Fully coupled-channels complex scaling method for the K−pp system

Abstract

We have developed a fully coupled-channels complex scaling method (ccCSM) for the study of the simplest (and thus most important) kaonic nucleus, $``{K}^{\ensuremath{-}}pp$'', which is a resonant state of a $\overline{K}NN\text{\ensuremath{-}}\ensuremath{\pi}\mathrm{\ensuremath{\Sigma}}N\text{\ensuremath{-}}\ensuremath{\pi}\mathrm{\ensuremath{\Lambda}}N$ coupled-channel system based on theoretical viewpoint. By employing the ccCSM and imposing the correct boundary condition for a resonance, the coupled-channel problem is solved using a phenomenological energy-independent potential. As a result of the ccCSM calculation of $``{K}^{\ensuremath{-}}pp$'', in which all three channels are treated explicitly, we have obtained a three-body resonance as a Gamow state. The resonance pole indicates that the binding energy of $``{K}^{\ensuremath{-}}pp$'' and the half value of its mesonic decay width are 51 and 16 MeV, respectively. In the analysis of the ccCSM resonant wave function, we clarify the spatial configuration and channel composition of $``{K}^{\ensuremath{-}}pp$''. Compared with past single-channel calculations based on effective $\overline{K}N$ potentials, the current study provides a guideline for the determination of the $\overline{K}N$ energy to be used in such effective potentials.