Leading twist coherent diffraction on nuclei in deep inelastic scattering at small x and nuclear shadowing

We extend the theory of leading twist nuclear shadowing to calculate leading twist nuclear diffractive parton distribution functions (nDPDFs). We observe that the quark and gluon nPDFs have different patterns of the $A$-dependence. It is found that the probability of diffraction in the quark channel increases with $A$, reaching about 30% at $x \sim 10^{-4}$ for $A \sim 200$, and weakly decreases with $Q^2$. In the gluon channel, the probability of diffraction is large for all nuclei ($\sim 40$% for heavy nuclei at $x \sim 10^{-4}$ and $Q_0^2 \sim 4$ GeV$^2$), it weakly depends on $A$ and it decreases rather fast with increasing $Q^2$ -- the probability decreases by approximately a factor of two as $Q^2$ changes from 4 GeV$^2$ to 100 GeV$^2$. We also find that nuclear shadowing breaks down Regge factorization of nDPDFs, which is satisfied experimentally in the nucleon case. All these novel effects in nDPDFs are large enough to be straightforwardly measured in ultraperipheral collisions at the LHC.