Isospin breaking, coupled-channel effects, and X(3872)

We reinvestigate the possibility of X(3872) as a D (D) over bar* molecule with J(PC) = 1(++) within the framework of both the one-pion-exchange model and the one-boson-exchange model. After careful treatment of the S-D wave mixing, the mass difference between the neutral and charged D((D) over bar)* mesons and the coupling of the D (D) over bar* pair to D*(D) over bar*, a loosely bound molecular state X(3872) emerges quite naturally with large isospin violation in its flavor wave function. For example, the isovector component is 26.24% if the binding energy is 0.30 MeV, where the isospin breaking effect is amplified by the tiny binding energy. After taking into account the phase space difference and assuming the 3 pi and 2 pi come from a virtual omega and rho meson respectively, we obtain the ratio of these two hidden-charm decay modes: B(X(3872) -> pi(+) pi(-) pi(-) pi(0) J/psi)/B(X(3872) -> pi(+) pi(-) J/psi = 0.42 for the binding energy being 0.3 MeV, which is consistent with the experimental value.