Theoretical investigations of the nnΛ/NNΣ system

No published nΛ scattering data exist, so that the JLab tritium K⁺ electroproduction of nnΛ was undertaken in an effort to observe a nnΛ resonance that would provide constraints on the nΛ interaction. We will discuss Faddeev-type calculations of such a resonance based upon pairwise potentials of rank-one separable form that fit effective range parameters of the nn data and effective range parameters for four NΛ potentials from the Nijmegen and Juelich groups that fit pΛ scattering data. Utilizing rank-one separable potentials allows one to analytically continue the nnΛ Faddeev equations into the second complex energy plane in search of resonance poles by examining the eigenvalue spectrum of the kernel of the equations. Modeling the position and width of the K⁺ spectrum was found to provide significant constraints on the heretofore unmeasured nΛ interaction.

The recent tritium K⁺ spectrum measurement exhibited an additional structure that was interpreted to be a NNΣ resonance. Such a resonance could have isospin T=0 or T=1. Afnan et al. had found such a T=0 resonance while exploring Λ-deuteron elastic scattering in the 1990s. Garcilzo et al. later suggested that only the spin-1/2 T=0 and T=1 NNΣ channels might support near threshold resonances, based upon a constituent quark model. We have revisited the Λ-d scattering calculation and located the T=1 NNΣ resonance pole. The two poles are close to one another in terms of the real part of the energy, so that interpreting the isospin properties of the observed structure in the K⁺ spectrum would be difficult.