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, $R_{ A/p}=(f_{ i/A}^{ D(3)}/f_{ i/A})/(f_{ i/p}^{ D(3)}/f_{ i/p})$, for coherent and summed (coherent plus quasi-elastic) nuclear deep-inelastic scattering. We find that $R_{ A/p} \approx 0.5-1$ for quarks as well as for the ratio of the diffractive and total cross sections $[(d\sigma_{ \rm diff}/dM_X^2)/\sigma_{ \rm tot}]_{ eA}/[(d\sigma_{ \rm diff}/dM_X^2)/\sigma_{ \rm tot}]_{ ep}$ and $R_{ A/p} \approx 0.5-1.3$ 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 $R_{ A/p}$ predicted in the gluon saturation framework. We demonstrate that the magnitude of $R_{ A/p}$ is controlled by the cross section of the interaction of hadronic fluctuations of the virtual photon with target nucleons, which explains an enhancement of $R_{ A/p}$ in the color dipole model and its suppression in LTA. We argue that the black disk limit corresponds to $R_{ A/p}=1$ and $R^{ \rm coh}_{ A/p}=0.86$ 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 $Q_{ sA}^2(b)/Q_{ sp}^2(b) \approx 1$ at small impact parameters $b$ due to the strong leading twist nuclear shadowing and diluteness of the nuclear density.
Categories: hep-ph hep-ex nucl-ex