Rapidity($y$) dependence of $v_1$ (top panels) and $v_2$ (bottom panels) of proton and $\Lambda$ baryons (left panels), pions (middle panels) and kaons (right panels) in 10-40% centrality for the $\sqrt{s_{NN}}$ = 3GeV Au+Au collisions. Statistical and systematic uncertainties are shown as bars and gray bands, respectively. Some uncertainties are smaller than the data points. The UrQMD and JAM results are shown as bands:golden, red and blue bands stand for JAM mean-field, UrQMD mean-field and UrQMD cascade mode, respectively. The value of the incompressibility $\kappa$ = 380 MeV is used in the mean-field option. More detailed model descriptions and data comparisons can be found in Supplemental Material.

Rapidity($y$) dependence of $v_1$ (top panels) and $v_2$ (bottom panels) of proton and $\Lambda$ baryons (left panels), pions (middle panels) and kaons (right panels) in 10-40% centrality for the $\sqrt{s_{NN}}$ = 3GeV Au+Au collisions. Statistical and systematic uncertainties are shown as bars and gray bands, respectively. Some uncertainties are smaller than the data points. The UrQMD and JAM results are shown as bands:golden, red and blue bands stand for JAM mean-field, UrQMD mean-field and UrQMD cascade mode, respectively. The value of the incompressibility $\kappa$ = 380 MeV is used in the mean-field option. More detailed model descriptions and data comparisons can be found in Supplemental Material.

Rapidity($y$) dependence of $v_1$ (top panels) and $v_2$ (bottom panels) of proton and $\Lambda$ baryons (left panels), pions (middle panels) and kaons (right panels) in 10-40% centrality for the $\sqrt{s_{NN}}$ = 3GeV Au+Au collisions. Statistical and systematic uncertainties are shown as bars and gray bands, respectively. Some uncertainties are smaller than the data points. The UrQMD and JAM results are shown as bands:golden, red and blue bands stand for JAM mean-field, UrQMD mean-field and UrQMD cascade mode, respectively. The value of the incompressibility $\kappa$ = 380 MeV is used in the mean-field option. More detailed model descriptions and data comparisons can be found in Supplemental Material.

$v_2$ scaled by the number of constituent quarks, $v_2/n_q$ , as a function of scaled transverse kinetic energy ($(m_T − m_0)/n_q$) for pions, kaons and protons from Au+Au collisions in 10-40% centrality at $\sqrt{s_{NN}}$ = 3, 27, and 54.4 GeV for positive charged particles (left panel) and negative charged particles (right panel). Colored dashed lines represent the scaling fit to data in 7.7, 14.5, 27, 54.4, and 200 GeV Au+Au collisions from STAR experiment at RHIC [43–45]. Statistical and systematic uncertainties are shown as bars and gray bands, respectively. Some uncertainties are smaller than the data points.

$v_2$ scaled by the number of constituent quarks, $v_2/n_q$ , as a function of scaled transverse kinetic energy ($(m_T − m_0)/n_q$) for pions, kaons and protons from Au+Au collisions in 10-40% centrality at $\sqrt{s_{NN}}$ = 3, 27, and 54.4 GeV for positive charged particles (left panel) and negative charged particles (right panel). Colored dashed lines represent the scaling fit to data in 7.7, 14.5, 27, 54.4, and 200 GeV Au+Au collisions from STAR experiment at RHIC [43–45]. Statistical and systematic uncertainties are shown as bars and gray bands, respectively. Some uncertainties are smaller than the data points.

$v_2$ scaled by the number of constituent quarks, $v_2/n_q$ , as a function of scaled transverse kinetic energy ($(m_T − m_0)/n_q$) for pions, kaons and protons from Au+Au collisions in 10-40% centrality at $\sqrt{s_{NN}}$ = 3, 27, and 54.4 GeV for positive charged particles (left panel) and negative charged particles (right panel). Colored dashed lines represent the scaling fit to data in 7.7, 14.5, 27, 54.4, and 200 GeV Au+Au collisions from STAR experiment at RHIC [43–45]. Statistical and systematic uncertainties are shown as bars and gray bands, respectively. Some uncertainties are smaller than the data points.

$v_2$ scaled by the number of constituent quarks, $v_2/n_q$ , as a function of scaled transverse kinetic energy ($(m_T − m_0)/n_q$) for pions, kaons and protons from Au+Au collisions in 10-40% centrality at $\sqrt{s_{NN}}$ = 3, 27, and 54.4 GeV for positive charged particles (left panel) and negative charged particles (right panel). Colored dashed lines represent the scaling fit to data in 7.7, 14.5, 27, 54.4, and 200 GeV Au+Au collisions from STAR experiment at RHIC [43–45]. Statistical and systematic uncertainties are shown as bars and gray bands, respectively. Some uncertainties are smaller than the data points.

$v_2$ scaled by the number of constituent quarks, $v_2/n_q$ , as a function of scaled transverse kinetic energy ($(m_T − m_0)/n_q$) for pions, kaons and protons from Au+Au collisions in 10-40% centrality at $\sqrt{s_{NN}}$ = 3, 27, and 54.4 GeV for positive charged particles (left panel) and negative charged particles (right panel). Colored dashed lines represent the scaling fit to data in 7.7, 14.5, 27, 54.4, and 200 GeV Au+Au collisions from STAR experiment at RHIC [43–45]. Statistical and systematic uncertainties are shown as bars and gray bands, respectively. Some uncertainties are smaller than the data points.

$v_2$ scaled by the number of constituent quarks, $v_2/n_q$ , as a function of scaled transverse kinetic energy ($(m_T − m_0)/n_q$) for pions, kaons and protons from Au+Au collisions in 10-40% centrality at $\sqrt{s_{NN}}$ = 3, 27, and 54.4 GeV for positive charged particles (left panel) and negative charged particles (right panel). Colored dashed lines represent the scaling fit to data in 7.7, 14.5, 27, 54.4, and 200 GeV Au+Au collisions from STAR experiment at RHIC [43–45]. Statistical and systematic uncertainties are shown as bars and gray bands, respectively. Some uncertainties are smaller than the data points.

$v_2$ scaled by the number of constituent quarks, $v_2/n_q$ , as a function of scaled transverse kinetic energy ($(m_T − m_0)/n_q$) for pions, kaons and protons from Au+Au collisions in 10-40% centrality at $\sqrt{s_{NN}}$ = 3, 27, and 54.4 GeV for positive charged particles (left panel) and negative charged particles (right panel). Colored dashed lines represent the scaling fit to data in 7.7, 14.5, 27, 54.4, and 200 GeV Au+Au collisions from STAR experiment at RHIC [43–45]. Statistical and systematic uncertainties are shown as bars and gray bands, respectively. Some uncertainties are smaller than the data points.

$v_2$ scaled by the number of constituent quarks, $v_2/n_q$ , as a function of scaled transverse kinetic energy ($(m_T − m_0)/n_q$) for pions, kaons and protons from Au+Au collisions in 10-40% centrality at $\sqrt{s_{NN}}$ = 3, 27, and 54.4 GeV for positive charged particles (left panel) and negative charged particles (right panel). Colored dashed lines represent the scaling fit to data in 7.7, 14.5, 27, 54.4, and 200 GeV Au+Au collisions from STAR experiment at RHIC [43–45]. Statistical and systematic uncertainties are shown as bars and gray bands, respectively. Some uncertainties are smaller than the data points.

$v_2$ scaled by the number of constituent quarks, $v_2/n_q$ , as a function of scaled transverse kinetic energy ($(m_T − m_0)/n_q$) for pions, kaons and protons from Au+Au collisions in 10-40% centrality at $\sqrt{s_{NN}}$ = 3, 27, and 54.4 GeV for positive charged particles (left panel) and negative charged particles (right panel). Colored dashed lines represent the scaling fit to data in 7.7, 14.5, 27, 54.4, and 200 GeV Au+Au collisions from STAR experiment at RHIC [43–45]. Statistical and systematic uncertainties are shown as bars and gray bands, respectively. Some uncertainties are smaller than the data points.

$v_2$ scaled by the number of constituent quarks, $v_2/n_q$ , as a function of scaled transverse kinetic energy ($(m_T − m_0)/n_q$) for pions, kaons and protons from Au+Au collisions in 10-40% centrality at $\sqrt{s_{NN}}$ = 3, 27, and 54.4 GeV for positive charged particles (left panel) and negative charged particles (right panel). Colored dashed lines represent the scaling fit to data in 7.7, 14.5, 27, 54.4, and 200 GeV Au+Au collisions from STAR experiment at RHIC [43–45]. Statistical and systematic uncertainties are shown as bars and gray bands, respectively. Some uncertainties are smaller than the data points.

$v_2$ scaled by the number of constituent quarks, $v_2/n_q$ , as a function of scaled transverse kinetic energy ($(m_T − m_0)/n_q$) for pions, kaons and protons from Au+Au collisions in 10-40% centrality at $\sqrt{s_{NN}}$ = 3, 27, and 54.4 GeV for positive charged particles (left panel) and negative charged particles (right panel). Colored dashed lines represent the scaling fit to data in 7.7, 14.5, 27, 54.4, and 200 GeV Au+Au collisions from STAR experiment at RHIC [43–45]. Statistical and systematic uncertainties are shown as bars and gray bands, respectively. Some uncertainties are smaller than the data points.

$v_2$ scaled by the number of constituent quarks, $v_2/n_q$ , as a function of scaled transverse kinetic energy ($(m_T − m_0)/n_q$) for pions, kaons and protons from Au+Au collisions in 10-40% centrality at $\sqrt{s_{NN}}$ = 3, 27, and 54.4 GeV for positive charged particles (left panel) and negative charged particles (right panel). Colored dashed lines represent the scaling fit to data in 7.7, 14.5, 27, 54.4, and 200 GeV Au+Au collisions from STAR experiment at RHIC [43–45]. Statistical and systematic uncertainties are shown as bars and gray bands, respectively. Some uncertainties are smaller than the data points.

$v_2$ scaled by the number of constituent quarks, $v_2/n_q$ , as a function of scaled transverse kinetic energy ($(m_T − m_0)/n_q$) for pions, kaons and protons from Au+Au collisions in 10-40% centrality at $\sqrt{s_{NN}}$ = 3, 27, and 54.4 GeV for positive charged particles (left panel) and negative charged particles (right panel). Colored dashed lines represent the scaling fit to data in 7.7, 14.5, 27, 54.4, and 200 GeV Au+Au collisions from STAR experiment at RHIC [43–45]. Statistical and systematic uncertainties are shown as bars and gray bands, respectively. Some uncertainties are smaller than the data points.

$v_2$ scaled by the number of constituent quarks, $v_2/n_q$ , as a function of scaled transverse kinetic energy ($(m_T − m_0)/n_q$) for pions, kaons and protons from Au+Au collisions in 10-40% centrality at $\sqrt{s_{NN}}$ = 3, 27, and 54.4 GeV for positive charged particles (left panel) and negative charged particles (right panel). Colored dashed lines represent the scaling fit to data in 7.7, 14.5, 27, 54.4, and 200 GeV Au+Au collisions from STAR experiment at RHIC [43–45]. Statistical and systematic uncertainties are shown as bars and gray bands, respectively. Some uncertainties are smaller than the data points.

$v_2$ scaled by the number of constituent quarks, $v_2/n_q$ , as a function of scaled transverse kinetic energy ($(m_T − m_0)/n_q$) for pions, kaons and protons from Au+Au collisions in 10-40% centrality at $\sqrt{s_{NN}}$ = 3, 27, and 54.4 GeV for positive charged particles (left panel) and negative charged particles (right panel). Colored dashed lines represent the scaling fit to data in 7.7, 14.5, 27, 54.4, and 200 GeV Au+Au collisions from STAR experiment at RHIC [43–45]. Statistical and systematic uncertainties are shown as bars and gray bands, respectively. Some uncertainties are smaller than the data points.

$v_2$ scaled by the number of constituent quarks, $v_2/n_q$ , as a function of scaled transverse kinetic energy ($(m_T − m_0)/n_q$) for pions, kaons and protons from Au+Au collisions in 10-40% centrality at $\sqrt{s_{NN}}$ = 3, 27, and 54.4 GeV for positive charged particles (left panel) and negative charged particles (right panel). Colored dashed lines represent the scaling fit to data in 7.7, 14.5, 27, 54.4, and 200 GeV Au+Au collisions from STAR experiment at RHIC [43–45]. Statistical and systematic uncertainties are shown as bars and gray bands, respectively. Some uncertainties are smaller than the data points.

$v_2$ scaled by the number of constituent quarks, $v_2/n_q$ , as a function of scaled transverse kinetic energy ($(m_T − m_0)/n_q$) for pions, kaons and protons from Au+Au collisions in 10-40% centrality at $\sqrt{s_{NN}}$ = 3, 27, and 54.4 GeV for positive charged particles (left panel) and negative charged particles (right panel). Colored dashed lines represent the scaling fit to data in 7.7, 14.5, 27, 54.4, and 200 GeV Au+Au collisions from STAR experiment at RHIC [43–45]. Statistical and systematic uncertainties are shown as bars and gray bands, respectively. Some uncertainties are smaller than the data points.

Collision energy dependence of (top panel) directed flow slope $dv_1/dy|_{y=0}$ for p, $\Lambda, \pi$(combined from $\pi^{\pm}$), K(combined from $K^{\pm}$ and $K_S^0$), $\phi$ and $\Xi^−$, and (bottom panel) elliptic flow $v_2$ for p, $\pi$(combined from $\pi^{\pm}$) in heavy- ion collisions. Collision centrality for all data from RHIC is 10-40%, except for 4.5 GeV where 10-30% is for $dv_1/dy|_{y=0}$ and 0-30% is for $v_2$. Statistical and systematic uncertainties are shown as bars and gray bands, respectively. Some uncertainties are smaller than the data points. The JAM and UrQMD results are shown as colored bands:golden, red and blue bands stand for JAM mean-field, UrQMD mean-field and UrQMD cascade mode, respectively. For clarity the x-axis value of the data points have been shifted.

Collision energy dependence of (top panel) directed flow slope $dv_1/dy|_{y=0}$ for p, $\Lambda, \pi$(combined from $\pi^{\pm}$), K(combined from $K^{\pm}$ and $K_S^0$), $\phi$ and $\Xi^−$, and (bottom panel) elliptic flow $v_2$ for p, $\pi$(combined from $\pi^{\pm}$) in heavy- ion collisions. Collision centrality for all data from RHIC is 10-40%, except for 4.5 GeV where 10-30% is for $dv_1/dy|_{y=0}$ and 0-30% is for $v_2$. Statistical and systematic uncertainties are shown as bars and gray bands, respectively. Some uncertainties are smaller than the data points. The JAM and UrQMD results are shown as colored bands:golden, red and blue bands stand for JAM mean-field, UrQMD mean-field and UrQMD cascade mode, respectively. For clarity the x-axis value of the data points have been shifted.

Collision energy dependence of (top panel) directed flow slope $dv_1/dy|_{y=0}$ for p, $\Lambda, \pi$(combined from $\pi^{\pm}$), K(combined from $K^{\pm}$ and $K_S^0$), $\phi$ and $\Xi^−$, and (bottom panel) elliptic flow $v_2$ for p, $\pi$(combined from $\pi^{\pm}$) in heavy- ion collisions. Collision centrality for all data from RHIC is 10-40%, except for 4.5 GeV where 10-30% is for $dv_1/dy|_{y=0}$ and 0-30% is for $v_2$. Statistical and systematic uncertainties are shown as bars and gray bands, respectively. Some uncertainties are smaller than the data points. The JAM and UrQMD results are shown as colored bands:golden, red and blue bands stand for JAM mean-field, UrQMD mean-field and UrQMD cascade mode, respectively. For clarity the x-axis value of the data points have been shifted.

Collision energy dependence of (top panel) directed flow slope $dv_1/dy|_{y=0}$ for p, $\Lambda, \pi$(combined from $\pi^{\pm}$), K(combined from $K^{\pm}$ and $K_S^0$), $\phi$ and $\Xi^−$, and (bottom panel) elliptic flow $v_2$ for p, $\pi$(combined from $\pi^{\pm}$) in heavy- ion collisions. Collision centrality for all data from RHIC is 10-40%, except for 4.5 GeV where 10-30% is for $dv_1/dy|_{y=0}$ and 0-30% is for $v_2$. Statistical and systematic uncertainties are shown as bars and gray bands, respectively. Some uncertainties are smaller than the data points. The JAM and UrQMD results are shown as colored bands:golden, red and blue bands stand for JAM mean-field, UrQMD mean-field and UrQMD cascade mode, respectively. For clarity the x-axis value of the data points have been shifted.

Collision energy dependence of (top panel) directed flow slope $dv_1/dy|_{y=0}$ for p, $\Lambda, \pi$(combined from $\pi^{\pm}$), K(combined from $K^{\pm}$ and $K_S^0$), $\phi$ and $\Xi^−$, and (bottom panel) elliptic flow $v_2$ for p, $\pi$(combined from $\pi^{\pm}$) in heavy- ion collisions. Collision centrality for all data from RHIC is 10-40%, except for 4.5 GeV where 10-30% is for $dv_1/dy|_{y=0}$ and 0-30% is for $v_2$. Statistical and systematic uncertainties are shown as bars and gray bands, respectively. Some uncertainties are smaller than the data points. The JAM and UrQMD results are shown as colored bands:golden, red and blue bands stand for JAM mean-field, UrQMD mean-field and UrQMD cascade mode, respectively. For clarity the x-axis value of the data points have been shifted.

Collision energy dependence of (top panel) directed flow slope $dv_1/dy|_{y=0}$ for p, $\Lambda, \pi$(combined from $\pi^{\pm}$), K(combined from $K^{\pm}$ and $K_S^0$), $\phi$ and $\Xi^−$, and (bottom panel) elliptic flow $v_2$ for p, $\pi$(combined from $\pi^{\pm}$) in heavy- ion collisions. Collision centrality for all data from RHIC is 10-40%, except for 4.5 GeV where 10-30% is for $dv_1/dy|_{y=0}$ and 0-30% is for $v_2$. Statistical and systematic uncertainties are shown as bars and gray bands, respectively. Some uncertainties are smaller than the data points. The JAM and UrQMD results are shown as colored bands:golden, red and blue bands stand for JAM mean-field, UrQMD mean-field and UrQMD cascade mode, respectively. For clarity the x-axis value of the data points have been shifted.

Collision energy dependence of (top panel) directed flow slope $dv_1/dy|_{y=0}$ for p, $\Lambda, \pi$(combined from $\pi^{\pm}$), K(combined from $K^{\pm}$ and $K_S^0$), $\phi$ and $\Xi^−$, and (bottom panel) elliptic flow $v_2$ for p, $\pi$(combined from $\pi^{\pm}$) in heavy- ion collisions. Collision centrality for all data from RHIC is 10-40%, except for 4.5 GeV where 10-30% is for $dv_1/dy|_{y=0}$ and 0-30% is for $v_2$. Statistical and systematic uncertainties are shown as bars and gray bands, respectively. Some uncertainties are smaller than the data points. The JAM and UrQMD results are shown as colored bands:golden, red and blue bands stand for JAM mean-field, UrQMD mean-field and UrQMD cascade mode, respectively. For clarity the x-axis value of the data points have been shifted.

Collision energy dependence of (top panel) directed flow slope $dv_1/dy|_{y=0}$ for p, $\Lambda, \pi$(combined from $\pi^{\pm}$), K(combined from $K^{\pm}$ and $K_S^0$), $\phi$ and $\Xi^−$, and (bottom panel) elliptic flow $v_2$ for p, $\pi$(combined from $\pi^{\pm}$) in heavy- ion collisions. Collision centrality for all data from RHIC is 10-40%, except for 4.5 GeV where 10-30% is for $dv_1/dy|_{y=0}$ and 0-30% is for $v_2$. Statistical and systematic uncertainties are shown as bars and gray bands, respectively. Some uncertainties are smaller than the data points. The JAM and UrQMD results are shown as colored bands:golden, red and blue bands stand for JAM mean-field, UrQMD mean-field and UrQMD cascade mode, respectively. For clarity the x-axis value of the data points have been shifted.

Collision energy dependence of (top panel) directed flow slope $dv_1/dy|_{y=0}$ for p, $\Lambda, \pi$(combined from $\pi^{\pm}$), K(combined from $K^{\pm}$ and $K_S^0$), $\phi$ and $\Xi^−$, and (bottom panel) elliptic flow $v_2$ for p, $\pi$(combined from $\pi^{\pm}$) in heavy- ion collisions. Collision centrality for all data from RHIC is 10-40%, except for 4.5 GeV where 10-30% is for $dv_1/dy|_{y=0}$ and 0-30% is for $v_2$. Statistical and systematic uncertainties are shown as bars and gray bands, respectively. Some uncertainties are smaller than the data points. The JAM and UrQMD results are shown as colored bands:golden, red and blue bands stand for JAM mean-field, UrQMD mean-field and UrQMD cascade mode, respectively. For clarity the x-axis value of the data points have been shifted.

(Color online) $\Lambda$ and $\overline{\Lambda}$ spectra on the deuteron and on the gold side in $d$ + Au minimum bias collisions. The data points on the gold side are multiplied by 2 for better visibility. The statistical errors are smaller than the points marking the measurements. The curves show a fit with a Boltzmann function in transverse mass to the data points.

(Color online) (a) Comparison of the measured $\overline{\Lambda}$ yield with model calculations. Statistical errors are shown as vertical error bars, the vertical caps show the quadratic sum of statistical and systematic er- rors including the overall normalization uncertainty. In both panels the target and projectile beam rapidities are indicated by arrows.

(Color online) (b) Comparison of the net $\Lambda$ yield with model calculations. Statistical errors are shown as vertical error bars, the vertical caps show the quadratic sum of statistical and systematic er- rors including the overall normalization uncertainty. In both panels the target and projectile beam rapidities are indicated by arrows.

(Color online) Comparison of $\overline{\Lambda}$ and net $\Lambda$ yields to model calculations for all three centrality classes. Statistical errors are shown as vertical error bars, the vertical caps show the quadratic sum of statistical and systematic errors. Beam rapidity is indicated by arrows.

(Color online) Comparison of $\overline{\Lambda}$ and net $\Lambda$ yields to model calculations for all three centrality classes. Statistical errors are shown as vertical error bars, the vertical caps show the quadratic sum of statistical and systematic errors. Beam rapidity is indicated by arrows.

(Color online) Comparison of $\overline{\Lambda}$ and net $\Lambda$ yields to model calculations for all three centrality classes. Statistical errors are shown as vertical error bars, the vertical caps show the quadratic sum of statistical and systematic errors. Beam rapidity is indicated by arrows.

(Color online) Comparison of $\overline{\Lambda}$ and net $\Lambda$ yields to model calculations for all three centrality classes. Statistical errors are shown as vertical error bars, the vertical caps show the quadratic sum of statistical and systematic errors. Beam rapidity is indicated by arrows.

(Color online) Comparison of $\overline{\Lambda}$ and net $\Lambda$ yields to model calculations for all three centrality classes. Statistical errors are shown as vertical error bars, the vertical caps show the quadratic sum of statistical and systematic errors. Beam rapidity is indicated by arrows.

(Color online) Comparison of $\overline{\Lambda}$ and net $\Lambda$ yields to model calculations for all three centrality classes. Statistical errors are shown as vertical error bars, the vertical caps show the quadratic sum of statistical and systematic errors. Beam rapidity is indicated by arrows.

(Color online) Minimum bias $\overline{\Lambda}/\Lambda$ ratio compared to model calculations. On the deuteron side HIJING/BB shows the best agreement with the results, while on the Au side only AMPT and EPOS give a satisfactory description of the data.

$\overline{\Lambda}/\Lambda$ ratio and net $\Lambda$ and $\overline{\Lambda}$ yields as a function of collision centrality on both the deuteron (left) and the gold side (right). On the deuteron side, centrality is expressed by the number of collisions per deuteron participant, while on the gold side the number of Au participants is chosen. Only statistical errors are shown. The increase in baryon number transport with centrality, shown by the net $\Lambda$ yield, is matched by the increase of $\overline{\Lambda}$-$\Lambda$ pair production, thus keeping the $\overline{\Lambda}/\Lambda$ ratio constant over a wide centrality range.

$\overline{\Lambda}/\Lambda$ ratio and net $\Lambda$ and $\overline{\Lambda}$ yields as a function of collision centrality on both the deuteron (left) and the gold side (right). On the deuteron side, centrality is expressed by the number of collisions per deuteron participant, while on the gold side the number of Au participants is chosen. Only statistical errors are shown. The increase in baryon number transport with centrality, shown by the net $\Lambda$ yield, is matched by the increase of $\overline{\Lambda}$-$\Lambda$ pair production, thus keeping the $\overline{\Lambda}/\Lambda$ ratio constant over a wide centrality range.

$\overline{\Lambda}/\Lambda$ ratio and net $\Lambda$ and $\overline{\Lambda}$ yields as a function of collision centrality on both the deuteron (left) and the gold side (right). On the deuteron side, centrality is expressed by the number of collisions per deuteron participant, while on the gold side the number of Au participants is chosen. Only statistical errors are shown. The increase in baryon number transport with centrality, shown by the net $\Lambda$ yield, is matched by the increase of $\overline{\Lambda}$-$\Lambda$ pair production, thus keeping the $\overline{\Lambda}/\Lambda$ ratio constant over a wide centrality range.

$\overline{\Lambda}/\Lambda$ ratio and net $\Lambda$ and $\overline{\Lambda}$ yields as a function of collision centrality on both the deuteron (left) and the gold side (right). On the deuteron side, centrality is expressed by the number of collisions per deuteron participant, while on the gold side the number of Au participants is chosen. Only statistical errors are shown. The increase in baryon number transport with centrality, shown by the net $\Lambda$ yield, is matched by the increase of $\overline{\Lambda}$-$\Lambda$ pair production, thus keeping the $\overline{\Lambda}/\Lambda$ ratio constant over a wide centrality range.

(Color online) Net $\Lambda dN/dy$ for central, mid-central and peripheral events on both the deuteron and the Au side of the collision. The data are compared to calculations of the distribution of net baryons obtained with the Multichain model [16] with $\alpha$ = 2.9, scaled by 0.1 to account for the conversion from net baryons to net $\Lambda$. An overall scale uncertainty of 10% on the model curves from this conversion is not shown. See text for details.

(Color online) Global polarization of $\Lambda$–hyperons as a function of centrality given as fraction of the total inelastic hadronic cross section. Filled circles show the results for Au+Au collisions at $\sqrt{s_{NN}}$=200 GeV (centrality region 20-70%) and open squares indicate the results for Au+Au collisions at $\sqrt{s_{NN}}$=62.4 GeV (centrality region 0-80%). Only statistical uncertainties are shown.

(Color online) Global polarization of $\overline{\Lambda}$–hyperons as a function of $\overline{\Lambda}$ transverse momentum $p^{\overline{\Lambda}}_{t}$. Filled circles show the results for Au+Au collisions at $\sqrt{s_{NN}}$=200 GeV (centrality region 20-70%) and open squares indicate the results for Au+Au collisions at $\sqrt{s_{NN}}$=62.4 GeV (centrality region 0-80%). Only statistical uncertainties are shown.

(Color online) Global polarization of $\overline{\Lambda}$–hyperons as a function of $\overline{\Lambda}$ pseudorapidity $\eta^{\overline{\Lambda}}$. Filled circles show the results for Au+Au collisions at $\sqrt{s_{NN}}$=200 GeV (centrality region 20-70%). A constant line fit to these data points yields $P_{\Lambda}=(1.8\pm 10.8)\times 10^{-3}$ with $\chi^{2}/ndf=5.5/10$. Open squares show the results for Au+Au collisions as $\sqrt{s_{NN}}$=62.4 GeV (centrality region 0-80%). A constant line fit gives $P_{\Lambda}=(-17.6\pm 11.1)\times 10^{-3}$ with $\chi^{2}/ndf=8.0/10$. Only statistical uncertainties are shown.

(Color online) Global polarization of $\overline{\Lambda}$–hyperons as a function of as a function of centrality. Filled circles show the results for Au+Au collisions at $\sqrt{s_{NN}}$=200 GeV (centrality region 20-70%) and open squares indicate the result for Au+Au collisions at $\sqrt{s_{NN}}$=62.4 GeV (centrality region 0-80%). Only statistical uncertainties are shown.

(Color online) Acceptance correction function $A_{0}(p^{H}_{t}, \eta^{H})$ defined in (10) as a function of $\Lambda$ (filled circles) and $\overline{\Lambda}$ (open squares) transverse momentum (top) and pseudorapidity (bottom). The deviation of this function from unity affects the overall scale of the measured global polarization according to Eq. 9. See the text for details and discussions on $A_{0}$ $p^{H}_{t}$ and $\eta^{H}$ dependence.

(Color online) Acceptance correction function $A_{0}(p^{H}_{t}, \eta^{H})$ defined in (10) as a function of $\Lambda$ (filled circles) and $\overline{\Lambda}$ (open squares) transverse momentum (top) and pseudorapidity (bottom). The deviation of this function from unity affects the overall scale of the measured global polarization according to Eq. 9. See the text for details and discussions on $A_{0}$ $p^{H}_{t}$ and $\eta^{H}$ dependence.

(Color online) Function $A_{2}(p^{H}_{t}, \eta^{H})$ defined in (11) as a function of $\Lambda$ (filled circles) and $\overline{\Lambda}$ (open squares) transverse momentum (top) and pseudorapidity (bottom). The deviation of this function from zero defines the contribution to the observable (3) from $P^{(2)}_{H} (p^{H}_{t}, \eta^{H})$ in the expansion (6).

(Color online) Function $A_{2}(p^{H}_{t}, \eta^{H})$ defined in (11) as a function of $\Lambda$ (filled circles) and $\overline{\Lambda}$ (open squares) transverse momentum (top) and pseudorapidity (bottom). The deviation of this function from zero defines the contribution to the observable (3) from $P^{(2)}_{H} (p^{H}_{t}, \eta^{H})$ in the expansion (6).

High transverse-momentum spectra ($p_{T} > 2.5$ GeV/c) of charged pions, protons, and antiprotons for the rapidity regions $|y| < 0.5$ (solid symbols) and $0.5 < |y| < 1.0$ (open symbols) for $d+Au$ collisions and various event centrality classes at $\sqrt{s_{NN}}=200$ GeV.

High transverse-momentum spectra ($p_{T} > 2.5$ GeV/c) of charged pions, protons, and antiprotons for the rapidity regions $|y| < 0.5$ (solid symbols) and $0.5 < |y| < 1.0$ (open symbols) for $d+Au$ collisions and various event centrality classes at $\sqrt{s_{NN}}=200$ GeV.

High transverse-momentum spectra ($p_{T} > 2.5$ GeV/c) of charged pions, protons, and antiprotons for the rapidity regions $|y| < 0.5$ (solid symbols) and $0.5 < |y| < 1.0$ (open symbols) for $d+Au$ collisions and various event centrality classes at $\sqrt{s_{NN}}=200$ GeV.

High transverse-momentum spectra ($p_{T} > 2.5$ GeV/c) of charged pions, protons, and antiprotons for the rapidity regions $|y| < 0.5$ (solid symbols) and $0.5 < |y| < 1.0$ (open symbols) for $d+Au$ collisions and various event centrality classes at $\sqrt{s_{NN}}=200$ GeV.

High transverse-momentum spectra ($p_{T} > 2.5$ GeV/c) of charged pions, protons, and antiprotons for the rapidity regions $|y| < 0.5$ (solid symbols) and $0.5 < |y| < 1.0$ (open symbols) for $d+Au$ collisions and various event centrality classes at $\sqrt{s_{NN}}=200$ GeV.

High transverse-momentum rapidity asymmetry factor ($Y_{\scriptsize{\mbox{Asym}}}$) for $\pi^{+}+\pi^{-}$ and $p+\bar{p}$ for $|y| < 0.5$ and $0.5 < |y| < 1.0$ for minimum bias $d+Au$ collisions at $\sqrt{s_{NN}}=200$ GeV. For comparison the inclusive charged hadron results from STAR [5] are also shown by the curves.

Centrality dependence of high transverse-momentum rapidity asymmetry factor ($Y_{\scriptsize{\mbox{Asym}}}$) for $\pi^{+}+\pi^{-}$ and $p+\bar{p}$ for $|y| < 0.5$ (left panels) and $0.5 < |y| < 1.0$ (right panels) for $d+Au$ collisions at $\sqrt{s_{NN}}=200$ GeV.

Centrality dependence of high transverse-momentum rapidity asymmetry factor ($Y_{\scriptsize{\mbox{Asym}}}$) for $\pi^{+}+\pi^{-}$ and $p+\bar{p}$ for $|y| < 0.5$ (left panels) and $0.5 < |y| < 1.0$ (right panels) for $d+Au$ collisions at $\sqrt{s_{NN}}=200$ GeV.

Variation of nuclear modification factor ($R_{CP}$) for $\pi^{+}+\pi^{-}$ and $p+\bar{p}$ with rapidity for $p_{T} > 2.5$ GeV/c for $d+Au$ collisions at $\sqrt{s_{NN}}=200$ GeV. Also shown for comparison are the $R_{CP}$ values for inclusive charged hadrons as a function of pseudorapidity [5]. The errors shown as boxes are the systematic errors. The error due to number of binary collisions is $\sim 14\%$ and is not shown in the figure.

Variation of $\pi^{-} / \pi^{+}$ and $\bar{p} / p$ with rapidity for $2.5 < p_{T} < 10$ GeV/c for peripheral ($40-100\%$) and n-tag events for $d+Au$ collisions at $\sqrt{s_{NN}}=200$ GeV. Also shown for comparison are the $\bar{p} / p$ for minimum bias $p+p$ collisions. The boxes are the systematic errors. The ratios for n-tag events are shifted by 0.05 units in rapidity and those for $p+p$ collisions by -0.05 units in rapidity for clarity of presentation.

Variation of $\pi^{-} / \pi^{+}$ and $\bar{p} / p$ with rapidity for $2.5 < p_{T} < 10$ GeV/c for peripheral ($40-100\%$) and n-tag events for $d+Au$ collisions at $\sqrt{s_{NN}}=200$ GeV. Also shown for comparison are the $\bar{p} / p$ for minimum bias $p+p$ collisions. The boxes are the systematic errors. The ratios for n-tag events are shifted by 0.05 units in rapidity and those for $p+p$ collisions by -0.05 units in rapidity for clarity of presentation.

Variation of double ratio $(\pi^{-} / \pi^{+})_{\scriptsize{\mbox{n-tag}}}/(\pi^{-} / \pi^{+})_{40-100\%}$ and $(\bar{p} / p)_{\scriptsize{\mbox{n-tag}}}/(\bar{p} / p)_{40-100\%}$ with rapidity for $2.5 < p_{T} < 10$ GeV/c for $d+Au$ collisions at $\sqrt{s_{NN}}=200$ GeV. The boxes are the systematic errors.

The purity and momentum-resolution corrected correlation functions $C_{true}(k^{*})$ for $p-\Lambda$, $\bar{p}-\bar{\Lambda}$ (a), $\bar{p}-\Lambda$, $p-\bar{\Lambda}$ (b). Curves correspond to fits done using the Lednicky and Lyuboshitz analytical model [12].

$(p-\Lambda) \oplus (\bar{p}-\bar{\Lambda})$ and $(\bar{p}-\Lambda) \oplus (p-\bar{\Lambda})$ combined correlation functions. Correlation functions are corrected for purity and momentum resolution. Curves correspond to fits done using the Lednicky and Lyuboshitz analytical model [12].

The combined $(\bar{p}-\Lambda) \oplus (p-\bar{\Lambda})$ spin-averaged $s$-wave scattering length compared with the previous measurements for the $p-\bar{p}$ system [24-27]. The curves show the one standard deviation contours. Note that for $(\bar{p}-\Lambda) \oplus (p-\bar{\Lambda})$ only, one should read $0.1973 \times \mbox{Im}f_{0}$ instead of $\mbox{Im}f_{0}$ on the x-axis.

The combined $(\bar{p}-\Lambda) \oplus (p-\bar{\Lambda})$ spin-averaged $s$-wave scattering length compared with the previous measurements for the $p-\bar{p}$ system [24-27]. The curves show the one standard deviation contours. Note that for $(\bar{p}-\Lambda) \oplus (p-\bar{\Lambda})$ only, one should read $0.1973 \times \mbox{Im}f_{0}$ instead of $\mbox{Im}f_{0}$ on the x-axis.

Pion source size [5] compared with proton and lambda source sizes as a function of the mean transverse mass $(\langle m_{t}\rangle)$ The curve shows the $\langle m_{t}\rangle^{-1/2}$ dependence with an arbitrary normalization.

$m_{\rm inv}$ dependences of $\Delta\gamma$ in 20-50$\%$ Au+Au collisions at 200 GeV.

The $\pi$ pair $\Delta\gamma$ at $m_{\rm inv} > m_{\rm inv}^{\rm low}$ for the data identified by TPC and more extended $p_T$ range identified by TPC and TOF.

The elliptic flow $v_2$ in bins of $q_2$ for the three centrality bins in the 20-50$\%$ range of Au+Au collisions at 200 GeV.

$m_{\rm inv}$ dependences of the $\Delta\gamma$ from ESE-selected event samples A (50$\%$ largest $q_{2}$) and B (50$\%$ smallest $q_{2}$) in 20-50$\%$ Au+Au collisions at 200 GeV.

$m_{\rm inv}$ dependences of the $\rm \Delta\gamma_{A} - \Delta\gamma_{B}$ in 20-50$\%$ Au+Au collisions at 200 GeV.

$\Delta\gamma_{\rm A}$ versus $\Delta\gamma_{\rm B}$ in 20-50$\%$ Au+Au collisions at 200 GeV. (The data are arranged as function of mass)

Parton dijet $M_{inv}$ vs $A_{LL}$ values with associated uncertainties, for topology C.

Parton dijet $M_{inv}$ vs $A_{LL}$ values with associated uncertainties, for topology D.

The correlation matrix for the point-to-point uncertainties (statistical and systematics) for the inclusive jet measurements.The relative luminosity and beam polarization uncertainties are not included because they are the same for all points.

The correlation matrix for the point-to-point uncertainties (statistical and systematics) for the inclusive jet measurements coupling with the forward-forward dijet measurements (topology A). The relative luminosity and beam polarization uncertainties are not included because they are the same for all points.

The correlation matrix for the point-to-point uncertainties (statistical and systematics) for the inclusive jet measurements coupling with the forward-forward dijet measurements (topology B). The relative luminosity and beam polarization uncertainties are not included because they are the same for all points.

The correlation matrix for the point-to-point uncertainties (statistical and systematics) for the inclusive jet measurements coupling with the forward-forward dijet measurements (topology C). The relative luminosity and beam polarization uncertainties are not included because they are the same for all points.

The correlation matrix for the point-to-point uncertainties (statistical and systematics) for the inclusive jet measurements coupling with the forward-forward dijet measurements (topology D). The relative luminosity and beam polarization uncertainties are not included because they are the same for all points.

The correlation matrix for the point-to-point uncertainties (systematics only) for forward-forward dijet measurements (topology A). The relative luminosity and beam polarization uncertainties are not included because they are the same for all points.

The correlation matrix for the point-to-point uncertainties (systematics only) coupling forward-forward dijet measurements (topology A) with forward-central dijet measurements (topology B). The relative luminosity and beam polarization uncertainties are not included because they are the same for all points.

The correlation matrix for the point-to-point uncertainties (systematics only) coupling forward-forward dijet measurements (topology A) with forward-central dijet measurements (topology C). The relative luminosity and beam polarization uncertainties are not included because they are the same for all points.

The correlation matrix for the point-to-point uncertainties (systematics only) coupling forward-forward dijet measurements (topology A) with forward-central dijet measurements (topology D). The relative luminosity and beam polarization uncertainties are not included because they are the same for all points.

The correlation matrix for the point-to-point uncertainties (systematics only) for forward-forward dijet measurements (topology B). The relative luminosity and beam polarization uncertainties are not included because they are the same for all points.

The correlation matrix for the point-to-point uncertainties (systematics only) coupling forward-forward dijet measurements (topology B) with forward-central dijet measurements (topology C). The relative luminosity and beam polarization uncertainties are not included because they are the same for all points.

The correlation matrix for the point-to-point uncertainties (systematics only) coupling forward-forward dijet measurements (topology B) with forward-central dijet measurements (topology D). The relative luminosity and beam polarization uncertainties are not included because they are the same for all points.

The correlation matrix for the point-to-point uncertainties (systematics only) for forward-forward dijet measurements (topology C). The relative luminosity and beam polarization uncertainties are not included because they are the same for all points.

The correlation matrix for the point-to-point uncertainties (systematics only) coupling forward-forward dijet measurements (topology C) with forward-central dijet measurements (topology D). The relative luminosity and beam polarization uncertainties are not included because they are the same for all points.

The correlation matrix for the point-to-point uncertainties (systematics only) for forward-forward dijet measurements (topology D). The relative luminosity and beam polarization uncertainties are not included because they are the same for all points.

The centrality dependence of Global $\Lambda$-hyperon Polarization at $\sqrt{s_{\rm NN}}=3$ GeV.

The $p_{\rm T}$ dependence of Global $\Lambda$-hyperon Polarization at $\sqrt{s_{\rm NN}}=3$ GeV.

The rapidity dependence of Global $\Lambda$-hyperon Polarization at $\sqrt{s_{\rm NN}}=3$ GeV.

Centrality dependence of the proton cumulant ratios for Au+Au collisions at $\sqrt{s_{NN}}$ = 3.0 GeV. Protons are from $-0.5 < y < 0$ and $0.4 < p_{T} < 2.0$ GeV/$c$. Systematic uncertainties are represented by gray bars. Statistical uncertainties are smaller than marker size. CBWC is applied to all cumulant ratios. While open squares represent the data without the VFC correction, blue triangles and red circles are the results with VFC using the $\langle N_{\rm{part}} \rangle$ distributions from the UrQMD and Glauber models, respectively. UrQMD model results are represented as gold dashed line.

Centrality dependence of the proton cumulant ratios for Au+Au collisions at $\sqrt{s_{NN}}$ = 3.0 GeV. Protons are from $-0.5 < y < 0$ and $0.4 < p_{T} < 2.0$ GeV/$c$. Systematic uncertainties are represented by gray bars. Statistical uncertainties are smaller than marker size. CBWC is applied to all cumulant ratios. While open squares represent the data without the VFC correction, blue triangles and red circles are the results with VFC using the $\langle N_{\rm{part}} \rangle$ distributions from the UrQMD and Glauber models, respectively. UrQMD model results are represented as gold dashed line.

Rapidity and transverse momentum dependence of the proton cumulant ratios for 0–5% central collisions. Black-squares, red-dots and blue-triangles stand for data without and with the VFC using Glauber and UrQMD, respectively.

Rapidity and transverse momentum dependence of the proton cumulant ratios for 0–5% central collisions. Black-squares, red-dots and blue-triangles stand for data without and with the VFC using Glauber and UrQMD, respectively.

Rapidity and transverse momentum dependence of the proton cumulant ratios for 0–5% central collisions. Black-squares, red-dots and blue-triangles stand for data without and with the VFC using Glauber and UrQMD, respectively.

Rapidity and transverse momentum dependence of the proton cumulant ratios for 0–5% central collisions. Black-squares, red-dots and blue-triangles stand for data without and with the VFC using Glauber and UrQMD, respectively.

Collision energy dependence of the ratios of cumulants, $C_4/C_2$, for proton (squares) and net-proton (red circles) from top 0-5% Au+Au collisions at RHIC. The points for protons are shifted horizontally for clarity. The new result for proton from $\sqrt{s_{NN}}$ = 3.0 GeV collisions is shown as a filled square. HADES data of $\sqrt{s_{NN}}$ = 2.4 GeV 0-10% collisions is also shown. The vertical black and gray bars are the statistical and systematic uncertainties, respectively. In addition, results from the HRG model, based on both Canonical Ensemble (CE) and Grand-Canonical Ensemble (GCE), and transport model UrQMD are presented.