Regge Poles and Complex Singularities

We investigate the analyticity in complex angular momentum for the case in which complex singularities are present in double-spectral representations of scattering amplitudes. The simple example we consider is $\Sigma -\Sigma$ scattering. We show that Regge continuation exists and has the same qualitative characteristics as for the case of no complex singularities. In particular, we find no direct connection between the presence of complex singularities and the existence of the branch cuts in angular momentum.