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, correlation functions, $\kappa_n$, 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, 62.4 200 GeV. The $C_{n}$ $\kappa_n$ are presented as function collision energy, centrality kinematic acceptance rapidity, $y$, transverse momentum, $p_{T}$. data were taken during first phase Beam Energy Scan (BES) program (2010 -- 2017) BNL Relativistic Heavy Ion Collider (RHIC) facility. measurements carried out midrapidity ($|y| <$ 0.5) momentum 0.4 $<$ $p_{\rm T}$ 2.0 GeV/$c$, using STAR detector RHIC. observe non-monotonic energy dependence ($\sqrt{s_{\mathrm 7.7 GeV) net-proton $C_{4}$/$C_{2}$ with significance 3.1$\sigma$ 0-5\% central collisions. This is consistent expectations critical fluctuations QCD-inspired model. Thermal transport model calculations show monotonic variation {NN}}}$. For multiparticle we significant negative values two-particle function, $\kappa_2$, protons antiprotons, which mainly due effects baryon number conservation. Furthermore, it found that four-particle $\kappa_4$, plays role determining $C_4/C_1$ below 19.6 GeV, cannot be understood by effect