Dynamical coupled-channels study of pi N --> pi pi N reactions

TL;DR

This paper develops a dynamical coupled-channels model to analyze pi N to pi pi N reactions, successfully describing experimental data and highlighting the importance of channel interference effects in nucleon resonance studies.

Contribution

It extends previous models by incorporating multiple resonant and non-resonant channels, providing a comprehensive framework for analyzing pi N to pi pi N reactions.

Findings

Successfully describes total cross sections and invariant mass distributions up to 2 GeV

Demonstrates significant interference effects among channels and amplitudes

Highlights the importance of coupled-channels effects in reaction analysis

Abstract

As a step toward performing a complete coupled-channels analysis of the world data of pi N, gamma^* N --> pi N, eta N, pi pi N reactions, the pi N --> pi pi N reactions are investigated starting with the dynamical coupled-channels model developed in Phys. Rev. C76, 065201 (2007). The channels included are pi N, eta N, and pi pi N which has pi Delta, rho N, and sigma N resonant components. The non-resonant amplitudes are generated from solving a set of coupled-channels equations with the meson-baryon potentials defined by effective Lagrangians. The resonant amplitudes are generated from 16 bare excited nucleon (N^*) states which are dressed by the non-resonant interactions as constrained by the unitarity condition. The data of total cross sections and pi N and pi pi invariant mass distributions of pi^+ p --> pi^+ pi^+ n, pi^+ pi^0p and pi^- p --> pi^+ pi^- n, pi^- pi^0 n, pi^0 pi^0 n reactions from threshold to the invariant mass W = 2 GeV can be described to a very large extent. We show the importance of the coupled-channels effects and the strong interference between the contributions from the pi Delta, sigma N, and rho N channels. The large interference between the resonant and non-resonant amplitudes is also demonstrated. Possible future developements are discussed.