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

Jan Bolz; Peter Kroll; Gerhard A. Schuler

doi:doi:10.1007/s100529800716

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2022 Impact factor 4.4

Particles and Fields

Eur. Phys. J. C 2, 705-719
DOI 10.1007/s100529800716

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

Jan Bolz¹ - Peter Kroll¹ - Gerhard A. Schuler²

¹ Fachbereich Physik, Universität Wuppertal, D-42097 Wuppertal, Germany (e-mail: kroll@theorie.physik.uni-wuppertal.de)
² Theory Division, CERN, CH-1211 Geneva 23, Switzerland (e-mail: Gerhard.Schuler@cern.ch)

Received: 25 April 1997 / Published online: 20 February 1998

Abstract
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 $\vert\mathrm{Q}\overline{\mathrm{Q}}\mathrm{g}\rangle$ 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 $\chi_{\c J}$ decays into pairs of pions, kaons, and etas. We also comment on $J/\psi$ decays into two pions.