Strange-baryon spectroscopy through Bethe-Salpeter approach under harmonic confinement

The unequal-quark-mass problem of excited $\Lambda$ and $\Sigma$ states is treated through a multichannel generalization of a relativistic Bethe-Salpeter treatment of the simpler (equal-mass) problem of $N$ and $\Delta$ as well as meson states recently found to give excellent fits to the corresponding spectra. The present fits to the $\Lambda$ and $\Sigma$ masses are fully in tune with the quality of the $N_L$ and ${\Delta }_L$ results, as evidenced by the highly consistent values of the appropriate universal function $F\left(M\right)\mathrm{}$ representing the central ${\mathrm{}\left(\mathrm{mass}\right)\mathrm{}}^2$ for each $N$ supermultiplet, calculated with the same reduced spring constant and quark masses as employed earlier for $N_L$, ${\Delta }_L$, and meson states. These $F\left(M\right)\mathrm{}$ values now include the one-gluon-exchange corrections which help in improving the $F\left(M\right)\mathrm{}$ regularities over the pure harmonic-oscillator prediction. The $F\left(M\right)\mathrm{}$ representation also brings out rather succinctly a modest symmetry-breaking trend (∼5-10%) at the collective supermultiplet level with little scatter among individual members.