$K^{-}$\textit{pp} studied with Coupled-Channel Complex Scaling Method

$K^{bar}$ nuclei (nuclear system with anti-kaon) might have lots of interesting properties due to the strong $K^{bar}N$ attraction in $s$-wave isoscalar channel. Recently, people are focusing on the most essential $K^{bar}$ nucleus ``$K^{-}$\textit{pp}''. A variational calculation with an effective $K^{bar}N$ potential derived from chiral SU(3) theory, performed by one of authors (A. D.), concluded the shallow binding of $K^{-}$\textit{pp}. (only 20 MeV) However, a Faddeev (AGS) calculation, also constrained by chiral SU(3) theory, reported 80 MeV binding energy. Such a large discrepancy is considered to be caused by the \underline {\textit{$\pi \Sigma $N}}\underline { three-body dynamics}. Since the \textit{$\pi \Sigma $} degree is not explicitly dealt with in the variational calculation and is incorporated in the effective $K^{bar}N$ potential, the \textit{$\pi \Sigma $N} three-body dynamics might be lack in the previous study. We will perform a coupled channel calculation treating \underline {the }\underline {\textit{$\pi \Sigma $N}}\underline { channel explicitly}. Since the obtained $K^{-}$\textit{pp}-\textit{$\pi \Sigma $N} coupled state is expected to appear above the \textit{$\pi \Sigma $N} threshold as \underline {a resonant state}, we employ ``Complex Scaling Method'' (CSM) which has succeeded in the treatment of resonances in nuclear physics. Studying $K^{-}$\textit{pp} with ``\textbf{\textit{Coupled-Channel Complex Scaling Method}}'' using a reliable \textit{NN} potential (Av18 potential) and theoretical/phenomenological $K^{bar}N$ potentials, we will report its binding energy and decay width. Then, analyzing the CSM wave function, detailed property of $K^{-}$\textit{pp} will be investigated.