| Since Belle Collaboration discovered the exotic state X(3872)?BaBar,Belle,BES?,CDF and LHCb collaborations have reported numbers of 'XYZ' exotic states.The common character of the new states is that c(b)quark and its antiquark are found in the decay product,so we call them charmonium-like state or bottomium-like state,such as X(3915),Y(4260),Zb(10610)and so on.A common explanation of the new particles are candidates of tetraquark.The report of these states not only provides chances to search for tetraquark,but also arise the interesting on the exotic states.Actually,once the establishment of quark model,the physicists made research on multiquark states.In 1964,Dyson put forward the concept of six quark state D03 etc.In 1972,Strottman studied a pentaquark state composed of light quarks(qqqqq).In 1977,Jaffe predicted H particle(uuddss)with MIT bag model.In 1989,Goldma,n thought that d*(uuuddd)is a inevitable dibaryon state.What' s more,LEPS collaboration claimed the existence of(?)+ consists of uudds,which was denied by more experiments with high precision measurements.How to study the properties of the exotic states?How to provide theoretical guide for experiment searching of new particles?Although Chromodynamics(QCD)is well known fundamental theory for strong interaction,it is very difficult to cope with the low energy hadron physics form the first principle of QCD.In the past years,lattice QCD made great progresses on the properties of hadrons,but it has trouble to deal with the hadron-hadron interaction and multiquark states.Another way to study the the properties of hadrons is QCD sum rule,nevertheless it only works on ground state of hadrons rather than excited states.The 'QCD inspired' phenomenological quark model offers a convenient way for studying the property of exotic states.When quark model was put forward,it successfully predicted the particle ?.After that it had gone continuous improvements,it has achieved great success in hadron spectra,and hadron-hadron interactions.Not only study the ground state,the quark model but also explains the excited states,and it could be easily expended to multiquark states.All in all,the article is working on quark model.The main purpose of this paper is studying the property of Zc(3900).which is reported by BESIII collaboration.The Zc(3900),a charged charmioum-like state,is a special state,if it is a qua.rk-antiquark state.the minimum contents of it is udcc,a tetraquark st ate.The previous work always assume the structure of the state before calculation,so the structure is artificial.In this work,we consider Zc(3900)as tetraquark state with quark contents of udcc and quantum numbers JP is 1+ and Gaussian expansion method is employed to do the calculation.In this approach,the structure of the state is fixed by the dynamics of the system.Two structures,meson-meson and diquark-antidiquark,are considered in the present calculation,and all possible color coupling and their mixing for each structure are also taken into account.The results show that we cannot obtain molecular state or resonance consistent with Zc(3900)in the SU(3)chiral quark model.For meson-meson structure,there are not enough attraction between two color-singlet mesons to form molecular states.The hidden-color states have high masses compared with Zc(3900),and the coupling with color-singlet channel is too weak to push the color-singlet state below the threshold.For diquark-antidiquark structure,the resonances can be formed due to the color structure.Nevertheless,the masses of the states are higher than that of Zc(3900).The channel coupling helps a little,but not enough.In the present work,the flavor symmetry is limited to SU(3),because the mass of c quark is much heavier than that of u,d quark.Generalizing the flavor symmetry from SU(3)to SU(4),and introducing the scalar meson exchange,the attraction between two clusters will be increased.The state Zc(3900)maybe explained in this way.This work is left for future. |
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