Hadronic Decays of the X(3872) to chi_{cJ} in Effective Field Theory

TL;DR

This paper develops an effective field theory approach to calculate the hadronic decays of the X(3872) to P-wave quarkonia, revealing nontrivial pion energy dependence and specific decay rate hierarchies.

Contribution

It introduces a novel effective theory framework (X-EFT) for analyzing X(3872) decays, connecting heavy hadron chiral perturbation theory with decay calculations, and reproduces factorization theorems for these processes.

Findings

Decay to chi_{c1} + 2 pions dominates among two-pion final states.

Nontrivial pion energy dependence affects heavy quark symmetry predictions.

Decays to other two-pion states are highly suppressed.

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 (HHchiPT) amplitudes for D^0 bar{D}^{*0} -> chi_{cJ} + (pi^0,pi+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 HHchiPT 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 chi_{c1} + pi^0 + pi^0, with a branching fraction just below that for the decay to chi_{c1} + pi^0. Decays to all other final states with two pions are highly suppressed.