Abstract
A certain two-channel $s$-wave scattering model containing a resonance at low energy is studied, and it is shown that both the multichannel effective range approximation and the $K$ matrix pole test for compositeness of the resonance fail for this model. When the model is applied to the low-energy $I=0$ $\overline{\mathrm{K}}$N interaction, it leads to a $K$ matrix which is very different from those used in the phenomenological $K$ matrix parametrizations hitherto carried out. Implications of this are discussed.
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