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The missing mass spectrum measured in high resolution studies of the reactionpp -> K^+X is analyzed with respect to the strong final state interaction nearthe Lambda p production threshold. The observed spectrum can be described byfactorizing the reaction amplitude in terms of a production amplitude and afinal state scattering amplitude. Parametrizing the Lambda p final stateinteraction in terms of the inverse Jost function allows a direct extraction ofthe low-energy phase-equivalent potential parameters. Constraints on thesinglet and triplet scattering lengths and effective ranges are deduced in asimultaneous fit of the Lambda p invariant mass spectrum and the total crosssection data of the free Lambda p scattering using the effective rangeapproximation.Comment: 9 pages,6 figures, 2 table

Analysis of the $\Lambda p$ final-state interaction in the reaction $p + p\to K^ + (\Lambda p)$