Scalar resonances: scattering and production amplitudes

TL;DR

This paper derives a model-independent expression for scalar resonance production amplitudes, linking them to scattering phases and intermediate meson propagation, enhancing analysis of experimental data.

Contribution

It introduces a generalized, nearly model-independent formula for scalar resonance production amplitudes that extends the K-matrix unitarization approach.

Findings

The production amplitude is determined by the scattering phase and an additional meson propagation phase.

The new formula is simple, robust, and applicable to experimental data analysis.

It generalizes existing unitarization methods for scalar resonances.

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.