Analytical properties and the unitarity relation for a resonance-particle interaction amplitude

The physical amplitude of a resonance-particle interaction is determined. This amplitude in its turn through a SU-relation is included in the experimental resonance production amplitude. Different analytic continuations give rise to four various resonance interaction amplitudes. The SU-relations for all amplitudes are derived and it is cleared up which of the amplitudes is form part of the directly measured physical ampplitudes. The analytical properties of the total resonance-particle interaction amplitudes and their partial waves are investigated on example of using simplest diagrams (pole, triangular in t-, n-, and s-channels, and box-graphs. It is shown that the obtained singularities do not prevent from using dispersion relations in determination of the physical resonance-particle interaction amplitude