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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/ψππ and J/ψπππ 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/ψρ, and J/ψω. The effects of the ρ and ω 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/ψρ and J/ψω peaks appear very close to the D0Dbar*0 threshold for a wide range of variation in the parameter sets. The size of the J/ψρ peak is almost the same as that of J/ψω, which is consistent with the experiments. The large width of the ρ meson makes the originally small isospin violation by about five times larger.