Fully coupled-channel study of $K^{-}pp$ resonance in a chiral SU(3)-based $\bar{K}N$ potential

Abstract

We have investigated the most essential kaonic nucleus "$K^{-}pp$" as a resonant state of the $\bar{K}NN$-$\pi \Sigma N$-$\pi \Lambda N$ coupled channel system using a chiral SU(3)-based $\bar{K}N$ potential. We treat the "$K^{-}pp$" resonance adequately with a fully coupled-channel complex scaling method (full ccCSM). Self-consistency needs to be considered for the energy dependence of the chiral SU(3)-based potential. In the present study, we propose a simple prescription for the treatment of self-consistency, considering the {\it averaged threshold} and {\it averaged binding energy of mesons}. With this prescription, we have successfully found the self-consistent solutions of the "$K^{-}pp$" three-body resonance. The results indicate that the "$K^{-}pp$" system is bound rather shallowly. In particular, when the potential parameters are constrained with the latest $\bar{K}N$ scattering length, the binding energy and half of the mesonic decay width are obtained as $14-50$ MeV and $8-19$ MeV, respectively.

Comments: 7 pages, 2 figures, accepted by Phys. Lett. B