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

Abstract

We re-investigate the possibility of X(3872) as a $D{\bar{D}}^{\ast }$ molecule with $J^{PC}=1^{++}$ within the framework of both the one-pion-exchange (OPE) model and the one-boson-exchange (OBE) model. After careful treatment of the S-D wave mixing, the mass difference between the neutral and charged $D(D^{\ast })$ mesons and the coupling of the $D(D^{\ast })$ pair to $D^{\ast }{\bar{D}}^{\ast }$, 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: $\mathcal{B}(X(3872)\to {\pi }^{+}{\pi }^{-}{\pi }^{0}J/\psi )/\mathcal{B}(X(3872)\to {\pi }^{+}{\pi }^{-}J/\psi )=0.42$ for the binding energy being 0.3 MeV, which is consistent with the experimental value.

published in Phys. Rev. D

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