Anomalous enhancement of the isospin-violating $\Lambda(1405)$ production by a triangle singularity in $\Lambda_c\rightarrow\pi^+\pi^0\pi^0\Sigma^0$

TL;DR

This paper investigates an anomalous enhancement in the isospin-violating production of the $ ext{Lambda}(1405)$ resonance via a triangle singularity in $ ext{Lambda}_c^+$ decay, revealing insights into hadronic molecular structures and $ar{K}N$ interactions.

Contribution

It demonstrates how a triangle singularity can enhance isospin-violating $ ext{Lambda}(1405)$ production, providing evidence for its molecular nature and $ar{K}N$ dynamics.

Findings

A narrow peak in $ ext{pi}^0 ext{Sigma}^0$ invariant mass distribution.

The peak is tied to the triangle singularity and mass differences in $ar{K}$ and $N$ states.

Supports the hadronic molecular picture of $ ext{Lambda}(1405)$.

Abstract

The decay of $\Lambda_c^+$ into $\pi^+\pi^0\Lambda(1405)$ with the $\Lambda(1405)$ decay into $\pi^0\Sigma^0$ through a triangle diagram is studied. This process is initiated by $ \Lambda_c^+ \to \pi^+ \bar{K}^*N $, then the $\bar{K}^*$ decays into $\bar{K} \pi$ and $\bar{K} N$ produce the $\Lambda(1405)$ through a triangle loop containing $\bar{K}^*N\bar{K}$ which develops a singularity around $1890$ MeV. This process is prohibited by the isospin symmetry, but the decay into this channel is enhanced by the contribution of the triangle diagram, which is sensitive to the mass of the internal particles. We find a narrow peak in the $\pi^0\Sigma^0$ invariant mass distribution, which originates from the $\Lambda(1405)$ amplitude, but is tied to the mass differences between the charged and neutral $\bar{K}$ or $N$ states. The observation of the unavoidable peak of the triangle singularity in the isospin-violating $\Lambda(1405)$ production would provide further support for hadronic molecular picture of the $\Lambda(1405)$ and further information on the $\bar{K} N $ interaction.