Wounded parton scaling of multiplicities in ultra-relativistic light- and heavy-ion collisions

Technical Summary: Wounded Parton Scaling of Multiplicities in Ultra-Relativistic Light- and Heavy-Ion Collisions

Problem Statement
The paper addresses the challenge of achieving a universal description of bulk particle production (multiplicities) across diverse collision systems—from light ions (O+O, Ne+Ne) to heavy ions (Xe+Xe, Pb+Pb)—at ultra-relativistic energies ($\sqrt{s_{NN}} \sim 5$ TeV) at the LHC. While multiplicity is a fundamental observable reflecting initial entropy deposition, previous models often struggle to describe data uniformly across different system sizes and centralities. A specific difficulty arises in defining centrality bins for ultra-peripheral collisions due to the interference of Coulomb interactions with strong interactions, leading to normalization uncertainties. Furthermore, it remains to be determined whether a single set of physical parameters, based on partonic degrees of freedom, can describe the entire spectrum of collision systems without system-specific adjustments.

Methodology
The authors employ a Wounded Parton Model (WPM) implemented within the GLISSANDO 3 framework, overlaid with Negative Binomial (NB) fluctuations. The core methodology involves the following steps:

1. Initial State Modeling: Nucleons are modeled as consisting of $N_p$ constituent partons. The spatial distribution of these partons within a nucleon follows an exponential density profile, while the parton-parton inelastic collision profile is Gaussian. The nucleons themselves are distributed according to Woods-Saxon (Pb, Ne), Harmonic Oscillator (O), or deformed Woods-Saxon (Xe) distributions.
2. Entropy Deposition: The model assumes that each "wounded" parton (one that undergoes at least one inelastic collision) deposits entropy into the initial fireball. This entropy deposition is subject to quantum fluctuations, modeled by summing independent Negative Binomial distributions for each wounded parton. The total entropy $S$ is proportional to the final charged particle multiplicity ($N_{ch} = \beta S$).
3. Data Handling and Fitting Strategy: To avoid normalization issues associated with Coulomb interactions and detector efficiency at the lowest multiplicities (most peripheral events), the authors do not use pre-defined experimental centrality classes. Instead, they perform a direct fit to the uncorrected experimental multiplicity distributions (histograms) recorded by the ATLAS Collaboration.
4. Fit Range and Parameters: The fit is restricted to the centrality range of 1% to 80%, excluding the most peripheral events (to avoid Coulomb issues) and the most central events (where different production mechanisms like saturation might dominate). The fit minimizes a global $\chi^2$ function across four systems (O+O, Ne+Ne, Xe+Xe, Pb+Pb) simultaneously. The model parameters include:
   • $N_p$: Number of partons per nucleon (tested values: 3, 4, 5).
   • $\kappa$: The NB distribution parameter governing fluctuations.
   • $\beta$: The proportionality factor between entropy and multiplicity.
   • $\gamma_{AA}$: System-specific normalization factors to account for experimental histogram normalization uncertainties.

Key Contributions

• Universal Description: The paper demonstrates that a single set of model parameters (specifically $N_p=4$ or $5$, $\beta$, and $\kappa$) can simultaneously describe the full multiplicity distributions for light and heavy ion collisions at $\sqrt{s_{NN}} \approx 5$ TeV.
• Direct Histogram Fitting: By fitting directly to uncorrected experimental histograms and excluding the most peripheral range, the authors circumvent the ambiguities in normalizing cross-sections caused by electromagnetic effects, providing a more robust comparison between theory and data.
• Partonic Scaling: The study confirms that scaling based on wounded partons (rather than wounded nucleons) is necessary to describe the data, particularly for the high-energy Pb-Pb and p-Pb spectra, requiring approximately four partons per nucleon for the best fit.

Results

• Optimal Parameters: The best description is obtained with four partons per nucleon ($N_p=4$). The optimal parameters are $\beta = 2.51$ and $\kappa = 0.23$. The system-specific normalization factors are found to be $\gamma_{OO} \approx 1.0$, $\gamma_{NeNe} \approx 1.0$, $\gamma_{XeXe} \approx 1.27$, and $\gamma_{PbPb} \approx 0.86$.
• Model Performance:
  • For O+O and Ne+Ne, the model reproduces the experimental data within 5% across the 1–80% centrality range.
  • For Xe+Xe and Pb+Pb, the model describes the data well at lower multiplicities (higher centralities) but systematically overshoots the data at high multiplicities (centralities below $\approx 3\%$).
• Mean Multiplicity: When comparing mean multiplicities in standard centrality bins, the ratio of model to experiment is consistent with unity for all systems and centrality windows, confirming the validity of wounded parton scaling for average production.

Significance and Claims
The authors claim that the wounded-parton model with 4–5 partons per nucleon provides a proper description of average particle production across collisions with vastly different system sizes at LHC energies. This universality suggests that the initial entropy deposition within the wounded parton framework can serve as a reliable basis for initial conditions in hydrodynamic calculations for both light-ion and heavy-ion collisions.

The paper modestly notes that the discrepancy in the most central heavy-ion collisions (where the model overshoots data) may indicate the presence of saturation-like effects in the densest systems or unaccounted efficiency corrections in the uncorrected data. The work does not propose new experimental setups but validates a unified theoretical framework for interpreting existing LHC data.