Investigation of the $\bar{K}$--$^{6}$Li Interaction and the Search for the $\Lambda(1405)$ Resonance

TL;DR

This study models the interaction between an antikaon and a lithium-6 nucleus to predict the formation and signals of the $ ext{Lambda}(1405)$ resonance in a light nuclear environment, guiding future experiments.

Contribution

It provides theoretical predictions of $ar{K}N$ dynamics and $ ext{Lambda}(1405)$ signals within a $^{6}$Li nucleus, using various interaction models.

Findings

Predicted $ ext{Lambda}(1405)$ signals in $ ext{pi} ext{Sigma} n$ spectra.

Identified robust features of $ ext{Lambda}(1405)$ in light nuclei.

Guidance for future experimental detection of $ ext{Lambda}(1405)$.

Abstract

We investigate the interaction of an antikaon ($K^-$) with the $^{6}$Li nucleus, described as an $\alpha + d$ cluster system. The study aims to explore the formation of the $\Lambda(1405)$ resonance through the $K^-d$ subsystem in the presence of a spectator $\alpha$ particle. In the absence of dedicated experimental data for this reaction, particular attention is given to providing quantitative predictions for the manifestation of the $\Lambda(1405)$ structure in low-energy $\bar{K}N$ dynamics within a light nuclear environment. Employing different models of the $\bar{K}N-\pi\Sigma$ interaction, we calculate the $\pi\Sigma n$ invariant-mass spectra and the $\alpha$-particle missing-mass spectra, thereby identifying robust features of the $\Lambda(1405)$ signal and offering guidance for future experimental investigations.