A Rating Quality Methodology for the Theoretical Description of Experimental Data

Abstract

We introduce a novel multi-parameter rating methodology for comparing theoretical models with experimental data in heavy-ion collisions, addressing limitations of the global ${\chi }^2$/ndf criterion. The methodology divides phase space into seven physically motivated kinematic zones. Each zone receives a quality score $Q_i\in [10,1000]$ via logarithmic transformation of local ${\chi }_i^2/{\nu }_i$ statistics. A composite rating $R$ aggregates weighted average, geometric mean, and minimum scores with a bounded dispersion penalty. The seven-zone division is validated through boundary significance tests on CMS PbPb data at $\sqrt{s_{NN}}=5.02$ TeV: four of six physical boundaries are confirmed significant ($p<0.05$) while none of the data-driven $K=9$ candidates carry independent physical significance. Coefficient sensitivity: $\pm 20\%$ variations produce $\Delta R<2\%$ with zero rank changes. Applied to ALICE data for $K_S^0$ mesons and $\Lambda$ hyperons in p-Pb at $\sqrt{s_{NN}}=5.02$ TeV, the methodology reveals a hierarchy of model universality: PHSD (microscopic QGP transport + coalescence) achieves near-universal performance ($R=911$ for mesons, $R=893$ for baryons on a synthetic LHCb-kinematics benchmark), while PYTHIA8 ($R=878$) leads in the hard-fragmentation regime via nuclear PDFs. The baryon anomaly peak in zones 3--4 yields $Q_i\sim 950$--$1000$ for coalescence models versus $Q_i\sim 400$--$600$ for fragmentation generators. The near-universal performance of PHSD demonstrates that coalescence mechanisms are critical not only for baryon production but also for a globally consistent description of meson spectra. The methodology is transparent, reproducible, and ready for integration into standard analysis frameworks.

Comments: 24 pages, 8 figures, 10 tables; v3: Corrected Keff=6 zone-merging aggregation; updated model rankings (PHSD leads for mesons); clarified data sources for zones 5-7 in Table 9