Parton densities and dipole cross-sections at small x in large nuclei

TL;DR

The paper analyzes parton distributions in large nuclei at small x using the colour dipole model in the large-$N_c$ limit, where nucleus–dipole scattering is described by non-linear BFKL fan diagrams. It solves the evolution equation for the dipole cross-section in momentum space with two initial conditions, finding that the initial form quickly becomes irrelevant and that all observables exhibit geometric scaling governed by the saturation momentum $Q_s(y,b)$. The main findings are that $Q_s$ grows with energy and nuclear size, the gluon density and dipole cross-section saturate, and the quark density also approaches a saturated, universal form as $y$ increases. These results reinforce the saturation paradigm for high-energy nuclear collisions and provide quantitative scaling relations for $Q_s(y,b)$ and related densities.

Abstract

Unintegrated gluon densities in nuclei, dipole-nucleus cross-sections and quark densities are numerically investigated in the high-colour limit, with the scattering on a heavy nucleus exactly described by the sum of fan diagrams of BFKL pomerons. The initial condition for the evolution in rapidity is quickly forgotten, and the gluon density presents a "supersaturation" pattern, as previous studies indicated. Both dipole-nucleus cross-sections and quark densities present the expected saturation features. Identifying the position in transverse momentum $l$ of the maximum of the gluon distribution with the saturation momentum $Q_s(y,b)$, at large rapidities all distributions depend only on one variable $[l/Q_s(y,b)]$ or $[rQ_s(y,b)]$.

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