Exploring the unknown Lambda-neutron interaction

Abstract

No published \LambdaΛn scattering data exist. A relativistic heavy-ion experiment has suggested that a \LambdaΛnn bound state was seen. However, several theoretical analyses have cast serious doubt on the bound-state assertion. Nevertheless, there could exist a three-body \LambdaΛnn resonance. Such a resonance could be used to constrain the \LambdaΛn interaction. We discuss \LambdaΛnn calculations using nn and \LambdaΛn pairwise interactions of rank-one, separable form that fit effective range parameters of the nn system and those hypothesized for the as yet unobserved \LambdaΛn system based upon four different \LambdaΛN potentials. The use of rank-one separable potentials allows one to analytically continue the \LambdaΛnn Faddeev equations onto the second complex energy plane in search of resonance poles, by examining the eigenvalue spectrum of the kernel of the Faddeev equations. Although each of the potential models predicts a \LambdaΛnn sub-threshold resonance pole, scaling of the \LambdaΛn interaction by as little as \sim∼5% does produce a physical resonance. This suggests that one may use photo-(electro-)production of the \LambdaΛnn system from tritium as a tool to examine the strength of the \LambdaΛn interaction.