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Multi-Parameter Rating Methodology for Systematic Comparison of Theoretical Models with Experimental Data in Heavy-Ion Physics

V. M. Pugatch, S. O. Omelchenko

Abstract

We introduce a novel multi-parameter rating methodology for objective comparison of theoretical models with experimental data in heavy-ion collisions, addressing fundamental limitations of the traditional global $χ^2$/ndf criterion. The methodology divides phase space into seven physically motivated kinematic regions reflecting distinct production mechanisms from thermal freeze-out to perturbative QCD. Each region receives a quality score $Q_i \in [10, 1000]$ via logarithmic transformation of local $χ^2_i/ν_i$ statistics, ranging from 10 (very poor agreement) to 1000 (perfect agreement). A composite rating $R$ aggregates weighted average, geometric mean, and minimum scores with dispersion penalty, preventing compensation of poor agreement in one region by artificial success elsewhere. Demonstrated on real ALICE and representative LHCb data for $K^0_S$ mesons and $Λ$ hyperons at $\sqrt{s_{NN}} = 5.02$ TeV in p-Pb collisions, the methodology reveals that no universal model exists: PYTHIA8 excels for mesons ($R=879$) via nuclear PDFs, while models with coalescence are potentially superior for baryons. The baryon anomaly peak serves as critical discriminator, with highest quality scores $Q_i \sim 950\text{--}1000$ in zones $3\text{--}4$. The methodology is transparent, reproducible, fully algorithmic, and ready for integration into standard analysis frameworks.

Multi-Parameter Rating Methodology for Systematic Comparison of Theoretical Models with Experimental Data in Heavy-Ion Physics

Abstract

We introduce a novel multi-parameter rating methodology for objective comparison of theoretical models with experimental data in heavy-ion collisions, addressing fundamental limitations of the traditional global /ndf criterion. The methodology divides phase space into seven physically motivated kinematic regions reflecting distinct production mechanisms from thermal freeze-out to perturbative QCD. Each region receives a quality score via logarithmic transformation of local statistics, ranging from 10 (very poor agreement) to 1000 (perfect agreement). A composite rating aggregates weighted average, geometric mean, and minimum scores with dispersion penalty, preventing compensation of poor agreement in one region by artificial success elsewhere. Demonstrated on real ALICE and representative LHCb data for mesons and hyperons at TeV in p-Pb collisions, the methodology reveals that no universal model exists: PYTHIA8 excels for mesons () via nuclear PDFs, while models with coalescence are potentially superior for baryons. The baryon anomaly peak serves as critical discriminator, with highest quality scores in zones . The methodology is transparent, reproducible, fully algorithmic, and ready for integration into standard analysis frameworks.
Paper Structure (20 sections, 17 equations, 8 figures, 8 tables)

This paper contains 20 sections, 17 equations, 8 figures, 8 tables.

Table of Contents

  1. Introduction
  2. The Masking Problem
  3. Goal and Key Innovation
  4. Structure
  5. Methodology
  6. Why Exactly Seven $p_T$ Zones?
  7. Local Statistics and Quality Score Scale
  8. Weight Coefficients
  9. Aggregated Metrics and Composite Rating
  10. Visualization Tools
  11. Database Structure and Reproducibility
  12. Application to Real Data
  13. Nuclear Modification Factors for Mesons and Baryons
  14. The Baryon Anomaly as Critical Discriminator
  15. Models and Data Sources
  16. ...and 5 more sections

Figures (8)

  • Figure 1: Radar (spider) plot illustrating the multi-criteria comparison of models. Each axis corresponds to a normalized observable, highlighting the inherent trade-offs between different physics constraints.
  • Figure 2: Heatmap of quality scores $Q_i$ for seven theoretical models across seven $p_T$ zones. Viridis color scale: yellow indicates excellent agreement ($Q_i \geq 900$), purple indicates poor agreement ($Q_i \leq 500$). Reveals model complementarity: hydrodynamic models (EPOS-LHC, AMPT) excel at low $p_T$, pQCD generators (PYTHIA8, HIJING) at high $p_T$. Values are derived from Table \ref{['tab:start_params']} using Eq. \ref{['eq:qi_formula']}.
  • Figure 3: Scatter plot illustrating correlations and conflicts between different observables entering the analysis. The non-trivial structure motivates the use of an aggregated quality measure.
  • Figure 4: Nuclear Modification Factor $R_{pPb}$ for $K^0_S$ mesons in p-Pb (forward, red squares) and Pb-p (backward, blue circles) configurations at $\sqrt{s_{NN}} = 5.02$ TeV. Vertical dashed lines mark zone boundaries. Full 7-zone methodology (0 to $>$10 GeV/c); experimental data limited to 4.5 GeV/c (zones 1--4 fully covered, zone 5 partial); zones 5--7 extrapolated based on pQCD expectations. Boxed $Q_i$ values (850, 900, 950, 1000, 800, 750, 700) are illustrative scale labels showing the methodology's scoring range; computed values require model-specific $\chi^2_i/\nu_i$ comparisons.
  • Figure 5: Forward--backward asymmetry for $K^0_S$ mesons, contributing to the final quality indicator. The asymmetry pattern reflects the interplay of nuclear PDF effects and energy loss mechanisms. Values are averaged over data points in each zone.
  • ...and 3 more figures