On the basis of unitarity and the Mandelstam representation we discuss the analyticity and threshold behavior of the positions and residues of the poles of the scattering amplitude in angular momentum as a function of energy, separate the right and left cuts of the partial wave amplitude for complex $l$, and extend, in a model theory in which elastic unitarity holds, the domain of analyticity in the $l$ plane to the region $\mathrm{Re}l>\mathrm{}1\mathrm{}$.

• Received 27 February 1962

DOI:https://doi.org/10.1103/PhysRev.127.974