Search for promptly produced heavy quarkonium states in hadronic Z decays

A search has been made for direct production of heavy quarkonium states in more than 3 million hadronic Z^{0} decays in the 1991-1994 DELPHI data. Prompt J/\psi, \psi(2S) and \Upsilon candidates have been searched for through their leptonic decay modes using criteria based on the kinematics and decay vertex positions. New upper limits are set at the 90 \% confidence level for {Br( Z^0 \rightarrow \left( Q \bar{Q} \right) X ) / Br( Z^0 \rightarrow \mbox{hadrons})} for various strong production mechanisms of J/\psi and \Upsilon; these range down to 0.9 \times 10^{-4}. The limits are set in the presence of a small excess (\sim 1 \% statistical probability of a background fluctuation) in the sum of candidates from prompt J/\psi, \psi(2S), \Upsilon(1S), \Upsilon(2S) and \Upsilon(3S) relative to the estimated background.