Theoretical analysis on the $K^{-}{}^3\text{He}\to \mathrm{\Lambda }pn$ reaction for the $\bar{K}NN$ bound-state search in the J-PARC E15 experiment

We theoretically analyze the $K^{-}{}^3\text{He}\to \mathrm{\Lambda }pn$ reaction for the $\bar{K}NN$ bound-state search in the J-PARC E15 experiment. We find that, by detecting a fast and forward neutron in the final state, an almost on-shell $\bar{K}$ is guaranteed, which is essential to make a bound state with two nucleons from ${}^3\text{He}$. Then, this almost on-shell $\bar{K}$ can bring a signal of the $\bar{K}NN$ bound state in the $\Lambda p$ invariant-mass spectrum, although it inevitably brings a kinematic peak above the $\bar{K}NN$ threshold as well. As a consequence, we predict two peaks across the $\bar{K}NN$ threshold in the spectrum: the lower peak coming from the $\bar{K}NN$ bound state, and the higher one originating from the kinematics.