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

## TL;DR

This paper introduces a fully coupled-channel complex scaling method to accurately study the $K^-pp$ resonant state, explicitly treating all relevant channels and providing detailed insights into its structure and decay properties.

## Contribution

The paper develops a novel fully coupled-channel complex scaling method for resonant states, explicitly solving the $ar{K}NN$-$ar{K}N$-$ar{ ext{Y}} ext{N}$ system with all channels included.

## Key findings

- Resonance energy of $K^-pp$ is 51 MeV below threshold.
- Decay width's half value is 16 MeV.
- Clarifies the spatial structure and channel composition of $K^-pp$.

## 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.