Investigation of $K^{bar}NN$ resonances with a coupled-channel Complex Scaling Method + Feshbach projection

We have investigated a prototype of kaonic nuclei, “$K^{-}pp$”, with a coupled-channel Complex Scaling Method (ccCSM). Combining the ccCSM with Feshbach projection method, we can handle a coupled-channel problem effectively as a single-channel problem. By using an energy-dependent chiral SU(3)-based $\bar{K}N$ potential, the $K^{-}pp$ ($J^{\pi }=0^{-}$ and $T=1\mathrm{/}2$) is obtained to be shallowly bound with the binding energy of 20-30 MeV. The mesonic decay width depends on the interaction parameters and ansatz; the decay width is ranging from 20 to 65 MeV. In case of $J^{\pi }=1^{-}$ state, no three-body $\bar{K}NN$ resonant states are found.