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

The $1s$ level shift in kaonic deuterium was calculated using Coulomb Sturmian expansion of Faddeev equations. The convergence of the method yields an $\sim 1\mathrm{eV}$ accuracy for the level shifts. We used three different, realistic, multichannel $\overline{K}N$ interactions reproducing all known experimental two-body $K^{-}N$ data. The different results suggest that the level shift should be in the range $\mathrm{\Delta }E\sim (800\pm 30)-(480\pm 20)i\mathrm{eV}$. The exact level shifts were compared with values, given by the commonly used approximations.

Figure 1

The $K^{-}d$ three-body system.

Figure 2

Integration path for the channel Green operator $G_{np}^{ch}$. See details in the text.

Figure 3

Integration path for the channel Green operator $G_{K^{-}n}^{ch}$. See details in the text.