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This work elaborates on former remarks of ours regarding two sets ofpredictions for the observables of the charge-exchange reaction $\pi^- p \to\pi^0 n$ at low energy (pion laboratory kinetic energy $T \leq 100$ MeV). Thefirst prediction is obtained via the triangle identity from the results of fitsto low-energy $\pi^\pm p$ elastic-scattering data, whereas the second is basedon the same analysis of the combined low-energy $\pi^+ p$ and charge-exchangedatabases. Assuming the integrity of the data used in our fits (i.e., theabsence of significant systematic effects in the determination of the absolutenormalisation of the datasets) and the insignificance of residual effects inthe electromagnetic corrections, a significant difference between these twosets of predictions may be interpreted as departure from the isospin invariancein the low-energy $\pi N$ interaction. We examine the sensitivity of thestandard low-energy observables to the effect, and identify the kinematicalregions which are promising for experimental survey. Accurate experiments underthe suggested conditions will differentiate between the predictions, and thusprovide an independent test of the isospin invariance in the low-energy $\pi N$interaction.

Proposals for the test of the isospin invariance in the pion-nucleon interaction at low energy