Charmonium and meson-molecule hybrid tetraquarks - Vector meson width and the isospin breaking in the X(3872) decay

In the X(3872) decay, both of the J/\psi\pi\pi\ and J/\psi\pi\pi\pi
branching fractions are observed experimentally, and their sizes are comparable to each other. In order to clarify the mechanism to cause such a large isospin violation, we investigate X(3872) employing a model of coupled-channel two-meson scattering with a ccbar core. The two-meson states consist of D0Dbar0, D+Dbar-, J/\psi\rho, and J/\psi\omega. The effects of the \rho\ and \omega\ meson width are also taken into account. We calculate the transfer strength from the ccbar core to the final two-meson states. It is found that very narrow J/\psi\rho\ and J/\psi\omega\ peaks appear very close to the D0Dbar*0 threshold for a wide range of variation in the parameter sets. The size of the J/\psi\rho\ peak is almost the same as that of J/\psi\omega, which is consistent with the experiments. The large width of the \rho\ meson makes the originally small isospin violation by about five times larger.