Baryon Spectroscopy and the Origin of Mass

8 Pages·0.18 MB·English

by  Eberhard Klempt

Baryon Spectroscopy and the Origin of Mass
Eberhard Klempt
Helmholtz-InstitutfürStrahlen–undKernphysik,UniversitätBonn
Nußallee14-16,D-53115Bonn,GERMANY
e-mail: [email protected]
0
1
0 Abstract. Theprotonmassarisesfromspontaneous breaking ofchiralsymmetryandtheformationofconstituent quarks.
2 Theirdynamicscannotbetestedbyprotontomographybutonlybystudyingexcitedbaryons.However,thenumberofexcited
baryons is much smaller than expected within quark models; even worse, the existence of many known states has been
n challenged in a recent analysis which includes - compared to older analyses - high-precision data from meson factories.
a Hencep Nelasticscatteringdatadonotprovideawell-foundedstartingpointofanyphenomenologicalanalysisofthebaryon
J
excitation spectrum. Photoproduction experiments now start to fill in this hole. Often, they confirm the old findings and

9 evensuggestafewnewstates.Theseresultsencourageattemptstocomparethepatternofobservedbaryonresonanceswith
1 predictions from quark models, from models generating baryons dynamically from meson-nucleon scattering amplitudes,
frommodelsbasedongravitationaltheories,andwiththeconjecturethatchiralsymmetrymayberestoredathighexcitation

] energies.BestagreementisfoundwithasimplemassformuladerivedwithinAdS/QCD.Consequencesforourunderstanding
h
ofQCDarediscussedaswellasexperimentswhichmayhelptodecideonthevalidityofmodels.
p
- Keywords: Baryonresonances,exp.status,quarkmodel,AdS/QFT,dynamicallygeneratedresonances,chiralsymmetryrestoration
p PACS: 12.39.-x;13.60.-r;13.75.-n;14.20.-c
e
h
[
INTRODUCTION

1
v Baryonspectroscopyisatabifurcationpoint.TheParticleDataGroup[1]lists44NandD resonanceswhichstem
0
mostly from the old analyses of the Karlsruhe-Helsinki (KH) [2] and Carnegie-Mellon (CM) [3]collaborations.
9
ThemostrecentanalysisoftheSAIDgroupatGeorgeWashingtonUniversity(GWU)[4]includeshighprecision
2
3 datafrommesonfactoriesanddatawithmeasurementsoftheprotonrecoilpolarization.Soweshouldexpectthe
. numberofknownstatestoincrease.Instead,SAIDfinds20only.Thisisamuchsmallernumberthanthe72known
1
mesonicstates,nottospeakaboutthewealthofadditionalstatesrevealedfromtheQMC-St-Petersburganalysisof
0
Crystal-BarrelLEARdata.Ofcourse,amuchgreaternumberofstatesisexpectedfor(three-body)baryonsthan
0
1 for(two-body)mesons.Here,wewilladdressthequestionwetherwehavetoabandonalargefractionofbaryon
: resonanceslistedbythePDGorifweshouldincludethemwheninterpretingthedatainmodels.
v
Themostnaturalandmostpopularframetodiscussbaryonresonancesisthequarkmodel.Butotherconcepts
i
X havebeenproposed.Here,datawillbecomparedtoquark-modelpredictions,totheSkyrmemodel,toAdS/QCD.
r Attheend,Iwilladdressafewkeyissuesintheoryandwillproposekeyexperiments,whichmayhelptodecide
a
onthevalidityofthedifferentconcepts.
WHYBARYONSPECTROSCOPY?
We all have an intuitive knowledge of what “mass" means. But, as often in physics, Nature offers surprises.
AstronomersbelievethatonlyasmallfractionofthetotalmassoftheUniverseismatterintheformasweknow
it. Close galaxiesseem to driftapart faster than more remote galaxies(Fig. 1, left); the accelerationis assigned
to a mythic dark energy (accounting for 73% of the mass of the Universe). The rotational frequencies of stars
in galaxies do not depend on the distance from the galaxy center (Fig. 1, center); dark matter, e.g. in the form
ofsuper-symmetricparticles,isintroducedwhichgivesa23%masscontribution.“Normal"mattermakesupthe
remaining4%.Themyriadsofstarsinthenightlyheavenconstitutejust1%ofthetotalmass(Fig.1,right).
Thematterasweknowitprovidessurprisesforusaswell. We areaccustomedtothefactthatelectronscarry
onlyan atomicmassfractionof1/4000;theirbindingenergyisin thesub-ppmrange.Innucleons,itis thefield
energywhichoutcaststhequarkmassbya factorhundred.99%of thebaryonmassdoesnotcomeof thequark
FIGURE1. Left:TheHubbleconstantislargerforclose-bygalaxies.Center:Thevelocitiesofstarswithingalaxiesdoes
notdependontheirdistancetothecenter.Right:Massdistribution.
massesbutfromchiralsymmetrybreaking.Thesmallcurrentquarkmassduetothequark-Higgsinteractionisnot
veryimportantonthehadronicscale.
The fundamentaltheoryof stronginteractions,QCD, is chirallyin-
variant,itkeepshandiness,forthenearlymasslessquarks.Thissym-
metryisdynamicallybroken,givingtoquarksaneffectivemass.This
effect can be studied in lattice gauge calculations [5] which show
an increase in mass with decreasing momentum transfer (see Fig.
2). At small q, the effective mass is about 320MeV. This is called
theconstituentquarkmass.Itcanbeunderstoodusingdifferentlan-
guages.Thebagmodelassignstheconstituentquarkmasstoabsence
of quark condensates inside of the bag [6]; the Dyson Schwinger
equation approximatesthe effective gluon operator [7]; quarks hop
betweenspecialfieldconfigurationscalledinstantonsbyflippingthe Figure2.Thequarkmassasafunction
quarkspinandthus,theseacquiremass[8].Howcanwelearnabout ofthemomentumtransfer[5]
constituentquarks?Certainlynotbydeepinelasticscattering.Proton
tomographyrevealsthe distributionof linear andorbitalangularmomentabut informationon collectivedegrees
offreedomislost.Thewavelengthwithwhichtheprotonisexploredneedstomatchthesizeoftheconstituents.
Thisistherealmofspectroscopy.
EXPERIMENTAL STATUS
Table1.NandD resonances.Compilation:see[9].a:BnGa;b:GWU.
The Particle Data Group [1] lists 44 nu- Resonance Mass Resonance Mass Resonance Mass
cleonandD resonances,Table1presents N(940) 940 D (1232) 1232±1 N1/2+(1440) 1450±32
a recent compilation [9]. Evidence for N1/2−(1535) 1538±10 N3/2−(1520) 1522±4 N1/2−(1650) 1660±18
theexistenceofbaryonresonancesisde- N3/2−(1700) 1725±50 N5/2−(1675) 1675±5 D 1/2−(1620) 1626±23
rived mostly from elastic p N scattering. D 3/2−(1700) 1720±50 D 3/2+(1600) 1615±80 N3/2+(1720) 1730±30
Dependingontheconfidencewithwhich N5/2+(1680) 1683±3 N1/2+(1710) 1713±12 D 1/2+(1750)
their existence and their properties are N1/2−(1905) 1905±50 N3/2−(1860) 1850±40 N1/2+(1880)a
known, these resonances are decorated N3/2+(1900)a N5/2+(1910) 1880±40 N7/2+(1990) 2020±60
with one, two, three or four stars. Ex- D 1/2−(1900) 1910±50 D 3/2−(1940) 1995±60 D 5/2−(1930) 1930±30
ceptforthefour-starresonances,the ev- D 1/2+(1910) 1935±90 D 3/2+(1920) 1950±70 D 5/2+(1905) 1885±25
idence is challenged by a careful GWU D 7/2+(1950) 1930±16 N1/2+(2100) 2090±100 N1/2−(2090)
analysis [4] and only those boldfaced in N3/2−(2080) 2100±55 N5/2−(2060)a 2065±25 N7/2−(2190) 2150±30
Table1 survive.Spinandparityofreso- N5/2−(2200) 2160±85 N9/2−(2250) 2255±55 D 1/2−(2150)
nancesaregivenintheformN1/2−(1535) D 5/2−(2223)b D 7/2−(2200) 2230±50 N9/2+(2220) 2360±125
which gives spin and parity directly in- D 7/2+(2390) 2390±100 D 9/2+(2300) 2360±125 D 11/2+(2420) 2462±120
steadofN(1535)S11 usedbytheParticle D 9/2−(2400) 2400±190 D 3/2−(2350) 2310±85 N11/2−(2600) 2630±120
DataGroup. N13/2+(2800) 2800±160 D 13/2−(2750) 2720±100 D 15/2+(2950) 2920±100
For an interpretation of the resonance spectrum it is decisive to know if we need to abandon the 24 states not
seen by SAID. At present, we cannot decide if the KH and CM analyses pick up some noise or if resonances
arelostintheGWU analysisbytheappliedsmoothingprocedure.Butforafewresonances,seenintheKHand
CM analyses and not seen in the GWU analysis of elastic p N scattering data, this question can be studied. We
give three examples where resonances found by KH and CM and disclaimed by GWU are required in inelastic
reactions.Notethattherelevantp N→p Namplitudes[4]areincludedinthefit.KH,CM,andGWUfitonlythese
amplitudes; the inelasticity is unconstrained by data. In the BnGa analysis, most inelastic channels are known
fromphotoproductionandonlyfewinelasticchannels(mainlywithvectormesons)aretreatedas“blackbox".
TFihge.3D 3s/h2o+w(1s6t0h0e)imfraogminpar+ypp→artSo+fKth+e:elasticP33p N scatteringamplitude 0.25 Im T(P33 ) 0.12
above D (1232). Points (in red) with error bars represent the GWU am-
plitude, the thin (red) line a BnGa fit. The D (1232) tail is followed by a 0.2 0.08
continuum;thereisnoevidenceforfurtherstructures.TheKHamplitude
is represented by black triangles; the dominantD (1232) tail is removed. 0.15 0.04
The amplitude exhibits a peak in the imaginary part, evidencinga D 3/2+ 0
resonanceat1600MeVcouplingtop N.TheCMpartialwaveagreeswith 0.1
-0.04
KH in exhibitinga peakstructure.The questionis which analysisis cor-
recttheoldanalysesbyCMandKHfindingD 3/2+(1600)orGWUwhere 0.05 -0.08
theresonancedoesnotexist.Theamplitudesderivedfromelasticp Nscat- W(GeV)
tering are ambiguous. The BnGa fit includes data on the inelastic reac- 0 -0.12
1.4 1.5 1.6 1.7 1.8 1.9 2
tionp +p→S +K+.Duetothecharge,intermediateresonancesmusthave Figure3.TheP amplitude.
33
isospinI=3/2.Thedatawereincludedinageneralfittoalargenumber
ofdifferentinelasticreactionsandtotheGWUelasticamplitudes.TheresultingP amplitudeisshownasthick
33
(blue) curve. The amplitude follows closely the KH amplitude. The analysis requiresto introduceD (1600).
3/2+
The need for the resonancecan be seen fromthe differentialdistribution and the inducedS + polarization.Thus
webelievethattheD (1600)isdefinitelyconfirmedwithapolepositionatM=1540+40,G =230±40MeV.
3/2+ −80
TheN (1900)fromphotoproductionofhyperons:
3/2+
0 12 Very sensitive data on photoproduction of hyperons are now available on
2/10 10 KL +KS g p→L K+,g p→S 0K+,andg p→S +K0.Fig.4showsthe c 2 oftheBnGa
D c fit as a function of the assumed N3/2+(1900) mass. The data base includes
8 high-statistics angular distributions, several single (S ,T and P) and double
6 polarizationobservables(Cx,Cz,Ox,Oz).Alargedatabaseonotherreactions
isincludedinthefits.Butstill,thereisnotyetafullreconstructionofpartial
4 waveamplitude.Sotheevidenceisderivedfromac 2 minimization(seeFig.
2 KL 4).Thebestvaluesanderrors,M= 1915±50MeVandG =100±50MeV,
coverallsolutionswithreasonablec 2.
0
D (1920)andD (1940)fromg p→pp 0h :
-2 3/2+ 3/2−
1800 1850 1900 1950 2000 2050 Fits to this reaction with/without D 3/2+(1920) (left) or D 3/2−(1940) (right)
M(P ), MeV
13 representedbysolidlinesinFig.5arenotnotsatisfying,boththeseresonances
Figure4.c 2 asafunctionofthe are neededto achievea goodfit. The fits optimizesfor(M;G )=(1910±50;
imposedN3/2+(1900)mass. 330±50)(D 3/2+(1920))and(1985±30;390±50)MeV(D 3/2−(1940)).
1.7< W < 1.9 1.9< W < 2.1 2.1< W < 2.3 1.7< W < 1.9 1.9< W < 2.1 2.1< W < 2.3
400 600
800 800 400 800
300
600 600 300 600 400
200
400 400 200 400
200
200 a) 200 b) 100 c) 100 d) 200 e) f)
0 0 0 0 0 0
-1 0 1 -1 0 1 1.5 2 -1 0 1 -1 0 1 -1 0 1
cos q cos q M(h p), GeV/c2 cos q cos q cos q
p h h p h h p
Figure 5:Selectedmass and angulardistributions. A fit represented by solid lines without D 3/2+(1920)(left) or
D 3/2−(1940)(right)yieldsabadfit.Onlywhenbothresonancesareincluded(dashedlines),dataarereproduced.
We conclude that 1. it would be too early to abandon the resonances found in the KH and CM analyses
but missed in the GWU analysis, and that 2. photoproduction begins to make a significant impact on baryon
spectroscopy. For the interpretation of the baryon spectrum, all resonances of Table 1 will be used. For further
informationontheBnGaanalysis,seetalksbyAnisovichandSarantsevatthisconference.
INTERPRETATION
Quarkmodels:
The quarkmodelprovidesthe most naturaland mostaccepted picture of the baryonexcitationspectrum. Ingre-
dientsareconstituentquarkswithdefinedrestmasses,aconfinementpotential(mostlylinear)andsomeresidual
interaction.In the celebratedIsgur-Karlmodelandits later “relativized"refinements,an effectiveone-gluonex-
change is chosen as residual interaction. The Bonn group starts from a Bethe-Salpeter equation;the linear con-
finement potential has a full Dirac structure. Instanton-inducedinteractions are responsible for the N−D mass
splitting.Thequarkmodelsareverysuccessfulinexplainingthepropertiesofbaryongroundstatesandlow-mass
excitations;theyfailtoreproducethemassesofradialexcitationsandpredictmanymorebaryonresonancesthan
foundinexperiment.
AdS/QCD:
The Maldacena correspondence relates conformal strongly-coupled theories in space-time to a weakly-coupled
(“gravitational")theoryinafivedimensionalAnti-deSitterspaceembeddedinsixdimensions.Gravitationalthe-
ories can be solved analytically, the solutions can be mapped into space-time and compared to data. There is a
(heuristic)mappingofquantummechanicaloperatorstooperatorsinAds/QCD.ThefifthdimensioninAdScalled
zcanbeinterpretedasvirtualityordistancebetweenconstituents.Forz→0,constituentsareasymptoticallyfree.
Confinementcanbeenforcedbyahardboundaryz<z =1/L (hardwall)orbyasoftwallduetoadilation
max QCD
field(orpenaltyfunction)increasingasz2.
AdS/QCD relates masses to the orbital angular momentum L (Fig. 6). In quark models, relativity plays an
importantrole,andonlythetotalangularmomentumJisdefined.Experimentally,thereareafewstrikingexamples
wheretheleadingorbitalangularmomentumandthespincanbeidentified.Togiveoneexample:thefourstates
D 1/2+(1910),D 3/2+(1920),D 5/2+(1905),andD 7/2+(1950)areisolatedinmass.Theyobviouslyformaspin-quartet
ofresonanceswithL=2,S=3/2.Smalladmixturesofothercomponentsarenotexcluded.
9/2+
Figure6:One-parameterfittotheD exci- 11/2+
taopMafatt2iiebroar=anomr=fyasqoip1·sune(.0acsnLt4rewrk+euGsidmtNewehV.di+“t2Fhwgoa3hosrn/piod2cnidhn)ub−cdar=leineqbdodu1u·na.ica4srreo6DkessssGph"tohGi,enneVwaez2Vnmie.tcrh2aeoiss.as, 2468 M2 D(3G/2+e(V1223)2) DDDD 3131////2222++--((((N11117667=020500000)))) DDDDDDD 5317531///////2222222---++++(((((((1111111999999934050210000500))))))) DDD 575///222+--731(((///222222+++222020030))) DDDDD195971/////22222--++735+((((///(22222222--[phone]))))) 11975911////2222//22+++-+- D 15/21+3(/22ND+91=530/121)97-1//(22/22---750)
D resonanceshavenogooddiquarks. L+N
0
0 1 2 3 4 5 6
Dynamicallygeneratedresonances:
The properties of some resonances (and the meson-baryon system at low energies) can be understood very
successfullyusinganeffectivechiralLagrangian,relyingonanexpansioninincreasingpowersofmesonmasses
andmomenta.Aproblemariseswhenthesedynamicallygeneratedresonancesarepredictedatopthequark-model
states,orwhenthelightquarkbaryonsaredisregardedaltogetherandreplacedbyasystematicsofmeson–baryon
excitations. The pole structure of N1/2−(1535) and N1/2−(1650), e.g., was studied by Döring et al. [10]. They
generated N (1535) dynamically and introduced two additional poles, one for N (1650) and a third one.
1/2− 1/2−
The latter pole movesfar into the complexplane and providesan almost energyindependentbackgroundwhile
thedynamicallygeneratedN1/2−(1535)poleappearsasastableobject.ThiscouldmeanthatN1/2−(1535)isfully
understoodby the interactionof the baryonandmeson, into whichit disintegrates.It can be interpretedthatthe
observedN (1535)isdynamicallygeneratedandthestatepredictedbythequarkmodelismissing.Thelatter
1/2−
interpretationseemsunacceptabletome.
Restorationofchiralsymmetry?
Incontrarytoexpectationsbasedonthequarkmodelinharmonicoscillatorapproximation,themassesofbaryon
resonances do not increase with alternating states of even and odd parity; often, states having the same J but
oppositeparitiesareapproximatelydegenerateinmass(seeTable2).Atlowmass,N (1535)ismuchheavier
1/2−
than its chiral partner, the proton. In meson spectroscopy, the r mass is much below the a (1260) mass. The
1
massdifferenceisassignedtoaspontaneousbreakingofchiralsymmetry.Glozman[11]andothersarguethatat
high-mass excitations, details of the potential responsible for spontaneous chiral breaking are irrelevant: chiral
symmetrycouldberestoredinhighlyexcitedbaryons.Thealternativeinterpretationoftheoccurrencespin-parity
partners, AdS/QCD, is criticized because of Table2.Chiralmultiplets(doubletsorquartets)ofN∗ andD ∗
the use of orbital angular momentum, a non- resonancesofhighmass.Listandstarrating,see[9].
relativistic quantity [12], a view contested in
[13]. Parity doublets are only observed for J=12 N1/2+**(1*710) N1/2*−*(*1*650) D 1/2+(1750) D 1/2*−*(*1*620)
resonances on Regge daughter trajectories; J=32 N3/2*+*(*1*720) N3/2−**(1*700) D 3/2+**(1*600) D 3/2*−*(*1*700)
mReegsgoenstraajnedctobrayryhoanvsefnaollipnagritoynptahretnelre.aTdihnigs J=52 N5/2*+*(*1*680) N5/2*−*(*1*675) nochiralpartners
isachallengeforfutureexperiments. J=12 N1/2+*(*1880) N1/2−*(1905) D 1/2*+*(*1*910) D 1/2−*(*1900)
Modelsversusdata: J=32 N3/2+*(1900) N3/2−*(*1860) D 3/2+**(1*920) D 3/2−*(*1940)
Modelpredictionscanbeconfrontedwithdata. J=52 N5/2+*(*1870) noch.partner D 5/2*+*(*1*905) D 5/2−*(*1930)
Thepredictionsofchiralsymmetryrestoration J=72 N7/2+*(*1990) noch.partner D 7/2*+*(*1*950) noch.partner
gbiavreyoannsionftteernpraeptapteiaornaosfpoanrietyodboseurbvlaettiso.nT,htheraet J=72 noch.partner N7/2*−*(*2*190) noch.partner D 7/2−*(2200)
is no prediction where the masses should be J=92 N9/2*+*(*2*220) N9/2*−*(*2*250) D 9/2+*(*2300) D 9/2−*(*2400)
found.Forthisreason,wedonotincludethis
modelinthequantitativecomparison.Also,modelsgeneratingresonancesdynamicallyarenotsuitableforanu-
merical comparison with data, since only a part of the spectrum is calculated. Well suited are quark models,
AdS/QCD,andtheSkyrmemodel(eventhoughthismodelwasleftoutintheabovediscussionofmodels).Weuse
twoquarkmodelsforthecomparison,therelativizedquarkmodelofCapstickandIsgur[14]andtherelativistic
Bonnmodel[15].TheSkyrmemodel[16]hastwoparametersonlybutpredictslessthanhalfthenumberofthe
observedstates, andthemasspredictionsare ratherinaccurate.Thebestagreementis achievedwiththe gravita-
tionalmodel[17],seeTable3.Abreakdownofcontributionsofindividualresonancescanbefoundin[18].
TheagreementbetweenAdS/QCD andthe dataisabsolutelyamazing.Obviously,thetwo parametersusedto
describethedatacorrespondtoimportantphysicalquantities.TheparameterainfrontofL+N isrelatedtothe
maximumdistancebetweenconstituents,itisrelatedtothesizeofthebaryon.Thesecondparameterbisusedto
constructanoperatorinAdSwhichreducesthesizeproportionaltothediquarkfractionwithvanishingspinand
isospininthebaryon:inthisversionofAdS/QCD,“gooddiquark"aresmallerinsizecomparedtootherdiquarks.
The second observation is that the mass depends on the orbital angular momentum L implying that we have
a non-relativistic situation. We are used to describe the nucleon as bound state of three constituent quarkseach
having1/3 of the nucleonmass. The constituent-quarkis generatedby chiralsymmetrybreaking,by the energy
ofthe QCD fields. Thequarkmodelassumesthatthe constituentquarkisan objectwhichcan beacceleratedto
relativisticenergies;chiralsymmetryandchiralsymmetrybreakingisnoteffected.Thisdoesnotneedto bethe
case. Glozman assumes that chiral symmetry is restored. This is the assumption of a central Mexican-hat-like
potentialwherechiralsymmetryisdynamicallybrokenattheoriginofthehadron.Theuseofameanfieldwhich
leadstoaMexican-hatpotentialintherestframeofthenucleonisatleastadebateableassumption.Thesuccess
ofAdS/QCDsuggeststhatconstituentquarksexpandandbecomemoremassivewhenabaryonisexcitedtohigh
energy.Chiralsymmetryisbrokeninanextendedvolume,andthismightbethereasonfortheincreaseinmass.
Table3.ComparisonofmodelcalculationswiththemassspectrumofnucleonandD resonancesfromTable1.
Model Reference Nr.ofparameters “quality"
Quarkmodelwitheff.one-gluonexchange [14] 7 (d M/M)=5.6%
Quarkmodelwithinstantoninducedforces [15] 5 (d M/M)=5.1%
Skyrmemodel: [16] 2 (d M/M)=9.1%
AdS/QCDmodelwith“gooddiquarks": [17] 2 (d M/M)=2.5%
ThenucleonislighterthanD (1232),notbecauseofeffective-onegluonexchangeleadingtoamagnetichyperfine
splittingbutbecauseofthesmallersizeofthegooddiquarkitcontains(which50%probability).TheL (1405)has
suchalowmasssinceithasnotonlyonegooddiquarkbutallthreepairshavevanishingspinandisospin.
Multiplicityofresonancesandtheexistenceglueballsandhybrids:
Thereisthewell-knownproblemofthemissingresonances:thenumberofbaryonresonancespredictedinquark
models exceeds by far the number of observed states. The number of baryon resonances can be counted using
harmonic oscillator wave function, with two oscillators r and l . Quark models predict, for given~L and N, a
multitudeofstatessatisfying~lρ+~lλ=~Landnρ+nλ=N.WithincreasingLandN,thenumberofpredictedstates
explodes:expectedare, e.g. two N states in the second shell, seven N states in the third shell, ten N
1/2+ 1/2− 1/2+
statesintheforthshell.ThisproblemispartlycuredinAdS/QCDwhereatmosttwoJ=1/2statesareexpected
inanyshell.
There could be a second problem of too large a number of predicted states. In the quark model, there is e.g.
one nucleonresonancewith L=1, S=1/2,one state with L=1, S=3/2. Thepossibility of mixingadmitted,
we can still identify the N1/2−(1535) with the predicted L= 1, S = 1/2 quark model state, and N1/2−(1650)
with L=1, S=3/2. But there is evidence that N (1535) can be generated dynamically from Nh -L K-S K
1/2−
coupled-channelscatteringdynamics.Hencetherecouldbe a quarkmodelstate N (1535)anda dynamically
1/2−
generatedN1′/2−(1535).Zou[18]proposesthattheobservedN1/2−(1535)hasalarge(qqq)(qq¯)componentwithall
quarksinS-wave.IfN (1535)=a |qqq>+b |(qqq)(qq¯)>,isthereanorthogonalresonanceN′′ =b |qqq>
1/2− 1/2−
−a ∗|(qqq)(qq¯)>and,ifso,atwhichmass?DohybridconfigurationsN′′′ =a ′|qqq>+b ′|(qqq)(G)>addto
1/2−
thelistofexpectedresonances?Experimentally,noneoftheseadditionalstateshasbeenobserved.
Itseemstobeworthwhiletostressthatthenumberofbosonsisnotawell-definedquantity.Iproposeaviewin
whichtheinteractionsbetweenthree(current)quarksprovidetheprimaryforcestostabilizeabaryon.Thethree
quarks acquire their constituent dynamical mass. Gluons may polarize the vacuum, correlated quark-antiquark
pairs are created. Depending on the dynamics, these qq¯ pairs may have long-range correlations and may move
freely within a hadron as Cooper-pairsor massless Goldstone bosonsleading to a fast flavor exchange.Or they
mayevolveintomassivequarks.Iftheirmassesapproachthemassof“normal"constituentquarks,weratherspeak
abouta nucleon-mesonmoleculeor - invokingcolor chemistry - aboutfive-quarkstates. However,the originof
allbaryonsisthethree-quarkcomponent.TheactualdecompositionisaquestionhowtheQCDvacuumresponds
to the primarycolorsourceof threequarksata givenmassandwith givenquantumnumbers.Theresponsecan
be verydifferent,in particular it will dependcritically on the presence of close-by thresholds,but it is a unique
response.Thereisno“hiddenvariable"whichdecidesthatthreequarkswithL=1,S=1/2willgoeitherintoa
N,N′,N′′,orintoaN′′′configuration,orintodifferentmixturesoftheseFockcomponents.Thereisonlyonestate.
This view has attractive features; it reduces the number of expected but unobservedstates. It emphasizes the
viewthatquark-modelresonances,dynamicallygeneratedresonances,five-quarkstatesaredifferentapproachesto
understandthesameobjectwithitscomplicatedinternalstructure.Thedifferentapproachesarealllegitimate,none
ofthemcarriesthetruth,andeachapproachshouldbetestedifthepredictionsarenotinconflictwithfirmresults
ofotherapproaches.Iftheviewisextendedtothemesonicsector,therearesomeunfamiliarconclusions.First,the
raisond’etreofallscalarmesonsistheirqq¯component,evenofthes .Butthisisalsoatrivialstatement:without
QCD,therearenonuclearforces.Second,ifthereisonlyonescalarisoscalarstate(plusradialexcitations),withall
configurationsqq¯,qqq¯q¯,qq¯G,pp ,KK¯,etc.included,thenonefurtherpossibility,theGGglueball,islikelyalsoa
Fockcomponentinitswavefunction.Inthisview,alsotheGGcomponentdoesnotleadtoanextrastate,thereisno
supernumerocityofresonancesexpected.Iamawareofclaimsthatsupernumerocityhasbeenproven;theParticle
DataGroupisstronglybiassedintothisdirection.Imaintainthattheseclaimsareexperimentallynotsound,see
[20], for a review. Presumably,most scalar isoscalar mesons are realized as flavor singlets or octets. The SU(3)
flavorsingletsareverywideandformthecontinuousscalarbackground,a“narrow" f (1370)doesnotexist.Only
0
theoctetmesonshavenormalhadronicwidths;theseare f (1500), f (1760)(whichincludes f (1710), f (1790),
0 0 0 0
f (1810)),and f (2100).Theflavordecompositionofthelow-mass f (980)and f (500)arestronglyinfluenced
0 0 0 0
by the pp and KK¯ threshold.Scalar mesonshave a significantfour-quarkcomponentbuttheir qq¯ componentis
mandatory:in SU(3),there are nine qq¯ states and also nine qqq¯q¯ states respectingthe Pauli principle.In SU(4),
thereare16qq¯andtherecouldexist36qqq¯q¯states,butnoneofthese20additionalstateshasbeenobserved.
Interestingly,theviewforbidsnon-exotichybrids,sincetheyareabsorbedintothewavefunctionofqq¯mesons
carryingthesamequantumnumbers.Neithertheexistenceofexotichybridsisexcludedbytheargumentsgiven
above,northeexistenceofpentaquarksinanon-(qqq)configuration.
WHATISNEEDED?
Itain’tnecessarilybeso:
Theinterpretationdepends,ofcourse,heavilyontheexistingdata.Henceitisofgreatestimportancetoconfirm
orrefuteasmanyofthestatesseen inKH andCM andnotseeninGWU analysesaspossible.Photoproduction
experimentsstarttohaveasignificantimpact.Experimentswithpolarizedphotonbeamsandpolarizedtargetshave
alreadytakena significantamountofdata;resultsareeagerlywaited for.Hyperonphotoproductionexperiments
benefitfromtheself-analysingpowerofhyperondecays.Somedoublepolarizationvariableshitthevalue1.This
may indicate that a smaller number of observables (and not 8) is already sufficient to constrain the amplitudes
fully. At least, the BnGa PWA group noticed that there are much less ambiguities in defining the partial wave
amplitudesforhyperonphotoproductionwhentheamplitudesareconstrainedbyds /dW ,S ,P,C ,C ,O ,andO .
x z x z
HenceIbelieveweareatapointwherewesoonwillbeabletodecidewhichresonancesexistinthemassrange
below2GeVor,perhaps,2.2GeV.
Searchformissingquarkmodelstates:
InthesecondoscillatorshellwithL=2,quarkmodelspredictstatesinwhichthespatialwavefunctionarefully
antisymmetric,in which the orbitalangularmomenta~lρ and~lλ are bothone andcoupleto L=1. If these states
exist, they likely do not decay into Np but prefer a cascade where the two oscillators de-excite successively.
According to the AdS/QCD mass formula (and its interpretation) one can assume that the mass of this spin
doublet N and N should be between 1.7 and 1.8GeV. The preferred decay mode could be the cascade
1/2+ 3/2+
N →N (1535)p →Nhp orN →N (1520)p →Npp wherealldecaysproceedviaS-wave.
1/2+ 1/2− 3/2+ 3/2−
WhatisthemassofthefirstD resonance?
7/2−
We havealreadymentionedthequartetofstates D 1/2+(1910),D 3/2+(1920),D 5/2+(1905),andD 7/2+(1950).The
firstthreestateshavespin-paritypartnersD 1/2−(1900),D 3/2−(1940),D 5/2−(1930).Inquarkmodels,themassesof
positiveparitystatesarewellreproduced,thoseofthenegative-paritystatesareunexpectedlylow.InAdS/QCD,
thepositive-paritystateshaveL=2,N=0,thenegative-paritystatesL=1,N=1,respectively,andarepredicted
to bedegeneratein mass. Since~L+~S yieldsonlyJ =1/2−, J=3/2−, andJ =5/2− negative-paritystates, but
J =1/2+, ··· J =7/2+ forL=2,S=3/2,the absenceofa paritypartnerof D 7/2+(1950)isexpected.Instead,
2184MeVispredictedasD 7/2− mass,closetothePDGresonanceD 7/2−(2200).
If chiral symmetry were restored in high-mass baryons, the D mass would need to be degenerate
7/2−
in mass with D (1950). The mass is 2200MeV, hence we could conclude that AdS/QCD is favored.
7/2+
However,the D 7/2−(2200)mass determinationis notveryreliable.In
Table 4 we list the Particle Data group entries for D 7/2−(2200). The Table4:PDGentriesforD 7/2−(2200).
valuesaveryconsistentbuttheresonanceisgivenone-staronly.Inthe
Mass[MeV] Width[MeV] Ref.
GWU analysis[4],thestate isnotseen.Thisiscertainlynotthelevel
2200±80 450±100 [2]
ofconfidenceweneedinordertosettlethequestionifchiralsymmetry
2215±60 400±100 [3]
isrestoredorbrokeninhigh-masshadronresonances.
2280±80 400±150 [21]
Spin-paritydoubletsarealsoobservedinthemesonspectrum,formany
mesonsbutnotforthoseontheleadingReggetrajectory.Togivean
example:thereisaa (2040)mesonwithJPC=4++butthelowestmasspartnerwithJPC=4−+isp (2250),and
4 4
thesameobservationcanbemadeforthelowest-massstatesintheseriesJPC=1−−,JPC=2++,JPC=3−−,···.
Hence spin-parity partnersare missing for the most importantstates. The following argumentby Glozman [22]
suggests a dynamical reason why the postulated JPC = 4−+ state at 2040MeV was not observed: mesons in
the high-mass region stem mostly from the QMC-St-Petersburg analysis of Crystal-Barrel LEAR data on p¯p
annihilationin flight.And the p¯p system couplesto JPC =4++ with L=4 while forformationof a JPC =4−+
state,L=5isrequired.Hencep (2250)couldbesuppressed.Itisworthwhiletonotethattheobservedpatternis
4
isexpectedinAdS/QCD.Mesons–exceptscalarandpseudoscalarmesons–arewelldescribedbytheformulain
thecaptionofFig.6,ifthe”3/2"isreplacedby”1/2".
In photoproduction or pion-induced reactions, there is no such angular momentum suppression; hence the
search for the lowest-mass D resonance seems to be the most rewarding case to decide if quark models or
7/2−
AdS/QCDdescribebestthemassspectrum,orifchiralsymmetryisrestoredathighexcitationenergies.
Limitsofdynamicalgeneratedresonances:
Therangeofapplicabilityofthemethodtogenerateresonancesdynamicallyhastobeunderstood.Asexperimen-
talist, I am readyto believethat N (1535)can be generateddynamicallyfromits decayproducts,also thatit
1/2−
couldhave,atlargedistances,asizablefive-quarkormolecularcomponentinitsFock-spaceexpansion.Butitis
difficulttoacceptthatN1/2−(1535)andN3/2−(1520)arefundamentallydifferentobjects.Osetinhiscontribution
tothisconference[23]constructedscalarandtensormesonsfromvector-vectorinteractions.Theisoscalarscalar
mesons are found at 1512MeV and 1726MeV. This looks like a success as well as the tensor meson found at
1275MeV.However,thenexttensorat1525coupleswithsimilarstrengthtoK∗K∗,ww ,fw ,ff , butnottorr .
This is in striking conflict with whatwe knowabout f (1525):it is a ss¯state, the tensor mesons have a mixing
2
angle close to the ideal one. OZI rule violating couplings like the one into fw are highly suppressed. Also the
isovectorstatesareafailure.Ifrr generates f (1270),rw mustgeneratea (1320);thepredictedlowestisoscalar
2 2
tensormassis1567MeVanditsscalarcompanionispredictedtohave1777MeV.Inmyview,itisimportantto
findouttheconditionsforameaningfulunitarizationofchiralamplitudes,andnottoenjoytheachievementsand
toneglectthefailures.
Excitedstatesonthelattice:
Lattice gauge calculation have entered the difficult task to explore the spectrum of baryon resonances and
to address their finite width. In the Introduction, I showed how the mass of a quark evolves with decreasing
momentumtransfer.Thecalculationwasdoneforaquarkpropagatorirrespectiveofitsenvironment.According
tothediscussionabove,theconstituentquarkmassshoulddependonitsneighborhood;itshouldbelighterinthe
nucleonthanintheD (1232),andmassiveinhighlyexcitedstates.
CONCLUSIONS
Baryonshaveplayedaveryimportantroleinthedevelopmentofparticlephysics,startingfromthe-atthattime-
mysteriousprotonandneutronmagneticmoments,thediscoveryoftheD (1232)byFermiandhiscollaborators,to
thediscoveryofSU(3)andtheinsightthatquarksneedanextradegreeoffreedomwhichisnowknownascolor.
Theconceptofchiralsymmetryandchiralsymmetrybreakingisattherootofmodernstronginteractionphysics.
With the new tools,in experimentandtheory,we havethe chancefora new understandingofstronginteraction
dynamicsintheconfinementregion.
IwouldliketothankB.Metsch,E.Oset,H.Petry,andJ.M.Richardforclarifyingdiscussions,andallmembersof
SFB/TR16forcontinuousencouragement.FinancialsupportwithintheSFB/TR16iskindlyacknowledged.
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