Z_cs（4000）⁺ And Z_cs（4220）⁺ In A Multiquark Color Flux-Tube Model

The BESIII Collaboration observed a charged hidden-charm structure during the decay of e+e-→(D*0DS-/D0DS*-)K+,called as Zcs(3985)-.The charged structure can be treated as a partner structure with strangeness of Zcs(3885)-,which is produced and decayed in S-wave with quark contents ccsq(q for u,d quark).And Zcs(3985)-is the first candidate particle of the strange hidden-charm tetraquark state.In 2021,the LHCb collaboration reported two exotic structures Zcs(4000)+and Zcs(4220)+in the J/ψK+invariant mass spectrum of the B+→J/ψφK+decay.Zcs(4220)+ has the same quark content as Zcs(3985)+,is a state with hidden-charm and strangeness decay to the final state of J/ψK+and can be thought of as P-wave decay.Color confinement is still a difficult problem in theoretical physics.In the traditional constituent quark model(CQM),a two-body confinement potential proportional to the color charges was introduced to describe the quark confinement interaction.However,the model leads to power law van der Waals forces between color-singlet hadrons,and it only considers the long-range static multibody potential as a sum of the two-body ones,it is flawed phenomenologically and theoretically.Recently,LQCD calculations on mesons,baryons,multiquark states reveal flux-tube or string-like structure.The confinement is multibody interaction and can be simulated by a potential which is proportional to the minimum of the total length of strings connecting the quarks to form a multiquark system.The color flux-tube model we adopted is based on the traditional quark model and the color flux tube diagram of the lattice QCD,the two-body and restricted potentials of the traditional quark model are considered as the multi-body interaction.In this work,we systematically investigate the mass spectrum,spatial configuration and magnetic moment of the ground and P-wave states[cu][cs]with various color-spin configurations in a multiquark color flux-tube model.In order to improve the accuracy of the Schrodinger equation,the Gaussian expansion method will be used to deal with the orbital wave function of tetraquark states.Numerical results indicate that the state Zcs(4000)+can be described as the compact state[cu][cs]with 13S1.Its main colorspin configuration is[cu]6c1[cs]6c1 and its magnetic moment is 0.73 μN.The state Zcs(4220)+can be described as the compact state[cu][cs]with 11P1(or 13P1).Its main color-spin configuration is[cu]3c0[cs]3c0(or[cu]3c0[cs]3c1)and its magnetic moment is 0.12 μN(or 0.64 μN).The physical state should be the mixture of these two different color-spin configurations and deserves further investigation.In addition,we also predict the properties of the states[cu][cs]with other quantum numbers in the model.The structure of this paper is divided into five parts as follows:the first part is the introduction,which introduces the basic knowledge of hadron physics and the development of Zc state.The second part briefly describes the theoretical models of the common quantum chromodynamics,such as Naive constituent quark model,GlashowIsgur model,the chiral quark model and the color flux-tube model.And the third chapter introduces the Gauss expansion method,it includes two-body problems such as the meson system,three-body problems such as the system in which three particles are all the same particles,and the gauss expansion of a four-body system.In chapter 4,the wave functions of meson and tetraquark state[cu][cs]are described.The last part is the result and analysis by substituting the meson fitting parameter into the tetraquark state.