Energy Dependence of the Cronin Effect from Non-Linear QCD Evolution

TL;DR

For the resulting spectrum of produced gluons in p-A and A-A collisions, the nonlinear QCD evolution is unable to generate a Cronin-type enhancement, and it quickly erases any such enhancement which may be present at lower energies.

Abstract

The non-linear evolution of dense partonic systems has been suggested as one of the novel physics mechanisms relevant to the dynamics of hadron-nucleus and nucleus-nucleus collisions at collider energies. Here we study to what extent the description of Cronin enhancement in the framework of this non-linear evolution is consistent with the recent observation in 200 AGeV d--Au collisions at the Relativistic Heavy Ion Collider. We solve the Balitsky-Kovchegov evolution equation numerically for several initial conditions encoding Cronin enhancement. We find that the properly normalized nuclear gluon distribution is suppressed at all momenta relative to that of a single nucleon. Calculating the resulting spectrum of produced gluons in p-A and A-A collisions, we establish that the nonlinear QCD evolution is unable to generate a Cronin type enhancement, and that it quickly erases any such enhancement which may be present at lower energies.

Figures (3)

• Figure 1: Solutions of the BK equation. Upper-left: $h(k)$ evolved (left to right) from $y=0$ to 5 and 10 for different initial conditions: GBW with $Q_s^2=0.36$ GeV$^2$ (solid lines), MV with $Q_s^2=4$ GeV$^2$ (dashed lines) and MV with $Q_s^2=100$ GeV$^2$ (dotted lines). Upper-right: The same as upper left for $\phi(k)$. Lower-left: the scaled function $h(\rho)$ versus $\rho = k/Q_s$ for $y=4,6,8,10$ and the same initial conditions and conventions (lines cannot be distinguished). Lower-right: Ratio of $h(y,\rho)/h(y,\rho=1)$ over $h(y=10,\rho)/h(y=10,\rho=1)$ for $y=4$ (solid line), 6 (dashed line), 8 (dotted line) and 10 (dashed-dotted line), and initial condition MV with $Q_s^2=4$ GeV$^2$.
• Figure 2: Ratio of distributions $\phi$ and $h$ in nucleus and proton, normalized to 1 at $k \to \infty$. Upper plots: BK evolution, with MV as initial condition with $Q^2_s=0.1$ GeV$^2$ for p and 2 GeV$^2$ for A. Lines from top to bottom correspond to $y=0$, 0.05, 0.1, 0.2, 0.4, 0.6, 1, 1.4 and 2. Lower plots: BFKL evolution, with MV as initial condition with $Q_s^2=4$ GeV$^2$ for p and 100 GeV$^2$ for A. Lines from top to bottom correspond to $y=0$, 1 and 4.
• Figure 3: Ratios $R_{pA}$ and $R_{AA}$ of gluon yields in p--A (upper plot) and A--A (lower plot) for BK evolution, with MV as initial condition with $Q^2_s=0.1$ GeV$^2$ for p and 2 GeV$^2$ for A. Lines from top to bottom correspond to $y=0$, 0.05, 0.1, 0.2, 0.4, 0.6, 1, 1.4 and 2.