Eur. Phys. J. A (2005) 23: 79-111
https://doi.org/10.1140/epja/i2004-10055-3

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

¹ Atominstitut der Österreichischen Universitäten, Arbeitsbereich Kernphysik und Nukleare Astrophysik, Technische Universität Wien, Wiedner Hauptstr. 8-10, A-1040, Wien, Austria
² Institut für Mittelenergiephysik Österreichische Akademie der Wissenschaften, Boltzmanngasse 3, A-1090, Wien, Austria

^* e-mail: ivanov@kph.tuwien.ac.at

Received: 16 June 2004
Accepted: 6 December 2004
Published online: 7 December 2004

Abstract

We study kaonic deuterium, the bound K ^- d state A_{K 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 A _Kd → 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.