Can a Λnn Resonance Constrain the Λn Amplitude?

We address the question of constraints on the Λn amplitude as a result of observing a Λnn resonance above the Λnn three-body threshold. To examine this question, we will first demonstrate that by starting with a Λn interaction based upon the experimental Λp data and then scaling the Λn potential by ≈8% one can generate a Λnn resonance, and with a sufficiently large scaling one can generate a Λnn bound state. This is achieved using the three-body Faddeev equations with rank one separable potentials for all pairwise interactions. The use of separable potentials is motivated by two factors: (i) the Faddeev equations reduce to a set of one dimensional integral equations that can be analytically continued into the complex energy plane where resonances reside. (ii) The Λn amplitude can be defined in terms of the effective range parameters. As a result we can explore the question: What constraint can be placed on the Λn effective range parameters by the Λnn resonance parameters? (author)