Theoretical study on the contributions of $ω$ meson to the $X(3872) \to J/ψπ^+π^-$ and $J/ψπ^+π^-π^0$ decays

Abstract

With the newly measurements of $X(3872) \to J/ψπ^+π^-$ from LHCb Collaboration, in addition to the dominant contribution from the $ρ^0$ meson, we perform a theoretical study on the contribution of $ω$ meson in the $X(3872) \to J/ψπ^+π^-$ and $X(3872)\to J/ψπ^+π^-π^0$ processes. It is found that the recent experimental measurements on the $π^+ π^-$ invariant mass distributions can be well reproduced, and the ratio of the couplings between $X(3872) \to J/ψρ^0$ and $X(3872) \to J/ψω$ is also evaluated. Within the parameters extracted from the $π^+ π^-$ invariant mass distributions of the $X(3872) \to J/ψπ^+π^-$ process, the branching fractions of the $X(3872) \to J/ψω$ channel relative to that of the $X(3872) \to J/ψπ^+π^-π^0$ channel and the $π^+ π^- π^0$ invariant mass distributions of the $X(3872) \to J/ψπ^+π^-π^0$ decay are calculated, which gives a hint for the further high-statistic experiment.