Statistical properties of partonic configurations and diffractive dissociation in high-energy electron-nucleus scattering

In this thesis, we study the detailed partonic content of the quantum states of a quark-antiquark color dipole subject to high-energy evolution, which are represented by a set of dipoles generated by a stochastic binary branching process, in the scattering off a large nucleus, and produce predictions for diffractive dissociation in electron-ion collisions, based on the dipole picture of QCD. Our main results are as follows. First, the scattering events of a color dipole, when parameters are set in such a way that the total cross section is small, are triggered by rare partonic fluctuations, which look different as seen from different reference frames. It turns out that the freedom to select a frame allows to deduce an asymptotic expression for the rapidity distribution of the first branching of the slowest parent dipole of the set of those which scatter. In another aspect, such study implies the importance of the characterization of particle distribution in the frontier region in the states generated by the QCD dipole branching, and more generally, by any one-dimensional branching random walk model. To this aim, we develop a Monte Carlo algorithm to generate the frontier region of a branching random walk. Furthermore, we are able to calculate the diffractive cross section demanding a minimal rapidity gap $Y_0$ and the distribution of rapidity gaps $Y_{gap}$ in the diffractive dissociation of a small dipole off a large nucleus, in a well-defined parametric region. They are the asymptotic solutions to the so-called Kovchegov-Levin equation, which describes the diffractive dissociation at high energy. Finally, we present predictions for the rapidity gap distributionin realistic kinematics of future electron-ion machines, based on the numerical solutions of the original Kovchegov-Levin equation and of its next-to-leading extension taking into account the running of the strong coupling.