Energy Conservation and Saturation in Small-x Evolution

TL;DR

This work addresses the competition between non-leading BFKL corrections, notably energy-momentum conservation, and saturation in small-$x$ QCD. It develops a Monte Carlo scheme that embeds energy-momentum conservation into Mueller's coordinate-space dipole evolution and couples it to unitarity-induced saturation, yielding a dynamical suppression of the gluon density growth and a delayed onset of saturation. The key finding is that energy-momentum conservation alone can reproduce much of the observed damping of $F_2$ at low $x$ and low $Q^2$, with unitarity providing only a modest additional effect once EC is included; the model qualitatively matches HERA data and offers insights into dipole-dipole and dipole-nucleus scattering. This framework advances the understanding of high-energy QCD by linking momentum-space NLO corrections with coordinate-space saturation, guiding extrapolations to LHC energies and providing a path toward a frame-independent, fully dynamical description of small-$x$ phenomena.

Abstract

Important corrections to BFKL evolution are obtained from non-leading contributions and from non-linear effects due to unitarisation or saturation. It has been difficult to estimate the relative importance of these effects, as NLO effects are most easily accounted for in momentum space while unitarisation and saturation are easier in transverse coordinate space. An essential component of the NLO contributions is due to energy conservation effects, and in this paper we present a model for implementing such effects together with saturation in Mueller's dipole evolution formalism. We find that energy conservation severely dampens the small-x rise of the gluon density and, as a consequence, the onset of saturation is delayed. Using a simple model for the proton we obtain a reasonable qualitative description of the x-dependence of F2 at low Q^2 as measured at HERA even without saturation effects. We also give qualitative descriptions of the energy dependence of the cross section for gamma*-gamma* and gamma*-nucleus scattering.