Exact calculations of a quasi-bound state in the $\bar{K} \bar{K} N$ system

TL;DR

This paper performs exact three-body calculations of a $ar{K}ar{K}N$ quasi-bound state using Faddeev equations with various $ar{K}N$ and $ar{K}ar{K}$ potentials, predicting a state possibly related to $ ext{Xi}(1950)$.

Contribution

It provides the first exact calculation of the $ar{K}ar{K}N$ quasi-bound state using multiple realistic potentials and novel methods for pole detection.

Findings

Quasi-bound state with 12-26 MeV binding energy.

Width of the state is 61-102 MeV.

Potential connection to the $ ext{Xi}(1950)$ resonance.

Abstract

Dynamically exact calculations of a quasi-bound state in the $\bar{K}\bar{K}N$ three-body system are performed using Faddeev-type AGS equations. As input two phenomenological and one chirally motivated $\bar{K}N$ potentials are used, which describe the experimental information on the $\bar{K}N$ system equally well and produce either a one- or two-pole structure of the $\Lambda(1405)$ resonance. For the $\bar{K}\bar{K}$ interaction separable potentials are employed that are fitted to phase shifts obtained from two theoretical models. The first one is a phenomenological $\bar{K}\bar{K}$ potential based on meson exchange, which is derived by SU(3) symmetry arguments from the J\"ulich $\pi \pi - \bar{K} K$ coupled-channels model. The other interaction is a variant of the first one, which is adjusted to the $KK$ s-wave scattering length recently determined in lattice QCD simulations. The position and width of the $\bar{K}\bar{K}N$ quasi-bound state is evaluated in two ways: (i) by a direct pole search in the complex energy plane and (ii) using an "inverse determinant" method, where one needs to calculate the determinant of the AGS system of equations only for real energies. A quasi-bound state is found with binding energy $B_{\bar{K}\bar{K}N} = 12 - 26$ MeV and width $\Gamma_{\bar{K}\bar{K}N} = 61 - 102$ MeV, which could correspond to the experimentally observed $\Xi(1950)$ state.