Diffraction at HERA, color opacity and nuclear shadowing in DIS off nuclei

The QCD factorization theorem for diffractive processes in DIS is used to derive formulae for the leading twist contribution to the nuclear shadowing of parton distributions in the low thickness limit (due to the coherent projectile (photon) interactions with tare nucleons). Based on the current analyzes of diffraction at HERA we find that the average strength of the interactions which govern diffraction in the gluon sector at x less than or equal to 10(-3), Q(0) = 2GeV is similar to 50mb. This is three times larger than in the quark sector and suggests that applicability of DGLAP approximation requires significantly larger Q(0) in the gluon sector. We use this information on diffraction to estimate the higher order shadowing terms due to the photon interactions with N greater than or equal to 3 nucleons which are important for the scattering of heavy nuclei and to calculate nuclear shadowing and Q(2) dependence of gluon densities. For the heavy nuclei the amount of the gluon shadowing: G(A)(x, Q(0)(2))/AG(N) (x, Q(0)(2))\(x less than or equal to 10-3) similar to 0.25 - 0.4 is sensitive to the probability of the small size configurations within wave function of the gluon "partonometer" at the Q(0) scale. At this scale for A similar to 200 the nonperturbative contribution to the gluon density is reduced by a factor of 4 - 5 at x less than or equal to 10(-3) unmasking PQCD physics in the gluon distribution of heavy nuclei. We point out that the shadowing of this magnitude would strongly modify the first stage of the heavy ion collisions at the LHC energies, and also would lead to large color opacity effects in eA collisions at HERA. energies. In particular, the leading twist contribution to the cross section of the coherent J/psi, production off A 2 greater than or equal to 12 nuclei at root s greater than or equal to 70 GeV is strongly reduced as compared to the naive color transparency expectations. The Gribov black body limit for F-2A(x, Q(2)) is extended to the case of the gluon distributions in nuclei and shown to be relevant for the HERA kinematics of eA collisions. Properties of the final states are also briefly discussed.