Theoretical Developments on PentaquarksShi-Lin Zhu

Peking UniversityMENU2004

August 30, 2004

Outline of the Talk • Status of exotic hadron search• Pentaquarks: discovery or artifact• Lattice QCD • Chiral soliton model• Large Nc expansion• QCD sum rules• Diquark model vs reality• Narrow width puzzle• Summary

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Not covered: •Non-clustered QM •Production •Theta relatives •Heavy PentaQ

…

Quark Model And Beyond• Quark Model very successful in the classific

ation of hadron states• Any state with quark content other than qq_

bar, qqq is beyond QM• But quark model can’t be the whole story• QCD allows much richer hadron spectrum s

uch as: glueball, hybrid meson/baryon, multiquark states, hadron molecules…

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Non-conventional Hadron Candidates• f0(980)/a0(980): 10 MeV below threshold, Kao

n molecule/four quark state?• Hybrid meson: Pi(1400), Pi (1600) with JPC=

1-+ , lower than theoretical prediction, interpretation not unique

• Glueballs: f0(1500), f0(1700), no pure sca

lar glueballs due to mixing

• Lambda(1405): 30 MeV below KN thre

shold, kaon-nucleon molecule?

• N(1440) : JP=1/2+, hybrid baryon?

(Kisslinger & Li)• H particle and other dib

aryons (Jaffe, Wang, Goldman, Zhang etc)

Till the end of 2002, None of these non-conventional states has been pinned down without

controversy!

Till the end of 2002, NONE of these non-conventional states has been established without controversy!

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Advances in Hadron Spectroscopy Since 2003• BES: pp_bar near-threshold enhancement in J/Psigam

ma pp_bar decays, I=0 channel; p Lambda_bar threshold enhancement in J/Psi K p Lambda_bar

• BABAR/CLEO/BELLE: narrow states DsJ(2317), DsJ(2457) below threshold

• SELEX: narrow state DsJ(2632) above threshold with abnormal decay pattern

• BELLE/CDFII: new narrow charmonium state X(3872)• E852: two exotic mesons with JPC=1-+ at 1709/2001MeV i

n the decay channel f1(1285)Pi-

• LEPS and others found evidence of Pentaquarks!

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Experiments Claimed the Observation of θ5

(LEPS)

nK

Inconsistencies in Mθ and Γθ?

0SpK

Width of θ+(1540)

• Two “positive” experiments:HERMES: Γθ = 17 9 2 MeV

ZEUS: Γθ = 8 4 MeV

- Indirect constraint:- Analysis with K+D data: Γθ < 6 MeV (Nussinov)• KN scattering data: Γθ < 5 MeV (Haidenbauer, Krein)

• K+ Xenon: Γθ < 1.2 MeV;

K+D: Γθ < 4 MeV (Cahn, Trilling)• Full analysis of K+ scattering data:

Γθ <1 MeV (Arndt et al., Meissner et al.)

M(nK+)≠ M(pKs)?

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Γθ(direct) ≠ Γθ (indirect)?

NA49: -- H1: ThetaC

uuddc_bar, 3099 MeV ddssu_bar, 1862 MeV,

WA89: 400 times larger Xi-

data sample, no signal!

1620 Xi-

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Summary of Negative Results

How significant are these negative results?•Some negative expts didn’t see Sigma* (1670, 1660)(four or three-star states in PDG)!•Production mechanism could be different for pentaQ at high and low energy!

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Does θ Pentaquark Exist? (Two Surveys by F E Close)

Serious Theoretical Challenges if it exists:• Low mass• Very narrow width• Weird production mechanism• Parity, spin etc

• Time Hadron2003 ICHEP04• Audience Hadron Physicists Particle Physicists• YES 1/3, mainly junior 1/900• NO 1/3, mainly senior 1/3• Keep On Searching 1/3 2/3

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Lattice Studies of PentaquarksFive studies posted to HEP-archive• Csikor-Fodor-Katz-Kovacs, hep-lat/0309090, JHEP• Sasaki, hep-lat/0310014.• Chiu-Hsieh, hep-lat/0403020, 0404007.• Kentucky Collab., hep-ph/0406196.• Ishii et al. (TIT Collab.), hep-lat/0408030Three preliminary results reported at conferences• Sigaev-Jahn-Negele (MIT Collab.), Quark-Nuclear-Physics04• Alexandrou-Koutsou-Tsapalis, Lattice04• Takahashi et al. (YITP Collab.), Pentaquark04

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Comparison of lattice results

Signal Parity Operator• Csikor et al. YES negative color variant of KN• Sasaki YES negative diquark-diquark-antiquark• Kentucky NO not positive simple KN• Chiu-Hsieh YES positive diquark-diquark-antiquark• MIT YES negative diquark-diquark-antiquark• Ishii et al. NO not positive diquark-diquark-antiquark• Takahashi YES negative KN & color variant of KN

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•Present status very confusing! •Where is the predictive power of LQCD?

Chiral Soliton Model• DPP predicted θ pentaquark at 153

0 MeV in CSM with S=+1, B=1, JP

=1/2+, I=0, Γθ < 15 MeV!• Input: N(1710) mass and width as

benchmark

Updated Chiral Soliton Model (Ellis et al) •With reasonable parameters, there always exists a low-lying θ pentaquark: 1430< mθ <1660 MeV •The anti-decuplet spectrum (θ, Xi-- ) can be reproduced

with bigger value of sigma-term 79 MeV or 64 MeV •The narrow width arises from the cancellation of the coupling constant in the first three orders in the large NC expansion

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CSM, Collective Quantization & Large NC(Cohen; Izthaki et al; Poblylitsa)

• In CSM, the mass splitting for non-exotic excitation is O(1/Nc). For exotic excitaion, it is O(Nc0).

• For pentaquarks, collective (rotation) and vibration modes are not orthogonal. They mix at leading order of Nc due to Wess-Zumino term.

• Collective quantization is NOT legitimate for exotic motion in CSM.

• Successful prediction of θ properties in CSM is fortuitous. We don’t understand θ from first principle.

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Large NC and Pentaquarks

• Large Nc formalism does NOT predict θ pentaquark! (Cohen; Itzhaki et al. …)

• However, given the existence of θ, one can predict its large Nc partners in the same way that Delta is the Nc partner of nucleon (Cohen, Lebed; Manohar, Jenkins)

• The mass splitting between these states is O(1/Nc).• QCD consistency can be applied to scattering amplitudes to

derive relations between coupling constants etc

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QCD Sum Rules (Zhu; Oka; Lee …) • Important: QSR does NOT predict θ!• QSR can accommodate θ at 1530 MeV if it really exists and

yield the absolute mass scale without fit to data. • All QSR calculations receive continuum contamination bec

ause of the high dimension of five-quark interpolating currents.

• QSR with old-fashion perturbation approach favors negative parity for θ. But the slow convergence of OPE series is a serious problem (Maltman).

• Appropriate interpolating currents such as color-octet KN type, diquark-diquark type can minimize the coupling with the scattering states as indicated by lattice QCD

• Invoking soft pion theorem, contribution from KN scattering states is found to be small (Lee et al.)

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Jaffe & Wilczek’s Diquark Model: (Assumptions)

• Quarks, when possible, correlate strongly in the channel which is anti-symmetric in color, spin and flavor (OGE, Instanton exchange)

• Highly correlated light quarks form diquarks, which is a color and flavor anti-triplet with JP=0+

• Diquarks obey Bose statistics• (Implicit assumption) Diquarks are tightly bound objects. Ot

herwise difficult to explain the narrow width• The correlation is strongest for massless quarks, decreases as one of quar

k mass increases, scales like 1/m1m2 in the heavy quark limit• Diquarks with other color and spin quantum numbers are assumed to be l

ess favored energetically

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Pentaquarks in Diquark Model

• Antidecuplet + octet with JP=1/2+, 3/2+, nearly degenerate• Lowest state is N(1440), not θ• Besides Xi5

--, NA49 observed Xi5- Xi*0 Pi- ( 8 10 + 8 )

, indicating existence of both anti-decuplet and octet around 1862 MeV, supporting JW’s diquark model?

• NOTE: 4q total WF is not fully anti-symmetric!

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•Color, flavor, spin WF of two [ud] diquarks: anti-symmetric, symmetric, symmetric •Symmetric total WF of two [ud] diquarks orbital WF anti-symmetric

P=+

Diquark Model vs Real Life• Hard to dynamically generate the scalar diquark with a low mass 420

MeV even with models• Maybe difficult to accommodate θ and θC (3099) simultaneously di

quark mass too low; anti-quark related attraction is important and ignored in diquark model

• Some lattice simulations reproduced N(1440) using three quark interpolating currents, supporting Roper as nucleon’s first radial excitation (Liu et al; Sasaki)

• N(1440) has a width of 350 MeV while the upper bound of Theta width is 1 MeV. Hard to accommodate them simultaneously.

• Interpreting the other nucleon-like pentaquark as N(1710) may also be wrong (Cohen).

• Introduction of diquarks leads to many additional low-mass states beyond quark model such as four-quark states composed of a pair of diquark and anti-diquark. Where are they?

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JP=1/2- Pentaquarks in Diquark Model(Zhu et al; Stewart, Wise; Cohen)

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•Experimental discovery of them support of diquark model •Failure re-evaluate the relevance of this picture

•Nine additional pentaquark states lighter than θ, close to the orbitally excited three-quark states.

•Especially two additional Lambda pentaquarks around Lambda(1405). Lambda (1405) could be a pentaquark candidate!

•Two nucleon-like pentaquarks may be narrow •The lowest heavy pentaquark has JP=1/2- instead of JP=1/2+

•Flavor WF of two diquarks symmetric Anti-decuplet and octet with L=1, JP=3/2+,1/2+

•Flavor WF of two diquarks anti-symmetric Octet and singlet with L=0, JP=1/2-

Diquarks, Pentaquarks, Anti-baryons and Dibaryons (Zhu; Lichtenberg)

• Diquark and anti-quark are very similar in many respects: supersymmetry between diquark and anti-quark. If diquark model is correct, then:

• Replacing two diquarks by two anti-quarks, pentaquark can be related to anti-baryon.

• Replacing the anti-quark by the diquark, pentaquarks can be related to dibaryons composed of three diquarks

• With experimental constraint on H dibaryon P=- SU(3)F singlet pentaquark mass ~(1402-1542) MeV• With θ+ mass P=- dibaryon mass ~ (2270-2310) MeV

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Other Clustered Quark Models• Diquark-triquark model, two clusters k

ept apart by the P-wave angular momentum barrier (Lipkin, Karliner)

• Color magnetic interaction occurs within two clusters only; Color electric forces bind them into a color singlet with P=+; Anti-decuplet + octet.

• In order to get a low lying θ, they assumed orbital excitation to be 200 MeV to set scale. REAL spin-average: 500MeV

• θ mass is 1540 MeV without orbital excitation! (Hogaasen & Sorba)

• θ mass should be around 1800 MeV in KL model!

• Shuryak & Zahed: replacing one scalar diquark by a tensor one with J=1, m=570MeV

• One orbital excitation within the tensor diquark

• No orbital excitation needed, pentaquark mass lowered

• But now θ is in the 27 representation! Where are Theta’s isospin partners?

Non-clustered quark models: Riska, Stancu, Maltman, Zhang, Ping at this conference

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Narrow Width Puzzle•D-wave 3/2- Lambda(1520) KN, width 7 MeV•P-wave Lambda(1600) is 100 MeV•Both decays need qq_bar pair creation from vacuum•θ falls apart easily with similar phase space•Width: < 10 MeV (direct experiments); <1MeV (indirect)

Some attempts for narrow width puzzle

•Color flavor spin overlap suppression > 24 (Jaffe Wilzcek; Jennings Maltman; Carlson et al; Close Dudek;Buccella Stora)•Spatial overlap suppression (Stech et al;Dudek;Carlson et al)•Cancellation of coupling constants in the first three orders in the large NC expansion in CSM (DPP; Ellis et al.)

•Decoupling from the decay modes through the diagonalization of the mixing mass matrix between two degenerate pentaquarks (Lipkin, Karliner)

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What’s Next?• If θ confirmed and established, a new landscape of

multi-quark hadrons is emerging from the horizon! We MUST answer:• What’s the underlying dynamics leading to its low

mass, narrow width and special production mechanism?

• Do other multiquark hadrons exist: 4q, 6q, 7q…, N q? Is there an upper limit for N?• Study of these issues will deepen our understandin

g of the low-energy sector of QCD!

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Summary• NONE of theoretical models predicts the e

xistence of θ+(1530) reliably.• NONE of theoretical models explains its lo

w mass, narrow width and production mechanism convincingly if it really exists.

• θ+ spin & parity distinguish models• Now its existence is an experimental issue, r

equiring high-statistics experiments• It could be an artifact.

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Group Theory For Anti-Decuplet Pentaquarks (Four Quarks Anti-Symmetric)

• Negative parity, L=0• 4q Color WF: [211]C

• 4q Orbital WF: [4]O

• 4q SU(6)fS WF: [31]210fS

• 4q SU(3)f WF: [22]6f

• 4q SU(2)S WF: [31]3S

• [22]f * [11]f=[33]10f + [21]f

• [31]S*[1]S=[41]S+[32]S

• Positive parity, L=1• 4q Color WF: [211]C

• 4q Orbital WF: [31]O

• 4q SU(6)OfS WF: [31]OfS

• 4q SU(6)fS WF: [4], [31], [22], [211], not unique

• Four possible totally anti-symmetric 4q WFs, all can lead to [33]10

f + [21]8f

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One Example: Selection Rules from Mismatch of Flavor-Spin Wave Functions (Buccella, Sorba)

• When s_bar picks up a quark to form a kaon, the two quarks among the remaining 3q are in the SU(6)FS anti-symmetric rep.

• Orthogonal to the nucleon octet symmetric Flavor-Spin WFs

• Decays of anti-decuplet into nucleon and pion octet strictly forbidden in the SU(6) flavor-spin symmetry limit

• Theta’s finite width arises from the SU(3)F breaking effects

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Photo-Production (Oh, Kim, Lee)￭￭ ~10 ~10 times larger in P=+ Than P=-times larger in P=+ Than P=-

￭￭ K-exchange dominant in the neutronK-exchange dominant in the neutron

￭￭ K*-exchange : significant interference K*-exchange : significant interference when the protonwhen the proton

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