# Saturation of Gluon Densities and the Color Glass Condensate

A major discovery of the last decade is the dominant role of gluons in nucleons that are viewed by a high-energy probe. The density of gluons grows extremely rapidly as one probes gluons carrying progressively smaller fractions *x* of a proton’s overall momentum. This growth reflects a QCD cascade in which higher-momentum (harder) parent gluons successively split into two or more lower-momentum (softer) daughter gluons. But this growth cannot continue unabated without eventually violating fundamental rules of physics. Physicists expect the growth to be tamed because at sufficiently high gluon densities softer gluons will again recombine into harder ones. The competition between the splitting and recombination processes should lead to a saturation of gluon densities at small *x*. Recent theoretical breakthroughs suggest that this saturation regime is characterized by new physics that can be best studied at an EIC.

The onset of saturation depends not only on the gluon’s momentum fraction *x*, but also on the spatial resolution with which the nucleon is probed. Physicists can select that resolution by restricting their attention to partons that have been given a particular momentum kick *Q* by the beam electrons. As *Q* decreases, the resolution of structure details in the plane transverse to the beam direction gets coarser. This increases the sensitivity to the recombination of gluons. This sensitivity also increases when the target nucleons are contained within a heavy nucleus, where many closely spaced nucleons along the beam path can conspire to contribute gluons to the recombination cause, amplifying the gluon density. Combining these two effects yields a predicted *saturation scale*: *Q _{s}^{2}* ~ (A/

*x*)

^{1/3}. As the formula shows, this scale grows with increasing nuclear mass number A and with decreasing gluon momentum fraction

*x*(see the figure). When the probe has much finer spatial resolution,

*Q*>>

^{2}*Q*, the physics is described by the well-studied linear regime of QCD, dominated by gluon splitting. But as

_{s}^{2}*Q*decreases below

^{2}*Q*one enters the novel nonlinear regime of saturated gluonic matter.

_{s}^{2}Gluons are among the class of particles known as *bosons* that are permitted by quantum physics to have more than one particle in the same state. In fact, the occupancy of gluons in the saturation regime is proportional to the inverse of the QCD coupling strength. When *Q*_{s}^{2}is large, this coupling is weak, and therefore the occupancy is large and the behavior of the gluon ensemble is nearly classical. In this limit, theorists predict that one should gain access to a fascinating facet of *all* matter: a dense swarm of gluons, wherein the individual gluons interact weakly but collectively form a coherent classical color field whose intensity may be the *strongest allowed in nature*! This predicted universal facet of matter has much in common with Bose-Einstein condensates (whose study led to the 2001 Nobel Prize in Physics) and with glassy materials, and has thus been labeled the CGC.

To reach CGC conditions one needs a suitable combination of high beam energy (small *x*) and heavy-ion (large A) beams to collide with the probing electrons. A hypothetical observer co-moving with the electron will see a tidal wave of gluons from protons and neutrons along the entire depth of the nucleus. Using heavy nuclei as an *amplifier* of gluon densities allows us to reach this regime with 10 times lower beam energy than would be needed in an electron-proton collider.

The regimes probed in atomic nuclei at high energies are shown in figure 2.14 as a function of the resolving momentum *Q*^{2} of the probe, the gluon momentum fraction *x*, and the atomic number A. As suggested by the figure, the CGC regime is expected to be universal across all atomic nuclei and for resolving momenta below the saturation scale. The use of large nuclei and high energies together opens a wide window to explore, with unmatched precision, this novel regime. The figure also shows that the CGC regime of strong gluon fields lies adjacent to the confining regime of QCD, where the interactions among individual gluons grow very strong. The transition between the two regimes may hold the key to understanding the confining dynamics at the heart of all matter.