Quasi-bound state in the $\bar{K}NNN$ system

The paper is devoted to the $\bar{K}NNN$ system, which is an exotic system consisting of an antikaon and three nucleons. Dynamically exact four-body Faddeev-type equations were solved and characteristics of the quasi-bound state in the system were evaluated. Three antikaon-nucleon and three nucleon-nucleon potentials were used, so the dependence of the four-body pole positions on the two-body interaction models was studied. The resulting binding energies $B_{K^{-}ppn}^{\mathrm{C}\mathrm{h}\mathrm{i}\mathrm{r}\mathrm{a}\mathrm{l}}\sim 30.5-34.5$ MeV obtained with chirally motivated and $B_{K^{-}ppn}^{\mathrm{S}\mathrm{I}\mathrm{D}\mathrm{D}}\sim 46.4-52.0$ MeV obtained with phenomenological antikaon-nucleon potentials are close to those obtained for the $K^{-}pp$ system with the same $\bar{K}N$ and $NN$ potentials, while the four-body widths ${\mathrm{\Gamma }}_{K^{-}ppn}\sim 38.2-50.9$ MeV are smaller.