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

TL;DR

This paper investigates the mass splittings of SU(3) baryons using a chiral soliton model, deriving new mass relations, fitting parameters to known baryon masses, and predicting masses of other baryons without additional free parameters.

Contribution

It introduces a model-independent approach to analyze baryon mass splittings considering isospin and SU(3) symmetry breaking, and predicts masses of baryon decuplet and antidecuplet.

Findings

Derived new mass relations for SU(3) baryons.

Predicted baryon decuplet and antidecuplet masses without extra parameters.

Estimated pion-nucleon sigma term as 36.4±3.9 MeV.

Abstract

Considering simultaneously isospin and SU(3) flavor symmetry breakings, we investigate the complete mass splittings of SU(3) baryons within a chiral soliton model, a {}"model-independent approach" being employed. In linear order 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 and the masses of $\Omega^{-}$ 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. 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 $\Sigma_{\pi N} = 36.4\pm3.9\,\mathrm{MeV}$. We get the ratio of the current light quark masses $R = 58.1\pm1.3$. The present results indicate that the recent experimental data for the $\Theta^{+}(1524)$ are compatible with the experimental data of the octet and decuplet masses.