Resolution of an Ambiguity in Alternative Soft-Pion Approaches toπN→ππNnear Threshold

Abstract

A recent observation that the current-commutator and effective-Lagrangian results differ for low-energy pion production is discussed. A simple unitarity argument shows that the commutator result as calculated is incorrect. The present status of $\pi \pi$ scattering lengths determined by threshold pion production is reviewed. The $s$-wave scattering lengths, in inverse pion masses, are found to be $a_0=0.24\mathrm{}\pm 0.03$ and $a_2=-0.03\mathrm{}\pm 0.015$.