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Scaling properties of background- and chiral-magnetically-driven charge separation in heavy ion collisions at $\sqrt s_{\mathrm{NN}}=200$ GeV

The Anomalous Viscous Fluid Dynamics model, AVFD, is used in concert with the charge-sensitive correlator $R_{Ψ_2}(ΔS)$ to investigate the scaling properties of background- and chiral-magnetically-driven (CME) charge separation ($ΔS$), characterized by the inverse variance $\mathrm{σ^{-2}_{R_{Ψ_2}}}$ of the $R_{Ψ_{2}}(ΔS)$ distributions obtained in collisions at $\sqrt s_{\mathrm{NN}}=200$ GeV. The $\mathrm{σ^{-2}_{R_{Ψ_2}}}$ values for the background are observed to be event-shape-independent. However, they scale with the reciprocal charged-particle multiplicity $(1/\left< N_{\rm ch} \right>)$, indicating an essential constraint for discerning background from the signal and a robust estimate of the difference between the backgrounds in Ru+Ru and Zr+Zr collisions. By contrast, the $\mathrm{σ^{-2}_{R_{Ψ_2}}}$values for signal + background show characteristic $1/\left< N_{\rm ch} \right>$ scaling violations that characterize the CME-driven contributions. Corrections to recent ${R_{Ψ_2}(ΔS)}$ measurements \cite{STAR:2021mii} that account for the background difference in Ru+Ru and Zr+Zr collisions indicate a charge separation difference compatible with the CME. The results further suggest that $\mathrm{σ^{-2}_{R_{Ψ_2}}}$ measurements for peripheral and central collisions in concert with $1/\left< N_{\rm ch} \right>$ scaling, provides a robust constraint to quantify the background and aid characterization of the CME.