Toward a unified description of hadro- and photoproduction: S-wave π- and η-photoproduction amplitudes

The Chew-Mandelstam (CM) parametrization, which has been used extensively in the two-body hadronic sector, is generalized in this exploratory paper to the electromagnetic sector by simultaneous fits to the π- and η-photoproduction S-wave multipole amplitudes for center-of-mass energies from the pion threshold through 1.61 GeV. We review the CM parametrization in detail to clarify the theoretical content of the said hadronic amplitude analysis and to place the proposed generalized said electromagnetic amplitudes in the context of earlier employed parametrized forms. The parametrization is unitary at the two-body level, which employs four hadronic channels and the γN electromagnetic channel. We compare the resulting fit to the maid parametrization and find qualitative agreement; although, numerically, the solution is somewhat different. Applications of the extended parametrization to global fits of the photoproduction data and to global fits of the combined hadronic and photoproduction data are discussed.