A narrow $DNN$ quasi-bound state

TL;DR

This paper investigates the properties of a $DNN$ quasi-bound state, finding it to be a deeply bound system with a moderate width, using two different theoretical approaches to ensure robustness of results.

Contribution

The study introduces a detailed analysis of the $DNN$ quasi-bound state using fixed center approximation and variational methods, highlighting the formation of a $ar{D}N$ cluster similar to $ ext{Lambda}_c(2595)$.

Findings

The $DNN$ system is bound by about 250 MeV.

The width of the state is estimated to be 20-40 MeV.

The $DN$ pair forms a cluster akin to $ ext{Lambda}_c(2595)$.

Abstract

The energies and widths of $DNN$ quasi-bound states with isospin I=1/2 are evaluated in two methods, the fixed center approximation to the Faddeev equation and the variational method approach to the effective one-channel Hamiltonian. The $DN$ interactions are constructed so that they dynamically generate the $\Lambda_c(2595)$ (I=0, $J^{\pi} =1/2^-$) resonance state. We find that the system is bound by about 250 MeV from the $DNN$ threshold, $\sqrt{s} \sim 3500$ MeV. Its width including both the mesonic decay and the $D$ absorption, is estimated to be about 20-40 MeV. The I=0 $DN$ pair in the $DNN$ system is found to form a cluster that is similar to the $\Lambda_c(2595)$.