Kaon-Nucleon scattering lengths from the experiments on kaonic hydrogen and kaonic deuterium

Within the framework of a low-energy effective field theory we consider the procedure of extraction of the S-wave kaon-nucleon scattering lengths a0 and a1 from a combined fit to the kaonic hydrogen and kaonic deuterium data. It is demonstrated that, if the present DEAR central values for the kaonic hydrogen ground-state energy and width are used in the analysis of the data, a solution for a0 and a1 exists only in a restricted domain of input values for the kaon-deuteron scattering length. We therefore conclude that forthcoming measurement of this scattering length imposes stringent constraints on the theoretical description of the kaon-deuteron interactions at low energies.