Separable Potentials in the Complex $l$ Plane

The analytic behavior of a certain kind of nonlocal separable potentials previously considered by one of us (ANM) is studied in the complex angular momentum plane. The amplitude derived from such potentials has cuts only in the locations expected for the Mandelstam representation, including one corresponding to the crossed channel. The spectral functions are explicitly evaluated. A study of the singularities in the complex $l$ plane of the partial wave amplitudes shows that there is only one Regge trajectory to the right of the $\mathrm{Re}l=-\frac{3}{2}$, and that its behavior is that of the principal Regge trajectory corresponding to a Yukawa potential. This is confirmed through the evaluation of the high-energy limit of the total amplitude in the crossed channel.