Scaling properties of the $\mathrm{\Delta }\gamma$ correlator and their implication for detection of the chiral magnetic effect in heavy-ion collisions

The scaling properties of the $\mathrm{\Delta }\gamma$ correlator, inferred from the Anomalous Viscous Fluid Dynamics (AVFD) model, are used to investigate a possible chiral-magnetically-driven (CME) charge separation in $p$+Au, $d$+Au, Ru+Ru, Zr+Zr, and Au+Au collisions at ${\sqrt{s}}_{\mathrm{N}\mathrm{N}}=200$ GeV, and in $p$+Pb (${\sqrt{s}}_{\mathrm{N}\mathrm{N}}=5.02$ TeV) and Pb+Pb collisions at ${\sqrt{s}}_{\mathrm{N}\mathrm{N}}=5.02$ and $2.76$ TeV. The results indicate that the values of the quotient $\mathrm{\Delta }\gamma \mathrm{/}{v}_2$ with the elliptic flow coefficient $v_2$ for $p$+Au, $d$+Au, $p$+Pb, and Pb+Pb collisions, scale as $1\mathrm{/}{\mathrm{N}}_{\mathrm{c}\mathrm{h}}$ consistent with background-driven charge separation. By contrast, the $\mathrm{\Delta }\gamma \mathrm{/}{v}_2$ values for Ru+Ru, Zr+Zr, and Au+Au collisions show scaling violations consistent with the presence of background plus a CME-driven contribution. Quantifying this CME-driven component indicates that in mid-central collisions, the fraction of the measured $\mathrm{\Delta }\gamma \mathrm{/}{v}_2$ attributable to the CME is approximately 27% for Au+Au and roughly a factor of two smaller for Ru+Ru and Zr+Zr, which show similar magnitudes.