Finite partonic distribution functions at small-x

This thesis is concerned with the behaviour of parton distribution functions in the small-x domain. The relevant physics is that of dense partonic systems, for which interactions between the partons cannot be neglected. These interactions lead to a departure from the behaviour predicted by the standard linear evolution schemes, resulting in saturation of the gluon density. The discussion is centered on a recent approach introduced a few years ago by McLerran and Venugopalan, and later developed by Jalilian-Marian, Kovner, Leonidov and Weigert (JKLW) into a set of evolution equations for a statistical ensemble describing a hadron. We reconsider the evolution equations for multi-gluon correlators derived by JKLW, deriving them in terms of vector potentials avoiding the introduction of the concept of colour charge density in the intermediate steps. The two step procedure of deriving the evolution of the charge density correlators followed by the solution of classical equations for the vector potentials is shown to be consistent with direct derivation of evolution for vector potentials. We analyze the relation between these evolution equations and other approaches proposed in the last several years. We show that the equation derived by Balitsky and Kovchegov is obtained from the JKLW equation in the limit of small induced charge density. We argue that the higher non-linearities resummed by the JKLW equation correspond, in physical terms, to the breakdown of the eikonal approximation when the gluon fields in the target are large. (author)SIGLEAvailable from British Library Document Supply Centre- DSC:DN056528 / BLDSC - British Library Document Supply CentreGBUnited Kingdo