The Study Of The Four-quark System Containing (?) Or (?)

Since the establishment of quark model,finding multi-quark states has always been an important field of hadronic physics research,which is of irreplaceable value to reveal the structure of hadrons and study the strong interactions.In recent years,with the accumulation of more and more high-energy experimental data,a series of important advances have been made in the field of hadronic spectrum in high-energy physics exper-iments.A number of new hadronic states,such as X(1835),Y(2175),X(3872),Y(4160),Z(4430),and so on,which are the so-called”XYZ”states,have been reported by many large collaborations,such as BES,CLEO,Belle,CDF,DO,etc.Most of these states have some special properties and are difficult to be explained by the traditional constituent quark model.In 2015,the LHCb collaboration reported two hidden-charm pentaquark states:Pc(4380)and Pc(4450),which aroused people's attention to the five-quark sys-tem containing heavy quarks.In 2019,after improving the experimental accuracy,the LHCb updated their results,and reported three pentaquark states:Pc(4312),Pc(4440)and Pc(4457).In September 2017,the LHCb reported a baryon ?cc containing double charm quarks,which provided an important experimental basis for the study of the in-teraction between two heavy quarks,and indicated that there may be some tetraquark states containing two heavy quarks(QQqq or qqQQ,where Q=c,b and q=u,d,s)This observation arouses people's interest in the study of the double-heavy tetraquark statesFor the systems with hadron interactions,quantum chromodynamics(QCD)is rec-ognized as the basic theory.Experiments show that the high energy processes can be processed by perturbation QCD,while the low energy QCD is non-perturbation.How to solve the low energy non-perturbed QCD is an important problem in contemporary physics.People have developed many ways to solve this problem.In recent years,great progress has been made in the study of the systems with hadron interactions by lattice QCD,which starts from the first principle to disperse the space and time.The lattice QCD can describe the properties of hadrons well.When extending to the hadron-hadron interactions,the results are qualitatively consistent with the experimental data.Howev-er,it is not satisfactory in predicting new hadronic states,explaining exotic states,and it is difficult to provide the physical intuitive images of the systems with hadron inter-actions.The chiral perturbation theory,which starts from hadrons free and maintains various symmetry of QCD,has been successfully applied to the study of nucleon-nucleon interactions,and the results are completely consistent with the experimental results in the low-energy region.The application of this theory to the higher-energy region,such as the excited state of hadrons and the peculiar state,is still to be developed.In addi-tion,the equivalent field theory method,Dyson-Schwinger equation,QCD sum rule and other non-perturbing methods are also widely used in the study of systems with hadron interactions,and some important results are obtained.Another usually used method is the phenomenological quark model.Since the quark model was proposed by Gell-mann et al.,the quark model has achieved great success in describing hadronic spectrum and hadron-hadronic interactions through the efforts of Isgur et al..The quark models also describe the experimental data of nucleon-nucleon and nucleon-hyperon scattering phase shifts well,and predict dibaryons like d*.In this work,we investigate the four-quark systems with two heavy quark-s in the framework of the constituent quark models by using the Gaussian expan-sion method(GEM).The work also extend to the full-heavy tetraquarks.First-ly,the constituent quark model and the GEM are introduced in detail.Second-ly,the meson spectrum is calculated and the model parameters are determined by comparing the experimental data.Then it is directly extended to the study of the tetraquark system.We introduce how to construct the wave function of the tetraquark system and calculate the Hamiltonian matrix element.Since the ground s-tate energy is the lowest one,we first studied the tetraquark system in the S wave,namely:uuQQ?usQQ?ucQQ?ubQQ?ssQQ?scQQ?sbQQ?ccQQ?cbQQ?bbQQ,where Q=c or b.Both the single channel and channel-coupling calculations are carried out in our work.Our results show that most tetraquarks containing cc or bb are unbound,except two states.The one is the udcc with a quantum number of IJ=01,and another one is the udbb with IJ=01,both of which are likely to be shallow bound states.For the full-heavy tetraquarks,we cannot obtain any bound states in present work.In ad-dition,we also study the contribution to the formation of these two bound states.The meson-exchange interaction may be a major factor to provides attractive potentials.The one-gluon-exchange also provides attractions,while the kinetic energy term provides re-pulsion.Moreover,we also investigate the structure of these two states,and find that both of them tend to be in a molecular structures,and the distance between quarks in the udbb state is smaller than the one in the udcc state,indicating that they are more likely to form a compact bound states,and its binding energy is larger than that of udcc with IJ=01.We still have a lot of work to do in order to further explore the exotic states and provide more theoretical information for experiments.At present,we only study the tetraquark system of S-wave,and we will continue to study the systems with higher partial wave in the future.And we assume the tetraquarks are in a molecular structure,more structures,as well as the coupling of all structures are needed in our future work It is hoped that through this research,we can not only have a better understanding of the low-energy behavior of QCD,but also provide more useful information for the experimental search of the multi-quark states.