Lambda(1405) in a baryon-meson scattering with a bound state embedded in the continuum

TL;DR

This paper explores the nature of Lambda(1405) as a resonance in baryon-meson scattering, examining the effects of introducing a bound state embedded in the continuum (BSEC) and its implications for resonance properties and scattering lengths.

Contribution

It introduces a BSEC into baryon-meson scattering models and analyzes its impact on Lambda(1405) resonance characteristics, providing a novel approach to understanding its structure.

Findings

Resonance appears in Sigma pi scattering below N Kbar threshold with strong attraction.

Introducing BSEC results in a resonance with a large width and reproduces N Kbar scattering length.

BSEC coupling that remains finite at zero momentum transfer increases the resonance width.

Abstract

We investigate Lambda(1405) as a resonance in a coupled channel baryon-meson scattering with a `bound state embedded in the continuum'(BSEC). This BSEC is introduced by hand, as a state not originated from simple baryon-meson systems. We assume it comes from the three-quark state. There appears a resonance in the Sigma pi scattering below the N Kbar threshold when the N Kbar channel is taken to be strongly attractive. It occurs without introducing a BSEC, just like the chiral unitary approach. When a BSEC is introduced, a resonance also appears with a weaker baryon-meson interaction. The corresponding peak also has a large width, and the N Kbar scattering length is reproduced well. The interaction whose channel dependence is the same as the one originated from the color-magnetic interaction, where no N Kbar attraction exists, also gives a broad peak like Lambda(1405) with help of a BSEC. It is found that the BSEC coupling which does not vanish at the zero momentum transfer give a larger width. In order to reproduce the observed N Kbar scattering length, introducing a BSEC seems preferable. In our calculation, a model gives an appropriate value when the BSEC contribution to the resonance is roughly half of that of the N Kbar in size.