ar X iv : h ep - p h / 05 06 08 7 v 2 21 J ul 2 00 5 Factorization in the Production and Decay of the X ( 3872 )

Abstract The production and decay of the X(3872) are analyzed under the assumption that the X is a weakly-bound molecule of the charm mesons D0D̄∗0 and D∗0D̄0. The decays imply that the large D0D̄∗0 scattering length has an imaginary part. An effective field theory for particles with a large complex scattering length is used to derive factorization formulas for production rates and decay rates of X. If a partial width is calculated in a model with a particular value of the binding energy, the factorization formula can be used to extrapolate to other values of the binding energy and to take into account the width of the X. The factorization formulas relate the rates for production of X to those for production of D0D̄∗0 and D∗0D̄0 near threshold. They also imply that the line shape of X differs significantly from that of a Breit-Wigner resonance.