A Study On The Odd States Of Charm-like Quarks

In recent ten years,a lot of exotic hadronic states have been discovered one after another by major high energy and nuclear physics experimental collaborations in the world,such as(3?3872?,(5_c?3900?,(3?5568?,etc.Since the properties of these exotic states can not be explained well by conventional hadrons?mesons and baryons?,many researchers have begun to use various methods and models to study these exotic states found in experiments.In theory,quantum chromodynamics?QCD?is the theoretical basis for describing strong interactions.The phenomena of strong interaction in different energy ranges should be solved by different methods because of the complexity of QCD.The phenomena in high energy range can be solved by perturbation theory because the coupling coefficient for strong interaction is small in this energy range.However,the properties of hadrons is in low energy range,which belong to the non-perturbation field of QCD,can not be solved by perturbation theory.The properties of hadrons in ground state can be solved well by lattice QCD,Dyson-Schwinger equations and QCD sum rules,but these methods are not effective when the hadron excitation and multiquarks are taken into consideration.Since the establishment of constituent quark model,which contains the main properties of QCD,it has been an important non-perturbation method to study the low energy hadron issues.So far,the constituent quark model has not only achieved success in describing mesons and baryons,but also showed its own advantages in solving the issues such as multiquarks and hadron-hadron interactions.In this thesis work,first the fitting of the meson spectrum is performed in the chiral constituent quark model.The results obtained by fitting are in good agreement with the experimental data.A set of model parameters are obtained while the effectiveness test of the chiral constituent quark model is shown.It also laid the foundation for the further study of the tetraquark systems.Then,the wavefunctions for tetraquark systems are constructed.The orbital wave function are expanded by Gaussians and the wave functions for color,flavor and spin are obtained by using the knowledge of group theory.Finally,we investigate the(8?(8?tetraquark states based on the chiral constituent quark model to explain some charmonium-like exotic states found in the process of⁺?/⁺by LHCb Collaboration in 2016.According to the results obtained for^{P C}=1⁺⁺,we find that there are several(8?(8?ground states around 4300 Me V and they are suitable to explain(3?4274?.However,due to the low energy of(3?4140?,our results show that it can not be explained by the(8?(8?tetraquark states.From the excited S-wave energy with^{P C}=0⁺⁺,We find that a 2S excited state with energy 4719.4 Me V is very close to that of the(3?4700?in experiment.In addition,there are several 2S states with energy around4650 Me V that are not much different from X?4700?,so(3?4700?can be interpreted as a 2S radial excited state in our calculation.It's worth noting that we also find several 1S states with^{P C}=0⁺⁺are close to the mass of(3?4350?found in the process of?/by Belle Collaboration in 2011.If the^{P C}of(3?4350?in experiment can be determined to be 0⁺⁺,we believe that the(3?4350?can be regarded as a(8?(8?ground state.As for X?4500?,there is no matching result in our calculation and it can not be described as a(8?(8?tetraquark state.At present,in addition to LHCb,there are many other collaborations that have also found many charmonium-like exotic states.For these exotic states containing(8?(8 componen-t,people have not yet given a uniform interpretation to their internal structure.Therefore,the field of charmonium-like exotic states still has a high research value.At the same time,the constituent quark model,a non-perturbation theoretical model,shows good results when be used in a single structure system.However,in the face of some more complex structures,such as meson-tetraquark mixing systems,quark-gluon mixing states,etc.,the current model can not deal with these issues well.Therefore,the theoretical models and methods still need constant development and improvement to give a in-depth study of these exotic hadron states found in experiment.