We report the triton ($t$) production in mid-rapidity ($|y| <$ 0.5) Au+Au collisions at $\sqrt{s_\mathrm{NN}}$= 7.7--200 GeV measured by the STAR experiment from the first phase of the beam energy scan at the Relativistic Heavy Ion Collider (RHIC). The nuclear compound yield ratio ($\mathrm{N}_t \times \mathrm{N}_p/\mathrm{N}_d^2$), which is predicted to be sensitive to the fluctuation of local neutron density, is observed to decrease monotonically with increasing charged-particle multiplicity ($dN_{ch}/d\eta$) and follows a scaling behavior. The $dN_{ch}/d\eta$ dependence of the yield ratio is compared to calculations from coalescence and thermal models. Enhancements in the yield ratios relative to the coalescence baseline are observed in the 0%-10% most central collisions at 19.6 and 27 GeV, with a significance of 2.3$\sigma$ and 3.4$\sigma$, respectively, giving a combined significance of 4.1$\sigma$. The enhancements are not observed in peripheral collisions or model calculations without critical fluctuation, and decreases with a smaller $p_{T}$ acceptance. The physics implications of these results on the QCD phase structure and the production mechanism of light nuclei in heavy-ion collisions are discussed.

We report the energy dependence of mid-rapidity (anti-)deuteron production in Au+Au collisions at $\sqrt{s_\text{NN}} =\ $7.7, 11.5, 14.5, 19.6, 27, 39, 62.4, and 200 GeV, measured by the STAR experiment at RHIC. The yield of deuterons is found to be well described by the thermal model. The collision energy, centrality, and transverse momentum dependence of the coalescence parameter $B_2$ are discussed. We find that the values of $B_2$ for anti-deuterons are systematically lower than those for deuterons, indicating that the correlation volume of anti-baryons is larger than that of baryons at $\sqrt{s_\text{NN}}$ from 19.6 to 39 GeV. In addition, values of $B_2$ are found to vary with collision energy and show a broad minimum around $\sqrt{s_\text{NN}}=\ $20 to 40 GeV, which might imply a change of the equation of state of the medium in these collisions.

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.

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.

The two-particle angular correlation functions, $R_2$, of pions, kaons, and protons in Au+Au collisions at $\sqrt{s_{NN}}=$ 7.7, 11.5, 14.5, 19.6, 27, 39, 62.4, and 200 GeV were measured by the STAR experiment at RHIC. These correlations were measured for both like-sign and unlike-sign charge combinations and versus the centrality. The correlations of pions and kaons show the expected near-side ({\it i.e.}, at small relative angles) peak resulting from short-range mechanisms. The amplitudes of these short-range correlations decrease with increasing beam energy. However, the proton correlation functions exhibit strong anticorrelations in the near-side region. This behavior is observed for the first time in an A+A collision system. The observed anticorrelation is $p_{T}$-independent and decreases with increasing beam energy and centrality. The experimental results are also compared to the Monte Carlo models UrQMD, Hijing, and AMPT.

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 present two-particle $p_{\rm t}$ correlations as a function of event centrality for Au+Au collisions at $\sqrt{s_{\rm NN}}$ = 7.7, 11.5, 14.5, 19.6, 27, 39, 62.4, and 200 GeV at the Relativistic Heavy Ion Collider using the STAR detector. These results are compared to previous measurements from CERES at the Super Proton Synchrotron and from ALICE at the Large Hadron Collider. The data are compared with UrQMD model calculations and with a model based on a Boltzmann-Langevin approach incorporating effects from thermalization. The relative dynamical correlations for Au+Au collisions at $\sqrt{s_{\rm NN}}$ = 200 GeV show a power law dependence on the number of participant nucleons and agree with the results for Pb+Pb collisions at $\sqrt{s_{\rm NN}} = 2.76~ {\rm TeV}$ from ALICE. As the collision energy is lowered from $\sqrt{s_{\rm NN}}$ = 200 GeV to 7.7 GeV, the centrality dependence of the relative dynamical correlations departs from the power law behavior observed at the higher collision energies. In central collisions, the relative dynamical correlations increase with collision energy up to $\sqrt{s_{\rm NN}}$ = 200 GeV in contrast to previous measurements that showed little dependence on the collision energy.

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 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.

Density fluctuations near the QCD critical point can be probed via an intermittency analysis in relativistic heavy-ion collisions. We report the first measurement of intermittency in Au$+$Au collisions at $\sqrt{s_\mathrm{_{NN}}}$ = 7.7-200 GeV measured by the STAR experiment at the Relativistic Heavy Ion Collider (RHIC). The scaled factorial moments of identified charged hadrons are analyzed at mid-rapidity and within the transverse momentum phase space. We observe a power-law behavior of scaled factorial moments in Au$+$Au collisions and a decrease in the extracted scaling exponent ($\nu$) from peripheral to central collisions. The $\nu$ is consistent with a constant for different collisions energies in the mid-central (10-40%) collisions. Moreover, the $\nu$ in the 0-5% most central Au$+$Au collisions exhibits a non-monotonic energy dependence that reaches a possible minimum around $\sqrt{s_\mathrm{_{NN}}}$ = 27 GeV. The physics implications on the QCD phase structure are discussed.