Path-length dependence of parton energy loss across collision systems: a Bayesian analysis of charged-particle RAA, consistent with a universal exponent from O+O to Pb+Pb

Abstract

How parton energy loss in the quark-gluon plasma (QGP) scales with the in-medium path length $L$ encodes the mechanism: collisional ($ΔE \propto L$), radiative ($ΔE \propto L^2$), or strong-coupling ($ΔE \propto L^3$). Exploiting the new CERN LHC light-ion data, we extract this scaling from the system size itself, jointly analysing CMS charged-particle nuclear modification factors $R_{AA}$ in four systems - O+O, Ne+Ne, Xe+Xe and Pb+Pb - spanning mass number $A = 16$ to $208$. A Bayesian analysis with a data-driven spectral baseline and a Monte-Carlo Glauber geometry yields an effective system-size exponent $n = 1.78 \pm 0.15\,\mathrm{(stat)} \pm 0.05\,\mathrm{(syst)}$. Nested-sampling model selection decisively favours an effective exponent near the radiative value ($n = 2$) over the collisional ($n = 1$) and strong-coupling ($n = 3$) values, a conclusion stable across all 160 analysis variants. Because fluctuations can only lower the effective exponent below its microscopic counterpart, the measurement bounds the latter from below at fixed geometry, excluding purely collisional energy loss. The medium density and the path length are degenerate across system size, so we quote the effective exponent as our primary result. A Bayes-factor test finds no change of regime between small and large systems, consistent with a universal exponent; the same framework gives decisive evidence for non-zero energy loss in O+O alone, quantifying the onset of suppression in the smallest system. The energy-loss magnitude corresponds to $\hat{q}/T^3 \approx 2$--$5$, consistent with the JETSCAPE determination.