S-matrix and unitarity bounds for three-channel systems,with application to low-energy photoproduction of pions from nucleons

A parametrization of the S-matrix for three-channel systems is given, where we state explicitly the unitarity bounds on the free parameters. The free parameters are directly related to measurable quantities. The results are applied to low-energy photoproduction of pions from nucleons, and lower bounds for the electric dipole amplitudes E₀₊ for π⁰ production are obtained. These lower bounds follow without using the Fermi-Watson final-state theorem.