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

Abstract

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 $B_{K^{-}ppn}^{\mathrm{Chiral}}\sim 30.5-34.5$ MeV obtained with chirally motivated and $B_{K^{-}ppn}^{\mathrm{SIDD}}\sim 46.4-52.0$ 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 ${\Gamma }_{K^{-}ppn}\sim 38.2-50.9$ MeV are smaller.

Comments: 22 pages, 2 figures, 5 tables