Using the leading twist approach (LTA) to nuclear shadowing, we calculate the ratios of diffractive and usual parton distributions for a heavy nucleus (Pb) and the proton, RA/p=fi/AD3/fi/A/fi/pD3/fi/p\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {R}_{A/p}=\\left({f}_{i/A}^{D(3)}/{f}_{i/A}\\right)/\\left({f}_{i/p}^{D(3)}/{f}_{i/p}\\right) $$\\end{document}, for coherent and summed (coherent plus quasi-elastic) nuclear deep-inelastic scattering. We find that RA/p ≈ 0.5 − 1 for quarks as well as for the ratio of the diffractive and total cross sections dσdiff/dMX2/σtoteA/dσdiff/dMX2/σtotep\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\left[\\left({d\\sigma}_{\ extrm{diff}}/{d M}_X^2\\right)/{\\sigma}_{\ extrm{tot}}\\right]}_{eA}/{\\left[\\left({d\\sigma}_{\ extrm{diff}}/{d M}_X^2\\right)/{\\sigma}_{\ extrm{tot}}\\right]}_{ep} $$\\end{document} and RA/p ≈ 0.5 − 1.3 for gluons in a broad range of x, including the kinematics of the Electron-Ion Collider, which reaffirms the difference from the nuclear enhancement of RA/p predicted in the gluon saturation framework. We demonstrate that the magnitude of RA/p is controlled by the cross section of the interaction of hadronic fluctuations of the virtual photon with target nucleons, which explains an enhancement of RA/p in the color dipole model and its suppression in LTA. We argue that the black disk limit corresponds to RA/p = 1 and RA/pcoh\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {R}_{A/p}^{\ extrm{coh}} $$\\end{document} = 0.86 for the summed and coherent scattering, respectively. Relying on an intuitive definition of the saturation scale, we show that the ratio of the saturation scales of a heavy nucleus and proton QsA2b/Qsp2b≈1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {Q}_{sA}^2(b)/{Q}_{sp}^2(b)\\approx 1 $$\\end{document} at small impact parameters b due to the strong leading twist nuclear shadowing and diluteness of the nuclear density.
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