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

Based on the scenario that a $\bar{K} N N$ bound state is generated and it eventually decays into $Λp$, we calculate the cross section of the $K^{-} {}^{3} \text{He} \to Λp n$ reaction, which was recently measured in the J-PARC E15 experiment. We find that the behavior of the calculated differential cross section $d ^{2} σ/ d M_{Λp} d q_{Λp}$, where $M_{Λp}$ and $q_{Λp}$ are the $Λp$ 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 $Λp$ invariant mass spectrum in the momentum transfer window $350 \text{ MeV} /c < q_{Λp} < 650 \text{ MeV} /c$. These facts strongly suggest that the $\bar{K} N N$ bound state was indeed generated in the J-PARC E15 experiment.