Parton densities and saturation scale from non-linear evolution in DIS on nuclei

TL;DR

This work numerically solves the nonlinear QCD evolution equation for deep inelastic scattering on nuclei over $x$ from $10^{-2}$ to $10^{-7}$, illustrating substantial deviations from Glauber–Mueller initial conditions and identifying a density-driven saturation regime. By computing the gluon density $xG_A$ and the structure function $F_{2A}$ within the color-dipole framework, the authors quantify a modest energy gain for nuclear targets and demonstrate damping of parton densities at small $x$ relative to linear DGLAP predictions. The saturation scale is extracted as $Q_{s,A}(x)$ with $Q^2_{s,A}\propto A^{p(x)}$ and, for Au, $Q^2_{s, ext{Au}}\approx(1.5\ \mathrm{GeV})^2$ at $x=10^{-3}$, with $p(x)$ decreasing at smaller $x$ and a scaling behavior $\tilde N_A(r_\perp,x)$ as a function of $r_\perp Q_{s,A}(x)$. These findings imply a sizable high-density QCD influence in heavy nuclei and offer theoretical input for RHIC phenomenology, while cautioning that LO nonlinear evolution may require higher-order treatment for precision.

Abstract

We present the numerical solution of the non-linear evolution equation for DIS on nuclei for $x = 10^{-2} ÷10^{-7}$. We demonstrate that the solution to the non-linear evolution equation is quite different from the Glauber - Mueller formula which was used as the initial condition for the equation. We illustrate the energy profit for performing DIS experiments on nuclei. However, it turns out that the gain is quite modest: $x_{Au} \simeq 5 x_{\rm proton} $ for the same parton density. We find that the saturation scale $Q^2_s \propto A^{1/3}$. For gold the saturation scale $Q_{s,Au} \simeq 1.5 GeV$ at $x= 10^{-3}$. Such a large value leads to considerable contribution of the high density QCD phase to RHIC data and reveals itself in essential damping for both $xG_A$ and $F_{2A}$.

Figures (9)

• Figure 1: The nucleon transverse profile function inside the nucleus $S_A(b)$ is plotted as a function of $b$.
• Figure 2: The function $\tilde{N}_A$ is plotted versus distance. The four curves show the result for the nuclei $Ne$, $Ca$, $Mo$, and $Au$.
• Figure 3: The functions $\tilde{N}_A$ for $Au$ and $Ne$ (dashed lines) are plotted together with the corresponding Glauber formulas (dotted lines).
• Figure 4: The function $N_{Au}$ is plotted versus the impact parameter $b$. The solid line is the exact $b$ dependence, while the dashed line is the anzatz (\ref{['Nb']}).
• Figure 5: The gluon density $xG_A$ is plotted as a function of $\lg x$ for the nuclei $Ne$, $Ca$, $Zn$, $Mo$, $Nd$, and $Au$.