Unphysical Region in Heavy-Meson-Nucleon Dispersion Relations

The contribution to $K$-meson-nucleon dispersion relations from the unphysical region due to absorption is examined in perturbation theory; it is found that the contribution need not be negligible for scalar $K$ mesons or the case where $\Lambda$ has opposite relative parity from ($K, \Sigma$). The influence this has on a dispersion-theoretic analysis of $K$-meson scattering is noted. In the Appendix the mass relationships for a rigorous derivation of the dispersion relations are discussed.