Near-threshold $K^{-}d$ scattering and properties of kaonic deuterium

Abstract

We calculated the $1s$ level shifts and widths of kaonic deuterium, corresponding to accurate results on near-threshold antikaon - deuteron scattering. The Lippmann-Schwinger eigenvalue equation with a strong $K^{-}-d$ and Coulomb potentials was solved. The two-body $K^{-}-d$ potentials reproduce the near-threshold elastic amplitudes of $K^{-}d$ scattering obtained from the three-body Alt-Grassberger-Sandhas equations with the coupled channels using four versions of the $\bar{K}N-\pi \Sigma$ potentials. Both new $\bar{K}N-\pi \Sigma$ potentials reproducing the very recent SIDDHARTA data on kaonic hydrogen and our older potentials reproducing KEK data have one- or two-pole versions of the $\Lambda (1405)$ resonance and reproduce experimental data on $K^{-}p$ scattering.

Comments: 16 pages, 4 figures, 3 tables; changed in accordance with the wishes of referees; the results are unchanged