Study Of Hadron Interaction And Multi-quark Systems In Constituent Quark Models

Hadron (baryons and mesons) spectroscopy opens the gate for the development of the fundamental theory of the strong interaction: quantum chromodynamics (QCD). The unique color structure of the known hadrons makes the construction of quark models very efficient. However the unique color structure also limits our understanding of the properties of other color structures available in QCD. In order to understand various color structure of QCD. to study system with more quarks is indispensable. Hadron-hadron interaction provides a window on the nature of other color structures in the short (or intermediate) range, but it is not enough because it can mainly provides the information of the interacting colorless hadrons. Therefore, multi-quark systems are important samples for providing information on low energy QCD, especially the abundant color structures.Since the first theoretical prediction of H dibaryon by Jaffe in 1977, several dibaryon states such as d^', d^*, NΩ,ΩΩand so on have been proposed. Unfortunately there is no any convincing evidence in experiment to demonstrate the existence of the dibaryon so far. In 2003 LEPS group reported the "discovery" of a new resonanceθ⁺ with strangeness S=+1, study of pentaquark system had been one of the hot topics in particle physics. Many collaborations carried out experiments to find this state, but obtained different conclusions. Recently, a higher statistics experiment at the Jefferson Laboratory found no evidence to support the claims of the existence ofθ⁺. But the new result of LEPS group confirmed the "discovery" ofθ⁺. Theoretically, almost every quark model, nonperturbative method, including lattice QCD, have been applied to the study of pentaquark. However no conclusive answer is achieved.Scattering experiments play a very important role for the development of modern physics. In the microscopic physics, we study the interactions between particles and their structures by various scattering experiments. Many theoretical work can be tested by a great deal of scattering experimental data. Recently, in MENU2007, CELSIUSWASAgroup reported that a IJ^P=01⁺ or IJ^P=03⁺△△subthreshold resonance (with resonance mass～2.41 GeV and width～100 MeV) is needed to fit the total cross section of the pn→dÏ€⁰Ï€⁰ reaction. And the analysis of the reaction pp→dÏ€⁺ also indicate the existence of the Nâ–³resonance. In addition, the bump in the scattering cross-sections of pp and np between 2.1-2.4 GeV may imply the superposition of many broad resonances of Nâ–³and△△. So it is interesting to study NN scattering to locate the possible resonances by incorporating Nâ–³and△△channels. This is the most important object of this dissertation.Although Quantum chromodynamics (QCD) is generally accepted as the fundamentaltheory of the strong interaction, the direct use of QCD to low-energy phenomena: hadron-hadron interactions and multi-quark systems, is still impossible because of the nonperturbative properties and the complications of QCD. So at present and even in the future, the QCD-inspired model will be a useful tool to explore the secret of strong interactionsystems, especially the multi-quark systems, which have abundant color structures. The most commonly used quark models are the constituent quark models, and the chiral quark model is one of them. With the help of several adjustable parameters, the existed experimental data on meson and baryon properties and hadron-hadron interactions can be fitted well in model. To describe hadron-hadron interaction,σmeson is indispensable in various quark models. However the existence ofσmeson is still in controversial. Recently there are some progress, the signals ofσmeson are revealed, but the "discovered"σmeson which is identified as S-wave resonance of twoÏ€'s, can not introduce enough attractionin nucleon-nucleon (NN) interaction. Is there an alternative approach to the intermediate range attraction of NN interaction? It is an interesting problem. QCD tells us that the interaction between quarks is generally a multi-body interaction. The two-body approximation is proved as a good one in the hadron properties. However the validity of the generalization to multi-quark system is still an open question. The quark delocalization color screening model (QDCSM) was developed in 1990s on the basis of conventional constituent quark model by F. Wang et al. Applying to hadron, it is just the Glashow-Isgur model, which the hadron properties can be described well. Applying to NN interaction, the intermediate range attraction can be obtained withoutσmeson. The model takes into consideration of multi-body interaction among quarks, and assumes the q-q interaction depends on the states quark occupied. The screened color confinement is introduced to imitate the coupling effect of the various color structures. The main ad- vantage of QDCSM is that it allows the multi-quark system to choose its most favorable configuration (by variation the energy of the system to delocalization parameter) through its own dynamics. The model has few parameters and therefore has strong prediction power. It has been applied to the study of baryon-baryon interactions (deuteron properties,NN, NΛ, NΣ, etc.) and a good agreement with experimental data is obtained. Applying to dibaryon, several interesting dibaryon candidates are obtained. In this work, we use various quark models to study the five-quark states and the dibaryon system. On one hand, by comparing all the results from different models, we want to find out what is the general features, and try to provide more reliable results; on the other hand, by comparing various quark models, we try to understand the QCD theory in low-energy phenomena.For the pentaquark states, group theoretic method for the systematic study of five-quark states within u, d, s three-flavor world with different configurations: diquark (qq-qq-(?)) configuration and molecules (q(?)-qqq) configuration, was developed. The calculation was carried out by using the fractional parentage expansion technique. Three quark models: the naive quark model, the chiral quark model and quark delocalization color screening (QDCSM), were used to show the general applicability of the method and general results of constituent quark models for five-quark states are given. For one configuration, the chiral quark model and QDCSM give similar pentaquark mass spectroscopy,which means theσmeson effect can be replaced by quark delocalization and color screening mechanism as has been verified in NN intermediate range attraction. These calculation shows the group theoretic method is a powerful method which can be applied to a systematic study of multi-quark systems and all the constituent quark models. This is one of features of our group.For the dibaryon system, the NN (I = 0,1; J=1, 2, 3) S-wave and D-wave scatteringphase shifts were calculated with the chiral quark model and QDCSM. Two models obtained similar results in the low energy regin. Several resonance states appeared in the scattering phase shifts. In the NN⁺D₃(I =0) channel, the△△subthreshold resonance appeared in both models with the same decay width (～13MeV) but different resonance energy. In the chiral quark model, the resonance energy lowed by adding the hidden-color channels. If we enhanced the color confinement interaction between the hidden-color channels, the same results can be obtained as the one obtained in QDCSM, which only have color-singlet channels coupling. These results might mean that the quark delocalizationand color screening introduced in QDCSM is an effective description of the effect of hidden color channels coupling. In NN³S₁(I=0) and ¹S₀ (I=1) channels, the△△subthreshold resonances appeared only in QDCSM. In the NN³D₂ (I=2) channel, there is no subthreshold resonance appeared in either the chiral quark model or QDCSM. In NN¹D₂ (I=1) channel, a Nâ–³subthreshold resonances appeared only in QDCSM, with very narrow width. All these resonance states can be used to explain the new experimentalresults reported by CELSIUS-WASA group. More wide resonance states, such as Nâ–³,△△and so on can be used to explain the bump appeared in the np and pp scattering sections.During the calculation of NN scattering phase shifts, we propose a new methodmatrixmechanics in a discrete coordinate space. By using this method, we obtained similar results as the one given by KHK variational method. This method can study the scattering states in a limited space, and maybe it can find application in the calculation of lattice QCD. As we known, the lattice QCD can only solve the bound states problem. It is difficult for lattice QCD to study the scattering states problem. Our new method will give them some help. This is an innovation of our work.Finally, the symmetric spin-orbit interactions of one-gluon-exchange and confinement are included in the nucleon-nucleon phase shift calculation in the framework of quark delocalization color screening model. We found the latter has very little influence on the nucleon-nucleon phase shifts. For the S wave and D wave phase shifts, the spin-orbit interaction affects the phase shifts only a little bit. For the singlet P waves, QDCSM gives a qualitatively correct but too strong repulsive results.