A Study Of Charmonium In Quark Model

The discovery of J/? and ?(2S) in 1974 open the door of the study of charmonium family, it also push the development of QCD spectrum. As the increasing number of the states were observed, the charmonium family became enriching. Recently, the Belle, BaBar. BES, CLEO-c and other Collaborations have reported a number of new hadron states with c quark, the so-called XYZ particles. Most of them are difficult to fit the pattern of quark model calculations, for example, X(3872), Y(3940),Y(4160), Z(3930) and so on. It aroused extensive interest for theoretical and experimental physicists. A lot of research devote to explanation of the states.In terms of mass spectrum, one find that the states below the threshold of DD can be described well as cc states by quark model. However most of the states above the threshold are difficult to be compatible with the calculation of quark model. To assign the state report-ed by experiment to a cc state, two requirements have to be satisfied. One is the measured mass of the state need to be in agreement with the theoretical calculation, the another is the decay properties of the states are compatible. In this work, we calculate the charmonium and charmed meson spectra in the framework of nonrelativistic constituent quark model. In the calculation, a high precision numerical method for few-body problem, gaussian expansion method (GEM) is used. Using the wavefunctions obtained in the calculation of spectrum, the two-body strong decay width of the charmonia are obtained by means of quark-pair cre-ation model (3P0 model). By comparing the calculated results with the experimental data, we are trying to identify the states reported by experiments with the cc states in the quark model.According our calculation, the states ?(4040),?(4415), Z(3930)?(3770) and ?(4160) can be assigned as ?(3~3S1), ?(5~3S1), Xc2(2~3P2),?(1~3D1)??(2~3D1), and it is reasonable to assign X(3940) as ?c(31S0), X(4140) as ?c(41S0), X(4350) as Xco(4~3Po),X(4630) as ?(5~3D1). Other XYZ states cannot find their places in the pattern of quark model. To explain these states, channel-coupling effect and multi-quark states have to be taken into account.Absolutely, the innovation of our work lies in the consistency of the calculation. The wavefunctions obtained in the calculation of spectrum are used in the decay calculation, whereas the simple harmonic oscillator wavefunctions are used in the previous work.