Triple-charm molecular states composed of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mi>D</mml:mi><mml:mo>*</mml:mo></mml:msup><mml:msup><mml:mi>D</mml:mi><mml:mo>*</mml:mo></mml:msup><mml:mi>D</mml:mi></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mi>D</mml:mi><mml:mo>*</mml:mo></mml:msup><mml:msup><mml:mi>D</mml:mi><mml:mo>*</mml:mo></mml:msup><mml:msup><mml:mi>D</mml:mi><mml:mo>*</mml:mo></mml:msup></mml:math>
Si-Qiang Luo, Tian-Wei Wu, Ming-Zhu Liu, Li‐Sheng Geng, Xiang Liu
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 $S\text{\ensuremath{-}}D$ mixing and coupled channel effects are carefully assessed in our study. Our results show that the $I({J}^{P})=\frac{1}{2}({0}^{\ensuremath{-}},{1}^{\ensuremath{-}},{2}^{\ensuremath{-}}){D}^{*}{D}^{*}D$ and $I({J}^{P})=\frac{1}{2}({0}^{\ensuremath{-}},{1}^{\ensuremath{-}},{2}^{\ensuremath{-}},{3}^{\ensuremath{-}}){D}^{*}{D}^{*}{D}^{*}$ 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 $D\text{\ensuremath{-}}{D}^{*}$ and ${D}^{*}\text{\ensuremath{-}}{D}^{*}$, which further corroborate the molecular nature of these states. These predictions could be tested in the future at LHC or HL-LHC.