Three-body molecular states composed of $D^{(*)}$ and two nucleons

Abstract

We study the three-body systems $DNN$ and $D^{*}NN$ within a hadronic molecular framework by combining a realistic nucleon-nucleon interaction with a $D^{(*)}N$ potential constrained by heavy-quark symmetry. The three-body Schr\"odinger equation is solved with the Gaussian Expansion Method, and the analytic structure of the spectrum is investigated using the Complex Scaling Method. We find that the $DNN$ system supports a robust and compact bound state in the $I(J^{P})=\tfrac{1}{2}(1^-)$ channel over a broad range of cutoff values, even when the corresponding $DN$ subsystem is weakly bound or unbound. For $D^{*}NN$, the spin-$1$ nature of the heavy meson and the associated spin-dependent forces generate a clear spin hierarchy: deeply bound states appear in both $0^-$ and $2^-$ channels, while the $1^-$ channel exhibits a characteristic two-branch pattern with a strongly bound compact branch and a more weakly bound, spatially extended branch. The root-mean-square radii indicate pronounced spatial compression compared with the deuteron scale, highlighting the cooperative roles of realistic $NN$ correlations, the $D^{(*)}N$ interactions, and heavy-quark symmetry in forming compact heavy-flavor few-body bound states. No three-body resonances under complex scaling are found in the explored parameter space. Our results provide quantitative benchmarks for future experimental searches for such charmed-meson-nuclear bound states.