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

Abstract

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