Abstract
The kaonic cluster ppK^-ppK− is described by isospin-dependent N{\bar K}NK‾ potentials with significant difference between singlet and triplet components. The quasi-bound state energy of the system is calculated based on the configuration space Faddeev equations within isospin and averaged potential models. The isospin averaging of N{\bar K}NK‾ potentials is used to simplify the isospin model to isospinless one. We show that three-body bound state energy E_{3}E3 has a lower bound within the isospin formalism due to relation \left\vert E_{3}(V_{NN}=0)\right\vert<2\left\vert E_{2}\right\vert|E3(VNN=0)|<2|E2|, where E_{2}E2 is the binding energy of isospin singlet state of the N{\bar K}NK‾ subsystem. The averaged potential model demonstrates opposite relation between |E_{2}||E2| and |E_{3}(V_{NN}=0)||E3(VNN=0)|.
Highlights
The quasi-bound states in the kaonic cluster N N K defined by the spin sN N of nucleon pair are intensively debated during the last years
The properties of the kaonic cluster are defined by N Kinteraction, having significant difference for the isospin singlet and triplet channels
The isospin singlet component of the N Kpotential generates a quasi-bound state corresponding to the Λ(1405) resonance below the pK− threshold
Summary
Similar results have been obtained within similar phenomenological models [3, 4] taking into account the πΣ coupling directly This value is much smaller than the experimentally motivated value of about 100 MeV for the ppK− deeply bound state [5,6,7]. [12] as "t-averaging" is applied for two-body t-matrix within the impulse representation for treatment of the system These two types of averaging were proposed for simplification of isospin models describing three and four -body kaonic clusters. The result of such comparison is the different relations between E2 and E3(VN N = 0) satisfying for both types of the N Kpotential (AY and sHW). The Faddeev equations allow to separate components of the total wave function corresponding to the different particle rearrangements
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