The $K^- p \rightarrow \eta \Lambda$ reaction in an effective Lagrangian model

TL;DR

This paper uses an effective Lagrangian model to analyze the $K^- p o ext{eta} \Lambda$ reaction near threshold, successfully reproducing total cross sections but highlighting the need for higher partial waves to explain angular distribution features.

Contribution

It introduces a comprehensive effective Lagrangian approach considering multiple channels and identifies the necessity of higher partial waves, such as a $D_{03}$ resonance, to explain angular distribution structures.

Findings

Total cross sections are well reproduced.

Higher partial waves are needed to explain angular structures.

A narrow $D_{03}$ resonance can describe bowl structures with a small width.

Abstract

We report on a theoretical study of the $K^- p \to \eta \Lambda$ reaction near threshold by using an effective Lagrangian approach. The role of $s-$channel $\Lambda(1670)$, $t-$channel $K^*$ and $u-$channel proton pole diagrams are considered. We show that the total cross sections data are well reproduced. However, only including the $s-$wave $\Lambda(1670)$ state and the background contribution from $t-$ and $u-$channel are not enough to describe the bowl structures in the angular distribution of $K^- p \to \eta \Lambda$ reaction, which indicates that there should be higher partial waves contributing to this reaction in some energy region. Indeed, if we considered the contributions from a $D_{03}$ resonance, we can describe the bowl structures, however, a rather small width ($\sim 2$ MeV) of this resonance is needed.