The quark model study of multiquark system

Jialun Ping, Hongxia Huang, Chengrong DengNanjing Normal University

Fan WangNanjing University

2009.4.20

NSTAR 2009, Beijing

Outline Motivation Dibaryon Tetraquark Summary

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Motivation Quark models: success in describing hadron properties Glashow-Isgur-Karl model: constituent quark model

Bag model: Hadron: baryon (qqq) and meson (qq): unique color structures

two-body interaction: qqq a good approximation Casimir scaling ij qq

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NSTAR 2009, Beijing

Hadron-hadron interactions and multi-quark statesGlashow-Isgur-Karl model nucleon-nucleon interaction intermediate range attraction is missing. (-meson is introduced. s-wave resonance? correlated two-exchange doesnt introduce enough attraction NPA637(1998) 395; PTP103(2000)351; PRC70(2004) 014002)

Multiquark states H-particle has been searched for 30 years, not found. Other exotics: d*, N, ,, no confirmation. d, disappeared, , disappeared? tetraquark states? Something missing?

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qqqq qqqqqq

molecule states

Multi- quark

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Success and LimitationsThe Hamiltonian and the wave functions used are very good approximation, for qqq and Unique color structure

Multi-quark system: various color structures available What are the effects of various color structure?

Multi-quark system is indispensable for our understanding of QCD, especially the abundant color structures of QCD.

Multi-quark system needs new quark model

New states needs explanations.

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DibaryonCELSIUS-WASA Collaboration ABC anomaly: pn d00 or pn d+-

JP = 1+ or 3+ resonance?M 2.39 GeV, width 90 MeV PPNP61(2008)276; PRL102(2009)052301Our group: d*(IJP=03+) PRC39(1989)1889; PRC51(1995)3411; NPA688(2001)871

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QDCSMQuark delocalization, color screening model: Quark delocalization:

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NN Phase shift calculations PRC79(2009)024001 QDCSM M=2357 MeV =14+96 MeV ChQM M=2393 MeV =14+136 MeV

PRC76(2007)065201

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TetraquarkThere is a long list of candidates of tetraquark states: f0(600), f0(980), X(1576), DsJ(2317), DsJ(2460), X(3872), Y(2175), Y(4260), Z(3930),

Constituent quark model success in describing the properties of baryon and meson generalized directly to study tetraquark states Casimir scaling: ij reasonable?

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Lattice CalculationThe results from LatticePRL 86(2001)18 arXiv:0802.3500 r

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String-like quark ModelConventional quark model

The two-body confinement potential

is replaced by

T. Goldman and S. Yankielowicz, PRD 12(1975)2910.

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Other parts of model Hamilton

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The Confinement of tetra-quark

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Jacobi ordinates

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Total wavefunction:Two channels:Orbital wavefunctions:

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Numerical results for ssssEnergy Channel I: 2275MeV; Channel II: 2193MeV Channel coupling: 2178MeVNave quark model: 2560 MeVChiral quark model: 2400 MeVSpatial structure

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Other statesNonstrange tetraquark: IJPC=00++: The two lowest states: 587 MeV, 1019 MeV f0 (600) f0(980) IJP=01-: The lowest state: 984 MeVqsqs: JP=0+ : The lowest state: 1306 MeV JP=1- : The lowest state: 1715 MeV---X(1576)ssss: JP=0+ : The lowest state: 1924 MeV JP=1- : The lowest state: 2176 MeV---Y(2175)cqcq: JP=0+ : The lowest state: 3688 MeV JP=1- : The lowest state: 3938 MeV---Y(4008)cscs: JP=0+ : The lowest state: 4078 MeV JP=1- : The lowest state: 4248 MeV---Y(4260)

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SummaryNN scattering (IJ=03) shows resonance structure by including in QDCSM and chiral quark model. The resonance can be used to explain the ABC effect seen in reaction pn d .

According to the suggestion of LQCD, a string-like quark model is proposed. They are the same as the conventional constituent quark model for ordinary baryon and meson.

In this model, f0 (600) , f0(980), X(1576), Y(2175), Y(4008), Y(4260) can be interpreted as tetraquark states.

Multi-body interaction may be dispensable for multiquark state study.

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Thanks!

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New color structure

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Zero-order approximation

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Numerical resultsSingle Channel calculation: Channel I: 2273 MeV; Channel II: 2216 MeV Channel coupling: 2196 MeVIt has similar energy as other color structures.

The coupling of different color structures is needed to account for the decay. It is difficult

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