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

TL;DR

This study uses a coupled-channel Complex Scaling Method combined with Feshbach projection to investigate kaonic nuclei, specifically the $K^-pp$ system, revealing shallow binding energies and decay widths, and finding no resonant states for certain quantum numbers.

Contribution

It introduces a novel combined approach of ccCSM and Feshbach projection to effectively analyze coupled-channel problems in kaonic nuclei.

Findings

$K^-pp$ is shallowly bound with 20-30 MeV energy

Decay widths range from 20 to 65 MeV depending on parameters

No resonant states found for $J^^-$ state

Abstract

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 $T=1/2$) 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.