Threshold and Pseudothreshold Relations for Meson-Baryon Scattering

Jackson and Hite have recently studied the problem of removing kinematic singularities from scattering amplitudes by using essentially nonrelativistic angular momentum arguments. For the case of meson-baryon scattering, their results depend on the sign of the mass difference between the meson and baryon. This dependence indicates the presence of remaining kinematic singularities in these amplitudes. For some purposes one wishes to complete the program of Jackson and Hite, and remove these singularities. By considering the amplitudes as functions of the energy $W$, rather than its square $s$, we are able to remove these additional singularities. The amplitudes we find have only dynamic singularities as a function of $s$ and $t$. There are, however, conditions between these amplitudes at thresholds and pseudothresholds. These conditions are adequately treated by Jackson and Hite, and do not concern us in this paper.