V. Quark Model Study

Since 2003, the study of pentaquark system has been one of the hot topics in particle physics. The chiral soliton model predicted the existence of the pentaquarkstate (?)⁺ . In 2003 LEPS group reported the discovery of a new resonance, now called (?)⁺, with strangeness S=+1, IJ=0(1/2) with mass of 1540 MeV inγn→K⁺K^-n. Itdecays into K⁺n or K⁰p with width less than 25MeV. Because of the strangenessS=+l, the minimal quark content of the exotic should be uudds. The "discovery" was confirmed subsequently by several groups. The NA49 Collaboration and HERA-B Collaboration reported the observation of (?)^- (1862), the antidecupletpartner of the (?)⁺. Recently, a higher statistics experiment at the Jefferson Laboratoryfound no evidence to support the claims of the existence of (?)⁺ Theoretically, almostevery quark model, nonperturbative method, including lattice QCD, have not been able to give a conclusive answer to the question whether there might exist pentaquarkstate (?)⁺ or not.Quantum chromodynamics (QCD) is generally accepted as the fundamental theory of the strong interaction. Because of the asymptotic freedom, the perturbation method can be applied, high-energy phenomena can be described very well by using its fundamental degrees of freedom, quarks and gluons. However, 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 interaction systems, especially the multi-quark systems, which have abundant color structures. The research of multi-quark system may play an important role in understanding the low-energy behavior of QCD.The commonly used quark models are: bag model, soliton model and potential model, etc.. Potential model is the most convenient and widely used model in hadron-hadron interaction and multi-quark system. According to the effective degrees of freedom employed in models, there are several versions of potential models. Because there exist adjustable parameters in models, the existed experimental data can be fitted by fine-tuning the parameters, so all of these models can describe the meson and baryon properties and hadron-hadron interactions. It is very difficult to discriminate among most models by using the existed experimental data, even the newest ones. Clearly the more are the parameters, the poorer is the capability to predict. To solve this problem, each model must carry out more calculations to explain the updated experiment data. At the same time we must locate some phenomena which depend on model sensitively. Multi-quark system may be a good place for this purpose, recent calculations by various models have shown that.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 two pions, can not introduce enough attraction in nucleon-nucleon (NN) interaction. Is there an alternative approach to the intermediate range attraction of NN interaction? 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 potential 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 advantage 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, NA, N∑, etc.) and a good agreement with experimental data is obtained. Applying to dibaryon, several interesting dibaryon candidates are obtained.This work presents the results of a systematic search of possible pentaquark candidates in the u,d,s 3-flavor world in the framework of QDCSM with the help of the fractional parentage expansion technique. In the calculation, some generalization is needed. The color screening, which is used originally for quark pair in two color singlet clusters, is extended to the colorful clusters. The adiabatic approximation is used to do systematic calculation. The model parameters are fixed by baryon properties and deuteron properties.The results show that some states in the particle listing of PDG can be explained as pentaquark states, which agrees with other calculations. Several interesting states are also proposed, for example. (?)₁ (uuuds, I = 1, J = 512).Dose the pentaquark really exist? More and elaborate experiments are needed to clarify the situation, if the pentaquark is confirmed experimentally, then our modification on the model is successful and it can be extended to other multi-quark systems, even can foretell more new multi-quark systems. If the pentaquark, and other multi-quark systems at last disappear, then we have to question our understanding of the QCD and we may ask: Is the Nature so stingy that only leave us the ordinary baryons and mesons? We also discussed the possibility the relation between QDCSM and the multi-channel and multi-structure calculation in the traditional constituent quark models. We do hope that QDCSM can bring some promethean opinions for the study of the nuclear structure and multi-quark state.