Abstract
In the framework of the Faddeev equations in configuration space we perform an analysis of quasi-bound state of the NN{\bar K}NNK‾ system within a particle model. In our approach, the system NN{\bar K}(s_{NN}=0)NNK‾(sNN=0) (NN{\bar K}(s_{NN}=1))NNK‾(sNN=1)) is described as a superposition of ppK^{-}ppK− and pn{\bar K}^0pnK‾0 (nn{\bar K}^{0}nnK‾0 and pn{ K}^-pnK−) states, which is possible due to a particle transition. The relation of the particle model to the theory of a two-state quantum system is addressed and discussed taking into account the possibilities of deep and shallow NN{\bar K}(s_{NN}=0)NNK‾(sNN=0) quasi-bound states.
Highlights
Over 50 years ago a study of three possible isospin configurations of the K N N system led Nogami [1] to the assumption of the possible existence of the bound state in this system: in a antikaon-nucleons system the presence of the K− meson attracts two unbound protons to form a K−pp cluster
Calculations performed by Akaishi and Yamazaki [2] have predicted the possible existence of discrete nuclear bound states of Kin few-body nuclear systems and this prediction was confirmed by several subsequent publications
The most recently, the J-PARC E15 collaboration reported the observation of a distinct peak in the Λp invariant mass spectrum of 3He(K−, Λp)n, well below mK + 2mp, i.e., the mass threshold of the K− meson to be bound to two protons
Summary
Over 50 years ago a study of three possible isospin configurations of the K N N system led Nogami [1] to the assumption of the possible existence of the bound state in this system: in a antikaon-nucleons system the presence of the K− meson attracts two unbound protons to form a K−pp cluster. The system ppK− is described using two potentials (vpp and vpK−), while for the description of the system npK 0 we are using three different potentials: vnp, vpK0 and vnK0. The Schrödinger equation for the ppK− and npK 0 systems can be written in the following matrix form: (H0 + Vpp, np + VpK−, pK 0 + VpK−, nK 0 − E)ψ = 0.
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