Fully coupled-channel complex scaling method for the $K^{-}pp$ system

Abstract

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

6 pages, 1 figure. Accepted version (Phys. Rev. C rapid communication)

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• Fully coupled-channel study of $K^{-}pp$ resonance in a chiral SU(3)-based $\bar{K}N$ potential
• Three- and four-body kaonic nuclear states: Binding energies and widths
• On mass polarization effect in three-body systems
• Quadruply charmed baryons as heavy quark symmetry partners of the $D_{s0}^{\ast }(2317)$
• Study of the p$-$p$-$K${}^{+}$ and p$-$p$-$K${}^{-}$ dynamics using the femtoscopy technique
• $\bar{K}\bar{D}N$ molecular state as a "$uuds\bar{c}$ pentaquark" in a three-body calculation
• Recent results and future prospects of kaonic nuclei at J-PARC
• Kaonic Nuclear Clusters --- a New Paradigm of Particle and Nuclear Physics ---
• Old and New in Strangeness Nuclear Physics