Universal characterization of Efimovian $D^0 nn$ System via Faddeev Techniques

Abstract

We demonstrate remnant structural universality in a putative S-wave $2n$-halo-bound $D^0nn$ system in the $J=0, T=3/2$ channel by invoking the zero-coupling limit (ZCL), which eliminates sub-threshold decay channels. Within this framework, we evaluate the one- and two-body matter density form factors, their associated root mean-square radii, and the $n$-$D^0$-$n$ opening angle. Our analysis is carried out at leading order using a quantum mechanical Faddeev technique in the momentum representation. Employing Jacobi momenta, we construct a complete partial-wave basis to expand the full three-body $D^0nn$ wave function across distinct rearrangement channels. Projection onto this basis yields a coupled set of Faddeev integral equations that govern the multiple-scattering dynamics of the constituent coupled spin-isospin subsystems. By introducing short-range separable interactions and expressing the two-body scattering amplitudes via spectator functions, we establish a direct correspondence with the familiar Skornyakov-Ter-Martirosyan equations from halo-EFT approach at leading order. A regulator-dependent analysis highlights the Efimov-like character of the three-body observables, with ground state properties exhibiting marked sensitivity to cutoff variations. However, the inclusion of a three-body force suppresses this dependence, as expected from renormalization-group invariance. We thereby conclude that, for sufficiently shallow three-body binding, the $D^0nn$ system in the ZCL exhibits a universal halo-bound structure. The subtle implications of range-like corrections at LO are addressed at a qualitative level in this analysis.