Mass splittings of SU(3) baryons within a chiral soliton model

초록

Considering simultaneously isospin and SU(3) flavor symmetry breakings to the second order, we investigate the mass splittings of the baryon decuplet and antidecuplet within a chiral soliton model ($\chi$SM), a "model-independent approach" being employed. Several new mass relations are derived, which are mostly generalizations of existing mass formulae. The dynamical quantities appearing in the expressions for the masses are fixed by fitting them to the masses of the baryon octet, those of the decuplet baryon ${\Omega }^{-}$ and ${\Theta }^{+}$ as input rather than by extracting them from a calculated self-consistent soliton profile. In particular, the consideration of isospin symmetry breaking allows us to use the experimental data of the whole octet baryon masses as input. The second-order corrections of SU(3) symmetry breaking make the analysis more compatible with the data. We predict the masses of the baryon decuplet and antidecuplet without any further adjustable free parameter. In addition, we also obtain the pion-nucleon sigma term which turns out to be ${\Sigma }_{\pi N}=(50.5\pm 5.4)\mathrm{MeV}$.