Three- and four-body kaonic nuclear states: Binding energies and widths

Abstract

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...

Structure of $Λ$(1405) resonance and $γ{p}\rightarrow K^{+}+(πΣ)^{0}$ reaction

“…Here, the operators K α,β i,j;Ii,Ij are three-body transition amplitudes which describe the elastic and re-arrangement processes [41][42][43] and the operators M α i,j;Ii,Ij are Born terms which describe the effective potential realized by exchanged particle. In this equation, W is the three-body energy and W −…”

Four-body Faddeev-type calculation of the $\bar{K}NNN$ system: Preliminary results

“…The lower indices α, β in Eqs. (4,5,6) similarly to the case of the three-body equations (1,2,3) define two-body subsystems of the full system. The upper indices τ, σ, ρ define a partition of the four-body system which can be of 3 + 1 or 2 + 2 type.…”

“…The next step is study of a four-body K N N N system. Some calculations were already performed for it [1,4,5], but more accurate calculations are needed. We use four-body Faddeev-type equations in AGS form [6].…”

Four-body Faddeev-type calculation of the $\bar{K}NNN$ system

“…The detection of the heavier four-body K 𝑁 𝑁 𝑁 system could be easier than in the case of K 𝑁 𝑁 since direct scattering of 𝐾 − on three-body nuclei (such as 3 He or 3 H) can be performed. Some theoretical works were devoted to the question of the quasi-bound state in the K 𝑁 𝑁 𝑁 system with different quantum numbers [3][4][5][6], but more accurate calculations within Faddeev-type equations are needed. The reason is that only these dynamically exact equations in momentum representation can treat energy dependent K 𝑁 potentials, necessary for this system, exactly.…”