New measurements of directed flow for charged hadrons, characterized by the Fourier coefficient \vone, are presented for transverse momenta $\mathrm{p_T}$, and centrality intervals in Au+Au collisions recorded by the STAR experiment for the center-of-mass energy range $\mathrm{\sqrt{s_{_{NN}}}} = 7.7 - 200$ GeV. The measurements underscore the importance of momentum conservation and the characteristic dependencies on $\mathrm{\sqrt{s_{_{NN}}}}$, centrality and $\mathrm{p_T}$ are consistent with the expectations of geometric fluctuations generated in the initial stages of the collision, acting in concert with a hydrodynamic-like expansion. The centrality and $\mathrm{p_T}$ dependencies of $\mathrm{v^{even}_{1}}$, as well as an observed similarity between its excitation function and that for $\mathrm{v_3}$, could serve as constraints for initial-state models. The $\mathrm{v^{even}_{1}}$ excitation function could also provide an important supplement to the flow measurements employed for precision extraction of the temperature dependence of the specific shear viscosity.

We report systematic measurements of bulk properties of the system created in Au+Au collisions at $\sqrt{s_{\mathrm{NN}}}$ = 14.5 GeV recorded by the STAR detector at the Relativistic Heavy Ion Collider (RHIC).The transverse momentum spectra of $\pi^{\pm}$, $K^{\pm}$ and $p(\bar{p})$ are studied at mid-rapidity ($|y| < 0.1$) for nine centrality intervals. The centrality, transverse momentum ($p_T$),and pseudorapidity ($\eta$) dependence of inclusive charged particle elliptic flow ($v_2$), and rapidity-odd charged particles directed flow ($v_{1}$) results near mid-rapidity are also presented. These measurements are compared with the published results from Au+Au collisions at other energies, and from Pb+Pb collisions at $\sqrt{s_{\mathrm{NN}}}$ = 2.76 TeV. The results at $\sqrt{s_{\mathrm{NN}}}$ = 14.5 GeV show similar behavior as established at other energies and fit well in the energy dependence trend. These results are important as the 14.5 GeV energy fills the gap in $\mu_B$, which is of the order of 100 MeV,between $\sqrt{s_{\mathrm{NN}}}$ =11.5 and 19.6 GeV. Comparisons of the data with UrQMD and AMPT models show poor agreement in general.

We report a systematic measurement of cumulants, $C_{n}$, for net-proton, proton and antiproton multiplicity distributions, and correlation functions, $\kappa_n$, 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 $\kappa_n$ 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 ($|y| <$ 0.5) and transverse momentum 0.4 $<$$p_{\rm T}$$<$ 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$\sigma$ 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, $\kappa_2$, 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, $\kappa_4$, 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.

Azimuthal anisotropy of produced particles is one of the most important observables used to access the collective properties of the expanding medium created in relativistic heavy-ion collisions. In this paper, we present second ($v_{2}$) and third ($v_{3}$) order azimuthal anisotropies of $K_{S}^{0}$, $\phi$, $\Lambda$, $\Xi$ and $\Omega$ at mid-rapidity ($|y|<$1) in Au+Au collisions at $\sqrt{s_{\text{NN}}}$ = 54.4 GeV measured by the STAR detector. The $v_{2}$ and $v_{3}$ are measured as a function of transverse momentum and centrality. Their energy dependence is also studied. $v_{3}$ is found to be more sensitive to the change in the center-of-mass energy than $v_{2}$. Scaling by constituent quark number is found to hold for $v_{2}$ within 10%. This observation could be evidence for the development of partonic collectivity in 54.4 GeV Au+Au collisions. Differences in $v_{2}$ and $v_{3}$ between baryons and anti-baryons are presented, and ratios of $v_{3}$/$v_{2}^{3/2}$ are studied and motivated by hydrodynamical calculations. The ratio of $v_{2}$ of $\phi$ mesons to that of anti-protons ($v_{2}(\phi)/v_{2}(\bar{p})$) shows centrality dependence at low transverse momentum, presumably resulting from the larger effects from hadronic interactions on anti-proton $v_{2}$.

We present STAR measurements of strange hadron ($\mathrm{K}^{0}_{\mathrm S}$, $\Lambda$, $\overline{\Lambda}$, $\Xi^-$, $\overline{\Xi}^+$, $\Omega^-$, $\overline{\Omega}^+$, and $\phi$) production at mid-rapidity ($|y| < 0.5$) in Au+Au collisions at $\sqrt{s_{_{\mathrm{NN}}}}$ = 7.7 - 39 GeV from the Beam Energy Scan Program at the Relativistic Heavy Ion Collider (RHIC). Transverse momentum spectra, averaged transverse mass, and the overall integrated yields of these strange hadrons are presented versus the centrality and collision energy. Antibaryon-to-baryon ratios ($\overline{\Lambda}$/$\Lambda$, $\overline{\Xi}^+$/$\Xi^-$, $\overline{\Omega}^+$/$\Omega^-$) are presented as well, and used to test a thermal statistical model and to extract the temperature normalized strangeness and baryon chemical potentials at hadronic freeze-out ($\mu_{B}/T_{\rm ch}$ and $\mu_{S}/T_{\rm ch}$) in central collisions. Strange baryon-to-pion ratios are compared to various model predictions in central collisions for all energies. The nuclear modification factors ($R_{\textrm{CP}}$) and antibaryon-to-meson ratios as a function of transverse momentum are presented for all collision energies. The $\mathrm{K}^{0}_{\mathrm S}$$R_{\textrm{CP}}$ shows no suppression for $p_{\rm T}$ up to 3.5 $\mathrm{GeV} / c$ at energies of 7.7 and 11.5 GeV. The $\overline{\Lambda}$/$\mathrm{K}^{0}_{\mathrm S}$ ratio also shows baryon-to-meson enhancement at intermediate $p_{\rm T}$ ($\approx$2.5 $\mathrm{GeV} / c$) in central collisions at energies above 19.6 GeV. Both observations suggest that there is likely a change of the underlying strange quark dynamics at collision energies below 19.6 GeV.

Rapidity-odd directed flow measurements at midrapidity are presented for $\Lambda$, $\bar{\Lambda}$, $K^\pm$, $K^0_s$ and $\phi$ at $\sqrt{s_{NN}} =$ 7.7, 11.5, 14.5, 19.6, 27, 39, 62.4 and 200 GeV in Au+Au collisions recorded by the STAR detector at the Relativistic Heavy Ion Collider. These measurements greatly expand the scope of data available to constrain models with differing prescriptions for the equation of state of quantum chromodynamics. Results show good sensitivity for testing a picture where flow is assumed to be imposed before hadron formation and the observed particles are assumed to form via coalescence of constituent quarks. The pattern of departure from a coalescence-inspired sum-rule can be a valuable new tool for probing the collision dynamics.

We report the first measurements of a complete second-order cumulant matrix of net-charge, net-proton, and net-kaon multiplicity distributions for the first phase of the beam energy scan program at RHIC. This includes the centrality and, for the first time, the pseudorapidity window dependence of both diagonal and off-diagonal cumulants in Au+Au collisions at \sNN~= 7.7-200 GeV. Within the available acceptance of $|\eta|<0.5$, the cumulants grow linearly with the pseudorapidity window. Relative to the corresponding measurements in peripheral collisions, the ratio of off-diagonal over diagonal cumulants in central collisions indicates an excess correlation between net-charge and net-kaon, as well as between net-charge and net-proton. The strength of such excess correlation increases with the collision energy. The correlation between net-proton and net-kaon multiplicity distributions is observed to be negative at \sNN~= 200 GeV and change to positive at the lowest collision energy. Model calculations based on non-thermal (UrQMD) and thermal (HRG) production of hadrons cannot explain the data. These measurements will help map the QCD phase diagram, constrain hadron resonance gas model calculations, and provide new insights on the energy dependence of baryon-strangeness correlations. An erratum has been added to address the issue of self-correlation in the previously considered efficiency correction for off-diagonal cumulant measurement. Previously considered unidentified (net-)charge correlation results ($\sigma^{11}_{Q,p}$ and $\sigma^{11}_{Q,k})$ are now replaced with identified (net-)charge correlation ($\sigma^{11}_{Q^{PID},p}$ and $\sigma^{11}_{Q^{PID},k}$)

We report the measurement of $K^{*0}$ meson at midrapidity ($|y|<$ 1.0) in Au+Au collisions at $\sqrt{s_{\rm NN}}$~=~7.7, 11.5, 14.5, 19.6, 27 and 39 GeV collected by the STAR experiment during the RHIC beam energy scan (BES) program. The transverse momentum spectra, yield, and average transverse momentum of $K^{*0}$ are presented as functions of collision centrality and beam energy. The $K^{*0}/K$ yield ratios are presented for different collision centrality intervals and beam energies. The $K^{*0}/K$ ratio in heavy-ion collisions are observed to be smaller than that in small system collisions (e+e and p+p). The $K^{*0}/K$ ratio follows a similar centrality dependence to that observed in previous RHIC and LHC measurements. The data favor the scenario of the dominance of hadronic re-scattering over regeneration for $K^{*0}$ production in the hadronic phase of the medium.

According to first-principle lattice QCD calculations, the transition from quark-gluon plasma to hadronic matter is a smooth crossover in the region μB ≤ T c. In this range the ratio, C6=C2, of net-baryon distributions are predicted to be negative. In this Letter, we report the first measurement of the midrapidity net-proton C6=C2 from 27, 54.4, and 200 GeV Au þ Au collisions at the Relativistic Heavy Ion Collider (RHIC). The dependence on collision centrality and kinematic acceptance in (p T , y) are analyzed. While for 27 and 54.4 GeV collisions the C6=C2 values are close to zero within uncertainties, it is observed that for 200 GeV collisions, the C6=C2 ratio becomes progressively negative from peripheral to central collisions. Transport model calculations without critical dynamics predict mostly positive values except for the most central collisions within uncertainties. These observations seem to favor a smooth crossover in the high-energy nuclear collisions at top RHIC energy.

Balance functions have been measured in terms of relative pseudorapidity ($\Delta \eta$) for charged particle pairs at the Relativistic Heavy-Ion Collider (RHIC) from Au+Au collisions at $\sqrt{s_{\rm NN}}$ = 7.7 GeV to 200 GeV using the STAR detector. These results are compared with balance functions measured at the Large Hadron Collider (LHC) from Pb+Pb collisions at $\sqrt{s_{\rm NN}}$ = 2.76 TeV by the ALICE Collaboration. The width of the balance function decreases as the collisions become more central and as the beam energy is increased. In contrast, the widths of the balance functions calculated using shuffled events show little dependence on centrality or beam energy and are larger than the observed widths. Balance function widths calculated using events generated by UrQMD are wider than the measured widths in central collisions and show little centrality dependence. The measured widths of the balance functions in central collisions are consistent with the delayed hadronization of a deconfined quark gluon plasma (QGP). The narrowing of the balance function in central collisions at $\sqrt{s_{\rm NN}}$ = 7.7 GeV implies that a QGP is still being created at this relatively low energy.