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

The X(3872) formation and decay processes in B-decay are investigated by a c (c) over bar -two-meson hybrid model. The two-meson state consists of the D-0(D) over bar*(0), D+ D*(-), J/psi rho, and J/psi omega channels. The energy-dependent decay widths of the rho and omega mesons are introduced. The D-(D) over bar* interaction is taken to be consistent with a lack of the B (B) over bar* bound state. The coupling between the D (D) over bar* and J/psi rho or the D (D) over bar* and J/psi omega channels is obtained from a quark model. The c (c) over bar -D (D) over bar* 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(D) over bar*(0) threshold. The size of the J/psi pi(3) peak that we calculated is 1.27-2.24 times as large as that of 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* 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 information on the X(3872) mass or the size of the c (c) over bar -D (D) over bar* coupling.