Paper detail

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

The $X$(3872) formation and decay processes in the $B$-decay are investigated by a $c\bar c$-two-meson hybrid model. The two-meson state consists of the $D^0{\bar D}^*{}^0$, $D^+D^{*-}$, $J/ψρ$, and $J/ψω$ channels. The energy-dependent decay widths of the $ρ$ and $ω$ mesons are introduced. The $D$-${\bar D}^*$ interaction is taken to be consistent with a lack of the $B{\bar B}^*$ bound state. The coupling between the $D{\bar D}^*$ and $J/ψρ$ or the $D{\bar D}^*$ and $J/ψω$ channels is obtained from a quark model. The $c{\bar c}$-$D{\bar D}^*$ coupling is taken as a parameter to fit the $X$(3872) mass. The spectrum is calculated up to 4 GeV. It is found that very narrow $J/ψρ$ and $J/ψω$ peaks appear around the $D^0{\bar D}^*{}^0$ threshold. The size of the $J/ψπ^3$ peak we calculated is 1.29-2.38 times as large as that of the $J/ψπ^2$. The isospin symmetry breaking in the present model comes from the mass difference of the charged and neutral $D$ and $D^*$ mesons, which gives a sufficiently large isospin mixing to explain the experiments. It is also found that values of 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.