Comparing partial-wave amplitude parametrization with dynamical models of meson-nucleon scattering

TL;DR

This paper explores the relationship between partial-wave amplitude parametrizations, especially the Chew-Mandelstam approach, and dynamical coupled-channel models in meson-nucleon scattering, highlighting their close connection despite model dependencies.

Contribution

It establishes and investigates the relationship between phenomenological parametrizations and dynamical models, focusing on the Delta(1232) resonance in meson-nucleon scattering.

Findings

The bare pole for Delta(1232) in dynamical models closely matches that in SAID parametrization.

Model dependence affects the direct connection between approaches.

Dynamical and phenomenological descriptions are closely related despite differences.

Abstract

Relationships between partial-wave amplitude parametrizations, in particular the Chew-Mandelstam approach, and dynamical coupled-channel models are established and investigated. A bare pole corresponding to the Delta(1232) resonance, found in a recent dynamical-model fit to pion- and omega-meson production reactions, compares closely to one found in a unitary multichannel partial-wave amplitude parametrization of SAID. The model dependence of the bare pole precludes a direct connection between the approaches but is suggestive that the dynamical description and the phenomenological parametrization are closely related.