The Octet Meson and Octet Baryon Interaction with strangeness and the $\Lambda(1405)$

TL;DR

This paper investigates the interactions of octet mesons and baryons with strangeness S=-1 using a relativistic chiral Lagrangian and Bethe-Salpeter approach, confirming the two-pole structure of the $ ext{Λ}(1405)$ resonance.

Contribution

It applies a relativistic Bethe-Salpeter framework with chiral Lagrangian to study strangeness S=-1 interactions and clarifies the two-pole nature of the $ ext{Λ}(1405)$ resonance.

Findings

Confirmed the two-pole structure of $ ext{Λ}(1405)$ at 1383+99i and 1423+14i MeV.

Identified the origins of the two poles from $ ext{Σ}π$ and $ar{ ext{K}}N$ interactions.

Theoretical results agree with experimental data.

Abstract

The octet meson and baryon interaction with strangeness $S=-1$ is studied fully relativistically with chiral Lagrangian. In this work, a Bethe-Salpeter equation approach with spectator quasipotential approximation is applied to study the reactions $K^-p\to MB$ with $MB=K^-p,\bar{K}^0n, \pi^-\Sigma^+,\pi^0\Sigma^0, \pi^+\Sigma^-$ and $\eta \Lambda$ with all possible partial waves and theoretical results are comparable with experimental data. It is found that the Weinberg-Tomozawa potential derived from the lowest order chiral Lagrangian only provides the contributions from partial waves with spin-parities $J^P=1/2^+$ and $1/2^-$. Two-pole structure of the $\Lambda(1405)$ is confirmed with poles at $1383+99 i$ and $1423+14i$ MeV. The lower and higher poles originate from $\Sigma \pi$ interaction as a resonance and $\bar{K}N$ interaction as a bound state, respectively.