On kaonic deuterium. Quantum field-theoretic and relativistic covariant approach

We study kaonic deuterium, the bound K(-)d state A(Kd). Within a quantum field-theoretic and relativistic covariant approach vie derive the energy level displacement of the ground state of kaonic deuterium in terms of the amplitude of K-d scattering for arbitrary relative momenta. Near threshold our formula reduces to the well-known DGBT formula. The S-wave amplitude of K-d scattering near threshold is defined by the resonances Lambda(1405), Sigma(1750) and a smooth elastic background, and the inelastic channels K(-)d --> NY and K(-)d --> NYpi, where Y = Sigma(+/-), Sigma(0) and Lambda(0), where the final-state interactions play an important role. The Ericson-Weise formula for the S-wave scattering length of K-d scattering is derived. The total width of the energy level of the ground state of kaonic deuterium is estimated using the theoretical predictions of the partial widths of the two-body decays AKd NY and experimental data on the rates of the NY pair production in the reactions K(-)d --> NY. We obtain Gamma(1s) = (630 +/- 100) eV. For the shift of the energy level of the ground state of kaonic deuterium we predict epsilon(1s) = (325 +/- 60) eV.