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The J/ψ ω Decay Channel of the X(3872) Charm Meson Molecule

Analyses of the J/ψ π+ π- decay channel of the X(3872) resonance by the CDF, Belle, and LHCb collaborations have established its J^{PC} quantum numbers as 1^{++}. An analysis of the π+ π- π0 invariant mass distribution in the J/ψ π+ π- π0 decay channel by the Babar collaboration indicated a preference for 2^{-+} over 1^{++}. We point out that a proper evaluation of the chi^2 in that analysis increases the probability for 1^{++} from 7.1% to about 18.7%. In the case of quantum numbers 1^{++}, where the X has an S-wave coupling to J/ψ ω, the proximity of the J/ψ ω threshold to D^* Dbar thresholds and the narrow width of the ω suggest that the effects of scattering between J/ψ ω and charm meson pairs could be significant. We derive invariant mass distributions for J/ψ π+ π- and π+ π- π0 that take into account S-wave scattering between the D^{*0} Dbar^0, D^{*+} D^-, and J/ψ ω channels. We also analyze the effects of scattering through the chi_{c1}(2P) charmonium resonance. We find that scattering effects are unable to produce significant changes in the shape of the π+ π- π 0 invariant mass distribution.