Sum rules for weak NNπ amplitudes and theoretical descriptions of nonleptonic hyperon decays

The sum rule based on current algebra predicts the p → n + π+ amplitude to be A (p+/sub +/) = -α3.02 x 10-7 (h = c = 1). The weak-interaction-model--dependent parameter α can have the same value α = tan theta/sub C/√2 for the Weinberg-Salam as for the Cabibbo model if the observed vertical-barΔIvertical-bar = 12, vertical-barΔSvertical-bar = 1 enhancement is explained by using PCAC (partially conserved axial-vector current). When the Melosh transformation is used with the soft-pion and infinite-momentum techniques, a very small amplitude A (p+/sub +/) = -α3.02 x 10-9 is found. A simple description of SU(3) -symmetry breaking, reproducing the observed nonleptonic decay amplitudes again, predicts A (p+/sub +/) = -α3.04 x 10-8. Useful insights may be gained from ΔI = 1 parity-violating experiments, such as γ asymmetry in the n + p → d + γ reaction