Chiral-Symmetry Breaking and the Ambiguity of Alternative Soft-Pion Approaches to ThresholdπN→ππN

The alternative soft-pion approaches to threshold $\pi N\to \pi \pi N$ provided by the phenomenological-Lagrangian and current-commutator theories are shown to differ only in their pion-pole contributions. Since the data for the reaction ${\pi }^{-}p\to {\pi }^{-}{\pi }^{+}n$ seem well fitted by the former theory for $\xi =0\mathrm{}$, and by the latter for $\xi =-\frac{1}{2}$, where $\xi$ is the chiral-symmetry-breaking parameter introduced by Olsson and Turner, threshold total-cross-section data for this charge state will not be able to determine a unique $\xi$ value.