Coupling constants andS-matrix zeros

A connection between coupling constants andS-matrix zeros is demonstrated to exist in the case of elastic scattering of neutral, scalar particles. From analyticity and unitarity arguments, the most general solution for a partial-wave phase shift is written in terms of the given discontinuities across the dynamical and inelastic branch cuts. The coupling constants associated with the simple poles follow directly from these phase shift solutions. Under certain conditions, it is shown that the arbitrariness in the solutions can be exhibited entirely by the position and number ofS-matrix zeros. A simple dynamical assumption is introduced as an illustrative example of a possible physical restriction on these zeros, and two coupling constants are calculated with use of very rough approximations.