Production of the X(3872) in B Meson Decay by the Coalescence of Charm Mesons

If the recently-discovered charmonium state X(3872) is a loosely-bound S-wave molecule of the charm mesons \bar D^0 D^{*0} or \bar D^{*0} D^0, it can be produced in B meson decay by the coalescence of charm mesons. If this coalescence mechanism dominates, the ratio of the differential rate for B^+ \to \bar D^0 D^{*0} K^+ near the \bar D^0 D^{*0} threshold and the rate for B^+ \to X K^+ is a function of the \bar D^0 D^{*0} invariant mass and hadron masses only. The identification of the X(3872) as a \bar D^0 D^{*0}/\bar D^{*0} D^0 molecule can be confirmed by observing an enhancement in the \bar D^0 D^{*0} invariant mass distribution near the threshold. An estimate of the branching fraction for B^+ \to X K^+ is consistent with observations if X has quantum numbers J^{PC} = 1^{++} and if J/\psi \pi^+ \pi^- is one of its major decay modes.