Benchmark for a quasi-bound state of the $\overset{\_}{K}pp$ system

TL;DR

This paper compares two computational methods for analyzing the ${K^-}pp$ system, revealing its strong dependence on the $ar{K}N$ interaction and providing insights into its binding energy and structure.

Contribution

It introduces a benchmark comparison of hyperspherical harmonics and Faddeev methods for the ${K^-}pp$ system, highlighting the dominant $ar{K}N$ interaction influence.

Findings

Ground state energy agrees between methods

Energy is insensitive to $NN$ interaction

Strong dependence on $ar{K}N$ potential

Abstract

We present three-body nonrelativistic calculations within the framework of a potential model for the kaonic cluster ${K^-}pp$ using two completely different methods: the method of hyperspherical harmonics in the momentum representation and the method of Faddeev equations in configuration space. To perform a numerical benchmark, different $NN$ and antikaon-nucleon interactions are applied. The results of the calculations for the ground state energy for the ${K^-}pp$ system obtained by both methods are in reasonable agreement. Although the ground state energy is not sensitive to the $NN$ interaction, it shows very strong dependence on the $\overset{\_}{K}N$ potential. We show that the dominant clustering of the ${K^-}pp$ system in the configuration $\Lambda (1405)+p$ allows us to calculate the binding energy to good accuracy within a simple cluster approach for the differential Faddeev equations. The theoretical discrepancies in the binding energy and width for the ${K^-}pp$ system related to the different $NN$ and $\overset{\_}{K}N$ interactions are addressed.