Abstract
The relative importance of J P = 1 2 ± baryon resonances in nonleptonic hyperon decays is investigated within a dispersion relation formulation of the current algebra-PCAC method with a view to establishing which resonances can be neglected. The dispersion relation formulation is reviewed, equal-time commutator and octet baryon pole terms are calculated, and then pion-octet baryon intermediate states are included in the calculation of the imaginary parts of the amplitudes for the dispersion relations. The imaginary parts of the amplitudes then involve pion-octet baryon scattering amplitudes for which a resonance approximation is used and weak nonleptonic amplitudes which are approximated by the equal-time commutator and octet baryon pole terms. An evaluation of the resulting dispersion integrals shows that it is safe to neglect resonances with J P = 1 2 + (J P = 1 2 − ) in S-wave ( P-wave) decays and, also, that the P-wave amplitude of Σ + → n + π + may be substantially enhanced by the resonance N′(1470).
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