Non-perturbative renormalization of the average color charge and multi-point correlators of color charge from a non-Gaussian small-x action

Abstract The McLerran-Venugopalan (MV) model is a Gaussian effective theory of color charge fluctuations at small-x in the limit of large valence charge density, i.e., a large nucleus made of uncorrelated color charges. In this work, we explore the effects of the first non-trivial (even C-parity) non-Gaussian correction on the color charge density to the MV model (“quartic” term) in SU(2) and SU(3) color group in the non-perturbative regime. We compare our (numerical) non-perturbative results to (analytical) perturbative ones in the limit of small or large non-Gaussian fluctuations. The couplings in the non-Gaussian action, μ ¯ for the quadratic and κ 4 for the quartic term, need to be renormalized in order to match the two-point function in the Gaussian theory. We investigate three different choices for the renormalization of these couplings: i) κ 4 is proportional to a power of μ ¯ ; ii) κ 4 is kept constant and iii) μ ¯ is kept constant. We find that the first two choices lead to a scenario where the small-x action evolves towards a theory dominated by large non-Gaussian fluctuations, regardless of the system size, while the last one allows for controlling the deviations from the MV model.