Higher Fock states and power counting in exclusive P -wave quarkonium decays

Exclusive processes at large momentum transfer Q factor into perturbatively calculable short-distance parts and long-distance hadronic wave functions. Usually, only contributions from the leading Fock states have to be included to leading order in 1/Q. We show that for exclusive decays of P -wave quarkonia the contribution from the next-higher Fock state |QQg〉 contributes at the same order in 1/Q. We investigate how the constituent gluon attaches to the hard process in order to form colour-singlet final-state hadrons and argue that a single additional long-distance factor is sufficient to parametrize the size of its contribution. Incorporating transverse degrees of freedom and Sudakov factors, our results are perturbatively stable in the sense that soft phase-space contributions are largely suppressed. Explicit calculations yield good agreement with data on χcJ decays into pairs of pions, kaons, and etas. We also comment on J/ψ decays into two pions. a Supported by Deutsche Forschungsgemeinschaft. b Heisenberg Fellow. CERN–TH/97–64 April 1997