Broken SU(3) sum rules involving the baryon resonances with [formula omitted

Abstract

By using an asymptotic symmetry for the SU(3) raising and lowering operator and a chiral SU(3) ⊗ SU(3) algebra, we investigate the effects of SU(3) symmetry breaking for the decay of the resonances J P = 3 + 2 , 3 + 2 , 5 + 2 , 5 − 2 into respectively baryons J P = 1 + 2 , 1 − 2 , 3 + 2 , 3 + 2 and a pion. Sum rules involving the physical masses of the particles of the 5 ± 2 octet and the 3 ± 2 decuplet and their decay coupling constants are derived. The correction to the decay amplitudes due to the breaking of SU(3) symmetry is found to be of the order of only a few percent if there is no particle mixing. Comparison with experiments (when available) is carried out. For the 3 + 2 → 1 + 2 + 0 − decays the correction is in the right direction to improve the discrepancy between the present experimental data and the prediction of exact SU(3) symmetry. However it is not enough to remove the entire discrepancy which seems to indicate the necessity of introducing some mixing effect. The sum rule for the decay 5 2 → 3 2 + 0 − shows that the F-wave decay is negligible compared to the P-wave decay. The Gürsey-Radicati type intermultiplet mass formulas for the 5 2 octet and 3 2 decuplet are deduced from current algebra and the ( 5 + 2 )Ξ particle is predicted to have a mass around 2.030 MeV. This value is consistent with the value obtained from the Gell-Mann/Okubo formula and agrees well with the mass of recently found Ξ(2030).