Decays of the X(3872) into J/psi and Light Hadrons

If the X(3872) is a loosely-bound molecule of the charm mesons D^0 \bar D^{*0} and D^{*0} \bar D^0, it can decay through the decay of a constituent in a hadronic channel with a nearby threshold, such as J/\psi \omega or J/\psi \rho. The differential decay rates of the X into J/\psi \pi^+\pi^-, J/\psi \pi^+\pi^-\pi^0, J/\psi \pi^0 \gamma, and J/\psi \gamma are calculated in terms of X J/\psi \rho and X J/\psi \omega coupling constants using an effective lagrangian that reproduces the decay rates of the \omega and the \rho. The dependence of the coupling constants on the binding energy and the total width of the X is determined by a factorization formula. Results from a model by Swanson are used to predict the partial width of X into J/\psi \pi^+\pi^-\pi^0 as a function of the binding energy and the total width of the X.