We study the property of the $X(3872)$ meson by analyzing the $B\to KD{\overline{D}}^{*}$ and $B\to KJ/\psi {\pi }^{+}{\pi }^{-}$ decay processes. The competition between the rescattering mediated through a Breit-Wigner resonance and the rescattering generated from a local $D{\overline{D}}^{*}\to D{\overline{D}}^{*}$ interaction is carefully studied through an effective Lagrangian approach. Three different fits are performed: pure Breit-Wigner case, pure $D{\overline{D}}^{*}$ molecule case with only local rescattering vertices (generated by the loop chain), and the mixed case. It is found that data supports the picture where $X(3872)$ is mainly a ($\overline{c}c$) Breit-Wigner resonance with a small contribution to the self-energy generated by $\overline{D}{D}^{*}$ final state interaction. For our optimal fit, the pole mass and width are found to be: $M_X=3871.2\pm 0.7\mathrm{MeV}$ and ${\mathrm{\Gamma }}_X=6.5\pm 1.2\mathrm{MeV}$.

• Received 14 November 2014

DOI:https://doi.org/10.1103/PhysRevD.92.034020