Baryons in the Constituent-Quark Model

Abstract

An elementary constituent-quark (CQ) model of mesons was previously presented. In this paper, we continue research into a study of the baryons in the constituent-quark model. Mac Gregor proposed a comprehensive model of elementary particles for which both mesons and baryons shared common mass-band structure in quantized units of m = 70 MeV, B= 140 MeV and X = 420 MeV. A review of the baryon data is under taken for comparison with the CQ model. It is shown in this paper that baryons possess an isospin I related to the mass quantum m = 70 MeV and to the B = 140 MeV quantum (or the mass of the pion). In order to establish a consistency with the quark model of Gell-Mann, we identify the SU(3) baryon decuplet as a standard feature to be maintained with only slight changes to the constituent-quark masses. By insisting on the J = 3/2, P-states of the SU(3) baryon decuplet to be in the same CQ excitation states, we are lead to establish baryon cores in the P-states with J = 1/2. Core corrections to Mac Gregor's CQ model of baryons are presented. Exact shell structure is found among all the baryons regardless of isospin as evidenced in the data from the Particle Data Group listing. New baryons are predicted to exist.