Tetraquark states in Quark Model

Jialun Ping

Youchang Yang, Yulan Wang, Yujia ZaiNanjing Normal University

中高能核物理大会 November 5-7, 2009, Hefei

Outline

I. Introduction

II. Quark Models and calculation method

III. Results

IV. Summary and outlook

I. Introduction

• Since 2003, a lot of work focus on mesons with charm quark(s)

• These states are difficult to be understood as conventional mesons.

• Explanation:

exotic four-quark states,

hybrid states with gluonic degrees of freedom,

molecules• Our goal: looking for tetraquark states

Summary of the Charmonium-like XY Z states

• Charmonium-like states: Z+(4430), Z1+(4050), Z2

+(4250)

Belle observed, but BaBar finds no conclusive evidence in their data for the Z+(4430)

minimum quark contents: ccud

Isospin symmetry breaks?

• Other charmonium states:

minimum quark contents: cc

no isospin partner?• Annihilation interactions play an important role.

2+4 mixing needed.

methods: OGE: qqqq

3P0

calculations are going on.

The tetraquark states: QQnn

• Q=b, c, s, n=u, d• No annihilation• The minimum quark contents: four quarks• Many proposals to explore the states experiment

ally have been put forward.

Boris A. et al, Phys. Lett. B 551,296 (2003).

A. Del Fabbro, et al., Phys. Rev. D71, 014008 (2005).

D. Janc, et al., Few-Body Systems 35, 175 (2004)

……

References

J. Carlson, et al., Phys. Rev. D 37, 744(1988)A. V. Manohar, M. B. Wise, Nucl. Phys. B 399, 17(1993).B. Silvestre-Brac and C. Semay, Z. Phys. C 57, 273-282(1993); 59, 457-470 (1993); 61, 271-275 (1994).S. Pepin, et al., Phys.Lett. B 393, 119 (1997).D. M. Brink, et al., Phys. Rev. D 49, 4665; 57, 6778(1998). D. Janc, M. Rosina, Few-Body Systems 35, 175-196(2004).J. Vijande, et al., Eur. Phys. J. A19, 383-389 (2004); PRD79,074010 (2

009)A.Del Fabbro, et al., Phys. Rev. D71, 014008 (2005).

• bbnn is bound state, • ccnn uncertain.

Tetraquark states

• In quark models, Two configurations are used: diquark-antidiquark: qq-qq dimeson and hidden color channels: qq-qq• Completeness? All the excited states are included completeness

• Over-completeness? configurations mixing, low-lying states are included, calculation tractable over-completeness Orthogonalization: Eigenfunction method

Quark Models

• Bhaduri, Cohler, and Nogami (BCN) quark model

• Advantages: simple, powerful Applied to conventional meson, baryon and four-quark sy

stem range from light quarks u, d to b with same set of parameters.

Chiral quark model

Quark delocalization color screening model

• Hamiltonian is same as ChQM

replace σ-meson exchange,

introduce color screening

Calculation method

• Gaussian expansion method: high precision numerical method for few body system.

E. Hiyama, et al., Prog. Part. Nucl. Phys. 51 223 (2003).• Wavefunction:

• Relative motion coordinates

Color, spin, flavor wavefunctions

• Color

• Spin

• Flavor

set (a) set (b)

• Total wavefunctions

• set (a)

• Set (b)

• Variational principle

• Binding energy

Model parameters

mesons

S-wave QQnn

• Systematic calculations

• Diquark-antidiquark configuration

• Dimeson configuration

• Configuration mixing

Configuration mixing

• Over-completeness• Orthogonalization: Eigenfunction method

construct the overlap matrix of all the bases,

diagonalize the overlap matrix,

delete the eigenfunctions with eigenvalue zero,

use the remain eigenfunctions to construct the hamiltonian matrix and diagonalize it to obtain the eigenenergies.

Configuration mixing

QQQQ, QQQn, Qnnn states

• No bound state is found.

• Annihilation interactions are not taken into account.

• The existence of open charm states imply that the annihilation interactions are important.

Summary and outlook

• A systematic calculation of tetraquark states in quark models is done.

• For QQQQ,QQQn,Qnnn, no bound state is found.

(without annihilation interactions)• For QQnn, bbnn with (I,J)=(0,1) is always bound in the q

uark models used. ccnn with (I,J)=(0,1) is bound state with smaller binding energy, ssnn with (I,J)=(0,1) is bound in ChQM after configuration mixing.

• Configuration mixing introduces more attraction.• Orthogonalization with eigenfunction method is used to o

vercome the problem of over-completeness.• 2+4 mixing is important for exotic tetraquark states

Thanks !!!