J/Ψ production in an equilibrating partonic system

Any color singlet or octet cc-bar pair is created at short distances and then expands to a full size of J/Ψ. Such a dynamical evolution process is included here in calculations for the J/Ψ number distribution as a function of transverse momentum and rapidity in central Au-Au collisions at both RHIC and LHC energies. The cc-bar pairs are produced in the initial collision and in the partonic system during the prethermal and thermal stages through the partonic channels ab → cc-bar[2S+1LJ] and ab → cc-bar[2S+1LJ]x, and then they dissociate in the latter two stages. Dissociation of cc-bar in the medium occurs via two reactions: (a) color singlet cc-bar plus a gluon turns to color octet cc-bar, (b) color octet cc-bar plus a gluon persists as color octet. There are modest yields of cc-bar in the prethermal stage at RHIC energy and through the reactions ab → cc-bar[2S+1LJ] at LHC energy for partons with large average momentum in the prethermal stage at both collider energies and in the thermal stage at LHC energy. Production from the partonic system competes with the suppression of the initial yield in the deconfined medium. Consequently, a bulge within -1.5 < y < 1.5 has been found for the J/Ψ number distribution and the ratio of J/Ψ number distributions for Au-Au collisions to nucleon-nucleon collisions. This bulge is caused by the partonic system and is thus an indicator of a deconfined partonic medium. Based on this result we suggest the rapidity region worth measuring in future experiments at RHIC and LHC to be -3 < y < 3