Hadronic decays of theX(3872)toχcJin effective field theory

Abstract

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 ($\mathrm{HH}\ensuremath{\chi}\mathrm{PT}$) amplitudes for ${D}^{0}{\overline{D}}^{*0}\ensuremath{\rightarrow}{\ensuremath{\chi}}_{cJ}({\ensuremath{\pi}}^{0},\ensuremath{\pi}\ensuremath{\pi})$ 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 $\mathrm{HH}\ensuremath{\chi}\mathrm{PT}$ 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 ${\ensuremath{\chi}}_{c1}{\ensuremath{\pi}}^{0}{\ensuremath{\pi}}^{0}$, with a branching fraction just below that for the decay to ${\ensuremath{\chi}}_{c1}{\ensuremath{\pi}}^{0}$. Decays to all other final states with two pions are highly suppressed.