Production of the X(3870) at the Upsilon(4S) by the Coalescence of Charm Mesons

If the recently-discovered charmonium state X(3870) is a loosely-bound molecule of the charm mesons D^0 and \bar D^{*0} or \bar D^0 and D^{*0}, it can be produced in e^+ e^- annihilation at the \Upsilon(4S) 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 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). 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 the B factories.