If the recently discovered charmonium state $X\left(3870\right)\mathrm{}$ is a loosely bound molecule of the charm mesons $D^0$ and $D^{*0}$ or $D^0$ and $D^{*0},$ it can be produced in $e^{+}{e}^{-}$ annihilation at the ${\rm Y}\mathrm{}\left(4S\right)\mathrm{}$ resonance by the coalescence of charm mesons produced in the decays of $B^{+}$ and $B^{-}$ mesons. Remarkably, in the case of 2-body decays of the B mesons, the leading contribution to the coalescence probability depends only on the hadron masses and on the width and branching fractions of the B meson. As the binding energy $E_b$ of the molecule goes to zero, the coalescence probability scales as $E_b^{1/2}\log {(E}_b).\mathrm{}$ Unfortunately, the coalescence probability is also suppressed by two powers of the ratio of the width to the mass of the B meson, and is therefore many orders of magnitude too small to be observed in current experiments at B factories.

• Received 17 February 2004

DOI:https://doi.org/10.1103/PhysRevD.69.114012