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

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.