Covariant formalism for F-wave quarkonium production and annihilation: Application to 3FJ→gg decays

We derive a covariant formalism to describe F-wave quarkonium production and annihilation processes in the context of nonrelativistic potential models. We apply it to evaluate the decay rates for the processes 3FJ→gg (where J=2,3,4). Such a calculation may be useful in evaluating the prospects of producing the predicted narrow F states in the Υ system. Related predictions for the two-photon widths of such F states could also be used in testing the validity of nonrelativistic potential models in the light quark system. We also explicitly calculate the two-photon decay width of the 1G4 state using similar techniques to compare to a recent general calculation