Coupled-channels Faddeev AGS calculation of $K^{-}ppn$ and $K^{-}ppp$ quasi-bound states

Abstract

Using separable $\bar{K}N-\pi \Sigma$ potentials in the Faddeev equations, we calculated the binding energies and widths of the $K^{-}pp$, $K^{-}ppn$ and $K^{-}ppp$ quasi-bound states on the basis of three- and four-body Alt-Grassberger-Sandhas equations in the momentum representation. One- and two-pole version of $\bar{K}N-\pi \Sigma$ interaction are considered and the dependence of the resulting few-body energy on the two-body $\bar{K}N-\pi \Sigma$ potential was investigated. The $s$-wave [3+1] and [2+2] sub-amplitudes are obtained by using the Hilbert-Schmidt expansion procedure for the integral kernels. As a result, we found a four-body resonance of the $K^{-}ppn$ and $K^{-}ppp$ quasi-bound states with a binding energy in the range $B_{K^{-}ppn}\sim 55-70$ and $B_{K^{-}ppp}\sim 90-100$ MeV, respectively. The calculations yielded full width of ${\Gamma }_{K^{-}ppn}\sim 16-20$ and ${\Gamma }_{K^{-}ppp}\sim 7-20$ MeV.

Comments: 16 pages, 4 figures