Charge separation measurements in $p$($d$)+Au and Au+Au collisions; implications for the chiral magnetic effect

Charge separation ($\mathrm{\Delta }S$) measurements, obtained relative to the $2^{\mathrm{n}\mathrm{d}}$-order (${\mathrm{\Psi }}_2$) and $3^{\mathrm{r}\mathrm{d}}$-order (${\mathrm{\Psi }}_3$) event planes with a new charge-sensitive correlator $R_{{\mathrm{\Psi }}_m}(\mathrm{\Delta }S)$, are presented for $p$($d$)+Au and Au+Au collisions at $\sqrt{s_{NN}}=200$~GeV. The correlator, which is sensitive to the hypothesized Chiral Magnetic Effect (CME), show the expected patterns of background-driven charge separation for the measurements relative to ${\mathrm{\Psi }}_3$ and those relative to ${\mathrm{\Psi }}_2$ for the $p$($d$)+Au systems. By contrast, the Au+Au measurements relative to ${\mathrm{\Psi }}_2$, show event-shape-independent $R_{{\mathrm{\Psi }}_2}(\mathrm{\Delta }S)$ distributions consistent with a CME-driven charge separation, quantified by widths having an inverse relationship to the Fourier dipole coefficient ${\tilde{a}}_1$, which evaluates the CME. The extracted values of these widths and their dependencies on centrality and event-shape give new constraints for possible CME-driven charge separation in relativistic heavy-ion collisions.