[Paper Review] Hadron multiplicities at the LHC

Dmitri E. Kharzeev, E. Levin+1 more|ArXiv.org|Jul 5, 2007

High-Energy Particle Collisions Research3 citations

TL;DR

This paper predicts hadron multiplicities in $pp$, $pA$, and $AA$ collisions at LHC energies using the Color Glass Condensate (CGC) framework, which models parton saturation at high energies. It derives a rapidity-dependent saturation scale $Q_s^2(Y)$ that leads to slower multiplicity growth than conventional models, with a transition from exponential rise to saturation at LHC energies.

ABSTRACT

We present the predictions for hadron multiplicities in pp, pA and AA collisions at the LHC based on our approach to the Color Glass Condensate.

Motivation & Objective

• To predict hadron multiplicities in $pp$, $pA$, and $AA$ collisions at LHC energies using the Color Glass Condensate (CGC) framework.
• To investigate the impact of non-linear parton evolution on multiplicity growth at high energies.
• To test the validity of the CGC approach in the regime of parton saturation at LHC energies.
• To examine the rapidity dependence of the saturation scale $Q_s(Y)$ and its implications for particle production.
• To compare predictions with conventional soft-plus-hard models and assess the role of longitudinal color fields.

Proposed method

• Models the initial wave functions of hadrons and nuclei as Color Glass Condensate (CGC) sheets with a specific ansatz for unintegrated parton distributions.
• Applies $k_{\perp}$-factorization to compute inclusive parton production cross sections.
• Implements hadronization via local parton-hadron duality, assuming angular distributions are preserved during fragmentation.
• Derives a rapidity-dependent saturation scale $Q_s^2(Y)$ from non-linear QCD evolution, incorporating longitudinal color fields.
• Uses the equation $Q_s^2(Y) = \frac{Q_s^2(Y_0) \exp\left(\frac{2\alpha_S}{\pi}(Y-Y_0)\right)}{1 + B Q_s^2(Y_0) \left(\exp\left(\frac{2\alpha_S}{\pi}(Y-Y_0)\right) - 1\right)}$, with $B = 1/(32\pi^2)(\pi R_A^2 / \alpha_S)$, to describe saturation dynamics.
• Evaluates multiplicity predictions by extrapolating from RHIC-tested CGC models to LHC energies.

Experimental results

Research questions

• RQ1 How does parton saturation in the CGC framework affect hadron multiplicity in $pp$, $pA$, and $AA$ collisions at LHC energies?
• RQ2 What is the role of longitudinal color fields in modifying the rapidity evolution of the saturation scale $Q_s(Y)$?
• RQ3 How does the predicted multiplicity growth at LHC energies compare to conventional soft-plus-hard models?
• RQ4 To what extent does the non-linear evolution of partons lead to a slowdown in multiplicity increase at high energies?
• RQ5 Can the CGC-based approach accurately describe total hadron multiplicities despite limitations in transverse momentum distributions?

Key findings

• The saturation scale $Q_s^2(Y)$ exhibits exponential growth at moderate energies but slows significantly at high energies due to non-linear effects.
• The resulting hadron multiplicity grows more slowly than predicted by conventional soft-plus-hard models, as shown in Fig. 1b.
• At LHC energies, the multiplicity growth transitions from exponential to saturated, with curve '2' in Fig. 1b showing a decrease in multiplicity rise due to evolution slowdown.
• The model predicts a total charged hadron multiplicity in central Pb-Pb collisions at $\sqrt{s} = 5.5$ TeV, consistent with expectations from the CGC framework (Fig. 1a).
• The inclusion of longitudinal color fields in the evolution leads to a modified $Q_s^2(Y)$ dependence that suppresses multiplicity growth at high rapidities.
• The results suggest that LHC data on multiplicities will be crucial for probing QCD in the strong color field regime and testing the CGC framework.