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Scattering lengths of strangeness S=-2 baryon-baryon interactions

We reconsider a method based on dispersion theory, that allows one to extract the scattering length of any two-baryon system from corresponding final-state interactions in production reactions. The application of the method to baryon-baryon systems with strangeness S=-2 and S=-3 systems is discussed. Theoretical uncertainties due to the presence of inelastic channels with near-by thresholds are examined for the specific situation of the reaction K^- d -> K^0 Lambda Lambda and the coupling of Lambda Lambda to the Xi N channel. The possibility to disentangle spin-triplet and spin-singlet scattering lengths by means of various polarization measurements is demonstrated for several production reactions in K^- d and gamma d scattering. Employing the method to available data on the Lambda Lambda invariant mass from the reaction ^{12}C(K^-,K^+ Lambda Lambda X), a 1S0 scattering length of a(Lambda Lambda)=-1.2\pm 0.6 fm is deduced.