In this work, we take the $X(3872)$ as the hidden-charm tetraquark state with both isospin $I=0$ and $I=1$ components, then investigate the strong decays $X(3872)\to J/\psi {\pi }^{+}{\pi }^{-}$, $J/\psi \omega$, ${\chi }_{c1}{\pi }^0$, $D^{*0}{\overline{D}}^0$, and $D^0{\overline{D}}^0{\pi }^0$ with the QCD sum rules. We take account of all the Feynman diagrams, and acquire four QCD sum rules based on rigorous quark-hadron duality. We obtain the total decay width about 1 MeV, which is in excellent agreement with the experiment data ${\mathrm{\Gamma }}_X=1.19\pm 0.21\mathrm{MeV}$ from the PDG, it is the first time to reproduce the tiny width of the $X(3872)$ via the QCD sum rules, which supports assigning the $X(3872)$ as the hidden-charm tetraquark state with the $J^{PC}=1^{++}$.

• Received 7 October 2023
• Accepted 4 January 2024

DOI:https://doi.org/10.1103/PhysRevD.109.014017

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Published by the American Physical Society