Abstract
The question of whether simple nearby singularities together with unitarity are generally capable of reproducing the masses and widths of observed low-energy resonances is studied. As a specific case, we study the $\ensuremath{\rho}$ meson. We replace the left-hand cut by one or two nearby poles and ask if the interaction-pole parameters can be adjusted to give the known mass and width of the $\ensuremath{\rho}$. If elastic unitarity is assumed, the answer is no. Calculations with inelastic unitarity are also made, and the observed $\ensuremath{\rho}$ can be reproduced if the inelastic amplitude provides an important contribution. These conclusions are reached without a detailed identification between known exchanged systems and the interaction pole parameters.
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