Research On The Effect Of Meson Exchange On The Binding Energy Of Peculiar Four Quark States

Exotic hadron states are still the hot subject of hadron physics research in recent years.Various(3(4(5 hadron states have been reported successively by BABAR,Belle,BES,L-HCb and other experimental collaborations.Especially,these charged charmonium-like or bottomonium-like states,(5_c?3885?,(5_c?4050?,(5_c?3900?,(3?5568?hadron states found by D0 experimental group,etc.cannot be explained in the quark-antiquark picture.New hadron states contain heavy quarks?c,b?are constantly being reported.So far,no unified explanation has been given for the internal structures of the exotic heavy hadron states,and the situation has attracted researchers over the world.Quantum chromodynamics?QCD?is a fundamental theory of strong interactions.However,due to the complexity of strong interactions,it is difficult to use QCD directly to deal with low-energy hadron physics problems.The development of the lattice QCD has made great progresses in the non-perturbation problem,but its description of hadron-hadron interactions and multiquark systems is not satisfactory.The constituent quark model which contains the main proper-ties of QCD,has achieved great successes in explaining the properties of mesons,baryons,and hadron-hadron interactions.The constituent quark model demonstrated its own ad-vantages in many experiments and theoretical research.In studying the charmonium-like states at the hadron level,Frank Close proposed that themeson exchange potential plays an important role,providing about 100 Me V binding energy to the four-quark exotic state systems consisting of,^*,₀,₁.However,there are some problems to study this issue from the hadron level,because the coupling constants betweenandmeson have to be extracted from the experimental data,which is scarce right now.Therefore,this thesis is based on the constituent quark model.In the framework of quark model,the powerful few-body method,gaussian expansion method?GEM?is employed to calculate the eigen-energies of the four-quark states which are composed ofmeson and their anti-particles.The effect of themeson exchange potential on the four-quark states are studied on the quark level.First,the meson spectrum is calculated by using GEM in the framework of the chiral constituent quark model.The model parameters are fixed by fitting the experimental data.We found that the results obtained are in good agreement with the experimental data,which show that the effectiveness of the quark model description.This step is the necessary prerequisite for the study of tetraquark states.Then for the given state with quantum numbers^{P C},we construct the total wave functions for the state by using the group representation theory method.The total wave function is the product of orbital,color,spin and flavor wave functions with necessary coupling.The infinitesimally-shifted Gaussian basis functions?ISG?are introduced to deal with the orbital wave functions for-wave mesons.The analytic formula of matrix elements of hamiltonian for tetraquark systems are derived.Two structures,meson-meson and diquark-antidiquark,and their mixing are also con-sidered in the calculation.In this way,the model space is enlarged and it allows the system choose its favored structure according its dynamics.The structure of the state can be unraveled by calculating the distances between quarks?antiquarks?.The procedure of our calculation is as follows.First the effective potentials of the state are obtained by the adiabatic calculation and we can have a qualitative knowledge of bounding of the state.Then the dynamic calculations are performed to determine whether the state is bound or not.To find the effect of themeson exchange potential,the contributions to the eigen-energy of each term in the hamiltonian are calculated.In the present work,the system with?^*,?₀^*,^*?^*and^*?₁are taken into account.For meson-meson structure,the interaction between the two mesons of the color singlet is not attractive enough to bind the two clusters,and the hidden-color channel can form resonances due to the color structure.The coupling between color-singlet channels and hidden-color channels does not push the state below the threshold.As for the resonances,the scattering calculation is needed to check the states can survive or not after coupling with the open channels.For diquark-antidiquark structure,the energies of the states are always higher than that of the states with the same quantum numbers in the meson-meson structure.There is on bound state in the diquark-antidiquark structure.There is also no bound state with the two-color structures mixing.But the resonance states are also possible.According to the results,meson exchange potential has attractive contribution to the energies of these systems,but it is not strong enough to make four-quark states bound.If the exotic states association withmeson and its antiparticle are confirmed by experiments,then looking for the new mechanism for the attraction is expected.Chiral constituent quark model has been proven as a successful method to describe the properties of hadrons and hadron-hadron interactions.To explain the exotic states found in experiments,the multiquark states,and even the mixing of quark-antiquark states and four-quark states,or quark-antiquark-gluon states has to be taken into account.With the improvement of the research and accumulation of experimental data,further development of quark model is expected.It is hope that the improved quark model can give a unified description of the low-lying spectrum of meson and the exotic states.