Net-Proton Number Cumulants in Strongly and Weakly Coupled QGP

Abstract: We provide a description of the QCD phase diagram across different energy regimes. Without any adjustable free parameters fitted to lattice or experimental data, we demonstrate that the net-proton number cumulant ratios from the Beam Energy Scan-I (BES-I) central ($0-5\%$) Au+Au collision experiments at RHIC, for center-of-mass energies $\sqrt{s} \geq 39\,\text{GeV}$, are well described by the $\textit{dynamical soft-wall}$ AdS black hole model, indicating the formation of a strongly coupled quark-gluon plasma (sQGP) dominated by gluons in the large $N_c$ limit. We identify a critical point at $\mu_B = 247\,\text{MeV}$ or $\sqrt{s}=16\,\text{GeV}$ in this model, where net-proton cumulant ratios show non-monotonic variation. However, for $\sqrt{s} < 39\,\text{GeV}$, the recent BES-II data does not exhibit the expected variation due to the critical point, suggesting instead a transition to a nearly-cold ($\mu_B \gg T$) weakly coupled QGP (wQGP), for $\sqrt{s} < 7.7\,\text{GeV}$, dominated by valence quarks. This prediction can be tested by the upcoming STAR Fixed-Target experimental data.