Progress and Issues in Hadronic Theory

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by  E. S. Swanson

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1 Progress and Issues in Hadronic Theory
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Eric Swanson∗
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h UniversityofPittsburgh
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E-mail: [email protected]
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Abriefreviewofprogressandissuesinhadronictheoryandphenomenologyispresented. New
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results for the X(3872), Zc(3900), and Zc(4020)are discussed and unresolvedissues are high-
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v lighted. A series of open problems in pQCD, NRQCD, and general phenomenology is given.
4 It is argued that these indicate that the currentunderstandingof hadronic dynamicsis poor. In
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9 particularoldideasaboutquarkannihilationandfactorisationappeartobeincorrect,pQCDlooks
3 limitedinscope,andtheconvergenceofsomeNRQCDcomputationsappearsjeapardisedbythe
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1 relativelightnessofthecharmquarkmass.
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XVInternationalConferenceonHadronSpectroscopy
4-8/11/2013
Nara,Japan
∗Speaker.
(cid:13)c Copyrightownedbytheauthor(s)underthetermsoftheCreativeCommonsAttribution-NonCommercial-ShareAlikeLicence. http://pos.sissa.it/
ProgressandIssuesinHadronicTheory EricSwanson
1. Introduction
Hadronsandtheirinteractionscontinuetochallengeourabilitytocomputeandmodelreliably
with quantum chromodynamics (QCD). The wealth of new data and states generated by the B
factories over the past decade is now being supplemented by new results from BESIII and the
LHCb,alongwithcontinuingcontributions fromBelle. Thenewresultshaveclarifiedsomeissues,
created newones,andleftmanyothersunresolved. Someofthesearereviewedhere.
2. Charged Onia
In examining the properties of the enigmatic Y(4260), the BESII collaboration has seen a
new enigma[1] in the process e+e− →Y(4260) →p +p −J/y in the p ±Jy spectrum, called the
Z (3900). The state was soon confirmed by Belle and CLEO-C[1]. Breit-Wigner fits yield M =
c
3899.0±3.6±4.9 MeVwithawidthG =46±10±20MeV.Thestatehasgeneratedmuchinterest
since, ifitisnotathreshold orotherdynamicaleffect,itmustconsistoffourquarks.
InthepastfewmonthsBESIIIhasfounda(possible)partnerstateine+e−→p ±Z (4020)∓→
c
p +p −h , called the Z (4020)[2] (see Fig. 1). The measured mass is M =4022.9±0.82.7 MeV
c c
andthewidthisG =7.9±2.7±2.6MeV.NotethattheZ (3900)wasnotseeninthischannel. The
c
stateisverylikelythesameastheZ (4025)whichwasseeninD∗D∗ byBESIII[3].
c
These states, along with the older Z (4050) and Z (4260) (seen in B→KZ →Kp ±c ) and
1 2 c1
Z(4430) (B→KZ →Kp ±y ′), are a strong indication that four-quark bound states must be taken
seriously aspossible realisations ofQCDdynamics. Furthermore, thisstoryseemstoberepeating
in the bottomonium sector, where the Z (10610) and Z (10650) appear as charged bottomonium
b b
resonances in¡ (5S)→p ±p ∓¡ (nS)andp ±p ∓h [4]. RecentlyBellereports thatJP=1+ forboth
b
statesandthepreferreddecaymodesaretoBB∗andB∗B∗respectively[5]. Furthermore,Bellehave
seentheneutralpartneroftheZ (10610) in¡ (10860)→¡ (nS)p 0p 0[6].
b
Although all of this evidence is encouraging, much work needs to be accomplished before a
coherent picture of charged onia emerges. For example, no simple dynamical understanding of
these states exists. Are they diquark-diquark, four-quark, or loosely bound? What dynamics pro-
videsthebinding–pionorothermesonexchange, two-quarkinteractions, multi-quarkinteraction,
or something new? At the phenomenological level it is disturbing that the Z states lie near (and
b
above) BB∗ and B∗B∗, while the Z(4430) has not been confirmed by BaBar[7], the Z(4050) and
Z(4250)looksomewhatdubious, theZ (4020)isnear(andabove)D∗D∗,andtheZ (3900)isnear
c c
(andabove)DD∗.
3. Other New Results
New developments have not been restricted to spectroscopy. For example, LHCb, which has
joinedthegame,hasrecentlydeterminedthatquantumnumbersoftheX(3872)areJPC=1++[8],
thereby resolving an old controversy and supporting the DD∗ molecular picture of this state[9].
Furthermore, BESIIIhave measured the process e+e− →g X(3872) and report that, “the X(3872)
might be from the radiative transition of the Y(4260) rather than from the y (4040) or Y(4360),
but continuum production ... cannot be ruled out by current data"[10]. If the decay Y(4260) →
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ProgressandIssuesinHadronicTheory EricSwanson
2)c 120
GeV/ 100 2)V/c50
5 Ge40
nts/(0.00 6800 nts/(0.005 123000
e e
Ev 40 Ev 30.8 3.9 4.0 4.1
M (GeV/c2)
p+hc
20
0
3.95 4.00 4.05 4.10 4.15 4.20 4.25
M (GeV/c2)
p –hc
Figure 1: Evidence for the Z (4020). Dots with error bars are data; shaded histograms are normalized
c
sidebandbackground;thesolidcurvesshowthetotalfit,andthedottedcurvesthebackgroundsfromthefit.
FigurefromRef. [2].
g X(3872) is confirmed it can have important implications for the structure of both states. For
example, if the X is a DD∗ molecule then it is natural to assume that the Y is also a molecule,
perhaps a DD [11]. Alternatively, if the Y is a hybrid state, then this process would require the
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photon emission to de-excite the gluonic degrees of freedom and create a light quark pair, which
seemsunlikely. InthiscaserunningtheprocessthroughacccomponentfortheX maybepreferred.
Thesagaofthepionelectromagneticformfactorcontinues. Recentdevelopmentsstartedwith
BaBar’s observation that Q2Fp (Q2) appears to rise with momentum. This has important implica-
tions for the applicability of perturbative QCD to exclusive processes[12] (including whether the
concept of exclusive pQCDeven exists). However, Belle have recently repeated themeasurement
and find a substantially slower rise with momentum[13]. Whether one interprets this as the ex-
pectedpQCDflatteningorarisethatdisagreeswithpQCDappearstobeamatterofpsychology at
present.
LHCb have contributed to a puzzle concerning the lifetime of the L baryon relative to the
b
B meson. While NRQCD predicts a ratio of nearly unity, old experimental results disagreed with
this. Theissuenowappears resolvedinfavouroftheNRQCDprediction[14].
Thehadroniclatticecommunityispoisedtobecomeanimportantcontributortohadronicphe-
nomenology. Themainissuesare(i)obtaininglight(andchiral)pions,(ii)incorporatingcontinuum
states in the computations, (iii) including ‘hairpin’ quark lines in the computations, (iv) develop-
ing methods to extract many excited states, and (iv) developing formalism to deal with complex
multichannel systems.
Theseareformidableproblems,butsteadyprogressisbeingmade. Recentsubstantiveprogress
in areas (iii) and (iv) are displayed in a computation of the isoscalar meson spectrum[15]. Simi-
larly, the hadronic scattering problem is being addressed. For example, isovector pp scattering
phase shifts have been recently computed yielding r resonance parameters of mr = 863 MeV,
grpp =4.83,andG r =10MeV.Theseresultshavebeenobtained witha391MeVpion[16].
Finally, the D meson represents a serious challenge for lattice computations since it lies
s0
nearDK threshold, solongdistanceeffectsareimportant,yetshortdistancegluon-mediated mass-
dependence isalsoexpected toaffectthestructure oftheD [17]. Asaresult, oldlatticecomputa-
s0
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ProgressandIssuesinHadronicTheory EricSwanson
tions ofthemass ofthis state tended toagree withsimple quark modelestimates (and hence were
approximately 200MeVhigh). HoweveranewlatticecalculationisabletoobtainalightD state
s0
byincludingtheDK continuumintheinterpolatorset;theyalsoworkinN =2+1QCDandhave
f
alightpionwithmass156MeV[18].
4. Unresolved Puzzles, Oldand New
A rather long list of problems in hadronic physics have resisted progress. Sometimes this is
duetolackofexperimentalfacilitiesandsometimesitisduetoourimmaturetheoreticaltoolkit. At
thesimplestlevelmanyofthenewstatesareofdubiousreliabilityandawaitconfirmationorfurther
exploration. AmongtheseIincludeG(3900),Y(4008),X(4160),Y(4274),X(4350),Y(4320),and
X(4630).
TheoldsuccessesofNRQCDinexplainingpromptJ/y production[19]havebeenextendedto
promptc c1andc productionbyATLAS[20]. HoweverNRQCDpredictionsforJ/y polarisation
c2
have not been successful[21]. This problem persists at the LHC[22]. Alternatively, ¡ (1S) and
¡ (2S) polarisations measured at CMS agree reasonably well with theory, while, curiously, ¡ (3S)
polarisationfails[23]. ThereisalsoaninterestingattemptbyATLAStomeasurepromptproduction
of J/y +W which yields results dramatically different from both colour singlet and colour octet
models[20]. Finally, CMShavemeasured theratios (c )B(c →¡ g )/s (c )B(c →¡ g )and
b2 b2 b1 b1
find quite different behaviour with respect to transverse ¡ momentum than expected (see the first
of Ref. [23]). One can of course add the old problem of NRQCD computations of the rate for
e+e−→J/y H attheBfactories thatfallanorderofmagnitudeshort.
In addition to the issues with some NRQCD computations, a long series of oddities has per-
sistedinthefield. AmongtheseIlist
• theeewidthsofy (2S)andy (3770),whichdisagreewithsimplequarkmodelexpectations.
• theratioofbranching ratios[24]
B(J/y →gh )
=0.21(4)
B(J/y →gh ′)
while
B(y (2S)→gh )
<0.018.
B(y (2S)→gh ′)
• thesimilarratios[25]
B(J/y →wh )
=9.56(16)
B(J/y →wh ′)
while
B(y (2S)→wh )
<0.343.
B(y (2S)→wh ′)
• theratioofBdecays[26].
B→h K ≫B→h ′K whileB→h K∗≪B→h ′K∗.
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ProgressandIssuesinHadronicTheory EricSwanson
• thep −r puzzle[27].
• node filtering in J/y decays. The Dalitz plot for J/y →ppp exhibits a strong r signal,
while the Dalitz plot for y (2S)→ppp shows a suppressed r and a strong r ′. The same
happens for the KKp final state (with K∗ and K∗′ mesons taking the place of the r and
r ′)[25].
• spinflipinthe¡ decay.
G (¡ (5S)→h (nP)pp ) 0.407(79)(60) h (1P)
b b
=
G (¡ (5S)→¡ (2S)pp ) 0.78(9)(15) h (2P)
( b
Thenumeratorinvolvesab-quarkspinflipandthusthisratioshouldbestronglysuppressed,
yetbothareoforderunity.
• oddities in¡ decays: thebranching fraction, B(¡ (5S)→B∗Bp )=7.3(2.3)(0.8) isanorder
ofmagnitudelarger thanexpected[28].
• oddities in ¡ decays: the rates for ¡ (5S) →¡ (1S,2S,3S)pp are two orders of magnitude
larger thanthoseof¡ (2S,3S,4S)→¡ (1S)pp [29].
• thepQCDprediction
G (c →gg ) 4
c2 = (1−1.76a )
G (c →gg ) 15 s
c0
disagrees withthemeasurementof0.278(50)(18)(31) (notethat4/15=0.27)[30].
• thebranchingfractionJ/y →ggg hasbeenmeasuredbyCLEO[31]andindicateslargeNLO
corrections topQCDcomputations[31].
5. Conclusions
Itisclearthathadronicspectroscopy remainsasourceofmuchinformation–andconfusion –
ontheQCDsectoroftheStandardModel. Asurveyoftheissuesraisedhereindicatethat
• pQCDappearstolargely failincomputations ofexclusive processes,
• the p −r puzzle and the decays of the J/y and y (2S) indicate that we do not completely
understand theprocessofhadronisation orfactorisation,
• NRQCDappearstofailinseveralareas,indicatingperhapsthatthecharmquarkisnotsuffi-
ciently heavytoprovideanaccurateexpansion inNRQCD,
• bound states continue toconfound modelbuilders. Dofour-quark states exist? Ifso, canwe
modelthemrobustly, canweobtainthemonthelattice?
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ProgressandIssuesinHadronicTheory EricSwanson
Ontheother sideoftheledger, lattice theorists continue toimprovetheircraftandcomputers
continue toget faster; effective fieldtheory has evolved into amature subject; and manyideas are
being generated by the community. It is certain that QCDwill continue to surprise and delight us
formanyyearstocome.
Acknowledgements
ThisresearchissupportedbytheUSDOEundergrantDE-FG02-00ER41135. Iamgratefulto
VeljkoDmitrašinovic´,RyanMitchell,ShoichiSasaki,andQiangZhaoforinformativediscussions.
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ProgressandIssuesinHadronicTheory EricSwanson
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