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

We report a systematic measurement of cumulants, C₍, for net-proton, proton, and antiproton multiplicity distributions, and correlation functions, ₍, for proton and antiproton multiplicity distributions up to the fourth order in Au+Au collisions at s₍₍=7. 7, 11. 5, 14. 5, 19. 6, 27, 39, 54. 4, 62. 4, and 200 GeV. The C₍ and ₍ are presented as a function of collision energy, centrality and kinematic acceptance in rapidity, y, and transverse momentum, pₓ. 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<pₓ<2. 04pt{0ex}GeV/c, using the STAR detector at RHIC. We observe a nonmonotonic energy dependence (s₍₍ = 7. 7--62. 4 GeV) of the net-proton C₄/C₂ with the significance of 3. 1 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 s₍₍. For the multiparticle correlation functions, we observe significant negative values for a two-particle correlation function, 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, ₄, of protons plays a role in determining the energy dependence of proton C₄/C₁ below 19. 6 GeV, which cannot be understood by the effect of baryon number conservation.