Hidden-charm Pentaquarks In The Constituent Quark Model

The theoretical study of multi-quark systems has begun since the establishment of the quark models,and the hadron spectrum is essential to analyze the internal structures and dynamic properties of multi-quark systems.Quantum chromodynamics(QCD)has three basic characteristics:asymptotic freedom,color confinement and spontaneous breaking of chiral symmetry.The perturbation method is applicable for the high energy processes due to the asymptotic freedom of QCD in the high energy region,but in the low energy region,QCD is highly nonperturbative,and hence various non-perturbation methods such as QCD sum rules,lattice QCD and constituent quark models are established to treat the low energy process.The constituent quark model has taken great success in explaining the properties of traditional hadrons,and hence it is natural to apply it to the multi-quark systems.With the improvement of experimental accuracy,many new resonances have been discovered,for example,the LHCb Collaboration in CERN reported two baryon resonances P_c(4380)and P_c(4450)in 2015 and later updated their data in 2019,reported the existence of P_c(4312)and revised the P_c(4450)into two narrow resonances of P_c(4440)and P_c(4457)and confirmed the existence of P_c,s(4459)in 2020.For these new baryon resonances,it is extremely difficult to describe them with the conventional quark models,which may contain at least five quarks.Many researchers speculated that these resonances may be a molecular structure composed of a charm baryon and a charm meson.Quantum number is very important for understanding the properties of particles.The LHCb Collaboration first suggested that P_c(4380)and P_c(4450)correspond to the quantum number J^Pof 3/2^-and 5/2^-respectively,but realized that it may need more research to get a conclusion.The new experimental discoveries once again sparked hot discussions on the molecules,the compact pentaquarks,the mixture of them,in particular,there exist debates on the quantum numbers and internal structures of these baryon resonances.In this thesis,the mass spectra of the five-quark systems are calculated by employing the constituent quark model.The space wave function of the system is expanded by using harmonic oscillator basis under the Jacobi coordinates,and the five-body Talmi-Monshinsky Bracket coefficients between different Jacobi coordinates are used to calculate the interaction between any quarks.The quark potential consists of one gluon exchange potential and the linear confinement potential with vector and scalar mixing Lorentz structure.Solving the Schrodinger equation by the variational method,we can obtain the mass spectra and the corresponding internal structures can be discussed.Under the[qqq][c(?)](q(28)u,d,s)configuration,there are two kinds of color structures:two colorless sub-clusters and two octet sub-clusters,both of them can construct a colorless five-quark system.We take both of them into account simultaneously and confirm their internal structures according to the ratios of each color configuration.We calculate the spectra corresponding to the J^P=1/2^-,3/2^-,5/2^-for different flavor configurations,and our results shows that the P_c(4312)may be a IJ^P=1/2,1/2^-molecule which contains a light baryon and a charmonium meson.The P_c(4440)and P_c(4457)can be the candidates of pentaquarks with a[[nnn]_8c(?)[c(?)]_8c]_1c(n=u,d)structure,P_c(4440)correspond to IJ^P=1/2,1/2^-and P_c(4457)correspond to IJ^P=1/2,1/2^-or IJ^P=1/2,3/2^-,while P_c,s(4459)is a[[nns]_8c(?)[c(?)]_8c]_1ccompact pentaquark of IJ^P=0,1/2^-.Under the same theoretical model,we also explore the hidden charm nssc(?) and sssc(?) five-quark systems.This organization of the thesis is as follows:We give an introduction to the basic knowledge of particle physics and the related research of pentaquarks firstly.The second part is our theoretical models,including the quark potentials and a relativistic correction of it.In the third part,we construct the wave functions under the symmetric limit and give an introduction of the main calculation methods.The fourth part is the discussions and analysis of our results.