  Besides the unitarity and symmetry requirements for a multi-resonance
scattering amplitude, several other natural conditions can easily exclude
unrealistic proposals. In particular, the behaviour of singularities under the
variation of model parameters yields important information. We discuss how
resonance poles should move in the complex-energy plane when coupling constants
and masses are varied, how resonances above threshold can turn into bound
states below threshold and how the light-quark spectrum can be turned into the
spectrum of heavy quarks, with one and the same analytic expression for the
scattering amplitude. Moreover, it is shown that perturbative approximations
usually do not satisfy those natural conditions.

High Energy Physics - Phenomenology;High Energy Physics - Experiment