Triple-charm molecular states composed of $D^{\ast }{D}^{\ast }D$ and $D^{\ast }{D}^{\ast }{D}^{\ast }$

Abstract

Inspired by the newly observed $T_{cc}^{+}$ state, we systematically investigate the $S$-wave triple-charm molecular states composed of $D^{\ast }{D}^{\ast }D$ and $D^{\ast }{D}^{\ast }{D}^{\ast }$. We employ the one-boson-exchange model to derive the interactions between $D(D^{\ast })$ and $D^{\ast }$ and solve the three-body Schrödinger 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 $I(J^P)=\frac{1}{2}(0^{-},1^{-},2^{-})$ $D^{\ast }{D}^{\ast }D$ and $I(J^P)=\frac{1}{2}(0^{-},1^{-},2^{-},3^{-})$ $D^{\ast }{D}^{\ast }{D}^{\ast }$ 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 $D$-$D^{\ast }$ and $D^{\ast }$-$D^{\ast }$, which further corroborate the molecular nature of these states. These predictions could be tested in the future at LHC or HL-LHC.

Comments: 12 pages, 3 figures, 6 tables. Published version in Phys. Rev. D