Abstract
A new evaluation of the 1s level shift and width of kaonic deuterium is presented based on an accurate K̅ NN three-body calculation, using as input a realistic antikaon-nucleon interaction constrained by the SIDDHARTA kaonic hydrogen data. The three-body Schrödinger equation is solved with a superposition of a large number of correlated Gaussian basis functions extending over distance scales up to several hundred fm. The resulting energy shift and width of the kaonic deuterium 1s level are △E ≃ 0:67 keV and Γ ≃ 1.02 keV, with estimated uncertainties at the 10 % level.
Highlights
Kaonic hydrogen and kaonic deuterium are the prototype K−-atomic systems to be studied in the quest for constraints on the low-energy antikaon-nucleon interaction near K N threshold
Isospin-breaking mass effects are important in the K N threshold physics that generates the 1s energy shift and width of kaonic hydrogen
Concerning the energy dependence of V K N(E), for kaonic hydrogen the results obtained by setting E ≡ EK N = 0 at threshold as input turn out to be equal to those using the self-consistent value of E
Summary
Kaonic hydrogen and kaonic deuterium are the prototype K−-atomic systems to be studied in the quest for constraints on the low-energy antikaon-nucleon interaction near K N threshold. Accurate data of the strong-interaction energy shift ∆E and width Γ of the 1s level in these kaonic atoms should provide, through their theoretical analysis, key information in order to fix basic K N scattering length parameters in both isospin I = 0, 1 channels. New K−d measurements are in preparation: SIDDHARTA-2 at LNF [2] and E57 at J-PARC [3] These developments call for advanced calculations of the coupled K− pn ↔ K 0nn system. Recent advanced Faddeev computations [8, 9] use separable potentials constrained by the SIDDHARTA kaonic hydrogen data and have evaluated the 1s K−d atomic state assuming isospin symmetry for the Kand nucleon doublets.
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