Non-leptonic hyperon decays and the baryon spectrum

Abstract

We propose a parallel treatment of S- and P-waves in non-leptonic hyperon decays through the commutator term plus pole contributions from the lowest levels of the baryon spectrum as described by the quark model: the positive parity ( 56,0 +) for P-waves, and the negative parity ( 70,1 −) for S-waves, connected to the ground state, respectively, by the parity conserving and the parity violating parts of H w. All these contributions satisfy the ΔI = 1 2 rule. The new piece we introduce, which comes from the ( 70, 1 −) intermediate states, provides a natural large correction to the soft pion limit for S-waves, of order δ m/ω ⋍ 0.5 relative to the commutator ( δm, SU(3) breaking parameter = pion energy; ω, mean baryon level spacing). We obtain a simple expression for this new term in the absence of spin-dependent perturbations, and we fix its magnitude from the properties of the baryon spectrum. We get a significant improvement of the relative magnitude of S- and P-waves, correcting the discrepancy of a relative factor of 2 which appears when considering only the commutator and 1 2 + poles. The new piece also leads to a correct D/ F ratio for S-waves.