Is two-poles' $\Lambda(1405)$ one state or two?

TL;DR

This paper investigates the two-pole structure of the $ ext{Lambda}(1405)$ resonance, revealing that it comprises a pure $ar{K}N$ molecule and a mainly $ ext{pi} ext{Sigma}$ state, suggesting it is effectively two overlapping states.

Contribution

The study provides a comprehensive analysis of the two-poles' properties across various coupled channel interactions, clarifying their nature and composition.

Findings

The higher-mass pole is a pure $ar{K}N$ molecule.

The lower-mass pole is mainly $ ext{pi} ext{Sigma}$ with a tiny $ar{K}N$ component.

The $ ext{Lambda}(1405)$} is effectively two overlapping states.

Abstract

To understand the nature of two poles for the $\Lambda(1405)$ state, we revisit the interactions of $\bar{K}N$ and $\pi\Sigma$ with their coupled channels, where two-poles structure is found in the second Riemann sheet. We also dynamically generate two poles in the single channel interaction of $\bar{K}N$ and $\pi\Sigma$, respectively. Moreover, we make a further study of two poles' properties by evaluating the couplings, the compositeness, the wave functions, and the radii for the interactions of four coupled channels, two coupled channels and the single channel. Our results show that the nature of two poles is unique. The higher-mass pole is a pure $\bar{K} N$ molecule, and the lower-mass one is a compositeness of mainly $\pi \Sigma$ with tiny component $\bar{K} N$. From our results, one can conclude that the $\Lambda(1405)$ state would be overlapped with two different states of the same quantum number.