1、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. IntroductionII. Quark Models and calculation methodIII. ResultsIV. Summary and outlook,I. Introduction,Since 2003, a lot of work focus on mesons wi
2、th 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, moleculesOur goal: looking for tetraquark states,Summary of the Charmonium-like XY Z states,Charmonium-like states: Z+(4430), Z1+(
3、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. met
4、hods: OGE: qqqq 3P0 calculations are going on.,The tetraquark states: QQnn,Q=b, c, s, n=u, dNo annihilationThe minimum quark contents: four quarksMany proposals to explore the states experimentally have been put forward. Boris A. et al, Phys. Lett. B 551,296 (2003). A. Del Fabbro, et al., Phys. Rev.
5、 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.
6、, 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 (2009)A.Del Fabbro, et al., Phys. Rev. D71, 014008 (2005).bbnn is bound state, ccnn un
7、certain.,Tetraquark states,In quark models, Two configurations are used: diquark-antidiquark: qq-qq dimeson and hidden color channels: qq-qqCompleteness? All the excited states are included completenessOver-completeness? configurations mixing, low-lying states are included, calculation tractable ove
8、r-completeness Orthogonalization: Eigenfunction method,Quark Models,Bhaduri, Cohler, and Nogami (BCN) quark model Advantages: simple, powerful Applied to conventional meson, baryon and four-quark system range from light quarks u, d to b with same set of parameters.,Chiral quark model,Quark delocaliz
9、ation color screening model,Hamiltonian is same as ChQM replace -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 coordin
10、ates,Color, spin, flavor wavefunctions,ColorSpinFlavor set (a) set (b),Total wavefunctionsset (a)Set (b),Variational principleBinding energy,Model parameters,mesons,S-wave QQnn,Systematic calculationsDiquark-antidiquark configurationDimeson configurationConfiguration mixing,Configuration mixing,Over
11、-completenessOrthogonalization: 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.,Config
12、uration 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
13、 QQQQ,QQQn,Qnnn, no bound state is found. (without annihilation interactions)For QQnn, bbnn with (I,J)=(0,1) is always bound in the quark 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 overcome the problem of over-completeness.2+4 mixing is important for exotic tetraquark states,Thanks !,
