Existence of solutions of partial-wave dispersion relations and singularN/D equations

Summary  It is shown that, for left-hand discontinuities which asymptotically exceed certain limits imposed by unitarity, the partial-wave dispersion relation admits no ghost-free solutions. However, for discontinuities which on the left tend to a limit λ, 0<λ<1, the singular integral equation that arises by application of the usualN/D approach is shown to lead to a one-parameter manifold of ghost-free solutions; in particular, a specific solution which is analytic at λ=0 belongs to this manifold. The variation of the zeros of theD function (for varying λ) is shown explicitly in a simple example.