Heavy quarkonium production and electromagnetic fragmentation in exclusive rare W-boson decays

We have updated theoretical studies of heavy vector quarkonium production, including [Formula: see text], [Formula: see text] and [Formula: see text], in the exclusive W-boson decays. Particularly, in the standard model the branching fraction of [Formula: see text] ([Formula: see text] or [Formula: see text]) has been predicted to be about [Formula: see text], which is substantially larger than those of two-body hadronic radiative W decays. Thus in the future high-luminosity experimental facilities, this rare channel could be very useful to search for the exclusive W-boson decays containing the hadronic final state. Furthermore, the surprisingly large decay rate can be explained by an electromagnetic fragmentation formalism. We have analyzed the lepton fragmentation and the photon fragmentation processes, and calculated their contributions to the differential decay rate of [Formula: see text] in the fragmentation limit. It is found that the fragmentation contribution agrees well with the result from the full calculation.