Research On Baryon Spectra In Relativistic Quark Model

Hadron spectroscopy is nature experimental laboratory to recognize internal structure and dynamics of hadrons.Quantum Chromodynamics?QCD?is regarded as foundational theory to describe the strong interaction.The basic features of QCD are asymptotic freedom,color confinement,chiral symmetry and its spontaneous breaking.For short range or high energy region processes,the perturbative QCD?pQCD?is applicable and have been confirmed by high energy experiments.However,pQCD fails for low energy processes due to QCD is highly non-perturbative in long range or low-energy processes.Hadron spectrum is in low-energy regions,the phenomenological models with the spirit of QCD have to be developed to treat non-perturbation calculation.Among them,the constituent quark model,which can treat the ground and excited states of hadron,is one of the most widely used models.In the constituent quark model,the current quark obtains constituent mass due to the spontaneous breaking of the QCD chiral symmetry.The interaction between them is described by a potential that equals to a chromatic Coulomb potential given by the non-relativistic reduction of leading order's one gluon exchange tree diagram in long range perturbation region plus a phenomenological linear potential introduced to describe the color confinement in long range non-perturbation region,and the meson exchange can be considered in middle range to obtain a Yukawa type potential.However,the constituent quark model under the non-relativistic limit is puzzled by the absent of spin-orbit coupling observed experimentally.Thus,the rough non-relativistic constituent quark model usually considers the spin-spin term and tensor term and artificially removes the spin-orbit term.The spin orbit coupling is a relativistic effect.Naturally,the Lorentz structure and its relativistic modification of the confining potential should be able to offset the spin-orbit coupling effect caused by one gluon exchange.Taking all of them into account may improve the calculation of baryon mass spectrum.The relativistic modified scalar-vector mixing confinement model have accurately given the mass spectrum of light mesons,heavy mesons and double heavy baryons.However,the quark-diquark approximation is uesd to study double heavy baryons,i.e.two quarks with stronger interaction are bound into diquark without radial excitation,and then interact with the third quark.In this paper,two-body reduction will not be used,and the baryon spectrum will be directly calculated by using the variational method in harmonic oscillator bases of different mass in three sets of Jaccobi coordinates.This method is easy to be extended to multi-quark systems,can give an analytic approximate wave function and allow radial excitation between any two quarks.Based on the quark potential model of one gluon exchange,the scalar-vector mixing and relativistic correction of phenomenological linear confining potential are introduced,and the three-body space wave function of baryon is constructed by harmonic oscillator basis in Jacobian coordinates.The expansion coefficients of harmonic oscillator bases from one Jacobian coordinate to another one are given by three-body generalized Talmi-Moshinsky coefficients.Only antisymmetry of the chromatic wave function and the exchanging symmetry between the first and the second quark in the remaining wave funcion are used to construct total wave function,this treatment is sufficient to distinguish baryons of different flavor components.Automatically,the symmetry of Hamiltonian will be reflected in the expansion coefficient.The spin wave function and spin operators are discussed in the direct product space of Pauli representation.The space operators are calculated in its eigenstates by expanding the space wave function into it in the help of the three-body generalized Talmi-Moshinsky coefficient,and finally the Hamiltonian matrix element will be obtained.The mass spectra of odd-parity states and even-parity states(J ^P?28?₂^1?,₂^3?,₂^5?)and their radial excited states of light baryons,strange bayons and heavy baryons are obtained.The calculation method in this paper lays a foundation for the study of mass spectrum of nonidentical multi-quark systems.