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.