Singularity of the Regge Amplitude

It is shown that the Regge amplitude $a(l, s)$ has singularities at certain fixed, real, physical values of $s$ for all nonphysical values of $l$. These singularities are not normal thresholds and are not singularities of the complete amplitude $A(s, t, u)$. They arise indirectly through unitarity. Their presence is deduced from the existence of a perturbation graph which satisfies the Mandelstam representation with spectral boundary curves having asymptotes other than the normal threshold lines.