Gluon saturation and inclusive hadron production at LHC

TL;DR

This work develops a Color Glass Condensate (CGC) based description of inclusive hadron production in high-energy collisions, positing that produced hadrons mainly originate from gluon mini-jets with transverse momentum of order the saturation scale $Q_s(x)$. It builds a $k_t$-factorization framework that relates unintegrated gluon densities to an impact-parameter dependent dipole amplitude $N(Y;r;b)$ via a BK-inspired model, enabling a prediction of gluon and hadron spectra governed by $Q_s(x)$ and geometric scaling. The approach successfully describes HERA DIS data and LHC pp measurements (ALICE/CMS/ATLAS) across energies, and provides predictions for 7–14 TeV, while incorporating nonperturbative elements through a mini-jet mass $m_{jet}$ and a Local Parton-Hadron Duality (LPHD) assumption to connect jets to hadrons. The results support saturation as a driving mechanism for particle production and offer a testable framework for CGC signals in current and future collider data, including potential extension to heavy-ion collisions. Overall, the paper provides a coherent, saturation-based account of multiplicities and transverse-m momentum spectra with implications for understanding QCD at high parton densities.

Abstract

In high density QCD the hadron production stems from decay of mini-jets that have the transverse momenta of the order of the saturation scale. It is shown in this paper that this idea is able to describe in a unique fashion both the inclusive hadron production for \sqrt{s} \geq 546 GeV including the first data from LHC and the deep inelastic scattering at HERA. Recently reported data from ALICE, CMS and ATLAS including inclusive charged-hadron transverse-momentum and multiplicity distribution in pp collisions are well described in our approach. We provide predictions for the upcoming LHC measurements.

Figures (6)

• Figure 1: Mini-jet production in hadron-hadron collisions in the transverse plane. The impact-parameter between two hadrons is $\vec{B}$.
• Figure 2: Right: shows the average impact parameter of the produced mini-jet $\langle b^2_{jet} \rangle$ given by Eq. (\ref{['PO5']}) as function of energy. Left: The comparison with the experimental data and prediction for $dN_{ch} / d y$ using Eq. (\ref{['PO1']}) with $\sigma_{nsd} = M\pi \langle b^2_{jet} \rangle$ for $|\eta|<2.4$. The curves are normalized by data at $\sqrt{s} = 546\,\text{GeV}$, see the text for the details. The experimental data are from Refs. AL1CMSparticleb. The error bars on the UA5 and ALICE data points are statistical. We show only systematic errors for the CMS data points.
• Figure 3: Right: Energy dependence of the charged hadrons multiplicity in the central region of rapidity $\eta=0$ in $pp$ collisions. The theoretical curve (Saturation model LR) is our prediction coming from the saturation model for the NSD interactions. The band indicates about $2\%$ theoretical error. The total theoretical uncertainties is less $6\%$ at high energies (see the text for the details). We also show the KLN prediction KLN with the same error band as ours. Left: Our prediction for the energy dependence of the average transverse momentum of charged hadrons. The CMS data CMS points and the theoretical curves in the left panel are for $|\eta|<2.4$. The experimental data are from Refs. CMSALICEparticlebua1ua5CDF1ecr. The experimental error bars indicate systematic uncertainties.
• Figure 4: The differential yield of charged hadrons for $|\eta|<2.4$. The experimental data are from CMS CMS at $2.36$ TeV for $|\eta|<2.4$. We show also our theoretical predictions for $7$ and $14$ TeV with $<z>=0.5$ and $m_{jet}=0.4$ GeV. The experimental error bars shown are systematic and statistical errors added linearly.
• Figure 5: Upper panel: The differential yield of charged hadrons in various $|\eta|$ bins for $\sqrt{s}=2.36$ TeV. The experimental data are from CMS CMS. We also show our predictions for $7$ TeV and $14$ TeV with $<z>=0.5$ and $m_{jet}=0.4$ GeV . The experimental error bars shown are systematic and statistical errors added linearly. Lower panel: The differential yield of charged hadrons for $|\eta|=0.1$ for two different value of mini-jet masses $m_{jet}$. The inserted plot in the lower panel figure shows the charged hadrons multiplicity again for two values of $m_{jet}$ for the same energy.