Using separable KΛNβΟΞ£ potentials in the Faddeev equations, we
calculated the binding energies and widths of the Kβpp, Kβppn and
Kβppp 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 KΛNβΟΞ£ interaction are considered and the
dependence of the resulting few-body energy on the two-body
KΛNβΟΞ£ 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
Kβppn and Kβppp quasi-bound states with a binding energy in the range
BKβppnββΌ55β70 and BKβpppββΌ90β100 MeV, respectively. The
calculations yielded full width of ΞKβppnββΌ16β20 and
ΞKβpppββΌ7β20 MeV.Comment: 16 pages, 4 figure