  The X(3872) seems to be a weakly-bound hadronic molecule whose constituents
are two charm mesons. Its binding energy is much smaller than all the other
energy scales in QCD. This separation of scales can be exploited through
factorization formulas for production and decay rates of the X. In a low-energy
effective field theory for the constituents of the X, the factorization
formulas can be derived using the operator product expansion. The derivations
are carried out explicitly for the simplest effective theory in which the
constituents interact through a contact interaction that produces a large
scattering length. The long-distance factors in the operator product expansions
for various observables are calculated nonperturbatively in the interaction
strength of the contact interaction. After renormalization of the coupling
constant, all remaining ultraviolet divergences can be absorbed into the
short-distance factors in the operator product expansions.
