The Peak Structure in the In-Flight ${}^{3}\text{He} ( K^{-} , \, \Lambda p ) n$ Reaction Around the $\bar{K} N N$ Threshold

We theoretically investigate the origin of the peak structure around the $K^{-} p p$ threshold observed in the in-flight ${}^{3}\text{He} ( K^{-} , \, \Lambda p ) n$ reaction in the recent E15 experiment at J-PARC. For this purpose, we consider two scenarios to produce the peak. One is that the $\Lambda (1405)$ is generated but it does not correlate with $p$, and the uncorrelated $\Lambda (1405) p$ system subsequently decays into $\Lambda p$. The other one is that the $\bar{K} N N$ bound state is indeed generated and decays into $\Lambda p$. As a result, the experimental signal is qualitatively well reproduced in the $\bar{K} N N$ bound scenario, definitely discarding the uncorrelated $\Lambda (1405) p$ one.