Coherence Phenomena in Charmonium Production off Nuclei at the Energies of RHIC and LHC

In the energy range of RHIC and LHC the mechanisms of nuclear suppression of charmonia are expected to be strikingly different from what is known for the energy of the SPS. One cannot think any more of charmonium produced on a bound nucleon which then attenuates as it passes through the rest of the nucleus. The coherence length of charmonium production substantially exceeds the nuclear radius in the new energy range. Therefore the production amplitudes on different nucleons, rather than the cross sections, add up and interfere, i.e. shadowing is at work. So far no theoretical tool has been available to calculate nuclear effects for charmonium production in this energy regime. We develop a light-cone Green function formalism which incorporates the effects of the coherence of the production amplitudes and of charmonium wave function formation, and is the central result of this paper. We found a substantial deviation from QCD factorization, namely, gluon shadowing is much stronger for charmonium production than it is in DIS. We predict for nuclear effects $x_2$ scaling which is violated at lower energies by initial state energy loss which must be also included in order to compare with available data. In this paper only the indirect J/Psi originating from decay of P-wave charmonia are considered. The calculated x_F-dependence of J/Psi nuclear suppression is in a good accord with data. We predict a dramatic variation of nuclear suppression with x_F in pA and a peculiar peak at x_F=0 in AA collisions at RHIC.