With the new measurements of $X(3872)\to J/\psi {\pi }^{+}{\pi }^{-}$ from LHCb Collaboration, in addition to the dominant contribution from the ${\rho }^0$ meson, we perform a theoretical study on the contribution of $\omega$ meson in the $X(3872)\to J/\psi {\pi }^{+}{\pi }^{-}$ and $X(3872)\to J/\psi {\pi }^{+}{\pi }^{-}{\pi }^0$ processes. For the $X(3872)\to J/\psi {\pi }^{+}{\pi }^{-}$ decay, in addition to the main contribution from ${\rho }^0$ meson, we consider also the $X(3872)J/\psi \omega$ coupling with $\omega$ meson decaying directly into ${\pi }^{+}{\pi }^{-}$. It is found that the recent experimental measurements on the ${\pi }^{+}{\pi }^{-}$ invariant mass distributions can be well reproduced, and the ratio of the couplings between $X(3872)\to J/\psi {\rho }^0$ and $X(3872)\to J/\psi \omega$ is also evaluated. Within the parameters extracted from the ${\pi }^{+}{\pi }^{-}$ invariant mass distributions of the $X(3872)\to J/\psi {\pi }^{+}{\pi }^{-}$ process, the branching fractions of the $X(3872)\to J/\psi \omega$ channel relative to that of the $X(3872)\to J/\psi {\pi }^{+}{\pi }^{-}{\pi }^0$ channel and the ${\pi }^{+}{\pi }^{-}{\pi }^0$ invariant mass distributions of the $X(3872)\to J/\psi {\pi }^{+}{\pi }^{-}{\pi }^0$ decay are calculated, which gives a hint for the further high-statistic experiment.

• Received 4 July 2022
• Accepted 13 September 2022

DOI:https://doi.org/10.1103/PhysRevD.106.056022

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Published by the American Physical Society