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.

中文翻译：

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ω介子对X(3872)→J/ψπ+π−和J/ψπ+π−π0衰变贡献的理论研究

随着新的测量$X(3872)\to Ĵ/\psi {\pi }^{+}{\pi }^{-}$来自 LHCb Collaboration，除了来自 LHCb 的主要贡献${\rho }^0$介子，我们对介子的贡献进行了理论研究$\omega$介子在$X(3872)\to Ĵ/\psi {\pi }^{+}{\pi }^{-}$和$X(3872)\to Ĵ/\psi {\pi }^{+}{\pi }^{-}{\pi }^0$过程。为了$X(3872)\to Ĵ/\psi {\pi }^{+}{\pi }^{-}$衰变，除了主要贡献来自${\rho }^0$介子，我们也考虑$X(3872)Ĵ/\psi \omega$与耦合$\omega$介子直接衰变为${\pi }^{+}{\pi }^{-}$. 发现最近的实验测量${\pi }^{+}{\pi }^{-}$可以很好地再现不变的质量分布，并且之间的耦合比$X(3872)\to Ĵ/\psi {\rho }^0$和$X(3872)\to Ĵ/\psi \omega$也被评估。在从参数中提取的${\pi }^{+}{\pi }^{-}$的不变质量分布$X(3872)\to Ĵ/\psi {\pi }^{+}{\pi }^{-}$过程中，分支部分的$X(3872)\to Ĵ/\psi \omega$通道相对于$X(3872)\to Ĵ/\psi {\pi }^{+}{\pi }^{-}{\pi }^0$频道和${\pi }^{+}{\pi }^{-}{\pi }^0$的不变质量分布$X(3872)\to Ĵ/\psi {\pi }^{+}{\pi }^{-}{\pi }^0$衰减被计算出来，这为进一步的高统计实验提供了提示。