Speakers
Description
The Rating Quality for Theoretical Description of Experimental Data
S. O. Omelchenko, V. M. Pugatch
Institute for Nuclear Research, National Academy of Sciences of Ukraine, Kyiv, Ukraine
$1.$ $Introduction.$ A new multi-parameter score-rating methodology for assessing the quality of theoretical description of experimental data in heavy-ion physics [1-11] is proposed. The approach overcomes the limitations of the traditional single-value criterion $\chi^2/\mathrm{ndf}$, which provides only an integral measure of agreement between theory and experiment.
The methodology is based on dividing the phase space into seven physically motivated kinematic regions of transverse momentum $p_T$ distributions and particle ratios, corresponding to different underlying physical regimes. For each region, the quality of agreement is quantified by a score $Q_i \in [10;1000]$ defined on a scale, ranging from very poor to excellent agreement.
A comprehensive rating $R$ is constructed through a systematic procedure that includes region definition, weighting according to physical significance, aggregation of local scores, uncertainty estimation, stability checks, and visualization. This framework enables a transparent and comparative assessment of theoretical models, revealing their region-specific performance and complementarity.
$2.$ $Methodology.$ The phase space is divided into seven kinematic regions corresponding to different physical regimes: thermal spectra ($p_T < 0.8$ GeV/$c$), radial flow, hard processes relevant to QGP formation ($2.5$--$4.0$ GeV/$c$), medium-energy jets, high-energy jets with quenching, and the perturbative QCD regime ($p_T > 10$ GeV/$c$).
For each region, the local statistic is defined as:
$$R_i = \frac{\chi_i^2}{\nu_i}, \qquad \nu_i = N_i - k$$
where $N_i$ is the number of data points and $k$ is the number of model parameters.
$3.$ $Score$ $Assignment.$ Based on the value of $R_i$, a quality score $Q_i$ is assigned using a scale, ranging from $Q_i = 1000$ for excellent agreement to $Q_i = 10$ for very poor agreement.
$4.$ $Weighting$ $and$ $Aggregation.$ Weight coefficients reflect the physical significance of different kinematic regions. The aggregated quality measures include weighted averaging, geometric mean, minimum score, and dispersion penalties.
$5.$ $Results$ $and$ $Discussion.$ The methodology was applied to LHC data for $K^0_S$
mesons and $\Lambda$ hyperons in $p$-$Pb$ collisions at $\sqrt{s_{NN}} = 5.02$ TeV. The analysis demonstrates model complementarity and sensitivity to nuclear shadowing effects.
$6.$ $Conclusions.$ The proposed score-rating methodology provides a transparent and robust framework for ranking theoretical models in heavy-ion physics and is well suited for systematic studies of LHC Run 3 data and beyond.
$References$
[1] ALICE Collaboration, Phys.Lett.B 846 (2024) 137875.
[2] U.Heinz, R.Snellings, Ann.Rev.Nucl.Part.Sci. 63 (2013) 123.
[3] J.E. Bernhard et al., Phys.Rev.C 103 (2021) 054904.
[4] K.Werner et al., Phys.Rev.C 85 (2013) 064907.
[5] Z.W.Lin et al., Phys.Rev.C 72 (2005) 064901.
[6] JET Collaboration, J.Phys.G 47 (2020) 065101.
[7] CMS Collaboration, JHEP 04 (2017) 039.
[8] T.Sjöstrand et al., Comput.Phys.Commun. 191 (2015) 159.
[9] X.N.Wang, M.Gyulassy, Phys.Rev.D 44 (1991) 3501.
[10] J.S.Moreland et al., Phys.Rev.C 92 (2015) 011901.
[11] W.Cassing, E.L.Bratkovskaya, Nucl.Phys.A 831 (2009) 215.
