Low-Energy Constraints on Pion Production Amplitudes inπNScattering

Using the hypothesis of the partially conserved axial-vector currents, and specific assumptions on the equal-time commutators of these currents, a calculation of the pion production amplitude near threshold of the $\pi N$ system has been attempted. The resulting matrix elements are contrasted with those obtained previously by other means, and a comparison with existing data on the total reaction cross section is made. Agreement is favorable for the energy range considered. Unlike previous studies of the production amplitudes where direct $\pi -\pi$ interactions are thought to play a substantial role, the present calculation ignores all possibilities of strong $\pi -\pi$ effects, and incorporates only those $\pi -\pi$ scattering effects required by the consistency of the current-algebra approach. The evaluation of these contributions requires some assumptions on the equal-time commutators of pseudoscalar and scalar densities. Finally, suggestions are made on extensions of the present approach based on resonance models.