We argue that the suppression of high p_t hadrons discovered recently in heavy ion collisions at RHIC may be a consequence of saturation in the Color Glass Condensate. We qualitatively and semi-quantitatively describe the data, in particular, the dependence upon the number of nucleon participants. We show that if parton saturation sets in at sufficiently small energy, then in nucleus-nucleus collisions at RHIC and LHC energies the cross sections of semi-hard processes should scale approximately with the number of participants, N_{part}. Our results provide a possible explanation of both the absence of apparent jet quenching at SPS energies and its presence at RHIC. Under the same assumption we predict that in semi–central and central pA (dA) collisions at collider energies the dependence of semi–hard processes on the number of participating nucleons of the nucleus will change to \sim (N_{part}^A)^{1/2}. The forthcoming data on dA collisions will provide a crucial test of this description.

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