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 two 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 cursive Greek chi ≤ 10^-3, Q₀ = 2GeV is ∼ 50mb. This is three times larger than in the quark sector and suggests that applicability of DGLAP approximation requires significantly larger Q₀ in the gluon sector. We use this information on diffraction to estimate the higher order shadowing terms due to the photon interactions with N ≥ 3 nucleons which are important for the scattering of heavy nuclei and to calculate nuclear shadowing and Q² dependence of gluon densities. For the heavy nuclei the amount of the gluon shadowing: G_A(cursive Greek chi, Q²₀)/AGN(cursive Greek chi, Q²₀)_{|cursive Greek chi≤10-3} ∼ 0.25 - 0.4 is sensitive to the probability of the small size configurations within wave function of the gluon "partonometer" at the Q₀ scale. At this scale for A ∼ 200 the nonperturbative contribution to the gluon density is reduced by a factor of 4 - 5 at cursive Greek chi ≤ 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/ψ production off A ≥ 12 nuclei at √s ≥ 70 GeV is strongly reduced as compared to the naive color transparency expectations. The Gribov black body limit for F_2A(cursive Greek chi, Q²) 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.