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 D0Dbar*0, 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. 
Sachiko Takeuchi, Kiyotaka Shimizu and Makoto Takizawa
hep-ph