Using separable potentials forKN − πΣ interaction, we investigated four-body kaonic nuclear systems such as K − ppn and K − K − pp, with the Faddeev AGS method in the momentum representation. The Faddeev calculations are based on the quasi-particle method and the method of the energy dependent pole expansion was used to obtain the separable representation for the integral kernels in the three-and four-body equations. Different types ofKN − πΣ potentials based on phenomenological and chiral SU(3) approach are used and it was shown that the kaonic nuclear systems under consideration are tightly bound. PACS numbers: 13.75.Jz, 14.20.Pt, 21.85.+d, 25.80.Nv TheKN interaction, which is affected by Λ(1405) resonance, plays an important role in the exotic systems, including the antikaon particle [1][2][3][4][5]. Thus, to study the kaonic systems, it is necessary to know theKN interaction. The first prediction of a quasi-bound state in kaonic nuclear systems was made in [3,[6][7][8], showing that these systems could be strongly bound. For the past two decades, many theoretical calculations were performed, focusing on the three-and four-body kaonic systems [9][10][11][12][13][14][15][16][17][18][19][20].Alongside theoretical studies, many experimental searches have been also carried out to investigate the possible existence of the quasi-bound state in the kaonic systems (especially K − pp system). The investigations for the K − pp quasi-bound state have been explored by FINUDA experiment at the DAPhNE collider [21] and also by OBELIX at CERN [22] and DISTO at SAT-URNE [23]. Further experimental results were obtained by E15 and E27 groups at J-PARC [24, 25]. However, the possible existence of the quasi-bound state in the K − pp systems is still highly uncertain and there are some doubts in the extracted experimental results. The new planned experiments by HADES [26] and LEPS [27] Collaborations, and also by J-PARC [24, 25] experiments may unravel this problem.The purpose of the present paper is to explore the binding energy and width of four-body kaonic nuclear systems including one or two antikaon particle. The problem can be solved using methods developed within four-body theories. To reduce the four-body Faddeev equations to a set of single-variable integral equations, one can employ different methods [28,29]. One can do the reduction procedure numerically by making use of the so-called HSE method proposed by Narodetsky [28] and also by using the energy-dependent pole expansion method which developed by Sofianos et al [29]. In Refs [16] and [17], the HSE method was employed to solve the Faddeev equations of K − ppn and K − K − pp systems, respectively. One can also perform the fourbody calculation using the energy-dependent pole expansion method [29] or the so-called EDPE method. In EDPE method the form factors are energy dependent. In the present study, K − ppn and K − K − pp quasi-bound state positions were calculated. Using the EDPE method, we found the separable expressions for the [3+1] and [2+2] subsystems. At the...

New calculations of the quasi-bound state positions in K − K − pp kaonic nuclear cluster are performed using non-relativistic four-body Faddeev-type equations in AGS form. The corresponding separable approximation for the integral kernels in the three-and four-body kaonic clusters is obtained by using the Hilbert-Schmidt expansion procedure. Different phenomenological models ofKN − πΣ potentials with one-and two-pole structure of Λ(1405) resonance and separable potential models forK-K and nucleonnucleon interactions, are used. The dependence of the resulting four-body binding energy on models of KN − πΣ interaction is investigated. We obtained the binding energy of the K − K − pp quasi-bound state ∼ 80-94 MeV with the phenomenologicalKN potentials. The width is about ∼ 5-8 MeV for the two-pole models of the interaction, while the one-pole potentials give ∼ 24-31 MeV width.