Scalar resonances: scattering and production amplitudes

Scattering and production amplitudes involving scalar resonances are known, according to Watson's theorem, to share the same phase \(\delta(s)\). We show that, at low energies, the production amplitude is fully determined by the combination of \(\delta(s)\) with another phase \(\omega(s)\), which describes intermediate two-meson propagation and is theoretically unambiguous. Our main result is a simple and almost model independent expression, which generalizes the usual \(K\)-matrix unitarization procedure and is suited to be used in analyses of production data involving scalar resonances.