Event-by-event analysis of chiral charge separation in $p^{\uparrow}+$Au collisions within an improved AMPT model
We study the charge separation induced by chiral magnetic effect (CME) in $p^{\uparrow}$+Au collisions at $\sqrt{s_{NN}}=200$ GeV event-by-event with an improved string-melting AMPT model. In this model, an impact-parameter-dependent formation-time delay is introduced to reduce the peak Bjorken energy density from $\sim$2 to $\sim$0.3 GeV/fm$^3$ and reproduces the illiptic flow $v_2(p_T)$ measured by PHENIX in $p+$Au simultaneously. The event-by-event CME source, whose quark momentum-exchange fraction scales with $|\mathbf{B}|_{\mathrm{event}}/|\mathbf{B}|_{\mathrm{max}}$ and is capped at the 7\% value from Au+Au, transmits the field geometry directly to the observable. We find that the initial correlator shows a clear scheme hierarchy tracking $B^2$. The parton cascade preserves $\sim$80--90\% of the signal, while coalescence and ART hadronic rescattering dissipate the bulk, leaving $\sim$10--30\% in the final state. The $γ_{OS}/γ_{SS}$ splitting remains visible. These results support the use of the inter-scheme difference $Δγ_{\mathrm{IV}}-Δγ_{\mathrm{II}}$ as an essentially background-free CME observable as we proposed in previous work.