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∆E ≈

By L. Gerl, H. Stöcker and W. Greiner


There are different time scales relevant for the production of quarkonium states: 1) the time needed to produce a heavy quark pair in a hard collision, 2) the time needed for a Q ¯ Q pair to form a bound state. The production time of a Q ¯ Q pair in its rest frame is given by τp = 1. Thisis0.13fm/cforc¯cand 0.05 fm/c for b mQ ¯b. The Lorentz factor of the pair at midrapidity in the rest frame of the target is γ ≈ 10, 100 and 3000 for a Quarkonium state at SPS, RHIC and LHC energies. At SPS fixed target energies γcτp is smaller than the average internucleon distance in nuclei rNN ≈ 1.8 fm. Thus, the production of heavy quark pairs is incoherent. At RHIC the production distance of c¯c pairsisalready as large as the diameter of a gold nucleus, and for b¯b pairs cτp> 1.8 fm, but this is still small as compared to the nuclear radius. At LHC both production distances exceed the diameter of a lead nucleus by an order of magnitude. The hadronisation time tH resp. the coherence length lc of heavy Quarkonium is γ ∆M with: lc = c · tH =

Year: 2011
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