Operator Product Expansion in the Production and Decay of the X(3872)

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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.