Theoretical study on the contributions of $\omega$ meson to the $X(3872)\to J/\psi {\pi }^{+}{\pi }^{-}$ and $J/\psi {\pi }^{+}{\pi }^{-}{\pi }^0$ decays

Abstract

With the newly 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. 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.

Comments: 8 pages, 3 figures