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

Abstract

Inspired by the experimental discoveries of ${T}_{cc}$, ${\mathrm{\ensuremath{\Sigma}}}_{c}(2800)$, and ${\mathrm{\ensuremath{\Lambda}}}_{c}(2940)$ and the theoretical picture where they are $D{D}^{*}$, $DN$, and ${D}^{*}N$ molecular candidates, we investigate the double-charm heptaquark system of $D{D}^{*}N$. We employ the one-boson-exchange model to deduce the pairwise $D\text{\ensuremath{-}}{D}^{*}$, $D\text{\ensuremath{-}}N$, and ${D}^{*}\text{\ensuremath{-}}N$ potentials and then study the $D{D}^{*}N$ system with the Gaussian expansion method. We find two good hadronic molecular candidates with $I({J}^{P})=\frac{1}{2}({\frac{1}{2}}^{+})$ and $\frac{1}{2}({\frac{3}{2}}^{+})$ $D{D}^{*}N$ with only $S$-wave pairwise interactions. The conclusion remains unchanged even taking into account the $S\text{\ensuremath{-}}D$ mixing and coupled channel effects. In addition to providing the binding energies, we also calculate the root-mean-square radii of the $D{D}^{*}N$ 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.