# Non-mesonic decay of the $\eta$-mesic $^{3}\hspace{-0.03cm}\mbox{He}$ via $pd\rightarrow(^{3}\hspace{-0.03cm}\mbox{He}$-$\eta)_{bound}\rightarrow$ $^{3}\hspace{-0.03cm}\mbox{He} 2\gamma (6\gamma$) reaction

## TL;DR

This paper develops a theoretical model for the non-mesonic decay of $ ext{eta}$-mesic helium-3, providing momentum distributions and branching ratios essential for experimental analysis and efficiency estimation.

## Contribution

The paper introduces a new theoretical framework for $ ext{eta}$-mesic helium-3 decay channels, including in-medium branching ratios and momentum distributions for experimental applications.

## Key findings

- Calculated relative momentum distribution of bound $ ext{He-3}$-$ ext{eta}$
- Provided in-medium branching ratios for $ ext{eta}$ decay modes
- Estimated detection efficiency for WASA-at-COSY detector

## Abstract

In this article a theoretical model for the $\eta$-mesic $^{3}\hspace{-0.03cm}\mbox{He}$ non-mesonic decay channels is presented. We present the resultant relative momentum distribution of bound $^{3}\hspace{-0.03cm}\mbox{He}$-$\eta$ as well as in-medium branching ratios of $\eta\rightarrow 2\gamma$ and $\eta\rightarrow 3\pi^0$, which are crucial for the Monte Carlo simulations of measured processes and thus for the experimental data interpretation. As an example we also apply the model for the estimation of the detection efficiency of the WASA-at-COSY detector.