Production of theX(3872)inB-MesonDecay 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 ${\overline{D}}^0{D}^{*0}$ or ${\overline{D}}^{*0}{D}^0$, 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 $B^{+}\to {\overline{D}}^0{D}^{*0}{K}^{+}$ near the ${\overline{D}}^0{D}^{*0}$ threshold and the rate for $B^{+}\to X{K}^{+}$ is a function of the ${\overline{D}}^0{D}^{*0}$ invariant mass and hadron masses only. The identification of the $X(3872)$ as a ${\overline{D}}^0{D}^{*0}$/${\overline{D}}^{*0}{D}^0$ molecule can be confirmed by observing an enhancement in the ${\overline{D}}^0{D}^{*0}$ 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.