The $\Lambda(1405)$ resonance as a genuine three-quark or molecular state

TL;DR

This paper investigates whether the $ ext{Lambda}(1405)$ resonance is a genuine three-quark state or a molecular state formed by meson-baryon interactions, using a chiral quark model and coupled-channel analysis.

Contribution

It demonstrates the importance of including three-quark octet states in modeling the $ ext{Lambda}(1405)$ and shows how the state can evolve into a molecular state with dominant $ar{K}N$ components.

Findings

The $ ext{Lambda}(1405)$ can be described as a molecular state with dominant $ar{K}N$ component.

Including three-quark states is crucial for reproducing scattering amplitudes.

The attraction in the $ar{K}N$ channel arises from $ar{K}N ext{Lambda}^*$ interactions.

Abstract

The mechanism for the formation of the $\Lambda(1405)$ resonance is studied in a chiral quark model that includes quark-meson as well as contact (four point) interactions. The negative-parity $S$-wave scattering amplitudes for strangeness $-1$ and $1$ are calculated within a unified coupled-channel framework that includes the $KN$, $\bar{K}N$, $\pi\Sigma$, $\eta\Lambda$, $K\Xi$, $\pi\Lambda$, and $\eta\Sigma$ channels and possible genuine three-quark bare singlet and octet states corresponding to $\frac12^-$ resonances. We show that in order to reproduce the scattering amplitudes in the $S_{01}$ partial wave it is important to include the pertinent three-quark octet states as well as the singlet state, while the inclusion of the contact term is not mandatory. The Laurent-Pietarinen expansion is used to determine the $S$-matrix poles. Following their evolution as a function of increasing interaction strength, the mass of the singlet state is strongly reduced due to the attractive self-energy in the $\pi\Sigma$ and $\bar{K}N$ channels; when it drops below the $KN$ threshold, the state acquires a dominant $\bar{K}N$ component which can be identified with a molecular state. The attraction between the kaon and the nucleon is generated through the $\bar{K}N\Lambda^*$ interaction rather than by meson-nucleon forces.