Color fluctuation approximation for multiple interactions in leading twist theory of nuclear shadowing

The leading twist theory of nuclear shadowing predicts the shadowing correction to nuclear parton distributions at small $x$ by connecting it to the leading twist hard diffraction in electron-nucleon scattering. The uncertainties of the predictions are related to the shadowing effects resulting from the interaction of the hard probe with $N \ge 3$ nucleons. We argue that the pattern of hard diffraction observed at HERA allows one to reduce these uncertainties. We develop a new approach to the treatment of these multiple interactions, which is based on the concept of the color fluctuations and accounts for the presence of both point-like and hadron-like configurations in the virtual photon wave function. Using the developed framework, we update our predictions for the leading twist nuclear shadowing in nuclear parton distributions of heavy nuclei at small $x$.