Analyticity of the Positions and Residues of Regge Poles

The amplitude $a(l, k)$ for scattering by a superposition of Yukawa potentials is considered as a meromorphic function of angular momentum l and linear momentum k. An N/D representation with the usual properties is explicitly given, and is then used to show that the position, α(k), and the residue, β(k), of its poles in l---the so-called Regge poles---are holomorphic functions of k, under a certain assumption. Further considered as functions of energy, α and βk^2α are shown to be real-analytic with no left-hand cut.