The $\Lambda_c^+\to\eta\pi^+\Lambda$ reaction and the $\Lambda a_0^+(980)$ and $\pi^+\Lambda(1670)$ contributions

TL;DR

This paper provides a theoretical analysis of the $ o ext{reaction}$ process, identifying contributions from resonances like $a_0(980)$ and $ ext{Lambda}(1670)$, and highlights the importance of interference effects and the spin flip component of $ ext{Sigma}(1385)$ in shaping the observed mass distributions.

Contribution

It introduces a model considering $a_0(980)$ and $ ext{Lambda}(1670)$ as dynamically generated resonances, explaining their production and interference effects in the reaction.

Findings

Large destructive interference between tree level and rescattering terms.

The spin flip part of $ ext{Sigma}(1385)$ significantly influences mass distribution shapes.

Internal emission has a minor role compared to external emission.

Abstract

We study from the theoretical point of view the $\Lambda_c^+\to \pi^+ \eta \Lambda$ reaction, recently measured by the Belle and BESIII Collaborations, where clear signals are observed for $a_0(980)$, $\Lambda(1670)$, and $\Sigma(1385)$ excitation. By considering the $a_0(980)$ and $\Lambda(1670)$ as dynamically generated resonances from the meson meson and meson baryon interaction, respectively, we are able to determine their relative production strength in the reaction, which is also tied to the strength of the $\pi^+ \eta \Lambda$ tree level contribution. We observe that this latter strength is very big and there are large destructive interferences between the tree level and the rescattering terms where the $a_0(980)$ and $\Lambda(1670)$ are generated. The $\Sigma(1385)$ contribution is included by means of a free parameter, the only one of the theory, up to a global normalization, when one considers only external emission, and we observe that the spin flip part of this term, usually ignored in theoretical and experimental works, plays an important role determining the shape of the mass distributions. Internal emission is also considered and it is found to play a minor role.