# Further Theoretical Analysis on the $K^{-} {}^{3} \text{He} \to \Lambda p n$ Reaction for the $\bar{K} N N$ Bound-State Search in the J-PARC E15 Experiment

## TL;DR

This paper provides a theoretical analysis supporting the existence of a $ar{K} N N$ bound state observed in the J-PARC E15 experiment by calculating reaction cross sections and matching experimental data.

## Contribution

The study offers a detailed theoretical calculation that aligns with experimental results, strengthening evidence for the $ar{K} N N$ bound state in the reaction.

## Key findings

- Calculated differential cross section matches experimental data.
- Reproduces the $ ext{Lambda} p$ invariant mass spectrum quantitatively.
- Supports the generation of the $ar{K} N N$ bound state in the experiment.

## Abstract

Based on the scenario that a $\bar{K} N N$ bound state is generated and it eventually decays into $\Lambda p$, we calculate the cross section of the $K^{-} {}^{3} \text{He} \to \Lambda p n$ reaction, which was recently measured in the J-PARC E15 experiment. We find that the behavior of the calculated differential cross section $d ^{2} \sigma / d M_{\Lambda p} d q_{\Lambda p}$, where $M_{\Lambda p}$ and $q_{\Lambda p}$ are the $\Lambda p$ invariant mass and momentum transfer in the $(K^{-} , \, n)$ reaction in the laboratory frame, respectively, is consistent with the experiment. Furthermore, we can reproduce almost quantitatively the experimental data of the $\Lambda p$ invariant mass spectrum in the momentum transfer window $350 \text{ MeV} /c < q_{\Lambda p} < 650 \text{ MeV} /c$. These facts strongly suggest that the $\bar{K} N N$ bound state was indeed generated in the J-PARC E15 experiment.