Precision Measurements of Kinematic Scan for Fluctuations of (Net-)proton Multiplicity Distributions in Au+Au Collisions from RHIC-STAR

This work presents measurements of the rapidity-window dependence of event-by-event net-proton cumulants and proton factorial cumulants in Au+Au collisions at $\sqrt{s_{\mathrm{N}\mathrm{N}}}=$7.7 – 27 GeV, using high-statistics data from RHIC BES-II. Protons and antiprotons are identified with improved detector performance within $0.4<p_{\mathrm{T}}<2.0$ GeV/$c$ and $\mathrm{\mid }y\mathrm{\mid }<0.6$, enabling a wide coverage in momentum space to probe long-range correlations near the QCD critical point. In the most central collisions, the proton number ${\kappa }_2\mathrm{/}{\kappa }_1$ and ${\kappa }_3\mathrm{/}{\kappa }_1$ exhibit power-law scaling with the rapidity window, but with exponents below the theoretical expectation, suggesting that the critical point, if it exists, may lie at higher baryon densities. A finite-size scaling analysis of the susceptibility and Binder cumulant study points out a critical baryon chemical potential region in 550 – 650 MeV.