Light Baryons Mass in a Non-Relativistic Quark Model within an Hypercentral Power Low Potential

TL;DR

This paper presents a non-relativistic quark model using a hypercentral power law potential and G"ursey Radicati mass formula to accurately calculate baryon masses, including excited states and resonances.

Contribution

It introduces a novel combination of hypercentral power law potential with the G"ursey Radicati mass formula for baryon mass spectrum calculations.

Findings

Successfully reproduces strange and non-strange baryon spectra

Accurately describes energies of excited multiplets up to 3 GeV

Provides a good estimate of Roper resonance positions

Abstract

In this work, we calculated the baryon mass within a non-relativistically quark model using an approach based on the G\"ursey Radicati mass formula (GR). The average energy value of each SU(6) multiplet is described using the SU(6) invariant interaction given by a hypercentral potential. In our series studies we investigate different interactions and situations to gain the best possible model. This goal can be obtained by checking and studying various potentials in different situations. In this paper we present the solution of the Schr\"odinger equation with an hypercentral power low potential. The results of our model (the combination of our proposed hypercentral Potential and generalized GR mass formula to description of the spectrum) show that the strange and non-strange baryons spectra are in general fairly well reproduced. The overall good description of the mass which we obtain shows that our model can also be used to give a fair description of the energies of the excited multiplets up to three GeV and the position of the Roper resonances of the nucleon.