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The doubly charmed exotic state $T_{cc}$ recently discovered by the LHCbCollaboration could well be a $DD^{*}$ molecular state long predicted invarious theoretical models, in particular, the $DD^*$ isoscalar axial vectormolecular state predicted in the one-boson-exchange model. In this work, westudy the $DDD^*$ system in the Gaussian Expansion Method with the $DD^*$interaction derived from the one-boson-exchange model and constrained by theprecise binding energy of $273\pm63$ keV of $T_{cc}$ with respect to the$D^{*+}D^0$ threshold. We show the existence of a $DDD^*$ state with a bindingenergy of a few hundred keV and spin-parity $1^-$. Its main decay modes are$DDD\pi$ and $DDD\gamma$. The existence of such a state could in principle beconfirmed with the upcoming LHC data and will unambiguously determine thenature of the $T_{cc}^+$ state and of the many exotic state of similar kind,thus deepening our understanding of the non-perturbative strong interaction.

Discovery of the doubly charmed $T_{cc}^+$ state implies a triply charmed $H_{ccc}$ hexaquark state