Comprehending Isospin breaking effects of $X(3872)$ in a Friedrichs-model-like scheme

Abstract

Recently, we have shown that the $X(3872)$ state can be naturally generated as a bound state by incorporating the hadron interactions into the Godfrey-Isgur quark model using the Friedrichs-like model combined with the QPC model, in which the wave function for the $X(3872)$ as a combination of the bare $c\bar{c}$ state and the continuum states can also be obtained. Under this scheme, we now investigate the isospin breaking effect of $X(3872)$ in its decays to $J/\psi {\pi }^{+}{\pi }^{-}$ and $J/\psi {\pi }^{+}{\pi }^{-}{\pi }^0$. By Considering its dominant continuum parts coupling to $J/\psi \rho$ and $J/\psi \omega$ through the quark rearrangement process, one could obtain the reasonable ratio of $\mathcal{B}(X(3872)\to J/\psi {\pi }^{+}{\pi }^{-}{\pi }^0)/\mathcal{B}(X(3872)\to J/\psi {\pi }^{+}{\pi }^{-})\simeq (0.58\sim 0.92)$. It is also shown that the $\bar{D}{D}^{\ast }$ invariant mass distributions in the $B\to \bar{D}{D}^{\ast }K$ decays could be understood qualitatively at the same time. This scheme may provide more insight to understand the enigmatic nature of the $X(3872)$ state.

13 pages, 4 figures

References in corpus (13)

• Multiquark Resonances
• Higher Charmonia and X,Y,Z states with Screened Potential
• X(3872) and Other Possible Heavy Molecular States
• Pion Interactions in the X(3872)
• Is the X(3872) Production Cross Section at Tevatron Compatible with a Hadron Molecule Interpretation?
• Is X(3872) {\sl Really} a Molecular State?
• Isospin breaking effects in the X(3872) resonance
• Line Shapes of the X(3872)
• Comprehensive analysis of the wave function of a hadronic resonance and its compositeness
• Isospin breaking, coupled-channel effects, and X(3872)
• Decays of the X(3872) and ${\chi }_{c1}(2P)$ charmonium
• Ambiversion of X(3872)
• Virtual states and generalized completeness relation in the Friedrichs Model

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