A doubly charmed strange molecule from coupled-channel dynamics

We investigate a doubly charmed molecular state $T_{cc\bar{s}}$ with $C=+2$, $\mathcal{S}=+1$, and $I=1/2$ in an off-shell coupled-channel formalism. Constructing the interaction kernel from a meson-exchange model based on an effective Lagrangian and solving the coupled-channel scattering equation in the Blankenbecler-Sugar reduction, we find a pole only for $J^P=1^+$ among $J^P=0^\pm$, $1^\pm$, and $2^\pm$. With the reduced cutoff mass of $600$~MeV, we obtain a mass of $3972.90$~MeV, which corresponds to a binding energy of $4.01$~MeV relative to the $D^*D_s$ threshold. Examining the relative signs and magnitudes of the $S$-wave channel couplings extracted from the pole residues, we demonstrate that the pole belongs predominantly to the triplet ($\mathbf{3}_A$) representation. We also discuss the relevance of heavy-quark spin symmetry to the bound state.