Triple-charm molecular states composed of $D^*D^*D$ and $D^*D^*D^*$

Abstract: Inspired by the newly observed $T_{cc}^+$ state, we systematically investigate the $S$-wave triple-charm molecular states composed of $D^*D^*D$ and $D^D^*D^$. We employ the one-boson-exchange model to derive the interactions between $D(D^*)$ and $D^*$ and solve the three-body Schr\"odinger equations with the Gaussian expansion method. The $S$-$D$ mixing and coupled channel effects are carefully assessed in our study. Our results show that the $I(J^P)=\frac{1}{2}(0^-,1^-,2^-)$ $D^*D^*D$ and $I(J^P)=\frac{1}{2}(0^-,1^-,2^-,3^-)$ $D^D^*D^$ systems could form bound states, which can be viewed as three-body hadronic molecules. We present not only the binding energies of the three-body bound states, but also the root-mean-square radii of $D $-$D^*$ and $D^$-$D^$, which further corroborate the molecular nature of these states. These predictions could be tested in the future at LHC or HL-LHC.