Five-quark components in baryons

0.19 MB·

by  B. S. Zou

Five-quark components in baryons
Bing-SongZou
InstituteofHighEnergyPhysics,CAS,P.O.Box918,Beijing100049,China;
TheoreticalPhysicsCenterforScienceFacilities,CAS,Beijing100049,China;
CenterofTheoreticalNuclearPhysics,NationalLabofHeavyIonAccelerator,Lanzhou730000,China
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1
Abstract
0
2
Evidencehasbeenaccumulatingfortheexistenceofsignificantintrinsicnon-perturbativefive-

n quarkcomponentsinvariousbaryons.Theinclusionofthefive-quarkcomponentsgivesanatural
a explanationoftheexcessofd¯overu¯,significantquarkorbitalangularmomentumintheproton,
J
theproblematicmassanddecaypatternofthelowest1/2−baryonnonet,etc.. Abreathingmode
7
ofqqq↔qqqqq¯issuggestedforthelowest1/2−baryonoctet.Evidenceofapredictedmember

] ofthenewscheme,Σ∗(1/2−)around1380MeV,isintroduced.
h
t Keywords: Baryon,five-quarkcomponents
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l PACS:14.20.-c,12.39.-x
c
u
n
[ 1. 5-quarkcomponentsintheproton

1
Inthe classicalquarkmodelspriorto QCD, eachprotonwas regardedas composedof two
v
4 u quarksandone d quark. The classical quarkmodelsgaveverygooddescriptionofthe mass
8 pattern and magnetic moments for the baryon SU(3) baryon 1/2+ octet and 3/2+ decuplet of
0 spatial ground states. Then the QCD introduces the gluon field which can fluctuate into sea
1
quarkqq¯pairsinadditiontothethreevalencequarksinsideaproton.Butuntilabouttheyearof
.
1 1992,u¯(x)=d¯(x)ands(x)= s¯(x)wereassumedfortheseaquarkpartondistributionfunctions.
0 However, evidence has been accumulating for the existence of significant intrinsic non-
0
perturbativefive-quarkcomponentsintheproton. Asurprisinglylargeasymmetrybetweenthe
1
u¯ andd¯seaquarkdistributionsintheprotonwithd¯−u¯ ∼0.12wasobservedfromdeepinelastic
:
v scatteringandDrell-Yanexperiments[1].Apopularexplanationfortheexcessofd¯overu¯ inthe
i
X proton was given by meson-cloudmodel[2] by includingin the protona mixture of nπ+ with
theπ+ composedofud¯. Recently,bystudyingstrangenessintheproton,anewconfigurationof
r
a diquark-diquark-antiquarkstructureisproposedforthefive-quarkcomponentsintheproton[3].
The diquarkclusterconfigurationsalso givea naturalexplanationforthe excessof d¯overu¯ in
the proton with a mixture of [ud][ud]d¯ component in the proton [3]. The measured value of
d¯−u¯ ∼0.12demandsthe5-quarkcomponentsintheprotontobemorethan12%.
Furtherevidencescamefromprotonspinproblemandsingle-spinasymmetryproblem,which
both indicate the presence of quark orbital angular momentum in the proton. The five-quark
uudqq¯ componentsin the proton with the q¯ of negative intrinsic parity demand either a quark
or anti-quark in the P-wave to make up the proton of positive intrinsic parity. So it gives nat-
urally the nonzero quark orbital angular momentum and hence a natural explanation to both
problems[3,4].
PreprintsubmittedtoNuclearPhysicsA January7,2010
To tell the relative importance of meson cloud and diquark cluster mixtures in the proton,
more precise experiments on the strangeness in the proton are needed. While the KΛ meson
cloud picture predicts strangeness magnetic moment and strangeness radius both negative [5],
thediquarkclusterpicturepredictsbothpositive[3]. Presentexperimentsarenotpreciseenough
todistinguishthetwopictures[6,7]. Theextremelysmallnessofthesestrangenessobservables
mayeitherindicateverysmallpercentageofthe strangenesscomponentin theprotonorabout
equallytheKΛmesoncloudand[ud][us]s¯contributionscancelingeachother.
2. NewschemeforN∗(1535)andits1/2−nonetpartnerswithlarge5-quarkcomponents
In the simple 3q constituent quark model, the lowest spatial excited baryon is expected to
bea(uud)N∗ statewithonequarkinorbitalangularmomentumL = 1state,andhenceshould
have negative parity. Experimentally, the lowest negative parity N∗ resonance is found to be
N∗(1535),whichisheavierthantwootherspatialexcitedbaryons:Λ∗(1405)andN∗(1440).This
isthelong-standingmassreverseproblemforthelowestspatialexcitedbaryons.
Recentlyalargevalueofg isdeduced[8,9]byasimultaneousfittoBESdataon
N∗(1535)KΛ
J/ψ → p¯pη, pK−Λ¯ +c.c., and COSY data on pp → pK+Λ. There is also evidence for large
g couplingfromγp → pη′ reactionatCLAS[10]and pp → ppη′ reaction[11],and
N∗(1535)Nη′
large g coupling from π−p → nφ, pp → ppφ and pn → dφ reactions [12, 13], but
N∗(1535)Nφ
smallercouplingofg fromcomparisonof pp→ pK+Λto pp→ pK+Σ0[14].
N∗(1535)KΣ
Themass reverseproblemcanbe easily understoodby considering5-quarkcomponentsin
them[8,15]. The N∗(1535)couldbethelowest L = 1orbitalexcited|uud >statewithalarge
admixtureof|[ud][us]s¯>pentaquarkcomponenthaving[ud],[us]ands¯inthegroundstate. The
N∗(1440)couldbethelowestradialexcited|uud >statewithalargeadmixtureof|[ud][ud]d¯>
pentaquarkcomponenthavingtwo[ud]diquarksintherelativeP-wave. WhilethelowestL= 1
orbitalexcited|uud>stateshouldhaveamasslowerthanthelowestradialexcited|uud >state,
the|[ud][us]s¯>pentaquarkcomponenthasahighermassthan|[ud][ud]d¯>pentaquarkcompo-
nent. ThelighterΛ∗(1405)1/2−isalsounderstandableinthispicture. Itsmain5-quarkconfigu-
rationis|[ud][us]u¯ >whichislighterthanthecorresponding5-quarkconfiguration|[ud][us]s¯>
intheN∗(1535)1/2−.
Thelargemixtureofthe |[ud][us]s¯ > pentaquarkcomponentin the N∗(1535)mayalso ex-
plainnaturallyitslargecouplingstotheNη, Nη′, NφandKΛtogetherwithitssmallcouplings
totheNπandKΣ. Inthedecayofthe|[ud][us]s¯>pentaquarkcomponent,the[ud]diquarkwith
isospinI =0isstableandkeepsunchangedwhilethe[us]diquarkisbrokentocombinewiththe
s¯toformeitherK+(us¯)Λ([ud]s)orφ(ss¯)p([ud]u).
Theinclusionofthelarge5-quarkcomponentsintheN∗(1535)causesanaturalcancelation
betweenthecontributionsoftheqqqandqqqqq¯ componentstotheaxialchargeoftheN(1535)
resonance[16] and introducesan importantnew mechanismas shownin Fig. 1 for its electro-
magnetictransitionγ∗N →N∗(1535)[17].
Theexperimentalmeasuredγ∗N → N∗(1535)amplitudehasamuchflatter Q2-dependence
than the classical qqq quark model predictions as shown in Fig. 2(left). The new mechanism
givesamuchflatterQ2-dependenceasshownbythedot-dashedcurveinFig.2. Withabout45%
5-quark componentsin N∗(1535) and 20% in proton, the measured electromagnetic transition
γ∗N →N∗(1535)amplitudeismuchbetterfittedasshowninFig.2(right).
Taking the qqqqq¯ components into account, the constituent quarks masses should be a bit
smaller than the ones employed in the case of pure qqq configuration. To reproducethe mass
2
q(p~4)
γ∗(~k)
q¯(~k−p~4) N∗(1535)(~0)
N(−~k)
Figure1:γ∗→qq¯mechanismfortheγ∗N→N∗(1535)transition.
180 3=340MeV 180 =340MeV,
160 3=246MeV 160
3=200MeV =600MeV
140 140 =246MeV,
-1/2GeV)110200 -1/2GeV)110200 ===613004000M0MMeeVeVV,
p-3 A (101/2 6800 p-3 A (101/2 6800
40
40
20
20
0
0-0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0
Q2 (GeV2) Q2 (GeV2)
Figure2:ThehelicityamplitudeAp forγ∗p→N∗(1535)withpureqqqconfiguration(left)andwith5-quarkcompo-
1/2
nentinaddition(right)wherethedot-dashedcurveisthecontributionfromtheγ∗→qq¯transition[17].
for the nucleon when the five-quark components have been included, the values m = m =
u d
m = 290MeVandm = 430MeVareused. Theoscillatorparameterfortheqqqcomponents,
s
ω , is from literature, basically determined from the proton radius. The oscillator parameter
3
for the qqqqq¯ components, ω , is treated as a free parameter, which is foundto be largerthan
5
ω . This is consistent with other empirical evidence favoring larger value of the ω [18, 19,
3 5
20, 21]. In our extended quark model with each baryon as a mixture of the three-quark and
five-quark components, the two components represent two different states of the baryon. For
the qqqqq¯ state, there are more color sources than the qqq state, and may make the effective
phenomenologicalconfinementpotentialstronger. Forthelowest1/2− baryonoctet, thelarger
ω value corresponds a smaller size for the 5-quark components. An intuitive picture for our
5
extendedquarkmodelis the qqq ↔ qqqqq¯ breathingmodelike this: the qqqstate with L = 1
andhigherkineticenergyhasweakerpotential;whenquarksexpand,aqq¯ pairispulledoutand
resultsinaqqqqq¯statewithL=0andstrongerpotential;thestrongerpotentialleadsqqqqq¯state
shrinkingtoamorecompactstatewhichthenmakestheq¯ toannihilatewithaquarkeasilyand
transitstotheqqqstate with L = 1andmorekineticenergytoexpand;thisleadstoconstantly
transitionsbetweenthesetwostates.
If this picture of large 5-quark mixture is correct, there should also exist the SU(3) nonet
partnersof the N∗(1535)and Λ∗(1405),i.e., anadditionalΛ∗ 1/2− around1570MeV, a triplet
Σ∗ 1/2− around1360MeVandadoubletΞ∗ 1/2− around1520MeV[15]. Thereisnohintfor
thesebaryonresonancesinthePDGtables[22]. However,aspointedoutinRef.[23],thereisin
factevidenceforalloftheminthedataofJ/ψdecaysanditcanbeeasilycheckedwiththehigh
3
statisticsBESIIIdatainnearfuture[24]. Recently,newevidenceforthepredictedΣ∗ resonance
with JP = 1/2− and mass around 1380 MeV was found in the old data of K−p → Λπ+π−
reaction[25],asintroducedinthenextsection.
3. EvidenceforthepredictedΣ∗(1/2−)ofthenewscheme
TheunquenchedmodelsgiveinterestingpredictionsfortheisovectorpartneroftheΛ∗(1405)
andN∗(1535). Whilethepenta-quarkmodels[15,26]predictaΣ∗(1/2−)resonancewithamass
aroundorlessthanitscorrespondingΛ∗partner,themesoncloudmodel[27]predictsittobenon-
resonantbroadstructure.Thepredictionsoftheseunquenchedmodelsandtheclassicalquenched
quarkmodelsaredistinctiveandneedtobecheckedbyexperiments.Hencewere-examinedthe
olddataofK−p→Λπ+π−reactiontoseewhetherthereisevidenceforitsexistenceornot[25].
The K−p → Λπ+π− reaction was studied extensively around 30 years ago for extracting
propertiesoftheΣ∗(1385)resonance,withK− beammomentumrangingfrom0.95GeVto8.25
GeV.IntheinvariantmassspectrumofΛπofthisreactionthereisastrongpeakwithmassaround
1385MeVandwidtharound40MeV.ThemassfitsinthepatternofSU(3)baryondecupletof
JP = 3/2+ predictedby the classical quarkmodelperfectly. The angulardistributionanalyses
also conclude thatthe spin of this resonanceis 3/2. Howeverwe foundthat all these analyses
are in fact assuming that there is only one resonance under the peak. Nobody has considered
thatthereareprobablytworesonancesthere. Thismaybebecausetherearenootherpredicted
Σ∗ resonancesaroundthismassregionintheclassicalquarkmodels. SincenowanewΣ∗ with
the JP = 1/2− around this mass region is predicted by various unquenched models, the old
K−p→Λπ+π−reactionshouldbere-scrutinizedcarefully.
WeexaminedpreviousexperimentalanalysesontheK−p→Λπ+π− reaction. Amongthem,
wefindthattheinvariantmassspectraofΛπ− withbeammomentumP = 1.0 ∼ 1.8GeV are
K−
differentfromothers.ThepeakaroundΣ∗(1385)inthesemassspectracannotbefitasperfectas
othersetsofdatawithasingleBreit-Wignerresonance. SinceRef.[28]presentsthelargestdata
sampleandthemosttransparentangulardistributionanalysisofthisreaction,were-fittheΛπ−
massspectrumandangulardistributionofRef.[28]bytakingintoaccountthepossibilityoftwo
Σ∗ resonancesinthismassregion.
Theresultsofthe fitswith a single andtwo Σ∗ resonancesaround1385MeVare shownin
Fig.3andTable1wherefittedparameterswithstatisticalerrorsaregiven. Thefitwithasingle
Σ∗resonance(Fit1)isalreadynotbad.ThefitwithtwoΣ∗resonances(Fit2)improvesχ2by10.5
comparedwiththeFit1for60datapointswith3morefittingparameters. Althoughthisisjusta
lessthan3σimprovement,apointfavoringFit2isthatwhilethesingleΣ∗ resonanceinFit1has
awidthlargerthanthePDGvalue[22]of36±5MeVfortheΣ∗(1385)resonance,thenarrower
Σ∗ resonanceinFit2givesa widthcompatiblewiththePDG valuefortheΣ∗(1385)resonance.
IntheFit2,thereisanadditionalbroaderΣ∗resonancewithawidthabout120MeV.
M Γ M Γ χ2/ndf(Fig.1) χ2/ndf(Fig.2)
Σ∗(3/2) Σ∗(3/2) Σ∗(1/2) Σ∗(1/2)
Fit1 1385.3±0.7 46.9±2.5 68.5/54 10.1/9
Fit2 1386.1+1.1 34.9+5.1 1381.3+4.9 118.6+55.2 58.0/51 3.2/9
−0.9 −4.9 −8.3 −35.1
Table1:Fittedparameterswithstatisticalerrorsandχ2overnumberofdegreeoffreedom(ndf)forthefitswithasingle
(Fit1)andtwoΣ∗resonances(Fit2)around1385MeV.
4
1.3 1.4 1.5 1.6 1.7 1.8
600 600 1.3 1.4 1.5 1.6 1.7 1.8
600 600
500 500 500 500
V
0 Me400 400 MeV 400 400
Events per 1123000000 123000000 vents per 10 123000000 123000000
E
0 0 0 0
1.3 1.4 1.5 1.6 1.7 1.8 1.3 1.4 1.5 1.6 1.7 1.8
M (GeV) M (GeV)
Figure3: FitstotheΛπ−massspectrumwithasingleΣ∗(left)andtwoΣ∗resonances(right)around1385MeVwith
fittingparameters listedinTable1. Theexperiment dataarefromRef.[28]on K−p → Λπ+π− withbeammomenta
around1.4GeV.
Thepreferredassignmentofspin J =3/2fortheΣ∗(1385)resonanceinRef.[28]isdemon-
stratedbythedistributionofthecosineoftheanglebetweentheΛdirectionandtheK−direction
forthereactionK−p → Λπ+π− with M intherangeof1385±45MeVandcosθ > 0.95.
Λπ− KΣ∗
For a Σ∗ with J = 3/2, the angular distribution is expected to be of the form (1+3cos2θ)/2;
whileforaΣ∗ with J = 1/2,aflatconstantdistributionispredicted. Thedata[28]asshownin
Fig.2clearlyfavorthecaseof J = 3/2ifonlyasingleΣ∗ resonanceisassumed. However,the
Fit2withtwoΣ∗ resonanceswiththenarroweroneofJ =3/2andthebroaderonewith J =1/2
reproducesthedataevenbetterasshownbythesolidcurveinFig.4. Theresultsshowthatthe
inclusionofanadditionalΣ∗(1/2−)besidesthewell-establishedΣ∗(1385)3/2+seemsimproving
thefittothedataof K− beammomentaaround1.4GeVforbothΛπ− invariantmassspectrum
andtheangulardistributionalthoughthelargeerrorbarsfortheangulardistributiondatamake
itnotveryconclusive.

-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0
35 35
30 30
25 25
nts 20 20
e
v 15 15
E
10 10
5 5
0 0
-1.0 -0.8 -0.6 -0.4 -0.2 (0.0 0.2) 0.4 0.6 0.8 1.0
Cos .K
Figure4: Predictions fortheangulardistribution forthe Figure5:TheoreticalΛπ−invariantmasssquareddistribu-
reaction K−p → Λπ+π− at beam momenta around 1.4 tionwithpureΣ∗(3/2+)(dottedline)andwithaΣ∗(1/2−)
GeVbyFit1(dashedcurve)andFit2(solidcurve),com- in addition (solid line) for the K−p → Λ∗(1520) →
paredwiththedatafromRef.[28]. Σ∗π→Λπ+π−reactionatbeammomentaaround0.4GeV,
comparedwithdata[30].
5
Furtherstrongerevidenceisfoundfromastudy[29]onthedataoftheK−p→Λ∗(1520)→
Σ∗π → Λπ+π− reactionatbeammomentaaround0.4GeV [30]. The theoreticalΛπ− invariant
masssquareddistributionwithpureΣ∗(3/2+)failstoreproducethedataasshownbythedotted
line in Fig. 5. With a Σ∗(1/2−) in addition, the data are perfectlyreproducedas shown by the
solidlineinFig.5.
Recently,theLEPScollaborationreportedameasurementofthereactionγn→K+Σ∗−(1385)
with linearlypolarizedphotonbeamatresonanceregion[31]. Thebeamasymmetryissizably
negativeatE = 1.8−2.4GeV,whichisingreatcontrasttothetheoreticalpredictionofavery
γ
smallbeamasymmetry[32]. ItisfoundthatincludinganadditionalΣ∗(1/2− givesnaturallythe
sizablynegativebeamasymmetry[33].
4. 5-quarkcomponentsinotherbaryons
The 5-quark componentsin other baryons are also found important. An admixture of 10-
20%ofqqqqq¯ componentsinthe∆(1232)resonanceisshowntoreducethewellknownunder-
predictionforthedecaywidthfor∆(1232)→Nγdecaybyabouthalfandthatofthecorrespond-
inghelicityamplitudesaboutafactor1.6.Themaineffectisduetothequark-antiquarkannihila-
tiontransitionsqqqqq¯ →qqqγ,theconsiderationofwhichbringstheratioA /A andconse-
3/2 1/2
quentlytheE2/M1ratioR intoagreementwiththeempiricalvalue[18].Thelargecontribution
EM
ofthequark-antiquarkannihilationtransitionsmayalsocompensatetheunder-predictionofthe
πN decaywidthof the ∆(1232)by the valencequarkmodel, oncethe ∆(1232)containsqqqqq¯
componentswith∼10%probability[19]. Thepresenceofsubstantialqqqqq¯componentsinthe
N∗(1440)canbringaboutareconciliationoftheconstituentquarkmodelwiththelargeempirical
decaywidthoftheN∗(1440)[20,34].
From a recentstudy [35] of the strong near-thresholdenhancementof pp → nK+Σ+ cross
section,theextraordinarylargecouplingofthe∆∗(1620)toρN obtainedfromtheπ+p → Nππ
isconfirmed. Doesthe∆∗(1620)containalargeρN molecularcomponentorrelatetosomeρN
dynamical generated state? If so, how about its SU(3) decuplet partners? In fact, from PDG
compilation[22] of baryonresonances,there are alreadysomeindicationsfora vector-meson-
baryonSU(3)decuplet.Whilethe∆∗(1620)1/2−isabout85MeVbelowtheNρthreshold,there
is a Σ∗(1750)1/2− about70 MeV below the NK∗ thresholdandthere is a Ξ∗(1950)?? about60
MeVbelowtheΛK∗ threshold. Iftheseresonancesareindeedthemembersofthe1/2− SU(3)
decupletvector-meson-baryonS-wavestates,wewouldexpectalsoaΩ∗1/2− resonancearound
2160 MeV. All these baryon resonances can be searched for in high statistic data on relevant
channelsfromvectorcharmoniumdecaysbyupcomingBES3experimentsinnearfuture.
Therearemanyotherbaryonresonanceswhichareproposedtobemeson-baryonstates[36],
i.e.,qqqqq¯regroupingintotwocolorlessclusters.
5. Conclusion
Fortheproton,thereshouldbeatleastabout20%mixtureofthefive-quarkcomponentsinthe
protontoreproduceitslargeu¯-d¯asymmetry(d¯−u¯ ≈0.12)ands-s¯asymmetry.Totelltherelative
importanceofmesoncloudanddiquarkclustermixturesintheproton,morepreciseexperiments
onthestrangenessradiusandstrangenessmagneticmomentoftheprotonareneeded.
Thereshouldbemorefive-quarkcomponentsinexcitedbaryons.Thestudyof1/2−baryons
seemstellingusthattheq¯qqqqinS-stateismorefavorablethanqqqwithL=1. Inotherwords,
6
forexcitedbaryons,theexcitationenergyforaspatialexcitationcouldbelargerthantodragout
aqq¯ pairfromgluonfield. Whethertheq¯qqqqcomponentsareindiquarkclusterconfiguration
or meson-baryon configuration depends on the strength of relevant diquark or meson-baryon
correlations. ForN∗(1535)andits1/2−SU(3)nonetpartners,thediquarkclusterpictureforthe
penta-quarkconfigurationgivesanaturalexplanationforthelongstandingmass-reverseproblem
of N∗(1535), N∗(1440) and Λ∗(1405) resonances as well as the unusual decay pattern of the
N∗(1535)resonance.For∆∗++(1620)andits1/2−SU(3)decupletpartners,theirSU(3)quantum
numbers do not allow them to be formed from two good scalar diquarks plus a q¯. Then their
q¯qqqqcomponentswouldbemainlyinmeson-baryonconfigurations.
Distinctivepatternsarepredictedbyquenchedquarkmodelsandunquenchedquarkmodels
forthelowestSU(3)baryonnonetwithspinparityJP =1/2−. Whilethequenchedquarkmodels
predict the lowest 1/2− Σ∗ resonance to be above 1600 MeV, the unquenched quark models
predictittobearoundΣ∗(1385)energy. Byre-examiningsomeolddataofthe K−p → Λπ+π−
reaction,itisfoundthatbesidesthewellestablishedΣ∗(1385)with JP = 3/2+, thereisindeed
somesomeevidenceforthepossibleexistenceofanewΣ∗resonancewithJP =1/2−aroundthe
same massbutwith broaderdecaywidth. Therearealso indicationsforsuchpossibilityin the
J/ψ →Σ¯Λπandγn → K+Σ∗− reactions. Atpresent,theevidenceisnotverystrong. Therefore,
high statistics studies on the relevant reactions, such as K−p → πΣ∗, γN → KΣ∗, ψ → Σ¯Σ∗
withΣ∗ →ΛπorΣπ,areurgedtobeperformedbyforthcomingexperimentsatJPARC,CEBAF,
BEPCII,etc.,toclarifythesituation.
AcknowledgementsIwouldliketothankD.O.Riska,B.C.Liu,J.J.Xie,C.S.An,J.J.Wu,F.X.Wei,
X.Cao, S.Dulat and H.C.Chiang for collaborationson relevantissues reported here, and thank
the Institute for Nuclear Theory at the University of Washington for its hospitality during the
completionofthispaper. ThisworkispartlysupportedbytheNationalNaturalScienceFoun-
dationofChina(NSFC)undergrantsNos. 10875133,10821063,10635080,andbytheChinese
Academy of Sciences (KJCX3-SYW-N2), and by the Ministry of Science and Technology of
China(2009CB825200).
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