Extraction of meson resonances from three-pions photo-production reactions

We investigate the model dependence of meson resonance properties extracted from the Dalitz-plot analysis of the three-pions photo-production reactions on the nucleon. Within a unitary model developed in our earlier work, we generate Dalitz-plot distributions as data to perform an isobar model fit that is similar to most of the previous analyses of three-pion production reactions. It is found that the resonance positions from the two models agree well when both fit the data accurately, except for the resonance poles near branch points. The residues of the resonant amplitudes extracted from the two models and by the usual Breit-Wigner procedure agree well only for the isolated resonances with narrow widths. For overlapping resonances, most of the extracted residues could be drastically different. Our results suggest that even with high precision data, the resonance extraction should be based on models within which the amplitude parametrization is constrained by a three-body unitarity condition.