The J/{\psi} {\omega} Decay Channel of the X(3872) Charm Meson Molecule

Analyses of the J/{\psi} {\pi}+ {\pi}- 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 \pi+ \pi- \pi 0 invariant mass distribution in the J/{\psi} \pi+ \pi- \pi 0 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/{\psi} {\omega}, the proximity of the J/{\psi} {\omega} threshold to D^* Dbar thresholds and the narrow width of the {\omega} suggest that the effects of scattering between J/{\psi} {\omega} and charm meson pairs could be significant. We derive invariant mass distributions for J/{\psi} \pi+ \pi- and \pi+ \pi- \pi 0 that take into account S-wave scattering between the D^{*0} Dbar^0, D^{*+} D^-, and J/{\psi} {\omega} 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 \pi+ \pi- {\pi} 0 invariant mass distribution.