Measurement of Fifth- and Sixth-Order Fluctuations of (Net-)proton Number in Au+Au Collisions from Phase II of the Beam Energy Scan Program at RHIC

Abstract

We report high-statistics measurements of fifth- and sixth-order factorial cumulants and cumulant ratios of (net-)proton multiplicity distributions in Au+Au collisions at $\sqrt{s_{NN}} = 7.7$--27 GeV, using data from the STAR experiment collected during the Beam Energy Scan Phase~II at RHIC. Protons and antiprotons are identified at midrapidity ($|y| < 0.5$) with transverse momentum $0.4 < p_T < 2.0$ GeV/$c$. The proton factorial cumulants $\kappa_4$, $\kappa_5$, and $\kappa_6$ increase with order but exhibit no sign alternation within current uncertainties, offering no evidence for a two-component structure in the proton multiplicity distribution, as might be expected near a first-order phase transition. The cumulant ratios $C_{5}/C_{1}$ and $C_{6}/C_{2}$ fluctuate around zero in collisions at 0--40\% centrality. The results are consistent with both the negative predictions from lattice QCD (LQCD) and the positive trends obtained from the Ultra-relativistic Quantum Molecular Dynamics (UrQMD) model. At $\sqrt{s_{NN}} \gtrsim 27$ GeV, the $C_4/C_2$ and $C_5/C_1$ results are compatible with predictions from lattice QCD, functional renormalization group (FRG), and hadron resonance gas (HRG) models, while UrQMD describes the data better at lower energies. These measurements place constraints on baryon number fluctuations and offer valuable insights into the QCD phase structure.