Cumulants and Correlation Functions of Net-proton, Proton and Antiproton Multiplicity Distributions in Au+Au Collisions at energies available at the BNL Relativistic Heavy Ion Collider

Abstract

We report a systematic measurement of cumulants, $C_n$, for net-proton, proton and antiproton multiplicity distributions, and correlation functions, $\hat{I}{º}_n$, for proton and antiproton multiplicity distributions up to the fourth order in Au+Au collisions at $\sqrt{s_{\mathrm{NN}}}$ = 7.7, 11.5, 14.5, 19.6, 27, 39, 54.4, 62.4 and 200 GeV. The $C_n$ and $\hat{I}{º}_n$ are presented as a function of collision energy, centrality and kinematic acceptance in rapidity, $y$, and transverse momentum, $p_T$. The data were taken during the first phase of the Beam Energy Scan (BES) program (2010 -- 2017) at the BNL Relativistic Heavy Ion Collider (RHIC) facility. The measurements are carried out at midrapidity ($|y|<$ 0.5) and transverse momentum 0.4 $<$ $p_{\mathrm{T}}$ $<$ 2.0 GeV/$c$, using the STAR detector at RHIC. We observe a non-monotonic energy dependence ($\sqrt{s_{\mathrm{NN}}}$ = 7.7 -- 62.4 GeV) of the net-proton $C_4$/$C_2$ with the significance of 3.1$\ddot{I}ƒ$ for the 0-5\% central Au+Au collisions. This is consistent with the expectations of critical fluctuations in a QCD-inspired model. Thermal and transport model calculations show a monotonic variation with $\sqrt{s_{\mathrm{NN}}}$. For the multiparticle correlation functions, we observe significant negative values for a two-particle correlation function, $\hat{I}{º}_2$, of protons and antiprotons, which are mainly due to the effects of baryon number conservation. Furthermore, it is found that the four-particle correlation function, $\hat{I}{º}_4$, of protons plays a role in determining the energy dependence of proton $C_4/C_1$ below 19.6 GeV, which cannot be understood by the effect of baryon number conservation.

34 pages, 25 figures, 8 tables