A Refined Analysis on the $X(3872)$ Resonance

We study the property of the $X(3872)$ meson by analyzing the $B\to K D\bar D^*$and$B\to K J/\psi \pi^+\pi^-$ decay processes. The competition between the rescattering mediated through a Breit-Wigner resonance and the rescattering generated from a local $D{\bar{D}}^{\ast }\to D{\bar{D}}^{\ast }$ interaction is carefully studied through an effective lagrangian approach. Three different fits are performed: pure Breit-Wigner case, pure $D{\bar{D}}^{\ast }$ 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 ($\bar cc$) Breit-Wigner resonance with a small contribution to the self-energy generated by $\bar{D}{D}^{\ast }$ final state interaction. For our optimal fit, the pole mass and width are found to be: $M_X=3871.2\pm 0.7$MeV and ${\mathrm{\Gamma }}_X=6.5\pm 1.2$MeV.