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A theoretical investigation is done to clarify the origin of the peakstructure observed near the $K^{-} p p$ threshold in the in-flight${}^{3}\text{He} ( K^{-}, \, \Lambda p ) n$ reaction of the J-PARC E15experiment, which could be a signal of the lightest kaonic nuclei, that is, the$\bar{K} N N (I=1/2)$ state. For the investigation, we evaluate the $\Lambda p$invariant mass spectrum assuming two possible scenarios to interpret theexperimental peak. One assumes that the $\Lambda (1405)$ resonance is generatedafter the emission of an energetic neutron from the absorption of the initial$K^-$, not forming a bound state with the remaining proton. This uncorrelated$\Lambda (1405) p$ system subsequently decays into the final $\Lambda p$. Theother scenario implies that, after the emission of the energetic neutron, a$\bar{K} N N$ bound state is formed, decaying eventually into a $\Lambda p$pair. Our results show that the experimental signal observed in the in-flight${}^{3}\text{He} ( K^{-} , \, \Lambda p ) n$ reaction at J-PARC isqualitatively well reproduced by the assumption that a $\bar{K} N N$ boundstate is generated in the reaction, definitely discarding the interpretation interms of an uncorrelated $\Lambda (1405) p$ state.

On the structure observed in the in-flight ${}^{3}\text{He} ( K^{-} , \, \Lambda p ) n$ reaction at J-PARC