A New Approach for Obtaining the Non-Strange Baryons Spectrum in a Phenomenological Interaction Potential

Abstract

In our work, we present the nonrelativistic quark model and a new mass formula for study the non-strange baryons octet and decuplet masses. Our model 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 which is inspired by early Lattice QCD calculations. For our purpose we introduced a spin independent description for SU(6) invariant part of the spectrum, we presented the analytical solution of three particle Schrödinger equation under the suitable phenomenological interaction potential by using the anzast method, through which the average energy values of the nonstrange resonances are reproduced. To describe the hyperfine structure of the baryon and splittings within the SU(6)-multiplets, we used the generalized Gürsey Radicati mass formula. A comparison between our calculations and the experimental data shows that the spectrum of the Roper resonances, the ground states and the excited multiplets up to three GeV are in general well reproduced and comparable with the experimental spectrum. Also one can conclude that; the interaction between the quark constituents of baryon resonances could be described adequately by using the combination of Killingbeck and isotonic oscillator potentials form.