The lattice QCD simulations of charmed states with $J^{PC} = 1^{++} $ have been performed in this study. Particularly, $X(3872)$ was investigated. The narrow state $X(3872)$ was discovered by the Belle Collaboration in B decay and subsequently confirmed by the BaBar Collaboration. Both the CDF and the $D0$ Collaboration saw a clear signal of inclusive $X(3872)$ production in pp collision. Since $X(3872)$ decays into $\pi^+\pi^−J/ψ$, it was the most natural to assign $X(3872)$ to one of the excited charmonia. Experiment has revealed unexpected properties of $X(3872)$. The mass of this state , $3872$ MeV, is very close to the sum of the masses of the $D^0$ and $\overline{D^{0}}$ mesons and decays to a $D^0$ and $\overline{D^{0}}$ were observed, giving rise to two other explanations for what the mysterious X could be: a loosely-bound “molecule” of $D^0$ and mesons, or a “tetra-quark” binding a di-quark and a di-antiquark. We also have proposed the approach to determine the nature of this state.

Hadron Spectroscopy and Interactions