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The $X$(3872) formation and decay processes in the $B$-decay are investigatedby a $c\bar c$-two-meson hybrid model. The two-meson state consists of the$D^0{\bar D}^*{}^0$, $D^+D^{*-}$, $J/\psi\rho$, and $J/\psi\omega$ channels.The energy-dependent decay widths of the $\rho$ and $\omega$ mesons areintroduced. The $D$-${\bar D}^*$ interaction is taken to be consistent with alack of the $B{\bar B}^*$ bound state. The coupling between the $D{\bar D}^*$and $J/\psi\rho$ or the $D{\bar D}^*$ and $J/\psi\omega$ channels is obtainedfrom a quark model. The $c{\bar c}$-$D{\bar D}^*$ coupling is taken as aparameter to fit the $X$(3872) mass. The spectrum is calculated up to 4 GeV.  It is found that very narrow $J/\psi\rho$ and $J/\psi\omega$ peaks appeararound the $D^0{\bar D}^*{}^0$ threshold. The size of the $J/\psi\pi^3$ peak wecalculated is 1.29-2.38 times as large as that of the $J/\psi\pi^2$. Theisospin symmetry breaking in the present model comes from the mass differenceof the charged and neutral $D$ and $D^*$ mesons, which gives a sufficientlylarge isospin mixing to explain the experiments. It is also found that valuesof the ratios of the transfer strengths can give the information on the$X$(3872) mass or the size of the $c{\bar c}$-$D{\bar D}^*$ coupling.

On the origin of the narrow peak and the isospin symmetry breaking of the $X$(3872)