Three-body hadronic structure of low-lying $1/2^+$ $\Sigma$ and $\Lambda$ resonances

TL;DR

This paper investigates the dynamical generation of low-lying $1/2^+$ $ ext{Sigma}$ and $ ext{Lambda}$ resonances through two-meson one-baryon systems, using coupled-channel Faddeev equations to identify resonance peaks.

Contribution

It introduces a novel coupled-channel Faddeev approach to dynamically generate and analyze low-lying $1/2^+$ $ ext{Sigma}$ and $ ext{Lambda}$ resonances in meson-baryon systems.

Findings

Resonance peaks align with known strangeness -1 $1/2^+$ resonances.

Dynamical generation of these states is supported by the calculated $T$-matrix.

The approach confirms the role of meson-baryon interactions in resonance formation.

Abstract

We discuss the dynamical generation of some low-lying $1/2^+$ $\Sigma$'s and $\Lambda$'s in two-meson one-baryon systems. These systems have been constructed by adding a pion in $S$-wave to the $\bar{K} N$ pair and its coupled channels, where the $1/2^-$ $\Lambda$(1405)-resonance gets dynamically generated. We solve Faddeev equations in the coupled-channel approach to calculate the $T$-matrix for these systems as a function of the total energy and the invariant mass of one of the meson-baryon pairs. This squared $T$-matrix shows peaks at the energies very close to the masses of the strangeness -1, $1/2^+$ resonances listed in the particle data book.