Saturation and parton level Cronin effect: enhancement vs suppression of gluon production in p-A and A-A collisions

TL;DR

This paper analyzes how perturbative saturation affects gluon production in proton–nucleus and nucleus–nucleus collisions, focusing on transverse momentum broadening and the Cronin effect. It compares a Glauber-Mueller saturation framework (McLerran-Venugopalan model) with evolved small-x gluon distributions (two parametrizations: NLEF and NLES) within a kt-factorization approach, to determine when Cronin enhancement arises versus suppression. The results show that, in the MV case, a Cronin-type enhancement appears for p_t above the saturation scale, while evolved distributions yield outcomes that strongly depend on the high-k_t tail outside the scaling window—some scenarios exhibit enhancement, others suppression. Centrality dependences can resemble N_part or N_coll scaling depending on p_t and model, and experimental d-Au data favor Cronin effects, suggesting significant final-state effects are needed to describe Au-Au data; overall, the work highlights the crucial role of the high-k_t tail in determining Cronin behavior in saturated systems.

Abstract

We note that the phenomenon of perturbative saturation leads to transverse momentum broadening in the spectrum of partons produced in hadronic collisions. This broadening has a simple interpretation as parton level Cronin effect for systems in which saturation is generated by the "tree level" Glauber-Mueller mechanism. For systems where the broadening results form the nonlinear QCD evolution to high energy, the presence or absence of Cronin effect depends crucially on the quantitative behavior of the gluon distribution functions at transverse momenta kt outside the so called scaling window. We discuss the relation of this phenomenon to the recent analysis by Kharzeev-Levin-McLerran of the momentum and centrality dependence of particle production in nucleus-nucleus collisions at RHIC.

Figures (6)

• Figure 1: a). The unintegrated gluon distribution function, normalized to the corresponding perturbative one, as function of $k_{t}$ for fixed $\rho_{\rm part} = 3.1~ {\rm fm^{-2}}$ and for $Q_s^2 \simeq 2~ {\rm GeV}^2$; solid curve: gluon distribution in the McLerran-Venugopalan model mv, dot-dashed curve: model (\ref{['eq10']}) - (\ref{['eq12']}) for the evolved gluon distribution. The dashed curve is for the anomalous dimension $\gamma = 0.5$. b). The ratio $R^{\rm periph}$ in Eq. (\ref{['rperiph']}) for the gluon distributions Eq. (\ref{['eq10']}) (dot-dashed curve) and Eq. (\ref{['slow']}) (solid curve).
• Figure 2: Cronin effect in the $p_{t}$-dependence of gluon production yields for head-on A-A collisions. Solid curve for the MV-gluon distribution normalized to the perturbative yield. The dot-dashed curve is for the evolved gluon distribution (\ref{['eq10']}), the dashed one for the evolved gluon distribution (\ref{['slow']}), both normalized as in Eq. (\ref{['eq21p']}).
• Figure 3: Centrality dependence of gluon production yields (\ref{['eq2']}) in A-A collisions as a function of $\rho_{\rm part}~ ({\rm fm^{-2}})$, normalized to the yield in peripheral collisions, Eq. (\ref{['eq20']}). Curves are calculated for the MV gluon distribution (\ref{['eq5']}) and different values of $p_t$: solid curve: $p_{t} = 0.25~{\rm GeV}$, dashed curve: $p_{t} = 1.0~{\rm GeV}$, dot-dashed curve: $p_{t} = 3.0~{\rm GeV}$.
• Figure 4: Centrality dependence as in Fig. \ref{['fig:Fig3']}, but with the gluons of Eq. (\ref{['eq10']}) and Eq. (\ref{['slow']}) for $p_t =$ 1 and 3 GeV. The solid and dashed lines correspond to Eq. (\ref{['eq10']}) for $p_t = 1$ GeV and $p_t = 3$ GeV, respectively. The short-dashed ($p_t =$ 1 GeV) and dot-dashed ($p_t = 3$ GeV) lines are calculated for the gluon distribution (\ref{['slow']}).
• Figure 5: Normalized yield for evolved gluon distributions as a function of $N_{\rm part}$. Legend the same as on Fig.4. The largest value $N_{\rm part}=380$ corresponds to $\rho_{\rm part}=3.1~ {\rm fm}^{-2}$ on Fig.\ref{['fig:Fig4']}.