Scaling Properties of the $\Delta\gamma$ Correlator: Constraints on Background and CME-Sensitive Charge Separation in Heavy-Ion Collisions

Abstract

The scaling properties of the $\Delta\gamma$ correlator are used to investigate charge separation associated with the chiral magnetic effect (CME) in $p$+Au, $d$+Au, Ru+Ru, Zr+Zr, and Au+Au collisions at $\sqrt{s_{\mathrm{NN}}}=200$~GeV, and in $p$+Pb and Pb+Pb collisions at $\sqrt{s_{\mathrm{NN}}}=5.02$ and $2.76$~TeV. Anomalous Viscous Fluid Dynamics (AVFD) calculations provide complementary benchmarks for background and signal+background behavior. Scaling $\Delta\gamma$ by the elliptic-flow coefficient $v_2$ reduces the leading flow-coupled background dependence, while the resulting $\Delta\gamma/v_2$ exhibits a common approximate $1/N_{\rm ch}$ scaling behavior for $p$+Au, $d$+Au, $p$+Pb, and Pb+Pb collisions, consistent with multiplicity dilution of background-driven charge correlations across markedly different collision systems and environments. In contrast, Ru+Ru, Zr+Zr, and Au+Au collisions exhibit systematic positive deviations from their respective $1/N_{\rm ch}$ background-scaling trends. These scaling violations are qualitatively similar to those generated by AVFD calculations with an input CME signal and, relative to the experimentally constrained background scaling, provide evidence for a CME contribution to the measured charge separation. The inferred CME fraction is approximately $27\%$ for mid-central Au+Au collisions and roughly a factor of two smaller for Ru+Ru and Zr+Zr, whose values are consistent within uncertainties. The inferred CME fractions reduce the expected Ru+Ru--Zr+Zr difference to only $\sim1.3\%$ in the total charge-separation signal, explaining its limited experimental sensitivity. These results demonstrate that scaling violations relative to an experimentally constrained background provide a quantitative strategy for isolating a CME contribution to charge separation in heavy-ion collisions.