# Studying the bound state of the $K^-p$ system in the Bethe-Salpeter formalism

## TL;DR

This paper investigates the $K^-p$ bound state using the Bethe-Salpeter formalism, finding a stable state with a mass of 1422 MeV and a narrow decay width, suggesting possible new structures beyond known resonances.

## Contribution

The study applies the Bethe-Salpeter formalism with ladder and instantaneous approximations to analyze the $K^-p$ bound state, providing new insights into its properties.

## Key findings

- The $K^-p$ bound state exists with a mass of 1422 MeV.
- The decay width of this state is smaller than that of $ ext{Lambda}(1405)$.
- Results imply potential new structures in observed resonances.

## Abstract

We study the $s$-wave kaon-nucleon bound state with the strangeness $S=-1$ in the Bethe-Salpeter formalism in the ladder and instantaneous approximations. We solve the Bethe-Salpeter equation of the bound state and obtain the Bethe-Salpeter amplitude. It is shown that the $K^-p$ bound state exists in this formalism. We also study the decay width of the bound state based on the Bethe-Salpeter techniques. The mass of this bound state is 1422 MeV and its decay width is obviously smaller than that of $\Lambda(1405)$. These results indicate that there may be some other structures in the observed resonance.