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.

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

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• Double-charm heptaquark states composed of two charmed mesons and one nucleon
• Molecular states of $D^{\ast }{D}^{\ast }{\bar{K}}^{\ast }$ nature
• Exotic states with triple charm
• Theoretical investigation of the molecular nature of $D_{s0}^{\ast }(2317)$ and $D_{s1}(2460)$ and the possibility of observing the $D\bar{D}K$ bound state $K_{c\bar{c}}(4180)$ in inclusive $e^{+}{e}^{-}\to c\bar{c}$ collisions
• Doubly charmed hexaquarks in the diquark picture
• Spectroscopic Properties of Double-Strangeness Molecular Tetraquarks
• Predictions of super-exotic heavy mesons from $K^{\ast }{B}^{\ast }{B}^{\ast }$ interactions
• Constraining the $DD{D}^{\ast }$ three-body bound state via the $Z_c(3900)$ pole
• Faddeev fixed-center approximation to the $\eta K^{\ast }{\bar{K}}^{\ast }$, $\pi K^{\ast }{\bar{K}}^{\ast }$ and $K{K}^{\ast }{\bar{K}}^{\ast }$ systems
• On the question of quark confinement in the Abelian U(1) QED gauge interaction
• Tri-meson state $\bar{\mathbf{B}}{\bar{\mathbf{B}}}^{\ast }{\bar{\mathbf{B}}}^{\ast }$
• Dynamically generated states from the $\eta K^{\ast }{\bar{K}}^{\ast }$, $\pi K^{\ast }{\bar{K}}^{\ast }$, and $K{K}^{\ast }{\bar{K}}^{\ast }$ systems within the fixed-center approximation
• Prospects for compact hexaquarks under the limitation imposed by quark confinement
• Correlation function for the $n{\bar{D}}_{s0}^{\ast }(2317)$ interaction and the issue of elastic unitarity