Dynamical source of mass splitting in an SU(3) bag model.

Abstract

The cloudy bag model of baryons is extended to include coupling to the kaons according to SU(3${)}_{L}$\ensuremath{\bigotimes}SU(3${)}_{R}$ symmetry. The breaking of chiral symmetry is imposed solely by allowing the pseudoscalar mesons to acquire their physical masses. The bare masses of the up, down, and strange quarks are therefore taken to be degenerate. Assuming that a single set of bag parameters describes both the baryon octet and decimet, self-energy corrections to the baryon masses are calculated to the level of virtual states containing two mesons (\ensuremath{\pi}, K, and K\ifmmode\bar\else\textasciimacron\fi{}). The four model parameters are fixed by fitting the NN\ensuremath{\pi} coupling constant, N mass, \ensuremath{\Delta} mass, and \ensuremath{\pi}N scattering phase shifts in the ${P}_{33}$ channel. These parameters give an excellent prediction for the baryon masses in the {8} and {10}. A consistent picture is thereby obtained in which the mass splitting between baryon isomultiplets arises exclusively from mesonic self-energy corrections, while the u, d, and s quarks are degenerate in mass.