The Intrinsic Glue Distribution at Very Small x

TL;DR

The work addresses the challenge of predicting gluon distributions at very small x by extending the classical-field MV framework to include extended longitudinal structure through renormalization-group methods. It shows how integrating out hard longitudinal modes produces a rapidity-dependent source density μ^2(y,Q^2) and a cumulative χ(y,Q^2), leading to nonlinear evolution that saturates at low transverse momentum and connects to perturbative DGLAP/BFKL dynamics. The resulting infrared-finite gluon correlators exhibit Lipatov-like enhancement and a nontrivial k_perp dependence, while ensuring unitarity in lepton-nucleus DIS and offering a path to estimating total multiplicities. The approach suggests a universal structure for small-x hadrons and provides a calculable framework bridging classical color fields and quantum evolution.

Abstract

We compute the distribution functions for gluons at very small x and not too large values of transverse momenta. We extend the McLerran-Venugopalan model by using renormalization group methods to integrate out effects due to those gluons which generate an effective classical charge density for Weizsäcker-Williams fields. We argue that this model can be extended from the description of nuclei at small x to the description of hadrons at yet smaller values of x. This generates a Lipatov like enhancement for the intrinsic gluon distribution function and a non-trivial transverse momentum dependence as well. We estimate the transverse momentum dependence for the distribution functions, and show how the issue of unitarity is resolved in lepton-nucleus interactions.

Figures (1)

• Figure 1: The distribution at fixed $x$ as a function of intrinsic transverse momentum $k_\perp^2$. We obtain considerable softening at small $k_\perp^2$ compared to the perturbative $1/k_\perp^2$ behavior