Decipher the width of the $X(3872)$ via the QCD sum rules

Abstract

In this work, we take the $X(3872)$ as the hidden-charm tetraquark state with both isospin $I=0$ and $1$ components, then investigate the strong decays $X(3872)\to J/\psi {\pi }^{+}{\pi }^{-}$, $J/\psi \omega$, ${\chi }_{c1}{\pi }^0$, $D^{\ast 0}{\bar{D}}^0$ and $D^0{\bar{D}}^0{\pi }^0$ 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 $1\mathrm{MeV}$, which is in excellent agreement with the experiment data ${\Gamma }_X=1.19\pm 0.21\mathrm{MeV}$ from the Particle Data Group, 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 $J^{PC}=1^{++}$.

Comments: 12 pages, 4 figures