The Color Flow Tube Model Studies The Four-quark State

Since the first exotic resonance X(3872)was observed in 2003 by Bell collaboration many other exotic sates have been discovered by the BaBar,Belle,BESIII,CDF,DO LHCb and other collaborations,these states are called "XYZ" states.In the traditional quark models,meson is made up by quark and antiquark,while baryon consists of three quarks.The "XYZ" states are difficult to be accommodated by the tranditional quark models.Our important work now is to explain these exotic states in quark models.The study of the exotic states is helpful for us to improve the quark model and will help us to understand better the quantum chromodynamics(QCD)theory as well.Despite the fact that QCD is widely accepted as the fundamental theory of strong interaction,it will face tremendous difficulty when deal with the multiquark states,which belong to the low-energy region of QCD,because of the non-perturbative properties and complexity of QCD in the low energy region.The QCD sum rule can handle the ground s-tate and the low energy states well but it has limited accuracy and cannot solve the highly excited states problems.In recent years,the lattice QCD has made impressive progresses on hadron physics,however,due to the limit of computing power and complexity of the problem,it is now not an ideal way to solve the multiquark problems.The phenomenolog-ical quark model offered another way to study the mutiquark states.The most successful and convenient one is the constituent quark model,with several adjustment parameter the existed experimental data on meson and baryon properties and hadron-hadron inter-action can be fitted well.The color flux-tube model,which is used in this paper,belongs to the constituent quark modelThe tetraquark consisted of two heavy quarks and two light antiquarks has aroused much interests.The question whether QQqq tetraquark are stable or unstable against decay into two Qq mesons has remained as a problem for a long time largely because of the lack of experimental data about the strength of the interaction between two heavy quarks.In 2017,the LHCb Collaboration at CERN discovered the doubly charmed baryon Ecc with quark contents cuu having mass of 3621.401±0.78MeV,which make the settlement of the problem possible.Shortly after that,Karliner and Rosner claimed that the discovery of the doubly charmed baryon Ξcc implied a stable bb(?) tetraquark exists.Eichten and Quigg also claimed that there exists stable heavy tetraquark QiQjqkql.The lattice QCD calculation shows that there are flux-tube-like structures existed in the multiquark systems,the interactions among quarks include multi-body interaction.the confinement potential can be represented as the sum of the flux tube lengths.Our group built a color flux-tube model based on the lattice QCD calculation.The numerical studies in the flux-tube model showed that the sum of the flux tube lengths can be replaced as the sum of the square of these flux tube lengths,the replacement will greatly simplify the calculation and introduces insignificant errors.The goal of this work is to study the tetraquark systems with two heavy quarks in the framework of the color flux-tube model,the powerful fow-body method with high precision:gaussian expansion method is employed.Three states,bcud,bb(?) and ccud are studied in the present work.The quantum numbers JP is limited to 0+,because we are interested in the bound states and the low-lying resonances.In the calculation,we take diquark-antidiquark structure as our starting point because of the characteristic of the color flux-tube model.All the color and spin configurations and their mixing are taken into account.Different approaches,effective potentials,the root-mean-square(rms)distance between quarks,the contribution of each term in the hamiltonian,are invoked to discuss the formation mechanism of the bound state and the structure of states.The results show that no bound state exists for the 1=1 bb(?),ccud and bcud systems,resonances are possible due to the color structure of the systems,the energies of the resonances are 11170 MeV,4158 MeV and 7490 MeV.For the I=0 bcud system,a bound state is found with energy 7090 MeV.The rms distances between quarks infer that the state is a compact tetraquark state.The calculations of the contribution of each term in hamiltonian show that the 7r meson exchange plays the dominant role in the formation of the bound state.The confinement with multi-body characteristic is helpful for the bound of the state.The present calculation is preliminary,the error from the variation of the parameters is not calculated.This is our next work.