Leading twist nuclear shadowing, nuclear generalized parton distributions, and nuclear deeply virtual Compton scattering at small<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>x</mml:mi></mml:mrow></mml:math>

We generalize the leading twist theory of nuclear shadowing and calculate quark and gluon generalized parton distributions (GPDs) of spinless nuclei. We predict very large nuclear shadowing for nuclear GPDs. In the limit of the purely transverse momentum transfer, our nuclear GPDs become impact-parameter-dependent nuclear parton distribution functions (PDFs). Nuclear shadowing induces nontrivial correlations between the impact parameter $b$ and the light-cone fraction $x$. We make predictions for the deeply virtual Compton scattering (DVCS) amplitude and the DVCS cross section on $^{208}\mathrm{Pb}$ at high energies. We calculate the cross section of the Bethe-Heitler (BH) process and address the issue of the extraction of the DVCS signal from the $eA\ensuremath{\rightarrow}e\ensuremath{\gamma}A$ cross section. We find that the $eA\ensuremath{\rightarrow}e\ensuremath{\gamma}A$ differential cross section is dominated by DVCS at the momentum transfer $t$ near the minima of the nuclear form factor. We also find that nuclear shadowing leads to dramatic oscillations of the DVCS beam-spin asymmetry, ${A}_{\mathit{LU}}$, as a function of $t$. The position of the points where ${A}_{\mathit{LU}}$ changes sign is directly related to the magnitude of nuclear shadowing.

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