QCD at small x and nucleus-nucleus collisions

At large collision energy √ s and relatively low momentum transfer Q, one expects a new regime of Quantum Chromo-Dynamics (QCD) known as “saturation”. This kinematical range is characterized by a very large occupation number for gluons inside hadrons and nuclei; this is the region where higher twist contributions are as large as the leading twist contributions incorporated in collinear factorization. In this talk, I discuss the onset of and dynamics in the saturation regime, some of its experimental signatures, and its implications for the early stages of Heavy Ion Collisions. 1. Hadrons and nuclei at high energy A nucleon at low energy can be seen as made of three valence quarks, constantly interacting via gluon exchanges and virtual fluctuations at all space-time scales smaller than the size of the nucleon itself. In an interaction process with a probe, only those fluctuations which are longer lived/larger than the resolution of the probe are actually relevant. In addition, interaction processes at low energy are made very complicated by the fact that the constituents of the nucleon can interact during the time seen by the probe. When one boosts the nucleon to a higher energy, all its internal time scales are dilated, which simplifies the interaction process with the probe: the interactions among the constituents of the nucleon now occur over much larger time-scales, and therefore the probe sees only a collection of free constituents. Moreover, the life-time of the quantum fluctuations is also time dilated, and thus the number of gluons taking part to the interaction process increases with the collision energy. Simultaneously, the fluctuations that were already important at the lower energy are now evolving so slowly that they can be considered static over the time-scale seen by the external probe. However, this growth with energy of the number of gluons in the wave-function of a nucleon (or nucleus) cannot continue indefinitely. Indeed, it would imply that nucleon-nucleon cross-sections grow faster than what is allowed by Froissart’s unitarity bound. In fact, an important aspect of the physics is missing in the above picture: gluons can recombine when their occupation number is large, a process known as gluon saturation [1]. To quantify when this new phenomenon occurs, one must compare the ‡ We assume that we are in a frame in which the probe has not changed QCD at small x and nucleus-nucleus collisions 2