Pole position of $\Lambda(1405)$ measured in $d(K^-,n)\pi\Sigma$ reactions

TL;DR

This study precisely measured the pole position of the $ ext{Lambda}(1405)$ resonance using $K^-$-induced reactions on deuteron, revealing it is closer to the $ar{K}N$ threshold than previously thought.

Contribution

It provides a new, more accurate determination of the $ ext{Lambda}(1405)$ pole position through invariant mass spectra analysis and coupled-channel scattering amplitudes.

Findings

Resonance pole at 1417.7 MeV/$c^2$, closer to $ar{K}N$ threshold.

Improved understanding of $ar{K}N$ and $ar{K}N ightarrowar{K}N$ scattering amplitudes.

Refined resonance parameters compared to Particle Data Group values.

Abstract

We measured a set of $\pi^\pm\Sigma^\mp$, $\pi^0\Sigma^0$, and $\pi^-\Sigma^0$ invariant mass spectra below and above the $\bar{K}N$ mass threshold in $K^-$-induced reactions on deuteron. We deduced the $S$-wave $\bar{K}N\rightarrow\pi\Sigma$ and $\bar{K}N\rightarrow\bar{K}N$ scattering amplitudes in the isospin 0 channel in the framework of a $\bar{K}N$ and $\pi\Sigma$ coupled channel. We find that a resonance pole corresponding to $\Lambda(1405)$ is located at 1417.7$^{+6.0}_{-7.4}$(fitting errors)$^{+1.1}_{-1.0}$(systematic errors) + $[-26.1^{+6.0}_{-7.9}$(fitting errors)$^{+1.7}_{-2.0}$(systematic errors)]$i$ MeV/$c^2$, closer to the $\bar{K}N$ mass threshold than the value determined by the Particle Data Group.