Description of Charged\text{-}Particle Multiplicity Distributions in High\text{-}Energy Proton\text{-}Proton Collisions Based on a Two-Component Model and Examination of Parton Distribution Functions

TL;DR

This paper addresses describing charged-particle multiplicities in high-energy $pp$ collisions using a minimal, gluon-driven two-component framework. The central component models gluon-gluon fusion with unintegrated gluon distributions derived from MD-DGLAP PDFs via the KMR scheme, while a secondary component accounts for soft valence-quark recombination in the fragmentation regions. The approach is validated against ATLAS data across energies from 0.9 to 13 TeV, showing good reproduction of the shape of the charged-particle pseudorapidity density $(1/N_{ev}) \, dN_{ch}/dta$, and it highlights the dominant role of gluon dynamics in the small-$x$ regime. The study also compares multiple PDF sets, demonstrating that high-energy data can constrain the small-$x$ behavior of gluons and discriminate among PDFs.

Abstract

High-energy proton-proton collisions at the LHC offer a stringent test of Quantum Chromodynamics (QCD) in the small-$x$, gluon-dominated regime. This study focus on a minimal, gluon-driven framework to describe the charged-particle multiplicities and their pseudorapidity densities in high energy collisions. The two-component model taken here includes the hard gluon-gluon fusion process and the soft quark recombination process, which directly relates to both integrated and unintegrated parton distributions. We begin by evolving Parton Distribution Functions (PDFs) using the Modified Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (MD-DGLAP) equations. These PDFs are then converted into unintegrated PDFs (UPDFs) via the Kimber-Martin-Ryskin (KMR) scheme. The resulting PDFs and UPDFs are incorporated into the two-component model to predict the charged-particle pseudorapidity density $\left(1 / N_{\mathrm{ev}}\right) d N_{\mathrm{ch}} / d η$ in $pp$ collisions at LHC energies. Our predictions are compared to the data from the ATLAS experiment, revealing that the model effectively captures the features of the observed pseudorapidity distributions, despite its simplicity. Within this framework, the gluon-gluon fusion processes are found to dominate particle production for $\sqrt { s } \ge 9 0 0 \ \mathrm { GeV }$.These findings provide phenomenological support for MD-DGLAP-based PDFs and the associated small-$x$ gluon dynamics. Furthermore,a comparative analysis of results from alternative PDF sets--including CTEQ, MSHT, NNPDF, HERAPDF, and GRV--is performed, with particular focus on examining their consistency with the relative shapes of experiment data in the small-$x$ region.

Figures (6)

• Figure 1: Integrated and unintegrated gluon distributions.Top: the integrated gluon distribution functions $xg(x,Q^{2})$, evolved using the MD-DGLAP equations (solid lines) and DGLAP equations (dashed lines)(shown for $Q^{2}=1,\,10,\,20~\mathrm{GeV}^{2}$). Bottom: the corresponding gluon unintegrated distribution functions , $f_{g}(x,k_{T}^{2},\mu^{2})/k_{T}^{2}$, obtained from the PDFs via the KMR prescription with higher-twist corrections (solid lines) and without higher-twist corrections (dashed lines) at $\mu^{2}=100~\mathrm{GeV}^{2}$ (shown for $k_{T}^{2}=1,\,10,\,20~\mathrm{GeV}^{2}$).
• Figure 2: Normalization coefficient $C(\sqrt{s})$ in the central component of the two-component model. The solid line represents a linear fit in logarithmic scale.
• Figure 3: Comparison of the scaled two-component model predictions with ATLAS data($n_{ch}\ge1,p_{t}>500 \ \mathrm{MeV}$) for $(1/N_{\mathrm{ev}}) \cdot (\mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta) \quad \text{vs.} \quad \eta$ at 0.9, 2.36, 7, 13 TeV respectively. The model is normalized to match the data at $\eta=0$.
• Figure 4: Predictions of Charged-Particle Pseudorapidity Spectra in pp Collisions at 0.9, 2.36, 7, 13 TeV respectively. Using Different PDF Sets, compared to ATLAS Measurements.
• Figure 5: Predictions of Charged-Particle Pseudorapidity Spectra in $pp$ Collisions, as in Fig. \ref{['fig:VariedPDFs']}, but calculated with the constant $C(\sqrt{s}) = 1$.