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The full complex phase structure of the meson-baryon reaction amplitude incoupled channels approach is investigated, including also the photon-baryonchannel. The result may be viewed as a generalization of the well-knownWatson's theorem. Furthermore, the complex phase structure is exhibited for thepole and nonpole parts of the reaction amplitude in such a way that it willserve as a convenient common starting point for constructing models withdifferent levels of approximation, in particular, for building isobar modelswhere the basic properties of the $S$-matrix can be maintained. Such modelsshould be useful, especially, in coupled multichannel calculations, where alarge amount of experimental data are considered in resonance analyses, asituation encountered in modern baryon spectroscopy. In particular, it is shownthat the unitarity of the pole part of the $T$-matrix arises automatically fromthe dressing mechanism inherent in the basic scattering equation. This impliesthat no separate conditions are required for making this part of the resonanceamplitude unitary as it has been done in some of the existing isobar models.

Complex phase structure of the meson-baryon $T$-matrix