Color-glass condensate beyond the Gaussian approximation

In the high-energy limit, perturbative calculations in QCD are conveniently done using the dipole picture which factorizes the scattering amplitude into a perturbative part and the nonperturbative scattering off the nuclear target, described using correlators of Wilson lines. These correlators can be computed in the color-glass condensate effective field theory by using a Gaussian model for the color density of the target. In this work, we generalize the Gaussian model to a generic function that is local in the transverse coordinates and the light-cone time, and show how to compute physical Wilson-line correlators in this model. We also consider a simple model for the color density based on stable probability distributions and show that the small-dipole behavior of the dipole amplitude is modified from quadratic to a power law, where the power is given by the stability parameter of the distribution. This generalization of the Gaussian model is suitable for numerical applications in the high-energy limit and can be used in future phenomenological studies of the nuclear structure.

💡 Research Summary

The paper addresses a fundamental limitation of the widely used McLerran‑Venugopalan (MV) model in the Color Glass Condensate (CGC) effective theory. The MV model assumes that the color charge density ρ of a high‑energy nucleus follows a Gaussian probability distribution, which enables analytic calculations of Wilson‑line correlators and, consequently, of observables such as the dipole scattering amplitude. However, the Gaussian assumption is only justified when the number of independent color sources n is large and its fluctuations are mild. In realistic nuclei, n fluctuates, and the distribution p(n) can have heavy tails, leading to non‑Gaussian statistics for ρ.

To go beyond this restriction, the authors propose a generalized weight functional W