Gluon Distribution Functions for Very Large Nuclei at Small Transverse Momentum

TL;DR

This paper develops a framework to compute gluon distribution functions for very large nuclei at small transverse momentum by mapping the problem to a two-dimensional ultraviolet-finite Euclidean field theory. The gluon distribution takes the form $\frac{1}{\pi R^2}\frac{dN}{dx d^2k_t} = \frac{N_c^2-1}{\pi^2} \frac{1}{x} \frac{1}{\alpha_s} H(k_t^2/(\alpha_s^2 \mu^2))$, with $H$ encoding density-driven modifications to the $q_t$-dependence and valid to all orders in density. In the weak-coupling regime, $H(y)=1/y$, while in the soft $k_t$ region the theory becomes strongly coupled but infrared-finite, enabling potential lattice Monte Carlo studies. The approach provides a non-perturbative handle on gluon distributions in heavy nuclei at small $x$ and small $q_t$, linking high-energy QCD phenomena to a tractable 2D field theory.

Abstract

We show that the gluon distribution function for very large nuclei may be computed for small transverse momentum as correlation functions of an ultraviolet finite two dimensional Euclidean field theory. This computation is valid to all orders in the density of partons per unit area, but to lowest order in $α_s$. The gluon distribution function is proportional to $1/x$, and the effect of the finite density of partons is to modify the dependence on transverse momentum for small transverse momentum.