Gluon saturation and energy dependence of hadron multiplicity in pp and AA collisions at the LHC

TL;DR

The study addresses the differing energy dependence of charged-hadron multiplicity in $pp$ and $AA$ collisions at the LHC within the Color Glass Condensate framework. By extending $k_T$-factorization to incorporate gluon-jet decay angular ordering (MLLA) through an energy-dependent gluon-jet hadron multiplicity $N^{Gluon}_h(E_{jet})$ derived from $e^+e^-$ data, the authors predict $dN_h/d\eta \propto s^{0.11}$ for $pp$ and $dN_h/d\eta \propto s^{0.145}$ for $AA$, with the latter enhanced by a larger saturation scale $Q_s$ in nuclei. Numerical results with the b-CGC model show good agreement with RHIC and LHC measurements, and predict a centrality-scaling collapse of $dN_{AA}/d\eta$ across energies; for 5.5 TeV Pb-Pb central collisions, $dN_{AA}/d\eta$ is predicted to be $1897 \pm 133$. This work demonstrates that CGC-based descriptions, augmented by gluon-jet decay dynamics, can coherently describe hadron production across $pp$ and $AA$ and reconcile energy-dependence trends observed at the LHC.

Abstract

The recent results in \sqrt{s}=2.76 TeV Pb+Pb collisions at the Large Hadron Collider (LHC) reported by the ALICE collaboration shows that the power-law energy-dependence of charged hadron multiplicity in Pb+Pb collisions is significantly different from p+p collisions. We show that this different energy-dependence can be explained by inclusion of a strong angular-ordering in the gluon-decay cascade within the Color-Glass-Condensate (or gluon saturation) approach. This effect is more important in nucleus-nucleus collisions where the saturation scale is larger than 1 GeV. Our prescription gives a good description of the LHC data both in p+p and Pb+Pb collisions.

Figures (6)

• Figure 1: The energy behaviour of charged particle pseudo-rapidity per participant pair for central $AA$ and non-singlet diffractive $pp$ collisions. The energy dependence can be described based on the saturation picture by $s^{0.11}$ for $pp$ and $s^{0.145}$ for $AA$ collisions. The saturation (CGC) curve for $pp$ collisions is taken from Ref. LRPP. The saturation curve for the $AA$ collisions was calculated from Eq. (\ref{['kt']}) having incorporated the effects of gluon-jet angular ordering which is important when the saturation scale $Q_s>1$ GeV, see the text for the details. The total theoretical uncertainties in the saturation model calculation is about $7\%$ (not shown here). The experimental data are from Refs. CMSAl1Apb1pakua1naphobbstarphen. The data from the PHENIX collaboration denoted by PHENIX 1 and 2 can be found in Ref. phen.
• Figure 2: Right: The mean charged hadron multiplicity of unbiased gluon $N^g_h$ and quark $N^q_h$ jets in $e^+e^-$ annihilation, as a function of the jet energy . For gluon jet we show experimental data obtained by two different methods, jet boost algorithm and subtracting multiplicities in two-jet $q\bar{q}$ events from three-jet $q\bar{q}g$ events eeee-plot. The experimental data for quark jet production in $e^+e^-$ annihilation are taken from Ref. pak. The energy behaviour of $N^{g}_h$ can be described by $E_{g}^{0.6\div 0.7}$ for $E_{g}\geq 0.85$ GeV. Left: The ratio of the mean charged particle multiplicities between unbiased gluon and quark jets as a function of scale. Various theoretical predictions pee based on perturbative QCD (pQCD) are also shown in the plot. The plot in the left panel is taken from Ref. ee-plot.
• Figure 3: Angular ordering in the gluon cascade in the MLLA ($\theta_1>\theta_2>\theta_3>...>\theta_n$) and the BFKL ($\theta_1<\theta_2<\theta_3<...<\theta_n$) regime.
• Figure 4: Pseudo-rapidity distribution of charged particles produced in Au-Au and Pb-Pb central collisions at RHIC $\sqrt{s}=130, 200$ GeV and the LHC energies $\sqrt{s}=2.75, 5.5$ TeV. The experimental data are from the PHOBOS rhic1 and the ALICE collaboration Apb1.
• Figure 5: Right: The scaled pseudo-rapidity density as a function of number of participant at midrapidity for $AA$ collisions at $0.2, 2.76$ and $5.5$ TeV. Left: The pseudo-rapidity distribution at RHIC $0.2$ TeV at different centralities. Both theoretical predictions and experimental data show gluon saturation-driven scaling property. We also show in the plots, the corresponding normalization product factors. The experimental data are from the PHOBOS rhic1rhic2 and ALICE Apb2 collaboration.