Three-body calculation of the $1s$ level shift in kaonic deuterium with realistic $\bar{K}N$ potentials

TL;DR

This paper calculates the 1s level shift in kaonic deuterium using advanced three-body methods with realistic antikaon-nucleon potentials, providing precise predictions and comparing them with approximate methods.

Contribution

It introduces a three-body calculation of kaonic deuterium level shifts using Coulomb Sturmian expansion and realistic potentials, improving accuracy over previous approximations.

Findings

Level shift estimated at approximately 800±30 eV with an imaginary part of about 480±20 eV.

Method achieves about 1 eV accuracy in level shift calculations.

Results suggest the level shift range is consistent across different realistic potentials.

Abstract

The $1s$ level shift in kaonic deuterium was calculated using Coulomb Sturmian expansion of Faddeev equations. The convergence of the method yields an $\sim\ 1\ eV$ accuracy for the level shifts. We used three different, realistic, multichannel $\bar{K}N$ interactions reproducing all known experimental two-body $\bar{K}N$ data. The different results suggest, that the level shift should be in the range $\Delta E\sim(800\pm30)-(480\pm20){\rm i}\ \ eV$. The (almost) exact level shifts were compared with values, given by the commonly used approximations.