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

Abstract

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 $D^0{\bar{D}}^{\ast }{}^0$, $D^{+}{D}^{\ast -}$, $J/\psi \rho$, and $J/\psi \omega$ channels. The energy-dependent decay widths of the $\rho$ and $\omega$ mesons are introduced. The $D$-${\bar{D}}^{\ast }$ interaction is taken to be consistent with a lack of the $B{\bar{B}}^{\ast }$ bound state. The coupling between the $D{\bar{D}}^{\ast }$ and $J/\psi \rho$ or the $D{\bar{D}}^{\ast }$ and $J/\psi \omega$ channels is obtained from a quark model. The $c\bar{c}$-$D{\bar{D}}^{\ast }$ 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 $J/\psi \rho$ and $J/\psi \omega$ peaks appear around the $D^0{\bar{D}}^{\ast }{}^0$ threshold. The size of the $J/\psi {\pi }^3$ peak we calculated is 1.29-2.38 times as large as that of the $J/\psi {\pi }^2$. The isospin symmetry breaking in the present model comes from the mass difference of the charged and neutral $D$ and $D^{\ast }$ 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 $c\bar{c}$-$D{\bar{D}}^{\ast }$ coupling.

33 pages, 12 figures

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