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

TL;DR

This paper predicts the existence of triple-charm molecular states composed of D and D* mesons using a three-body Schrödinger equation approach, inspired by the T_cc+ observation, and suggests they could be detected at LHC.

Contribution

It systematically investigates triple-charm molecular states with a detailed three-body analysis, including interactions, mixing, and coupled channels, providing new predictions for bound states.

Findings

Bound states for specific isospin and spin-parity configurations are predicted.

Calculated binding energies and radii support the molecular interpretation.

Predictions are testable at current high-energy physics experiments.

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.