Double-charm heptaquark states composed of two charmed mesons and one nucleon

Inspired by the experimental discoveries of $T_{cc}$, ${\mathrm{\Sigma }}_c(2800)$, and ${\mathrm{\Lambda }}_c(2940)$ and the theoretical picture where they are $D{D}^{\ast }$, $DN$, and $D^{\ast }N$ molecular candidates, we investigate the double charm heptaquark system of $D{D}^{\ast }N$. We employ the one-boson-exchange model to deduce the pairwise $D$-$D^{\ast }$, $D$-$N$, and $D^{\ast }$-$N$ potentials and then study the $D{D}^{\ast }N$ system with the Gaussian expansion method. We find two good hadronic molecular candidates with $I(J^P)=\frac{1}{2}({\frac{1}{2}}^{-})$ and $\frac{1}{2}({\frac{3}{2}}^{-})$ $D{D}^{\ast }N$ with only $s$-wave pairwise interactions. The conclusion remains unchanged even taking into account the $S$-$D$ mixing and coupled channel effects. In addition to providing the binding energies, we also calculate the root-mean-square radii of the $D{D}^{\ast }N$ system, which further support the molecular nature of the predicted states. They can be searched for at the upcoming LHC run 3 and run 4.