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

Zhong-Yu Wang, Hiwa A. Ahmed, C. W. Xiao

Published 2021-06-19Version 1

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. 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 cases 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 a compositeness of mainly $\pi \Sigma$ with tiny component $\bar{K} N$. From these findings, one can conclude that the $\Lambda(1405)$ state would be a degenerated state of two states with the same quantum number.