Can a $$\varLambda nn$$ Resonance Constrain the $$\varLambda n$$ Amplitude?

Abstract

We address the question of constraints on the $$\varLambda n$$ amplitude as a result of observing a $$\varLambda nn$$ resonance above the $$\varLambda nn$$ three-body threshold. To examine this question, we will first demonstrate that by starting with a $$\varLambda n$$ interaction based upon the experimental $$\varLambda p$$ data and then scaling the $$\varLambda n$$ potential by $$\approx 8\%$$ one can generate a $$\varLambda nn$$ resonance, and with a sufficiently large scaling one can generate a $$\varLambda nn$$ 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 $$\varLambda n$$ 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 $$\varLambda n$$ effective range parameters by the $$\varLambda nn$$ resonance parameters?