A simple semi-relativistic hypercentral constituent quark model for light baryons

Abstract

In this work, baryons as a three-body bound system have been investigated in a semi-relativistic approach. Our model, like all constituent quark models, contains a dominant SU(6)-invariant part accounting for the average multiplet energies, and a perturbative SU(6)-violating interaction for the splitting within the multiplets, a structure that is inspired by lattice QCD calculations. Introducing a spin-independent relativistic description for the SU(6)-invariant part of the spectrum, we presented the exact analytical solution of the three-particle Klein–Gordon equation, through which the average energy values of the nonstrange resonances are reproduced. To describe the hyperfine structure of the baryon, the splittings within the SU(6) multiplets are produced by the spin- and isospin-dependent SU(6)-violating interaction, which have been treated as perturbative terms. For the SU(6)-invariant potential, we have added a quadratic term to the popular “Coulombic-plus-linear” potential. The resulting description of the baryon spectrum is comparable with those obtained by other calculations and experimental spectrum.