Alternate form for the low-energy K¯N K matrix

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 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.