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 cc-bar–two-meson hybrid model. The two-meson state consists of the D⁰D-bar^∗0, D⁺D^∗−, J / ψρ, and J / ψω channels. The energy-dependent decay widths of the ρ and ω mesons are introduced. The D–D-bar^∗ interaction is taken to be consistent with a lack of the BB-bar^∗ bound state. The coupling between the DD-bar^∗ and J / ψρ or the DD-bar^∗ and J / ψω channels is obtained from a quark model. The cc-bar–DD-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 / ψρ and J / ψω peaks appear around the D⁰D-bar^∗0 threshold. The size of the J / ψπ³ peak that we calculated is 1.27–2.24 times as large as that of J / ψπ². 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 cc-bar–DD-bar^∗ coupling