Perturbative structure of two- and four-point functions of color charge in a non-Gaussian small-$x$ action

TL;DR

This paper analyzes the perturbative expansion of color charge correlators in the Color Glass Condensate framework, revealing divergence issues and applying Borel-Padé resummation to approximate non-perturbative solutions.

Contribution

It introduces a perturbative expansion including quartic corrections to the MV model and applies Borel-Padé resummation to handle divergence, providing a way to approximate non-perturbative results.

Findings

Perturbative series diverges at higher orders.

Borel-Padé resummation yields convergent approximations.

Non-perturbative solutions can be approximated by resummed series.

Abstract

We compute the perturbative expansion of the two- and four-point functions of color charges in the Color Glass Condensate framework considering the quartic correction to the McLerran-Venugopalan (MV) model of Gaussian color charge fluctuations. Expressions for these correlators in the perturbative expansion for small and large non-Gaussian color charge fluctuations are derived for arbitrary orders in perturbation theory. We explicitly show that the perturbative series does not converge at higher orders as expected. We apply the Borel-Pad\'e resummation method to our problem to construct a convergent series. It is shown that the fully non-perturbative solution can be described by the Borel-Pad\'e approximants constructed from the first few terms of the perturbative series for small non-Gaussian fluctuations.