Scalar resonances: scattering and production amplitudes

Abstract

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.

Comments: 10 pages, 4 figures. Minor changes, references added, version to appear in Phys. Rev. D