Hadronic decays of the X(3872) to χcJ in effective field theory

The decays of the X(3872) to P-wave quarkonia are calculated under the assumption that it is a shallow bound state of neutral charmed mesons. The X(3872) is described using an effective theory of nonrelativistic D mesons and pions (X-EFT). We calculate X(3872) decays by first matching heavy hadron chiral perturbation theory (HHχPT) amplitudes for D0D̄ *0→χcJ(π0,ππ) onto local operators in X-EFT, and then using these operators to calculate the X(3872) decays. This procedure reproduces the factorization theorems for X(3872) decays to conventional quarkonia previously derived using the operator product expansion. For single pion decays, we find nontrivial dependence on the pion energy from HHχPT diagrams with virtual D mesons. This nontrivial energy dependence can potentially modify heavy-quark symmetry predictions for the relative sizes of decay rates. At leading order, decays to final states with two pions are dominated by the final state χc1π0π0, with a branching fraction just below that for the decay to χc1π0. Decays to all other final states with two pions are highly suppressed.