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

TL;DR

This study uses a fully coupled-channel complex scaling method with a chiral SU(3)-based potential to investigate the $K^-pp$ resonance, revealing shallow binding in one picture and deeper binding in another, with implications for dense matter formation.

Contribution

It introduces a comprehensive coupled-channel approach with a chiral potential to analyze the $K^-pp$ resonance, accounting for energy dependence and different theoretical pictures.

Findings

$K^-pp$ resonance is a shallowly bound state with narrow width in the field picture.

In the particle picture, the binding energy can be as large as about 50 MeV.

Results have implications for the formation of dense kaonic nuclear matter.

Abstract

Nuclear system with antikaons, so-called kaonic nuclei, has been a longstanding issue in strange nuclear physics and hadron physics, because they might have exotic nature; In particular, they could be a doorway to the dense matter due to the strong attraction between antikaon and nucleon. Among kaonic nuclei, the three-body system composed of two protons and a single $K^-$ meson, $K^-pp$, is the most essential. In this article, we will report on the recent situation of $K^-pp$ studies in both theoretical and experimental sides. Afterwards, we will explain our latest study of the $K^-pp$ with a fully coupled-channel complex scaling method (Full ccCSM) using a chiral SU(3)-based $\bar{K}N$(-$\pi Y$) potential. In Full ccCSM, the $K^-pp$ is completely treated as a resonant state of a $\bar{K}NN$-$\pi\Sigma N$-$\pi\Lambda N$ coupled-channel system. The energy dependence involved in the chiral potential is handled with a self-consistent calculation in which two extreme ansatzes are examined: field picture and particle picture. With our chiral SU(3)-based potential constrained by the precise data of kaonic hydrogen atom (SIDDHARTA experiment), the $K^-pp$ resonance is obtained as a shallowly bound state measured from the $\bar{K}NN$ threshold with a narrow width, if the field picture is employed in the calculation: the binding energy is $14-28$ MeV and half value of the mesonic decay width are $8-15$ MeV. On the other hand, if the particle picture is employed, it is found that the binding energy could be as large as about 50 MeV, even though such a chiral potential is used. Based on these results of Full ccCSM calculation, we have discussed on the possibility for kaonic nuclei to form a dense matter and on the latest experimental result reported by J-PARC E15 collaboration.