Electromagnetic production of quarkonium in Z0 decay.

The decay Z → Q+ ll, where Q is a J = 1 quarkonium state, has a very clean final state, which should make it easy to detect. The branching ratio of this mode is greater than 10 for ρ, φ, and ψ, indicating that these processes may be detectable at LEP. Well over one million Z decay events have been accumulated at LEP, and further improvements are expected. This makes it possible to investigate rare decays of the Zboson with branching ratios as small as 10. Processes involving the production of the charmonium state J/ψ that have been considered previously are Z → ψ+gg, Z → ψ+cc̄, and Z → ψ+γ [1, 2, 3, 4, 5]. The production of a lepton pair and a ψ from a Z is another example of such a process. This decay is especially interesting because of its clean final state, and its relatively large branching ratio. In this paper the rates for Z → Q + ll, where Q is a J = 1 quarkonium state, are calculated to leading order in α in a model independent way. The branching ratios for ρ, φ, and ψ are greater than 10 which indicates that these processes may be detectable at LEP. The specific decay of Z → ψ + ll is calculated first, and later generalized to other quarkonium states with J = 1. The decay rate is Γ(Z → ψ + ll) = 1 2MZ ∫ [dk][dk′][dp] (2π)δ(Z − k − k′ − p) 1 3 ∑ |A|, (1) where k, k, p and Z are the 4-momenta of the l, l, ψ, and Z, and [dp] = dp/(16πp0) is the Lorentz invariant phase space element. The two Feynman diagrams that contribute to the amplitude A at leading order in α are shown in figure 1. Neglecting lepton mass, squaring the amplitude, averaging over initial spins, and summing over final spins gives