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

TL;DR

This paper analyzes the complex phase structure of the meson-baryon T-matrix in coupled channels, generalizing Watson's theorem, and provides a framework for constructing models that maintain unitarity in resonance analyses.

Contribution

It introduces a comprehensive analysis of the meson-baryon T-matrix phase structure, including pole and nonpole parts, facilitating improved model building in baryon spectroscopy.

Findings

The complex phase structure is characterized for pole and nonpole parts.

Unitarity of the pole part arises automatically from the dressing mechanism.

The framework aids in constructing models that preserve basic S-matrix properties.

Abstract

The full complex phase structure of the meson-baryon reaction amplitude in coupled channels approach is investigated, including also the photon-baryon channel. The result may be viewed as a generalization of the well-known Watson's theorem. Furthermore, the complex phase structure is exhibited for the pole and nonpole parts of the reaction amplitude in such a way that it will serve as a convenient common starting point for constructing models with different levels of approximation, in particular, for building isobar models where the basic properties of the $S$-matrix can be maintained. Such models should be useful, especially, in coupled multichannel calculations, where a large amount of experimental data are considered in resonance analyses, a situation encountered in modern baryon spectroscopy. In particular, it is shown that the unitarity of the pole part of the $T$-matrix arises automatically from the dressing mechanism inherent in the basic scattering equation. This implies that no separate conditions are required for making this part of the resonance amplitude unitary as it has been done in some of the existing isobar models.