB825200).
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