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

Abstract

We study kaonic deuterium, the bound K − d state A Kd . 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 wellknown 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 → N Y and K − d → N Y π, 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 → N Y and experimental data on the rates of the N Y -pair production in the reactions K − d → N Y . We obtain Γ 1s = (630 ± 100) eV. For the shift of the energy level of the ground state of kaonic deuterium we predict ǫ 1s = (353 ± 60) eV.

Energy-level displacement of excitednpstates of kaonic hydrogen

“…For the S-wave amplitude of K − N scattering near threshold, computed in [1,6], the energy level displacement of the ground state of kaonic hydrogen obtained by Meißner et al [3] is equal to −ǫ This agrees well with both our theoretical result (1.1) and experimental data (1.2) within 1.5 standard deviations for the shift and one standard deviation for the width. In this paper we compute the energy level displacement of the excited np states of kaonic hydrogen, where n is the principal quantum number and p corresponds to the excited state with ℓ = 1.…”

“…The S-wave scattering lengths a 0 0 and a 1 0 have been treated as free parameters of the approach. Using our results for the S-wave scattering lengths a 0 0 and a 1 0 [1,6] and keeping leading terms in QCD isospin-breaking and electromagnetic interactions, i.e. accounting for only the contribution of Coulombic photons, we have shown that the numerical value of the energy level displacement of the ns state of kaonic hydrogen, computed by Meißner et al [3], agrees well with both our theoretical prediction [1] and recent experimental data by the DEAR Collaboration [2] within 1.5 standard deviations for the shift and one standard deviation for the width.…”

“…We would like to emphasize that the baryon resonances we will treat as elementary particles defined by local fields and local phenomenological Lagrangians with phenomenological coupling constants [1,6]( see also [21]). The contribution of the octet of low-lying baryons baryons with spin 1/2 and positive parity (N(940), Λ 0 (1116), Σ(1193)) = B (8) we include to the elastic background.…”

On kaonic hydrogen. Phenomenological quantum field theoretic model revisited

“…This result is obtained without the specification of the numerical values of the coupling constants g 1 and g 2 and the masses of resonances, but using only physical masses of interacting particles for the calculation of phase volumes. 11) where A = − 6.02 fm is the contribution of the Λ(1405) resonance, calculated for g 1 = 0.91 and m Λ(1405) = 1405 MeV Ref. [1].…”

“…Using the results obtained in Section 2 for the S-wave scattering lengths of K − N scattering and in Ref. [11] we recalculate the S-wave scattering length a…”