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# The $X(3872)\rightarrow J/\psi \pi \gamma$ and $X(3872)\rightarrow J/\psi \pi\pi \gamma$ decays

Dec 2022

We study the $\rho$ and $\omega$ meson contribution to the radiative decays$X(3872)\rightarrow J/\psi \pi \gamma$ and $X(3872)\rightarrow J/\psi \pi\pi\gamma$. The $X(3872)\rightarrow J/\psi \pi \gamma$ is dominated by the$\omega$ meson. As for the $X(3872)\rightarrow J/\psi \pi\pi \gamma$, thecontributions of the cascade decays through the $\rho$ and $\omega$ mesons arestrongly suppressed with respect to the diagrams which proceed either throughthe $\psi(2S)$ or the three body decay of $\rho$. The branching ratios of$X(3872)\rightarrow J/\psi \pi \gamma$ and $X(3872)\rightarrow J/\psi \pi\pi\gamma$ are $(8.10^{+3.50}_{-2.88})\times10^{-3}$ and $(2.38\pm1.06)\%$, whichmay be accessible by the BESIII and LHCb Collaborations. Especailly, the$X(3872)\rightarrow J/\psi \pi \gamma$ and $X(3872)\rightarrow J/\psi\pi^+\pi^- \gamma$ decays can be employed to extract the couplings$g_{X\psi\omega}$ and $g_{X\psi\rho}$, which probe the isoscalar and isovectorcomponents of the X(3872) wave function respectively.

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