Cumulants and correlation functions of net-proton, proton, and antiproton multiplicity distributions in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>Au</mml:mi><mml:mo>+</mml:mo><mml:mi>Au</mml:mi></mml:mrow></mml:math> collisions at energies available at the BNL Relativistic Heavy Ion Collider

We report a systematic measurement of cumulants, ${C}_{n}$, for net-proton, proton, and antiproton multiplicity distributions, and correlation functions, ${\ensuremath{\kappa}}_{n}$, for proton and antiproton multiplicity distributions up to the fourth order in $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{{s}_{NN}}=7.7$, 11.5, 14.5, 19.6, 27, 39, 54.4, 62.4, and 200 GeV. The ${C}_{n}$ and ${\ensuremath{\kappa}}_{n}$ 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 ($|y|&lt;$ 0.5) and transverse momentum $0.4&lt;{p}_{T}&lt;2.0\phantom{\rule{4pt}{0ex}}\mathrm{GeV}/c$, using the STAR detector at RHIC. We observe a nonmonotonic energy dependence ($\sqrt{{s}_{NN}}$ = 7.7--62.4 GeV) of the net-proton ${C}_{4}/{C}_{2}$ with the significance of $3.1\ensuremath{\sigma}$ for the 0--5% central $\mathrm{Au}+\mathrm{Au}$ 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 $\sqrt{{s}_{NN}}$. For the multiparticle correlation functions, we observe significant negative values for a two-particle correlation function, ${\ensuremath{\kappa}}_{2}$, 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, ${\ensuremath{\kappa}}_{4}$, 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.