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

Abstract

We study kaonic deuterium, the bound K-d state AK d. Within a quantum field-theoretic and relativistic covariant approach we 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 Λ(1405), Σ(1750) and a smooth elastic background, and the inelastic channels K-d → NY and K-d → NYπ, where Y = Σ±,Σ{0} and Λ{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 Γ{1s} = (630±100)eV. For the shift of the energy level of the ground state of kaonic deuterium we predict ε{1s} = (325±60)eV.