Study On The Quark Model Of Meson-meson Interaction

Since 2003,the experimental groups Belle7 BaBar,BES,etc,have reported a lot of new hadron states,such as X(3915),Y(4260),Zc(3900)and so on.These reports of new hadron states have aroused widespread interest of the theoretical and experimental physicists.Although no new hadron states have been identified so far,theoretical and ex-perimental work has continued to find multiple quark states.Many theoretical physicists have studied multi-quark states from the perspective of molecular states.For example,assuming that the four-quark state is in a meson-meson structure,it can explain some new hadron states.In the light quark system,many theoretical physics regarded f0(980)and a0(980)as meson-meson structures,and did a lot of theoretical research.Smruti Pa-tel and others interpreted Zc(3900)as JPC(1+-)four-quark state with the meson-meson structure.Yang Youchang et al interpreted X(3915)as the D*D*molecular state with the meson-meson structure.From this point of view,studying the four-quark system with the meson-meson structure is a common way to explore the four-quark state.With this approach,we can not only find some new hadron states reported experimentally,but also further study the meson-meson interactionQuantum chromodynamics(QCD)is the basic theory describing strong interactions But low-energy hadron physics belongs to the non-perturbative region of QCD.Due to the complexity of the theory of non-perturbation QCD,it is very difficult to solve the low-energy hadron problem from the first-principles QCD.Although the lattice QCD theory has made great progress in recent years,it is still difficult to deal with the excited state problem.The phenomenological quark model based on QCD is an effective method for studying hadron-hadron interactions.It can well describe the properties of hadrons,such as nucleon-nucleon interactions,baryon spectrum,and heavy quark couplet energy spectrum.Our research group has done systematic research on both the six-quark system and the five-quark system in the framework of the constituent quark models.We obtained the nucleon-nucleon interaction,the properties of deuteron,the reported dibaryon d*,N?,etc,and the hidden-charm pentaquark states Pc(4310),Pc(4440),Pc(4457)etc Extending to the four-quark system,our research group studied many exotic states,such as X(3915),X(3872),and so on.And we also explained the experimental data well Based on the work above,we would like to conduct a systematic search of all four-quark systems to find the possible four-quark statesAs the first step,we systematically investigate the four-quark system composed of light quarks in this work.In the framework of the chiral quark model,we study the qq-qq(q=u,d,s)system with the help of the Gaussian expansion method(GEM).During our calculation,we not only carry out the bound state calculation,but also study the effective potentials of the meson-meson interaction.The results show that for all color-singlet channel,the interactions between two mesons are repulsive,and there is no any bound state in the system.Even the channel coupling calculation cannot help much The hidden-color channel coupling also has little effect on most systems,except for one system,the IJP=00+pp state,the color-singlet channel of which is also unbound,but the energy of the hidden-color channel is lower than the theoretical threshold of pp The channel coupling calculation further reduces the energy of the system.So this state is possible to be a resonance state with the energy of about 1311.37 MeV,and the decay channel is ??.We suggest looking for this state experimentally.Meanwhile,the effective potentials between pp show that the interaction between the color-singlet pp is repulsive,while the one for the hidden-color channel is attractive.And there is a very deep attraction for the pp system by the channel coupling calculation,which is a necessary condition for forming a bound state.In addition,we also study the contribution of each interaction item.We find that the color confinement potential,coulomb interaction,color-magnetic interaction,? meson exchange,and a meson exchange all provide attractions In particular,the attraction of the color-magnetic interaction term is very large,which is an important factor in the formation of bound states.Moreover,through the study of the effective potentials,we also find that it is possible for some hidden-color states qs-qs(q=u,d)to be the resonance states.Take the hidden-color channel IJP=01+K*K*for example,although the energy this state is above the threshold of K*K*,the attractive potential shows it is possible to be a resonance state.The investigation of the scattering process is needed to further confirm whether it is a resonance state or not,which is our work in future.In order to explore more new hadron states,we still have a lot of work to do.At present we have only studied the ground states of the four-quark system consisting of light quarks.In the future,we will continue to study the systems with higher partial wave,as well as the four-quark systems containing heavy quarks.Finally,we will do the systematical search for all four-quark systems.In addition,the current structure of the four-quark system in our work is the meson-meson structure.Other structures,as well as the coupling of all structures will be studied in future.It is hoped that through this research,we can not only explore possible four-quark states and provide theoretical information for the experiment,but also have a deeper understanding of the low-energy behavior of QCD.