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Nonlinear evolution and saturation for heavy nuclei in DIS

E. Levin, K. Tuchin

TL;DR

The paper analyzes nonlinear small-x evolution of the dipole-nucleus scattering amplitude in DIS within the double logarithmic approximation, focusing on the saturation regime and the A-dependence of the saturation scale. The authors solve Kovchegov's nonlinear evolution equation using a semiclassical characteristics method, identifying a critical line that separates linear growth from saturation and determines the scaling behavior. They show that the initial parton density in the nucleus crucially controls whether the saturation region exhibits geometric scaling (small density) or not (large density). They deduce the A-dependence of the saturation scale: for light nuclei, $Q_s^2(y,A) \sim A^{2/3}$ at all energies, while for heavy nuclei it starts as $A^{1/3}$ and asymptotically matches $A^{2/3}$, with a rough transition around $A\sim 70$. The work highlights how Glauber-Mueller initial conditions feed into nonlinear evolution and saturation onset in nuclei.

Abstract

The nonlinear evolution equation for the scattering amplitude of colour dipole off the heavy nucleus is solved in the double logarithmic approximation. It is found that if the initial parton density in a nucleus is smaller then some critical value, then the scattering amplitude is a function of one scaling variable inside the saturation region, whereas if it is greater then the critical value, then the scaling behaviour breaks down. Dependence of the saturation scale on the number of nucleons is discussed as well.

Nonlinear evolution and saturation for heavy nuclei in DIS

TL;DR

The paper analyzes nonlinear small-x evolution of the dipole-nucleus scattering amplitude in DIS within the double logarithmic approximation, focusing on the saturation regime and the A-dependence of the saturation scale. The authors solve Kovchegov's nonlinear evolution equation using a semiclassical characteristics method, identifying a critical line that separates linear growth from saturation and determines the scaling behavior. They show that the initial parton density in the nucleus crucially controls whether the saturation region exhibits geometric scaling (small density) or not (large density). They deduce the A-dependence of the saturation scale: for light nuclei, at all energies, while for heavy nuclei it starts as and asymptotically matches , with a rough transition around . The work highlights how Glauber-Mueller initial conditions feed into nonlinear evolution and saturation onset in nuclei.

Abstract

The nonlinear evolution equation for the scattering amplitude of colour dipole off the heavy nucleus is solved in the double logarithmic approximation. It is found that if the initial parton density in a nucleus is smaller then some critical value, then the scattering amplitude is a function of one scaling variable inside the saturation region, whereas if it is greater then the critical value, then the scaling behaviour breaks down. Dependence of the saturation scale on the number of nucleons is discussed as well.

Paper Structure

This paper contains 4 sections, 52 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Solution at $Q^2>Q_s^2(x_B)$.
  3. Solution at $Q^2<Q_s^2(x_B)$.
  4. Discussion

Figures (1)

  • Figure 1: The kinematical regions relevant in high parton density QCD. The initial condition Eq. (\ref{['INIT0']}) for the nonlinear evolution equation Eq. (\ref{['MAIN2']}) is set on the line $y=y_0$ (dashed line). Solid curves 1,2 are the critical lines $r=\left(\ln Q_s^2/4\Lambda^2\right)$ for different nuclei: $A_1<A_2$. Initial conditions for the solution to the left of the critical line are set along line 1 for nucleus $A_1$ or along line $ABC$ for nucleus $A_2$.