$v_{2}(p_{T})$ for $K_{S}^{0}$ (Centrality:0-80%)

$v_{3}(p_{T})$ for $K_{S}^{0}$ (Centrality:0-10%)

$v_{3}(p_{T})$ for $K_{S}^{0}$ (Centrality:10-40%)

$v_{3}(p_{T})$ for $K_{S}^{0}$ (Centrality:40-80%)

$v_{3}(p_{T})$ for $K_{S}^{0}$ (Centrality:0-80%)

$v_{2}(p_{T})$ for $\Lambda$ (Centrality:0-10%)

$v_{2}(p_{T})$ for $\Lambda$ (Centrality:10-40%)

$v_{2}(p_{T})$ for $\Lambda$ (Centrality:40-80%)

$v_{2}(p_{T})$ for $\Lambda$ (Centrality:0-80%)

$v_{3}(p_{T})$ for $\Lambda$ (Centrality:0-10%)

$v_{3}(p_{T})$ for $\Lambda$ (Centrality:10-40%)

$v_{3}(p_{T})$ for $\Lambda$ (Centrality:40-80%)

$v_{3}(p_{T})$ for $\Lambda$ (Centrality:0-80%)

$v_{2}(p_{T})$ for $\bar{\Lambda}$ (Centrality:0-10%)

$v_{2}(p_{T})$ for $\bar{\Lambda}$ (Centrality:10-40%)

$v_{2}(p_{T})$ for $\bar{\Lambda}$ (Centrality:40-80%)

$v_{2}(p_{T})$ for $\bar{\Lambda}$ (Centrality:0-80%)

$v_{3}(p_{T})$ for $\bar{\Lambda}$ (Centrality:0-10%)

$v_{3}(p_{T})$ for $\bar{\Lambda}$ (Centrality:10-40%)

$v_{3}(p_{T})$ for $\bar{\Lambda}$ (Centrality:40-80%)

$v_{3}(p_{T})$ for $\bar{\Lambda}$ (Centrality:0-80%)

$v_{2}(p_{T})$ for $\phi$ (Centrality:0-10%)

$v_{2}(p_{T})$ for $\phi$ (Centrality:10-40%)

$v_{2}(p_{T})$ for $\phi$ (Centrality:40-80%)

$v_{2}(p_{T})$ for $\phi$ (Centrality:0-80%)

$v_{3}(p_{T})$ for $\phi$ (Centrality:0-10%)

$v_{3}(p_{T})$ for $\phi$ (Centrality:10-40%)

$v_{3}(p_{T})$ for $\phi$ (Centrality:0-80%)

$v_{2}(p_{T})$ for $\Xi^{-}$ (Centrality:0-10%)

$v_{2}(p_{T})$ for $\Xi^{-}$ (Centrality:10-40%)

$v_{2}(p_{T})$ for $\Xi^{-}$ (Centrality:40-80%)

$v_{2}(p_{T})$ for $\Xi^{-}$ (Centrality:0-80%)

$v_{3}(p_{T})$ for $\Xi^{-}$ (Centrality:0-10%)

$v_{3}(p_{T})$ for $\Xi^{-}$ (Centrality:10-40%)

$v_{3}(p_{T})$ for $\Xi^{-}$ (Centrality:0-80%)

$v_{2}(p_{T})$ for $\bar{\Xi^{+}}$ (Centrality:0-10%)

$v_{2}(p_{T})$ for $\bar{\Xi^{+}}$ (Centrality:10-40%)

$v_{2}(p_{T})$ for $\bar{\Xi^{+}}$ (Centrality:40-80%)

$v_{2}(p_{T})$ for $\bar{\Xi^{+}}$ (Centrality:0-80%)

$v_{3}(p_{T})$ for $\bar{\Xi^{+}}$ (Centrality:0-10%)

$v_{3}(p_{T})$ for $\bar{\Xi^{+}}$ (Centrality:10-40%)

$v_{3}(p_{T})$ for $\bar{\Xi^{+}}$ (Centrality:0-80%)

$v_{2}(p_{T})$ for $\Omega^{-}$ (Centrality:0-10%)

$v_{2}(p_{T})$ for $\Omega^{-}$ (Centrality:10-40%)

$v_{2}(p_{T})$ for $\Omega^{-}$ (Centrality:40-80%)

$v_{2}(p_{T})$ for $\Omega^{-}$ (Centrality:0-80%)

$v_{3}(p_{T})$ for $\Omega^{-}$ (Centrality:0-10%)

$v_{3}(p_{T})$ for $\Omega^{-}$ (Centrality:10-40%)

$v_{3}(p_{T})$ for $\Omega^{-}$ (Centrality:0-80%)

$v_{2}(p_{T})$ for $\bar{\Omega^{+}}$ (Centrality:0-10%)

$v_{2}(p_{T})$ for $\bar{\Omega^{+}}$ (Centrality:10-40%)

$v_{2}(p_{T})$ for $\bar{\Omega^{+}}$ (Centrality:40-80%)

$v_{2}(p_{T})$ for $\bar{\Omega^{+}}$ (Centrality:0-80%)

$v_{3}(p_{T})$ for $\bar{\Omega^{+}}$ (Centrality:0-10%)

$v_{3}(p_{T})$ for $\bar{\Omega^{+}}$ (Centrality:10-40%)

$v_{3}(p_{T})$ for $\bar{\Omega^{+}}$ (Centrality:0-80%)

$v_{2}$ of $\phi$ to $\bar{p}$ ratio

Difference of $v_{2}$ between particle and anti-particle

Difference of $v_{3}$ between particle and anti-particle

Example of combinatorial background subtracted invariant mass distributions and the extracted yields as a function of $\cos \theta^*$ for $\phi$ and $K^{*0}$ mesons. \textbf{a)} example of $\phi \rightarrow K^+ + K^-$ invariant mass distributions, with combinatorial background subtracted, integrated over $\cos \theta^*$; \textbf{b)} example of $K^{*0} (\overline{K^{*0}}) \rightarrow K^{-} \pi^{+} (K^{+} \pi^{-})$ invariant mass distributions, with combinatorial background subtracted, integrated over $\cos \theta^*$; \textbf{c)} extracted yields of $\phi$ as a function of $\cos \theta^*$; \textbf{d)} extracted yields of $K^{*0}$ as a function of $\cos \theta^*$.

Example of combinatorial background subtracted invariant mass distributions and the extracted yields as a function of $\cos \theta^*$ for $\phi$ and $K^{*0}$ mesons. \textbf{a)} example of $\phi \rightarrow K^+ + K^-$ invariant mass distributions, with combinatorial background subtracted, integrated over $\cos \theta^*$; \textbf{b)} example of $K^{*0} (\overline{K^{*0}}) \rightarrow K^{-} \pi^{+} (K^{+} \pi^{-})$ invariant mass distributions, with combinatorial background subtracted, integrated over $\cos \theta^*$; \textbf{c)} extracted yields of $\phi$ as a function of $\cos \theta^*$; \textbf{d)} extracted yields of $K^{*0}$ as a function of $\cos \theta^*$.

Example of combinatorial background subtracted invariant mass distributions and the extracted yields as a function of $\cos \theta^*$ for $\phi$ and $K^{*0}$ mesons. \textbf{a)} example of $\phi \rightarrow K^+ + K^-$ invariant mass distributions, with combinatorial background subtracted, integrated over $\cos \theta^*$; \textbf{b)} example of $K^{*0} (\overline{K^{*0}}) \rightarrow K^{-} \pi^{+} (K^{+} \pi^{-})$ invariant mass distributions, with combinatorial background subtracted, integrated over $\cos \theta^*$; \textbf{c)} extracted yields of $\phi$ as a function of $\cos \theta^*$; \textbf{d)} extracted yields of $K^{*0}$ as a function of $\cos \theta^*$.

Efficiency corrected $\phi$-meson yields as a function of cos$\theta$* and corresponding fits with Eq.1 in the method section.

Efficiency and acceptance corrected $K^{*0}$-meson yields as a function of cos$\theta$* and corresponding fits with Eq.4 in the method section.

$\phi$-meson $\rho_{00}$ obtained from 1st- and 2nd-order event planes. The red stars (gray squares) show the $\phi$-meson $\rho_{00}$ as a function of beam energy, obtained with the 2nd-order (1st-order) EP.

$\phi$-meson $\rho_{00}$ with respect to different quantization axes. $\phi$-meson $\rho_{00}$ as a function of beam energy, for the out-of-plane direction (stars) and the in-plane direction (diamonds). Curves are fits based on theoretical calculations with a $\phi$-meson field. The corresponding $G_s^{(y)}$ values obtained from the fits are shown in the legend.

$\rho_{00}$ as a function of transverse momentum for $\phi$ for different collision energies. The gray squares and red stars are results obtained with the 1st- and 2nd-order EP, respectively.

$\rho_{00}$ as a function of transverse momentum for $\phi$ for different collision energies. The gray squares and red stars are results obtained with the 1st- and 2nd-order EP, respectively.

$\rho_{00}$ as a function of transverse momentum for $\phi$ for different collision energies. The gray squares and red stars are results obtained with the 1st- and 2nd-order EP, respectively.

$\rho_{00}$ as a function of transverse momentum for $\phi$ for different collision energies. The gray squares and red stars are results obtained with the 1st- and 2nd-order EP, respectively.

$\rho_{00}$ as a function of transverse momentum for $\phi$ for different collision energies. The gray squares and red stars are results obtained with the 1st- and 2nd-order EP, respectively.

$\rho_{00}$ as a function of transverse momentum for $\phi$ for different collision energies. The gray squares and red stars are results obtained with the 1st- and 2nd-order EP, respectively.

$\rho_{00}$ as a function of transverse momentum for $\phi$ for different collision energies. The gray squares and red stars are results obtained with the 1st- and 2nd-order EP, respectively.

$\rho_{00}$ as a function of transverse momentum for $\phi$ for different collision energies. The gray squares and red stars are results obtained with the 1st- and 2nd-order EP, respectively.

$\rho_{00}$ as a function of transverse momentum for $\phi$ for different collision energies. The gray squares and red stars are results obtained with the 1st- and 2nd-order EP, respectively.

$\rho_{00}$ as a function of transverse momentum for $\phi$ for different collision energies. The gray squares and red stars are results obtained with the 1st- and 2nd-order EP, respectively.

$\rho_{00}$ as a function of transverse momentum for $\phi$ for different collision energies. The gray squares and red stars are results obtained with the 1st- and 2nd-order EP, respectively.

$\rho_{00}$ as a function of transverse momentum for $\phi$ for different collision energies. The gray squares and red stars are results obtained with the 1st- and 2nd-order EP, respectively.

$\rho_{00}$ as a function of transverse momentum for $K^{*0}$ for different collision energies.

$\rho_{00}$ as a function of transverse momentum for $K^{*0}$ for different collision energies.

$\rho_{00}$ as a function of transverse momentum for $K^{*0}$ for different collision energies.

$\rho_{00}$ as a function of transverse momentum for $K^{*0}$ for different collision energies.

$\rho_{00}$ as a function of transverse momentum for $K^{*0}$ for different collision energies.

$\rho_{00}$ as a function of transverse momentum for $K^{*0}$ for different collision energies.

$\rho_{00}$ as a function of transverse momentum for $K^{*0}$ for different collision energies.

$\rho_{00}$ as a function of centrality for $\phi$ (upper panels) and $K^{*0}$ (lower panels). The solid squares and stars are results for the $\phi$ meson, obtained with the 1st- and 2nd-order EP, respectively. The solid circles are results for the $K^{*0}$ meson, obtained with the 2nd-order EP.}

$\rho_{00}$ as a function of centrality for $\phi$ (upper panels) and $K^{*0}$ (lower panels). The solid squares and stars are results for the $\phi$ meson, obtained with the 1st- and 2nd-order EP, respectively. The solid circles are results for the $K^{*0}$ meson, obtained with the 2nd-order EP.}

$\rho_{00}$ as a function of centrality for $\phi$ (upper panels) and $K^{*0}$ (lower panels). The solid squares and stars are results for the $\phi$ meson, obtained with the 1st- and 2nd-order EP, respectively. The solid circles are results for the $K^{*0}$ meson, obtained with the 2nd-order EP.}

$\rho_{00}$ as a function of centrality for $\phi$ (upper panels) and $K^{*0}$ (lower panels). The solid squares and stars are results for the $\phi$ meson, obtained with the 1st- and 2nd-order EP, respectively. The solid circles are results for the $K^{*0}$ meson, obtained with the 2nd-order EP.}

$\rho_{00}$ as a function of centrality for $\phi$ (upper panels) and $K^{*0}$ (lower panels). The solid squares and stars are results for the $\phi$ meson, obtained with the 1st- and 2nd-order EP, respectively. The solid circles are results for the $K^{*0}$ meson, obtained with the 2nd-order EP.}

$\rho_{00}$ as a function of centrality for $\phi$ (upper panels) and $K^{*0}$ (lower panels). The solid squares and stars are results for the $\phi$ meson, obtained with the 1st- and 2nd-order EP, respectively. The solid circles are results for the $K^{*0}$ meson, obtained with the 2nd-order EP.}

$\rho_{00}$ as a function of centrality for $\phi$ (upper panels) and $K^{*0}$ (lower panels). The solid squares and stars are results for the $\phi$ meson, obtained with the 1st- and 2nd-order EP, respectively. The solid circles are results for the $K^{*0}$ meson, obtained with the 2nd-order EP.}

Global spin alignment measurement of $\phi$ and $K^{*0}$ vector mesons in Au+Au collisions at 0-20\% centrality. The solid squares and stars are results for the $\phi$ meson, obtained with the 1st- and 2nd-order EP, respectively. The solid circles are results for $K^{*0}$-meson, obtained with the 2nd-order EP.

Global spin alignment measurement of $\phi$ and $K^{*0}$ vector mesons in Au+Au collisions at 0-20\% centrality. The solid squares and stars are results for the $\phi$ meson, obtained with the 1st- and 2nd-order EP, respectively. The solid circles are results for $K^{*0}$-meson, obtained with the 2nd-order EP.

Directed flow $v_1$ as a function of rapidity $y$ for $K^{+}$ in 10%–40% central Au+Au collisions at $\sqrt{s_{NN}} =$ 7.7, 11.5, 14.5, 19.6, 27, and 39 GeV.

Directed flow $v_1$ as a function of rapidity $y$ for $p$ in 10%–40% central Au+Au collisions at $\sqrt{s_{NN}} =$ 62.4 and 200 GeV.

Directed flow $v_1$ as a function of rapidity $y$ for $K^{+}$ in 10%–40% central Au+Au collisions at $\sqrt{s_{NN}} =$ 62.4 and 200 GeV.

Directed flow $v_1$ as a function of rapidity $y$ for $p$ in 40%–80% central Au+Au collisions at $\sqrt{s_{NN}} =$ 7.7, 11.5, 14.5, 19.6, 27, 39, 62.4 and 200 GeV.

Directed flow $v_1$ as a function of rapidity $y$ for $K^{+}$ in 40%–80% central Au+Au collisions at $\sqrt{s_{NN}} =$ 7.7, 11.5, 14.5, 19.6, 27, 39, 62.4 and 200 GeV.

Directed flow $v_1$ as a function of rapidity $y$ for $\bar{p}$ in 5%–10% central Au+Au collisions at $\sqrt{s_{NN}} =$ 7.7, 11.5, 14.5, 19.6, 27, 39, 62.4 and 200 GeV.

Directed flow $v_1$ as a function of rapidity $y$ for $K^{-}$ in 5%–10% central Au+Au collisions at $\sqrt{s_{NN}} =$ 7.7, 11.5, 14.5, 19.6, 27, 39, 62.4 and 200 GeV.

Directed flow $v_1$ as a function of rapidity $y$ for $\bar{p}$ in 10%–40% central Au+Au collisions at $\sqrt{s_{NN}} =$ 7.7, 11.5, 14.5, 19.6, 27, and 39 GeV.

Directed flow $v_1$ as a function of rapidity $y$ for $K^{-}$ in 10%–40% central Au+Au collisions at $\sqrt{s_{NN}} =$ 7.7, 11.5, 14.5, 19.6, 27, 39, and 200 GeV.

Directed flow $v_1$ as a function of rapidity $y$ for $\bar{p}$ in 10%–40% central Au+Au collisions at $\sqrt{s_{NN}} =$ 62.4 and 200 GeV.

Directed flow $v_1$ as a function of rapidity $y$ for $K^{-}$ in 10%–40% central Au+Au collisions at $\sqrt{s_{NN}} =$ 62.4 GeV.

Directed flow $v_1$ as a function of rapidity $y$ for $\bar{p}$ in 40%–80% central Au+Au collisions at $\sqrt{s_{NN}} =$ 7.7, 11.5, 14.5, 19.6, 27, 39, 62.4 and 200 GeV.

Directed flow $v_1$ as a function of rapidity $y$ for $K^{-}$ in 40%–80% central Au+Au collisions at $\sqrt{s_{NN}} =$ 7.7, 11.5, 14.5, 19.6, 27, 39, 62.4 and 200 GeV.

Directed flow $v_1$ as a function of rapidity $y$ for $\pi^{+}$ in 5%–10% central Au+Au collisions at $\sqrt{s_{NN}} =$ 7.7, 11.5, 14.5, 19.6, 27, 39, 62.4 and 200 GeV.

Directed flow $v_1$ as a function of rapidity $y$ for $K_0^s$ in 5%–10% central Au+Au collisions at $\sqrt{s_{NN}} =$ 7.7, 11.5, 14.5, 19.6, 27, 39, 62.4 and 200 GeV.

Directed flow $v_1$ as a function of rapidity $y$ for $\pi^{+}$ in 10%–40% central Au+Au collisions at $\sqrt{s_{NN}} =$ 7.7, 11.5, 14.5, 19.6, 27, and 39 GeV.

Directed flow $v_1$ as a function of rapidity $y$ for $K_0^s$ in 10%–40% central Au+Au collisions at $\sqrt{s_{NN}} =$ 7.7, 11.5, 14.5, 19.6, 27, 39, and 200 GeV.

Directed flow $v_1$ as a function of rapidity $y$ for $\pi^{+}$ in 10%–40% central Au+Au collisions at $\sqrt{s_{NN}} =$ 62.4 and 200 GeV.

Directed flow $v_1$ as a function of rapidity $y$ for $K_0^s$ in 10%–40% central Au+Au collisions at $\sqrt{s_{NN}} =$ 62.4 GeV.

Directed flow $v_1$ as a function of rapidity $y$ for $\pi^{+}$ in 40%–80% central Au+Au collisions at $\sqrt{s_{NN}} =$ 7.7, 11.5, 14.5, 19.6, 27, 39, 62.4 and 200 GeV.

Directed flow $v_1$ as a function of rapidity $y$ for $K_0^s$ in 40%–80% central Au+Au collisions at $\sqrt{s_{NN}} =$ 7.7, 11.5, 14.5, 19.6, 27, 39, 62.4 and 200 GeV.

Directed flow $v_1$ as a function of rapidity $y$ for $\pi^{-}$ in 5%–10% central Au+Au collisions at $\sqrt{s_{NN}} =$ 7.7, 11.5, 14.5, 19.6, 27, 39, 62.4 and 200 GeV.

Directed flow $v_1$ as a function of rapidity $y$ for $\Lambda$ in 5%–10% central Au+Au collisions at $\sqrt{s_{NN}} =$ 7.7, 11.5, 14.5, 19.6, 27, 39, 62.4 and 200 GeV.

Directed flow $v_1$ as a function of rapidity $y$ for $\pi^{-}$ in 10%–40% central Au+Au collisions at $\sqrt{s_{NN}} =$ 7.7, 11.5, 14.5, 19.6, 27, and 39 GeV.

Directed flow $v_1$ as a function of rapidity $y$ for $\Lambda$ in 10%–40% central Au+Au collisions at $\sqrt{s_{NN}} =$ 7.7, 11.5, 14.5, 19.6, 27, 39, and 200 GeV.

Directed flow $v_1$ as a function of rapidity $y$ for $\pi^{-}$ in 10%–40% central Au+Au collisions at $\sqrt{s_{NN}} =$ 62.4 and 200 GeV.

Directed flow $v_1$ as a function of rapidity $y$ for $\Lambda$ in 10%–40% central Au+Au collisions at $\sqrt{s_{NN}} =$ 62.4 GeV.

Directed flow $v_1$ as a function of rapidity $y$ for $\pi^{-}$ in 40%–80% central Au+Au collisions at $\sqrt{s_{NN}} =$ 7.7, 11.5, 14.5, 19.6, 27, 39, 62.4 and 200 GeV.

Directed flow $v_1$ as a function of rapidity $y$ for $\Lambda$ in 40%–80% central Au+Au collisions at $\sqrt{s_{NN}} =$ 7.7, 11.5, 14.5, 19.6, 27, 39, 62.4 and 200 GeV.

Directed flow $v_1$ as a function of rapidity $y$ for $K^{+}$ in 5%–10% central Au+Au collisions at $\sqrt{s_{NN}} =$ 7.7, 11.5, 14.5, 19.6, 27, 39, 62.4 and 200 GeV.

Directed flow $v_1$ as a function of rapidity $y$ for $\bar{\Lambda}$ in 5%–10% central Au+Au collisions at $\sqrt{s_{NN}} =$ 7.7, 11.5, 14.5, 19.6, 27, 39, 62.4 and 200 GeV.

Directed flow $v_1$ as a function of rapidity $y$ for $K^{+}$ in 10%–40% central Au+Au collisions at $\sqrt{s_{NN}} =$ 7.7, 11.5, 14.5, 19.6, 27, and 39 GeV.

Directed flow $v_1$ as a function of rapidity $y$ for $\bar{\Lambda}$ in 10%–40% central Au+Au collisions at $\sqrt{s_{NN}} =$ 7.7, 11.5, 14.5, 19.6, 27, 39, and 200 GeV.

Directed flow $v_1$ as a function of rapidity $y$ for $K^{+}$ in 10%–40% central Au+Au collisions at $\sqrt{s_{NN}} =$ 62.4 and 200 GeV.

Directed flow $v_1$ as a function of rapidity $y$ for $\bar{\Lambda}$ in 10%–40% central Au+Au collisions at $\sqrt{s_{NN}} =$ 62.4 GeV.

Directed flow $v_1$ as a function of rapidity $y$ for $K^{+}$ in 40%–80% central Au+Au collisions at $\sqrt{s_{NN}} =$ 7.7, 11.5, 14.5, 19.6, 27, 39, 62.4 and 200 GeV.

Directed flow $v_1$ as a function of rapidity $y$ for $\bar{\Lambda}$ in 40%–80% central Au+Au collisions at $\sqrt{s_{NN}} =$ 7.7, 11.5, 14.5, 19.6, 27, 39, 62.4 and 200 GeV.

Directed flow $v_1$ as a function of rapidity $y$ for $K^{-}$ in 5%–10% central Au+Au collisions at $\sqrt{s_{NN}} =$ 7.7, 11.5, 14.5, 19.6, 27, 39, 62.4 and 200 GeV.

Directed flow $v_1$ as a function of rapidity $y$ for $\phi$ in 5%–10% central Au+Au collisions at $\sqrt{s_{NN}} =$ 7.7 GeV.

Directed flow $v_1$ as a function of rapidity $y$ for $K^{-}$ in 10%–40% central Au+Au collisions at $\sqrt{s_{NN}} =$ 7.7, 11.5, 14.5, 19.6, 27, 39, and 200 GeV.

Directed flow $v_1$ as a function of rapidity $y$ for $\phi$ in 5%–10% central Au+Au collisions at $\sqrt{s_{NN}} =$ 11.5, 14.5, 19.6, 27, 39 and 62.4 GeV.

Directed flow $v_1$ as a function of rapidity $y$ for $K^{-}$ in 10%–40% central Au+Au collisions at $\sqrt{s_{NN}} =$ 62.4 GeV.

Directed flow $v_1$ as a function of rapidity $y$ for $\phi$ in 5%–10% central Au+Au collisions at $\sqrt{s_{NN}} =$ 200 GeV.

Directed flow $v_1$ as a function of rapidity $y$ for $K^{-}$ in 40%–80% central Au+Au collisions at $\sqrt{s_{NN}} =$ 7.7, 11.5, 14.5, 19.6, 27, 39, 62.4 and 200 GeV.

Directed flow $v_1$ as a function of rapidity $y$ for $\phi$ in 10%–40% central Au+Au collisions at $\sqrt{s_{NN}} =$ 7.7 GeV.

Directed flow $v_1$ as a function of rapidity $y$ for $K_0^s$ in 5%–10% central Au+Au collisions at $\sqrt{s_{NN}} =$ 7.7, 11.5, 14.5, 19.6, 27, 39, 62.4 and 200 GeV.

Directed flow $v_1$ as a function of rapidity $y$ for $\phi$ in 10%–40% central Au+Au collisions at $\sqrt{s_{NN}} =$ 11.5, 14.5, 19.6, 27, 39 and 62.4 GeV.

Directed flow $v_1$ as a function of rapidity $y$ for $K_0^s$ in 10%–40% central Au+Au collisions at $\sqrt{s_{NN}} =$ 7.7, 11.5, 14.5, 19.6, 27, 39, and 200 GeV.

Directed flow $v_1$ as a function of rapidity $y$ for $\phi$ in 10%–40% central Au+Au collisions at $\sqrt{s_{NN}} =$ 200 GeV.

Directed flow $v_1$ as a function of rapidity $y$ for $K_0^s$ in 10%–40% central Au+Au collisions at $\sqrt{s_{NN}} =$ 62.4 GeV.

Directed flow $v_1$ as a function of rapidity $y$ for $\phi$ in 40%–80% central Au+Au collisions at $\sqrt{s_{NN}} =$ 7.7 GeV.

Directed flow $v_1$ as a function of rapidity $y$ for $K_0^s$ in 40%–80% central Au+Au collisions at $\sqrt{s_{NN}} =$ 7.7, 11.5, 14.5, 19.6, 27, 39, 62.4 and 200 GeV.

Directed flow $v_1$ as a function of rapidity $y$ for $\phi$ in 40%–80% central Au+Au collisions at $\sqrt{s_{NN}} =$ 11.5, 14.5, 19.6, 27, 39 and 62.4 GeV.

Directed flow $v_1$ as a function of rapidity $y$ for $\Lambda$ in 5%–10% central Au+Au collisions at $\sqrt{s_{NN}} =$ 7.7, 11.5, 14.5, 19.6, 27, 39, 62.4 and 200 GeV.

Directed flow $v_1$ as a function of rapidity $y$ for $\phi$ in 40%–80% central Au+Au collisions at $\sqrt{s_{NN}} =$ 200 GeV.

Directed flow $v_1$ as a function of rapidity $y$ for $\Lambda$ in 10%–40% central Au+Au collisions at $\sqrt{s_{NN}} =$ 7.7, 11.5, 14.5, 19.6, 27, 39, and 200 GeV.

Directed flow slope $dv_1/dy$ as a function of beam energy in 10%–40% central Au+Au collisions.

Directed flow $v_1$ as a function of rapidity $y$ for $\Lambda$ in 10%–40% central Au+Au collisions at $\sqrt{s_{NN}} =$ 62.4 GeV.

Directed flow slope $dv_1/dy$ as a function of beam energy in 10%–40% central Au+Au collisions.

Directed flow $v_1$ as a function of rapidity $y$ for $\Lambda$ in 40%–80% central Au+Au collisions at $\sqrt{s_{NN}} =$ 7.7, 11.5, 14.5, 19.6, 27, 39, 62.4 and 200 GeV.

Directed flow slope $dv_1/dy$ as a function of beam energy in 10%–40% central Au+Au collisions.

Directed flow $v_1$ as a function of rapidity $y$ for $\bar{\Lambda}$ in 5%–10% central Au+Au collisions at $\sqrt{s_{NN}} =$ 7.7, 11.5, 14.5, 19.6, 27, 39, 62.4 and 200 GeV.

Directed flow slope $dv_1/dy$ as a function of beam energy in 10%–40% central Au+Au collisions.

Directed flow $v_1$ as a function of rapidity $y$ for $\bar{\Lambda}$ in 10%–40% central Au+Au collisions at $\sqrt{s_{NN}} =$ 7.7, 11.5, 14.5, 19.6, 27, 39, and 200 GeV.

Directed flow $v_1$ as a function of rapidity $y$ for $\bar{\Lambda}$ in 10%–40% central Au+Au collisions at $\sqrt{s_{NN}} =$ 62.4 GeV.

Directed flow $v_1$ as a function of rapidity $y$ for $\bar{\Lambda}$ in 40%–80% central Au+Au collisions at $\sqrt{s_{NN}} =$ 7.7, 11.5, 14.5, 19.6, 27, 39, 62.4 and 200 GeV.

Directed flow $v_1$ as a function of rapidity $y$ for $\phi$ in 5%–10% central Au+Au collisions at $\sqrt{s_{NN}} =$ 7.7 GeV.

Directed flow $v_1$ as a function of rapidity $y$ for $\phi$ in 5%–10% central Au+Au collisions at $\sqrt{s_{NN}} =$ 11.5, 14.5, 19.6, 27, 39 and 62.4 GeV.

Directed flow $v_1$ as a function of rapidity $y$ for $\phi$ in 5%–10% central Au+Au collisions at $\sqrt{s_{NN}} =$ 200 GeV.

Directed flow $v_1$ as a function of rapidity $y$ for $\phi$ in 10%–40% central Au+Au collisions at $\sqrt{s_{NN}} =$ 7.7 GeV.

Directed flow $v_1$ as a function of rapidity $y$ for $\phi$ in 10%–40% central Au+Au collisions at $\sqrt{s_{NN}} =$ 11.5, 14.5, 19.6, 27, 39 and 62.4 GeV.

Directed flow $v_1$ as a function of rapidity $y$ for $\phi$ in 10%–40% central Au+Au collisions at $\sqrt{s_{NN}} =$ 200 GeV.

Directed flow $v_1$ as a function of rapidity $y$ for $\phi$ in 40%–80% central Au+Au collisions at $\sqrt{s_{NN}} =$ 7.7 GeV.

Directed flow $v_1$ as a function of rapidity $y$ for $\phi$ in 40%–80% central Au+Au collisions at $\sqrt{s_{NN}} =$ 11.5, 14.5, 19.6, 27, 39 and 62.4 GeV.

Directed flow $v_1$ as a function of rapidity $y$ for $\phi$ in 40%–80% central Au+Au collisions at $\sqrt{s_{NN}} =$ 200 GeV.

Directed flow slope $dv_1/dy$ as a function of beam energy in 10%–40% central Au+Au collisions.

Directed flow slope $dv_1/dy$ as a function of beam energy in 10%–40% central Au+Au collisions.

Directed flow slope $dv_1/dy$ as a function of beam energy in 10%–40% central Au+Au collisions.

Directed flow slope $dv_1/dy$ as a function of beam energy in 10%–40% central Au+Au collisions.

Centrality dependence of efficiency corrected second-order diagonal cumulants of net-proton, net-kaon and net-pion (top to bottom) of the multiplicity distributions for Au+Au collisions at GeV (left to right) within kinematic range of |η| < 0.5 and 0.4 < pT < 1.6 GeV/c. The boxes represent the systematic error. The statistical error bars are within the marker size. The dashed lines represent scaling predicted by central limit theorem and the solid lines are UrQMD calculations.

Centrality dependence of second-order off-diagonal cumulants of net-proton, net-charge and net-kaon for Au+Au colli- sions at √sNN = 7.7, 11.5, 14.5, 19.6, 27, 39, 62.4 and 200 GeV (left to right) within kinematic range |η| < 0.5 and 0.4 < pT < 1.6 GeV/c. Error bars are statistical and boxes are systematic errors. The dashed lines represent scaling predicted by the central limit theorem and the solid lines are UrQMD calculations.

Centrality dependence of efficiency corrected second-order diagonal cumulants of net-proton, net-kaon and net-pion (top to bottom) of the multiplicity distributions for Au+Au collisions at GeV (left to right) within kinematic range of |η| < 0.5 and 0.4 < pT < 1.6 GeV/c. The boxes represent the systematic error. The statistical error bars are within the marker size. The dashed lines represent scaling predicted by central limit theorem and the solid lines are UrQMD calculations.

Centrality dependence of second-order off-diagonal to diagonal cumulants ratios of net-proton, net-charge and net-kaon for Au+Au collisions at √sNN = 7.7, 11.5, 14.5, 19.6, 27, 39, 62.4 and 200 GeV (left to right) within the kinematic range |η| < 0.5 and 0.4 < pT < 1.6 GeV/c. Error bars are statistical and boxes are systematic errors. The solid lines represent the UrQMD calculations.

Centrality dependence of efficiency corrected second-order diagonal cumulants of net-proton, net-kaon and net-pion (top to bottom) of the multiplicity distributions for Au+Au collisions at GeV (left to right) within kinematic range of |η| < 0.5 and 0.4 < pT < 1.6 GeV/c. The boxes represent the systematic error. The statistical error bars are within the marker size. The dashed lines represent scaling predicted by central limit theorem and the solid lines are UrQMD calculations.

Beam energy dependence of cumulant ratios (Cp,k,CQ,k and CQ,p; top to bottom) of net-proton, net-kaon and net-charge (identified) for Au+Au collisions at sNN = 7.7, 11.5, 14.5, 19.6, 27, 39, 62.4 and 200 GeV. The bands denote the UrQMD calculations for 0-5% and 70-80% central collisions and the HRG values are denoted by red dotted lines. The Poisson baseline is denoted by black dashed lines. Error bars are statistical and boxes are systematic errors.

Centrality dependence of efficiency corrected second-order diagonal cumulants of net-proton, net-kaon and net-pion (top to bottom) of the multiplicity distributions for Au+Au collisions at GeV (left to right) within kinematic range of |η| < 0.5 and 0.4 < pT < 1.6 GeV/c. The boxes represent the systematic error. The statistical error bars are within the marker size. The dashed lines represent scaling predicted by central limit theorem and the solid lines are UrQMD calculations.

Centrality dependence of efficiency corrected second-order diagonal cumulants of net-proton, net-kaon and net-pion (top to bottom) of the multiplicity distributions for Au+Au collisions at GeV (left to right) within kinematic range of |η| < 0.5 and 0.4 < pT < 1.6 GeV/c. The boxes represent the systematic error. The statistical error bars are within the marker size. The dashed lines represent scaling predicted by central limit theorem and the solid lines are UrQMD calculations.

Centrality dependence of efficiency corrected second-order diagonal cumulants of net-proton, net-kaon and net-pion (top to bottom) of the multiplicity distributions for Au+Au collisions at GeV (left to right) within kinematic range of |η| < 0.5 and 0.4 < pT < 1.6 GeV/c. The boxes represent the systematic error. The statistical error bars are within the marker size. The dashed lines represent scaling predicted by central limit theorem and the solid lines are UrQMD calculations.

Centrality dependence of efficiency corrected second-order diagonal cumulants of net-proton, net-kaon and net-pion (top to bottom) of the multiplicity distributions for Au+Au collisions at GeV (left to right) within kinematic range of |η| < 0.5 and 0.4 < pT < 1.6 GeV/c. The boxes represent the systematic error. The statistical error bars are within the marker size. The dashed lines represent scaling predicted by central limit theorem and the solid lines are UrQMD calculations.

Centrality dependence of efficiency corrected second-order diagonal cumulants of net-proton, net-kaon and net-pion (top to bottom) of the multiplicity distributions for Au+Au collisions at GeV (left to right) within kinematic range of |η| < 0.5 and 0.4 < pT < 1.6 GeV/c. The boxes represent the systematic error. The statistical error bars are within the marker size. The dashed lines represent scaling predicted by central limit theorem and the solid lines are UrQMD calculations.

Centrality dependence of second-order off-diagonal cumulants of net-proton, net-charge and net-kaon for Au+Au colli-sions at √sNN = 7.7, 11.5, 14.5, 19.6, 27, 39, 62.4 and 200 GeV (left to right) within kinematic range |η| < 0.5 and 0.4 < pT < 1.6 GeV/c. Bars represent statistical errors and boxes show systematic errors. The dashed lines represent scaling predicted by the central limit theorem and the solid lines are UrQMD calculations.

Centrality dependence of second-order off-diagonal cumulants of net-proton, net-charge and net-kaon for Au+Au colli-sions at √sNN = 7.7, 11.5, 14.5, 19.6, 27, 39, 62.4 and 200 GeV (left to right) within kinematic range |η| < 0.5 and 0.4 < pT < 1.6 GeV/c. Bars represent statistical errors and boxes show systematic errors. The dashed lines represent scaling predicted by the central limit theorem and the solid lines are UrQMD calculations.

Centrality dependence of second-order off-diagonal cumulants of net-proton, net-charge and net-kaon for Au+Au colli-sions at √sNN = 7.7, 11.5, 14.5, 19.6, 27, 39, 62.4 and 200 GeV (left to right) within kinematic range |η| < 0.5 and 0.4 < pT < 1.6 GeV/c. Bars represent statistical errors and boxes show systematic errors. The dashed lines represent scaling predicted by the central limit theorem and the solid lines are UrQMD calculations.

Centrality dependence of second-order off-diagonal cumulants of net-proton, net-charge and net-kaon for Au+Au colli-sions at √sNN = 7.7, 11.5, 14.5, 19.6, 27, 39, 62.4 and 200 GeV (left to right) within kinematic range |η| < 0.5 and 0.4 < pT < 1.6 GeV/c. Bars represent statistical errors and boxes show systematic errors. The dashed lines represent scaling predicted by the central limit theorem and the solid lines are UrQMD calculations.

Centrality dependence of second-order off-diagonal cumulants of net-proton, net-charge and net-kaon for Au+Au colli-sions at √sNN = 7.7, 11.5, 14.5, 19.6, 27, 39, 62.4 and 200 GeV (left to right) within kinematic range |η| < 0.5 and 0.4 < pT < 1.6 GeV/c. Bars represent statistical errors and boxes show systematic errors. The dashed lines represent scaling predicted by the central limit theorem and the solid lines are UrQMD calculations.

Centrality dependence of second-order off-diagonal cumulants of net-proton, net-charge and net-kaon for Au+Au colli-sions at √sNN = 7.7, 11.5, 14.5, 19.6, 27, 39, 62.4 and 200 GeV (left to right) within kinematic range |η| < 0.5 and 0.4 < pT < 1.6 GeV/c. Bars represent statistical errors and boxes show systematic errors. The dashed lines represent scaling predicted by the central limit theorem and the solid lines are UrQMD calculations.

Centrality dependence of second-order off-diagonal cumulants of net-proton, net-charge and net-kaon for Au+Au colli-sions at √sNN = 7.7, 11.5, 14.5, 19.6, 27, 39, 62.4 and 200 GeV (left to right) within kinematic range |η| < 0.5 and 0.4 < pT < 1.6 GeV/c. Bars represent statistical errors and boxes show systematic errors. The dashed lines represent scaling predicted by the central limit theorem and the solid lines are UrQMD calculations.

Centrality dependence of second-order off-diagonal cumulants of net-proton, net-charge and net-kaon for Au+Au colli-sions at √sNN = 7.7, 11.5, 14.5, 19.6, 27, 39, 62.4 and 200 GeV (left to right) within kinematic range |η| < 0.5 and 0.4 < pT < 1.6 GeV/c. Bars represent statistical errors and boxes show systematic errors. The dashed lines represent scaling predicted by the central limit theorem and the solid lines are UrQMD calculations.

Centrality dependence of second-order off-diagonal to diagonal cumulants ratios of net-proton, identified net-charge and net-kaon for Au+Au collisions at √sNN = 7.7, 11.5, 14.5, 19.6, 27, 39, 62.4 and 200 GeV (left to right) within the kinematic range |η| < 0.5 and 0.4 < pT < 1.6 GeV/c. Bars represent statistical errors and boxes show systematic errors. The solid lines represent the UrQMD calculations.

Centrality dependence of second-order off-diagonal to diagonal cumulants ratios of net-proton, identified net-charge and net-kaon for Au+Au collisions at √sNN = 7.7, 11.5, 14.5, 19.6, 27, 39, 62.4 and 200 GeV (left to right) within the kinematic range |η| < 0.5 and 0.4 < pT < 1.6 GeV/c. Bars represent statistical errors and boxes show systematic errors. The solid lines represent the UrQMD calculations.

Centrality dependence of second-order off-diagonal to diagonal cumulants ratios of net-proton, identified net-charge and net-kaon for Au+Au collisions at √sNN = 7.7, 11.5, 14.5, 19.6, 27, 39, 62.4 and 200 GeV (left to right) within the kinematic range |η| < 0.5 and 0.4 < pT < 1.6 GeV/c. Bars represent statistical errors and boxes show systematic errors. The solid lines represent the UrQMD calculations.

Centrality dependence of second-order off-diagonal to diagonal cumulants ratios of net-proton, identified net-charge and net-kaon for Au+Au collisions at √sNN = 7.7, 11.5, 14.5, 19.6, 27, 39, 62.4 and 200 GeV (left to right) within the kinematic range |η| < 0.5 and 0.4 < pT < 1.6 GeV/c. Bars represent statistical errors and boxes show systematic errors. The solid lines represent the UrQMD calculations.

Centrality dependence of second-order off-diagonal to diagonal cumulants ratios of net-proton, identified net-charge and net-kaon for Au+Au collisions at √sNN = 7.7, 11.5, 14.5, 19.6, 27, 39, 62.4 and 200 GeV (left to right) within the kinematic range |η| < 0.5 and 0.4 < pT < 1.6 GeV/c. Bars represent statistical errors and boxes show systematic errors. The solid lines represent the UrQMD calculations.

Centrality dependence of second-order off-diagonal to diagonal cumulants ratios of net-proton, identified net-charge and net-kaon for Au+Au collisions at √sNN = 7.7, 11.5, 14.5, 19.6, 27, 39, 62.4 and 200 GeV (left to right) within the kinematic range |η| < 0.5 and 0.4 < pT < 1.6 GeV/c. Bars represent statistical errors and boxes show systematic errors. The solid lines represent the UrQMD calculations.

Centrality dependence of second-order off-diagonal to diagonal cumulants ratios of net-proton, identified net-charge and net-kaon for Au+Au collisions at √sNN = 7.7, 11.5, 14.5, 19.6, 27, 39, 62.4 and 200 GeV (left to right) within the kinematic range |η| < 0.5 and 0.4 < pT < 1.6 GeV/c. Bars represent statistical errors and boxes show systematic errors. The solid lines represent the UrQMD calculations.

Centrality dependence of second-order off-diagonal to diagonal cumulants ratios of net-proton, identified net-charge and net-kaon for Au+Au collisions at √sNN = 7.7, 11.5, 14.5, 19.6, 27, 39, 62.4 and 200 GeV (left to right) within the kinematic range |η| < 0.5 and 0.4 < pT < 1.6 GeV/c. Bars represent statistical errors and boxes show systematic errors. The solid lines represent the UrQMD calculations.

Beam energy dependence of cumulant ratios (Cp,k,CQ,k and CQ,p; top to bottom) of net-proton, net-kaon and identified net-charge for Au+Au collisions at sNN = 7.7, 11.5, 14.5, 19.6, 27, 39, 62.4 and 200 GeV. The bands denote the UrQMD calculations for 0-5% and 70-80% central collisions and the HRG values are denoted by red dotted lines. The Poisson baseline is denoted by black dashed lines. Bars show statistical errors and boxes show systematic errors.

Event by event net-proton multiplicity, $\Delta N_{p}$, distributions for Au+Au collisions at √sNN = 27, 54.4, and 200 GeV in 0-10% and 30-40% centralities at midrapidity (|y| < 0.5) for the transverse momentum range of 0.4 < $p_{T}$ (GeV/c) < 2.0. These distributions are normalized by the corresponding numbers of events and are not corrected for detector efficiencies. Statistical uncertainties are shown as vertical lines. The dashed lines show the Skellam distributions for each collision energy and centrality. The bottom panel shows the ratio of the data to the Skellam expectations.

Event by event net-proton multiplicity, $\Delta N_{p}$, distributions for Au+Au collisions at √sNN = 27, 54.4, and 200 GeV in 0-10% and 30-40% centralities at midrapidity (|y| < 0.5) for the transverse momentum range of 0.4 < $p_{T}$ (GeV/c) < 2.0. These distributions are normalized by the corresponding numbers of events and are not corrected for detector efficiencies. Statistical uncertainties are shown as vertical lines. The dashed lines show the Skellam distributions for each collision energy and centrality. The bottom panel shows the ratio of the data to the Skellam expectations.

Event by event net-proton multiplicity, $\Delta N_{p}$, distributions for Au+Au collisions at √sNN = 27, 54.4, and 200 GeV in 0-10% and 30-40% centralities at midrapidity (|y| < 0.5) for the transverse momentum range of 0.4 < $p_{T}$ (GeV/c) < 2.0. These distributions are normalized by the corresponding numbers of events and are not corrected for detector efficiencies. Statistical uncertainties are shown as vertical lines. The dashed lines show the Skellam distributions for each collision energy and centrality. The bottom panel shows the ratio of the data to the Skellam expectations.

Net-proton $C_{6}/C_{2}$ as a function of rapidity (left) and transverse momentum acceptance (right) from $\sqrt{s_{NN}}$ = 27 GeV (crosses), 54.4 (open squares), and 200 GeV (filled circles) Au+Au collisions. The upper and lower plots are for 0-10% and 30-40% centralities, respectively. The error bars are statistical and caps are systematic errors. Points for different beam energies are staggered horizontally to improve clarity. UrQMD transport model results are shown as shaded and hatched bands. The Skellam expectation ($C_{6}/C_{2} = 1) is shown as long-dashed lines.

Net-proton $C_{6}/C_{2}$ as a function of rapidity (left) and transverse momentum acceptance (right) from $\sqrt{s_{NN}}$ = 27 GeV (crosses), 54.4 (open squares), and 200 GeV (filled circles) Au+Au collisions. The upper and lower plots are for 0-10% and 30-40% centralities, respectively. The error bars are statistical and caps are systematic errors. Points for different beam energies are staggered horizontally to improve clarity. UrQMD transport model results are shown as shaded and hatched bands. The Skellam expectation ($C_{6}/C_{2} = 1) is shown as long-dashed lines.

Net-proton $C_{6}/C_{2}$ as a function of rapidity (left) and transverse momentum acceptance (right) from $\sqrt{s_{NN}}$ = 27 GeV (crosses), 54.4 (open squares), and 200 GeV (filled circles) Au+Au collisions. The upper and lower plots are for 0-10% and 30-40% centralities, respectively. The error bars are statistical and caps are systematic errors. Points for different beam energies are staggered horizontally to improve clarity. UrQMD transport model results are shown as shaded and hatched bands. The Skellam expectation ($C_{6}/C_{2} = 1) is shown as long-dashed lines.

Net-proton $C_{6}/C_{2}$ as a function of rapidity (left) and transverse momentum acceptance (right) from $\sqrt{s_{NN}}$ = 27 GeV (crosses), 54.4 (open squares), and 200 GeV (filled circles) Au+Au collisions. The upper and lower plots are for 0-10% and 30-40% centralities, respectively. The error bars are statistical and caps are systematic errors. Points for different beam energies are staggered horizontally to improve clarity. UrQMD transport model results are shown as shaded and hatched bands. The Skellam expectation ($C_{6}/C_{2} = 1) is shown as long-dashed lines.

Net-proton $C_{6}/C_{2}$ as a function of rapidity (left) and transverse momentum acceptance (right) from $\sqrt{s_{NN}}$ = 27 GeV (crosses), 54.4 (open squares), and 200 GeV (filled circles) Au+Au collisions. The upper and lower plots are for 0-10% and 30-40% centralities, respectively. The error bars are statistical and caps are systematic errors. Points for different beam energies are staggered horizontally to improve clarity. UrQMD transport model results are shown as shaded and hatched bands. The Skellam expectation ($C_{6}/C_{2} = 1) is shown as long-dashed lines.

Net-proton $C_{6}/C_{2}$ as a function of rapidity (left) and transverse momentum acceptance (right) from $\sqrt{s_{NN}}$ = 27 GeV (crosses), 54.4 (open squares), and 200 GeV (filled circles) Au+Au collisions. The upper and lower plots are for 0-10% and 30-40% centralities, respectively. The error bars are statistical and caps are systematic errors. Points for different beam energies are staggered horizontally to improve clarity. UrQMD transport model results are shown as shaded and hatched bands. The Skellam expectation ($C_{6}/C_{2} = 1) is shown as long-dashed lines.

Collisions centrality dependence of net-proton $C_{6}/C_{2}$ in Au+Au collisions for |$y$| < 0.5 and 0.4 < $p_{T}$ (GeV/c) < 2.0. The error bars are statistical and caps are systematic errors. Points for different beam energies are staggered horizontally to improve clarity. A shaded band shows the results from UrQMD model calculations. UrQMD calculations from the above three collision energies are consistent among them so they are merged in order to reduce statistical fluctuations. Details on these calculations can be found in the Supplemental Material at [URL will be inserted by publisher]. The lattice QCD calculations [16, 17] for T = 160 MeV and $\mu_{B}$ < 110 MeV. are shown as a blue band at $\langle N_{part}\rangle$ $\approx$ 340.

Collisions centrality dependence of net-proton $C_{6}/C_{2}$ in Au+Au collisions for |$y$| < 0.5 and 0.4 < $p_{T}$ (GeV/c) < 2.0. The error bars are statistical and caps are systematic errors. Points for different beam energies are staggered horizontally to improve clarity. A shaded band shows the results from UrQMD model calculations. UrQMD calculations from the above three collision energies are consistent among them so they are merged in order to reduce statistical fluctuations. Details on these calculations can be found in the Supplemental Material at [URL will be inserted by publisher]. The lattice QCD calculations [16, 17] for T = 160 MeV and $\mu_{B}$ < 110 MeV. are shown as a blue band at $\langle N_{part}\rangle$ $\approx$ 340.

Collisions centrality dependence of net-proton $C_{6}/C_{2}$ in Au+Au collisions for |$y$| < 0.5 and 0.4 < $p_{T}$ (GeV/c) < 2.0. The error bars are statistical and caps are systematic errors. Points for different beam energies are staggered horizontally to improve clarity. A shaded band shows the results from UrQMD model calculations. UrQMD calculations from the above three collision energies are consistent among them so they are merged in order to reduce statistical fluctuations. Details on these calculations can be found in the Supplemental Material at [URL will be inserted by publisher]. The lattice QCD calculations [16, 17] for T = 160 MeV and $\mu_{B}$ < 110 MeV. are shown as a blue band at $\langle N_{part}\rangle$ $\approx$ 340.

Distributions of reconstructed protons (black circles) from embedding simulations in 200 GeV Au+Au collisions at 0-2.5% centrality. Red lines are fits with the binomial distribution, and green dotted lines represent the fit with the beta-binomial distributions using α that gives the minimal chi2/ndf. Each panel shows the result from the given combinations of embedded protons and antiprotons. The ratio of fits to the embedding data is shown for each panel.

Distributions of reconstructed protons (black circles) from embedding simulations in 200 GeV Au+Au collisions at 0-2.5% centrality. Red lines are fits with the binomial distribution, and green dotted lines represent the fit with the beta-binomial distributions using α that gives the minimal chi2/ndf. Each panel shows the result from the given combinations of embedded protons and antiprotons. The ratio of fits to the embedding data is shown for each panel.

Distributions of reconstructed protons (black circles) from embedding simulations in 200 GeV Au+Au collisions at 0-2.5% centrality. Red lines are fits with the binomial distribution, and green dotted lines represent the fit with the beta-binomial distributions using α that gives the minimal chi2/ndf. Each panel shows the result from the given combinations of embedded protons and antiprotons. The ratio of fits to the embedding data is shown for each panel.

Distributions of reconstructed protons (black circles) from embedding simulations in 200 GeV Au+Au collisions at 0-2.5% centrality. Red lines are fits with the binomial distribution, and green dotted lines represent the fit with the beta-binomial distributions using α that gives the minimal chi2/ndf. Each panel shows the result from the given combinations of embedded protons and antiprotons. The ratio of fits to the embedding data is shown for each panel.

Distributions of reconstructed protons (black circles) from embedding simulations in 200 GeV Au+Au collisions at 0-2.5% centrality. Red lines are fits with the binomial distribution, and green dotted lines represent the fit with the beta-binomial distributions using α that gives the minimal chi2/ndf. Each panel shows the result from the given combinations of embedded protons and antiprotons. The ratio of fits to the embedding data is shown for each panel.

Distributions of reconstructed protons (black circles) from embedding simulations in 200 GeV Au+Au collisions at 0-2.5% centrality. Red lines are fits with the binomial distribution, and green dotted lines represent the fit with the beta-binomial distributions using α that gives the minimal chi2/ndf. Each panel shows the result from the given combinations of embedded protons and antiprotons. The ratio of fits to the embedding data is shown for each panel.

Distributions of reconstructed protons (black circles) from embedding simulations in 200 GeV Au+Au collisions at 0-2.5% centrality. Red lines are fits with the binomial distribution, and green dotted lines represent the fit with the beta-binomial distributions using α that gives the minimal chi2/ndf. Each panel shows the result from the given combinations of embedded protons and antiprotons. The ratio of fits to the embedding data is shown for each panel.

Distributions of reconstructed protons (black circles) from embedding simulations in 200 GeV Au+Au collisions at 0-2.5% centrality. Red lines are fits with the binomial distribution, and green dotted lines represent the fit with the beta-binomial distributions using α that gives the minimal chi2/ndf. Each panel shows the result from the given combinations of embedded protons and antiprotons. The ratio of fits to the embedding data is shown for each panel.

Distributions of reconstructed protons (black circles) from embedding simulations in 200 GeV Au+Au collisions at 0-2.5% centrality. Red lines are fits with the binomial distribution, and green dotted lines represent the fit with the beta-binomial distributions using α that gives the minimal chi2/ndf. Each panel shows the result from the given combinations of embedded protons and antiprotons. The ratio of fits to the embedding data is shown for each panel.

Distributions of reconstructed protons (black circles) from embedding simulations in 200 GeV Au+Au collisions at 0-2.5% centrality. Red lines are fits with the binomial distribution, and green dotted lines represent the fit with the beta-binomial distributions using α that gives the minimal chi2/ndf. Each panel shows the result from the given combinations of embedded protons and antiprotons. The ratio of fits to the embedding data is shown for each panel.

Distributions of reconstructed protons (black circles) from embedding simulations in 200 GeV Au+Au collisions at 0-2.5% centrality. Red lines are fits with the binomial distribution, and green dotted lines represent the fit with the beta-binomial distributions using α that gives the minimal chi2/ndf. Each panel shows the result from the given combinations of embedded protons and antiprotons. The ratio of fits to the embedding data is shown for each panel.

Distributions of reconstructed protons (black circles) from embedding simulations in 200 GeV Au+Au collisions at 0-2.5% centrality. Red lines are fits with the binomial distribution, and green dotted lines represent the fit with the beta-binomial distributions using α that gives the minimal chi2/ndf. Each panel shows the result from the given combinations of embedded protons and antiprotons. The ratio of fits to the embedding data is shown for each panel.

Distributions of reconstructed protons (black circles) from embedding simulations in 200 GeV Au+Au collisions at 0-2.5% centrality. Red lines are fits with the binomial distribution, and green dotted lines represent the fit with the beta-binomial distributions using α that gives the minimal chi2/ndf. Each panel shows the result from the given combinations of embedded protons and antiprotons. The ratio of fits to the embedding data is shown for each panel.

Distributions of reconstructed protons (black circles) from embedding simulations in 200 GeV Au+Au collisions at 0-2.5% centrality. Red lines are fits with the binomial distribution, and green dotted lines represent the fit with the beta-binomial distributions using α that gives the minimal chi2/ndf. Each panel shows the result from the given combinations of embedded protons and antiprotons. The ratio of fits to the embedding data is shown for each panel.

Distributions of reconstructed protons (black circles) from embedding simulations in 200 GeV Au+Au collisions at 0-2.5% centrality. Red lines are fits with the binomial distribution, and green dotted lines represent the fit with the beta-binomial distributions using α that gives the minimal chi2/ndf. Each panel shows the result from the given combinations of embedded protons and antiprotons. The ratio of fits to the embedding data is shown for each panel.

Distributions of reconstructed protons (black circles) from embedding simulations in 200 GeV Au+Au collisions at 0-2.5% centrality. Red lines are fits with the binomial distribution, and green dotted lines represent the fit with the beta-binomial distributions using α that gives the minimal chi2/ndf. Each panel shows the result from the given combinations of embedded protons and antiprotons. The ratio of fits to the embedding data is shown for each panel.

Distributions of reconstructed protons (black circles) from embedding simulations in 200 GeV Au+Au collisions at 0-2.5% centrality. Red lines are fits with the binomial distribution, and green dotted lines represent the fit with the beta-binomial distributions using α that gives the minimal chi2/ndf. Each panel shows the result from the given combinations of embedded protons and antiprotons. The ratio of fits to the embedding data is shown for each panel.

Distributions of reconstructed protons (black circles) from embedding simulations in 200 GeV Au+Au collisions at 0-2.5% centrality. Red lines are fits with the binomial distribution, and green dotted lines represent the fit with the beta-binomial distributions using α that gives the minimal chi2/ndf. Each panel shows the result from the given combinations of embedded protons and antiprotons. The ratio of fits to the embedding data is shown for each panel.

Distributions of reconstructed protons (black circles) from embedding simulations in 200 GeV Au+Au collisions at 0-2.5% centrality. Red lines are fits with the binomial distribution, and green dotted lines represent the fit with the beta-binomial distributions using α that gives the minimal chi2/ndf. Each panel shows the result from the given combinations of embedded protons and antiprotons. The ratio of fits to the embedding data is shown for each panel.

Distributions of reconstructed protons (black circles) from embedding simulations in 200 GeV Au+Au collisions at 0-2.5% centrality. Red lines are fits with the binomial distribution, and green dotted lines represent the fit with the beta-binomial distributions using α that gives the minimal chi2/ndf. Each panel shows the result from the given combinations of embedded protons and antiprotons. The ratio of fits to the embedding data is shown for each panel.

Distributions of reconstructed protons (black circles) from embedding simulations in 200 GeV Au+Au collisions at 0-2.5% centrality. Red lines are fits with the binomial distribution, and green dotted lines represent the fit with the beta-binomial distributions using α that gives the minimal chi2/ndf. Each panel shows the result from the given combinations of embedded protons and antiprotons. The ratio of fits to the embedding data is shown for each panel.

Distributions of reconstructed protons (black circles) from embedding simulations in 200 GeV Au+Au collisions at 0-2.5% centrality. Red lines are fits with the binomial distribution, and green dotted lines represent the fit with the beta-binomial distributions using α that gives the minimal chi2/ndf. Each panel shows the result from the given combinations of embedded protons and antiprotons. The ratio of fits to the embedding data is shown for each panel.

Distributions of reconstructed protons (black circles) from embedding simulations in 200 GeV Au+Au collisions at 0-2.5% centrality. Red lines are fits with the binomial distribution, and green dotted lines represent the fit with the beta-binomial distributions using α that gives the minimal chi2/ndf. Each panel shows the result from the given combinations of embedded protons and antiprotons. The ratio of fits to the embedding data is shown for each panel.

Distributions of reconstructed protons (black circles) from embedding simulations in 200 GeV Au+Au collisions at 0-2.5% centrality. Red lines are fits with the binomial distribution, and green dotted lines represent the fit with the beta-binomial distributions using α that gives the minimal chi2/ndf. Each panel shows the result from the given combinations of embedded protons and antiprotons. The ratio of fits to the embedding data is shown for each panel.

Distributions of reconstructed protons (black circles) from embedding simulations in 200 GeV Au+Au collisions at 0-2.5% centrality. Red lines are fits with the binomial distribution, and green dotted lines represent the fit with the beta-binomial distributions using α that gives the minimal chi2/ndf. Each panel shows the result from the given combinations of embedded protons and antiprotons. The ratio of fits to the embedding data is shown for each panel.

Distributions of reconstructed protons (black circles) from embedding simulations in 200 GeV Au+Au collisions at 0-2.5% centrality. Red lines are fits with the binomial distribution, and green dotted lines represent the fit with the beta-binomial distributions using α that gives the minimal chi2/ndf. Each panel shows the result from the given combinations of embedded protons and antiprotons. The ratio of fits to the embedding data is shown for each panel.

Distributions of reconstructed protons (black circles) from embedding simulations in 200 GeV Au+Au collisions at 0-2.5% centrality. Red lines are fits with the binomial distribution, and green dotted lines represent the fit with the beta-binomial distributions using α that gives the minimal chi2/ndf. Each panel shows the result from the given combinations of embedded protons and antiprotons. The ratio of fits to the embedding data is shown for each panel.

Distributions of reconstructed protons (black circles) from embedding simulations in 200 GeV Au+Au collisions at 0-2.5% centrality. Red lines are fits with the binomial distribution, and green dotted lines represent the fit with the beta-binomial distributions using α that gives the minimal chi2/ndf. Each panel shows the result from the given combinations of embedded protons and antiprotons. The ratio of fits to the embedding data is shown for each panel.

Distributions of reconstructed protons (black circles) from embedding simulations in 200 GeV Au+Au collisions at 0-2.5% centrality. Red lines are fits with the binomial distribution, and green dotted lines represent the fit with the beta-binomial distributions using α that gives the minimal chi2/ndf. Each panel shows the result from the given combinations of embedded protons and antiprotons. The ratio of fits to the embedding data is shown for each panel.

Distributions of reconstructed protons (black circles) from embedding simulations in 200 GeV Au+Au collisions at 0-2.5% centrality. Red lines are fits with the binomial distribution, and green dotted lines represent the fit with the beta-binomial distributions using α that gives the minimal chi2/ndf. Each panel shows the result from the given combinations of embedded protons and antiprotons. The ratio of fits to the embedding data is shown for each panel.

Distributions of reconstructed protons (black circles) from embedding simulations in 200 GeV Au+Au collisions at 0-2.5% centrality. Red lines are fits with the binomial distribution, and green dotted lines represent the fit with the beta-binomial distributions using α that gives the minimal chi2/ndf. Each panel shows the result from the given combinations of embedded protons and antiprotons. The ratio of fits to the embedding data is shown for each panel.

Distributions of reconstructed protons (black circles) from embedding simulations in 200 GeV Au+Au collisions at 0-2.5% centrality. Red lines are fits with the binomial distribution, and green dotted lines represent the fit with the beta-binomial distributions using α that gives the minimal chi2/ndf. Each panel shows the result from the given combinations of embedded protons and antiprotons. The ratio of fits to the embedding data is shown for each panel.

Distributions of reconstructed protons (black circles) from embedding simulations in 200 GeV Au+Au collisions at 0-2.5% centrality. Red lines are fits with the binomial distribution, and green dotted lines represent the fit with the beta-binomial distributions using α that gives the minimal chi2/ndf. Each panel shows the result from the given combinations of embedded protons and antiprotons. The ratio of fits to the embedding data is shown for each panel.

Cumulants and their ratios up to the sixth order corrected for non-binomial efficiencies for 200 GeV Au+Au collisions at 0-5% centrality. The CBWC is applied for 2.5% centrality bin width. Results from the conventional efficiency correction are shown as black filled circles, results from the unfolding with the binomial detector response are shown as black open circles, and results from beta-binomial detector response with $\alpha+\sigma$, $\alpha$ and $\alpha-\sigma$ are shown in green triangles, red squares and blue triangles, respectively. C5, C6, C2/C1, C5/C1 and C6/C2 are scaled by constant shown in each column.

Collision centrality dependence of net-proton C6/C2 in Au+Au collisions for $\sqrt{s_{NN}}$ = 200 GeV within |y| < 0.5 and 0.4 < pT (GeV/c) < 2.0. Results with and without the CBWC are overlaid. The results are corrected for detector efficiencies. Points for different calculation methods are staggered horizontally to improve clarity.

Collision centrality dependence of net-proton C6/C2 in Au+Au collisions for $\sqrt{s_{NN}}$ = 27, 54.4, and 200 GeV within |y| < 0.5 and 0.4 < pT (GeV/c) < 2.0. Points for different beam energies are staggered horizontally to improve clarity. Shaded and hatched bands show the results from UrQMD model calculations The lattice QCD calculations [13, 14] for T = 160 MeV and $\mu_{B}$ < 110 MeV. are shown as a blue band at $\langle N_{part}\rangle$ $\approx$ 340.

Centrality dependence of single cumulants C1, of net-lambda multiplicity distributions at Au + Au collision 62.4 GeV. Values are shown with NBD, Poisson and UrQMD predictions.Npart values are from Phys. Rev. C 104, 024902 (2021) and they are little different than the values shown in the original paper.

Centrality dependence of single cumulants C1, of net-lambda multiplicity distributions at Au + Au collision 200 GeV. Values are shown with NBD, Poisson and UrQMD predictions.Npart values are from Phys. Rev. C 104, 024902 (2021) and they are little different than the values shown in the original paper.

Centrality dependence of single cumulants C2, of net-lambda multiplicity distributions at Au + Au collision 19.6 GeV. Values are shown with NBD, Poisson and UrQMD predictions.Npart values are from Phys. Rev. C 104, 024902 (2021) and they are little different than the values shown in the original paper.

Centrality dependence of single cumulants C2, of net-lambda multiplicity distributions at Au + Au collision 27 GeV. Values are shown with NBD, Poisson and UrQMD predictions.Npart values are from Phys. Rev. C 104, 024902 (2021) and they are little different than the values shown in the original paper.

Centrality dependence of single cumulants C2, of net-lambda multiplicity distributions at Au + Au collision 39 GeV. Values are shown with NBD, Poisson and UrQMD predictions.Npart values are from Phys. Rev. C 104, 024902 (2021) and they are little different than the values shown in the original paper.

Centrality dependence of single cumulants C2, of net-lambda multiplicity distributions at Au + Au collision 62.4 GeV. Values are shown with NBD, Poisson and UrQMD predictions.Npart values are from Phys. Rev. C 104, 024902 (2021) and they are little different than the values shown in the original paper.

Centrality dependence of single cumulants C2, of net-lambda multiplicity distributions at Au + Au collision 200 GeV. Values are shown with NBD, Poisson and UrQMD predictions.Npart values are from Phys. Rev. C 104, 024902 (2021) and they are little different than the values shown in the original paper.

Centrality dependence of single cumulants C3, of net-lambda multiplicity distributions at Au + Au collision 19.6 GeV. Values are shown with NBD, Poisson and UrQMD predictions.Npart values are from Phys. Rev. C 104, 024902 (2021) and they are little different than the values shown in the original paper.

Centrality dependence of single cumulants C3, of net-lambda multiplicity distributions at Au + Au collision 27 GeV. Values are shown with NBD, Poisson and UrQMD predictions.Npart values are from Phys. Rev. C 104, 024902 (2021) and they are little different than the values shown in the original paper.

Centrality dependence of single cumulants C3, of net-lambda multiplicity distributions at Au + Au collision 39 GeV. Values are shown with NBD, Poisson and UrQMD predictions.Npart values are from Phys. Rev. C 104, 024902 (2021) and they are little different than the values shown in the original paper.

Centrality dependence of single cumulants C3, of net-lambda multiplicity distributions at Au + Au collision 62.4 GeV. Values are shown with NBD, Poisson and UrQMD predictions.Npart values are from Phys. Rev. C 104, 024902 (2021) and they are little different than the values shown in the original paper.

Centrality dependence of single cumulants C3, of net-lambda multiplicity distributions at Au + Au collision 200 GeV. Values are shown with NBD, Poisson and UrQMD predictions.Npart values are from Phys. Rev. C 104, 024902 (2021) and they are little different than the values shown in the original paper.

Centrality dependence of net-lambda cumulant ratio C2/C1, as a function of net-lambda multiplicity distributions at Au + Au collision 19.6 GeV. Values are shown with NBD, Poisson and UrQMD predictions.Npart values are from Phys. Rev. C 104, 024902 (2021) and they are little different than the values shown in the original paper.

Centrality dependence of net-lambda cumulant ratio C2/C1, as a function of net-lambda multiplicity distributions at Au + Au collision 27 GeV. Values are shown with NBD, Poisson and UrQMD predictions.Npart values are from Phys. Rev. C 104, 024902 (2021) and they are little different than the values shown in the original paper.

Centrality dependence of net-lambda cumulant ratio C2/C1, as a function of net-lambda multiplicity distributions at Au + Au collision 39 GeV. Values are shown with NBD, Poisson and UrQMD predictions.Npart values are from Phys. Rev. C 104, 024902 (2021) and they are little different than the values shown in the original paper.

Centrality dependence of net-lambda cumulant ratio C2/C1, as a function of net-lambda multiplicity distributions at Au + Au collision 62.4 GeV. Values are shown with NBD, Poisson and UrQMD predictions.Npart values are from Phys. Rev. C 104, 024902 (2021) and they are little different than the values shown in the original paper.

Centrality dependence of net-lambda cumulant ratio C2/C1, as a function of net-lambda multiplicity distributions at Au + Au collision 200 GeV. Values are shown with NBD, Poisson and UrQMD predictions.Npart values are from Phys. Rev. C 104, 024902 (2021) and they are little different than the values shown in the original paper.

Centrality dependence of net-lambda cumulant ratio C3/C2, as a function of net-lambda multiplicity distributions at Au + Au collision 19.6 GeV. Values are shown with NBD, Poisson and UrQMD predictions.Npart values are from Phys. Rev. C 104, 024902 (2021) and they are little different than the values shown in the original paper.

Centrality dependence of net-lambda cumulant ratio C3/C2, as a function of net-lambda multiplicity distributions at Au + Au collision 27 GeV. Values are shown with NBD, Poisson and UrQMD predictions.Npart values are from Phys. Rev. C 104, 024902 (2021) and they are little different than the values shown in the original paper.

Centrality dependence of net-lambda cumulant ratio C3/C2, as a function of net-lambda multiplicity distributions at Au + Au collision 39 GeV. Values are shown with NBD, Poisson and UrQMD predictions.Npart values are from Phys. Rev. C 104, 024902 (2021) and they are little different than the values shown in the original paper.

Centrality dependence of net-lambda cumulant ratio C3/C2, as a function of net-lambda multiplicity distributions at Au + Au collision 62.4 GeV. Values are shown with NBD, Poisson and UrQMD predictions.Npart values are from Phys. Rev. C 104, 024902 (2021) and they are little different than the values shown in the original paper.

Centrality dependence of net-lambda cumulant ratio C3/C2, as a function of net-lambda multiplicity distributions at Au + Au collision 200 GeV. Values are shown with NBD, Poisson and UrQMD predictions.Npart values are from Phys. Rev. C 104, 024902 (2021) and they are little different than the values shown in the original paper.

Beam-energy dependence of net-lambda cumulant ratios C2/C1 in most central (0-5%) and peripheral (50-60%). Values are shown with NBD, Poisson and UrQMD predictions.

Beam-energy dependence of net-lambda cumulant ratios C3/C2 in most central (0-5%) and peripheral (50-60%). Values are shown with NBD, Poisson and UrQMD predictions.

Beam-energy dependence of net-lambda, net-proton and net-kaon cumulant ratios C2/C1 in most central (0-5%) collision.

Beam-energy dependence of net-lambda, net-proton and net-kaon cumulant ratios C3/C2 in most central (0-5%) collision.

Beam-energy dependence of net-lambda cumulant ratios C2/C1 in most central (0-5%) collision, along with results from HRG.

Beam-energy dependence of net-lambda cumulant ratios C3/C2 in most central (0-5%) collision, along with results from HRG.

Rapidity dependence of net-lambda cumulant ratios C2/C1 in most central (0-5%) collision, along with results from NBD.

Rapidity dependence of net-lambda cumulant ratios C3/C2 in most central (0-5%) collision, along with results from NBD.

Rapidity dependence of normalized C2 in most central (0-5%) collision at Au+Au 19.6 GeV.

Rapidity dependence of normalized C2 in most central (0-5%) collision at Au+Au 200 GeV.

Reference charged particle multiplicity distributions using only pions and kaons ...

Reference charged particle multiplicity distributions using only pions and kaons ...

Reference charged particle multiplicity distributions using only pions and kaons ...

Reference charged particle multiplicity distributions using only pions and kaons ...

Reference charged particle multiplicity distributions using only pions and kaons ...

Reference charged particle multiplicity distributions using only pions and kaons ...

$\Delta N_\mathrm{p}$ multiplicity distributions in Au+Au collisions at various $\sqrt{s_\text{NN}}$ for 0-5%, ...

$\Delta N_\mathrm{p}$ multiplicity distributions in Au+Au collisions at various $\sqrt{s_\text{NN}}$ for 0-5%, ...

$\Delta N_\mathrm{p}$ multiplicity distributions in Au+Au collisions at various $\sqrt{s_\text{NN}}$ for 0-5%, ...

$\Delta N_\mathrm{p}$ multiplicity distributions in Au+Au collisions at various $\sqrt{s_\text{NN}}$ for 0-5%, ...

$\Delta N_\mathrm{p}$ multiplicity distributions in Au+Au collisions at various $\sqrt{s_\text{NN}}$ for 0-5%, ...

$\Delta N_\mathrm{p}$ multiplicity distributions in Au+Au collisions at various $\sqrt{s_\text{NN}}$ for 0-5%, ...

$\Delta N_\mathrm{p}$ multiplicity distributions in Au+Au collisions at various $\sqrt{s_\text{NN}}$ for 0-5%, ...

$\Delta N_\mathrm{p}$ multiplicity distributions in Au+Au collisions at various $\sqrt{s_\text{NN}}$ for 0-5%, ...

$\Delta N_\mathrm{p}$ multiplicity distributions in Au+Au collisions at various $\sqrt{s_\text{NN}}$ for 0-5%, ...

$\Delta N_\mathrm{p}$ multiplicity distributions in Au+Au collisions at various $\sqrt{s_\text{NN}}$ for 0-5%, ...

$\Delta N_\mathrm{p}$ multiplicity distributions in Au+Au collisions at various $\sqrt{s_\text{NN}}$ for 0-5%, ...

$\Delta N_\mathrm{p}$ multiplicity distributions in Au+Au collisions at various $\sqrt{s_\text{NN}}$ for 0-5%, ...

$\Delta N_\mathrm{p}$ multiplicity distributions in Au+Au collisions at various $\sqrt{s_\text{NN}}$ for 0-5%, ...

$\Delta N_\mathrm{p}$ multiplicity distributions in Au+Au collisions at various $\sqrt{s_\text{NN}}$ for 0-5%, ...

$\Delta N_\mathrm{p}$ multiplicity distributions in Au+Au collisions at various $\sqrt{s_\text{NN}}$ for 0-5%, ...

$\Delta N_\mathrm{p}$ multiplicity distributions in Au+Au collisions at various $\sqrt{s_\text{NN}}$ for 0-5%, ...

$\Delta N_\mathrm{p}$ multiplicity distributions in Au+Au collisions at various $\sqrt{s_\text{NN}}$ for 0-5%, ...

$\Delta N_\mathrm{p}$ multiplicity distributions in Au+Au collisions at various $\sqrt{s_\text{NN}}$ for 0-5%, ...

$\Delta N_\mathrm{p}$ multiplicity distributions in Au+Au collisions at various $\sqrt{s_\text{NN}}$ for 0-5%, ...

$\Delta N_\mathrm{p}$ multiplicity distributions in Au+Au collisions at various $\sqrt{s_\text{NN}}$ for 0-5%, ...

$\Delta N_\mathrm{p}$ multiplicity distributions in Au+Au collisions at various $\sqrt{s_\text{NN}}$ for 0-5%, ...

$\Delta N_\mathrm{p}$ multiplicity distributions in Au+Au collisions at various $\sqrt{s_\text{NN}}$ for 0-5%, ...

$\Delta N_\mathrm{p}$ multiplicity distributions in Au+Au collisions at various $\sqrt{s_\text{NN}}$ for 0-5%, ...

$\Delta N_\mathrm{p}$ multiplicity distributions in Au+Au collisions at various $\sqrt{s_\text{NN}}$ for 0-5%, ...

$\Delta N_\mathrm{p}$ multiplicity distributions in Au+Au collisions at various $\sqrt{s_\text{NN}}$ for 0-5%, ...

$\Delta N_\mathrm{p}$ multiplicity distributions in Au+Au collisions at various $\sqrt{s_\text{NN}}$ for 0-5%, ...

$\Delta N_\mathrm{p}$ multiplicity distributions in Au+Au collisions at various $\sqrt{s_\text{NN}}$ for 0-5%, ...

$C_{n}$ of net-proton distribution in Au+Au collisions at $\sqrt{s_{NN}}$ = 7.7 GeV as a function of $N_{part}$.

$C_{n}$ of net-proton distribution in Au+Au collisions at $\sqrt{s_{NN}}$ = 7.7 GeV as a function of $N_{part}$.

$C_{n}$ of net-proton distribution in Au+Au collisions at $\sqrt{s_{NN}}$ = 7.7 GeV as a function of $N_{part}$.

$C_{n}$ of net-proton distribution in Au+Au collisions at $\sqrt{s_{NN}}$ = 7.7 GeV as a function of $N_{part}$.

$C_{n}$ of net-proton distribution in Au+Au collisions at $\sqrt{s_{NN}}$ = 19.6 GeV as a function of $N_{part}$.

$C_{n}$ of net-proton distribution in Au+Au collisions at $\sqrt{s_{NN}}$ = 19.6 GeV as a function of $N_{part}$.

$C_{n}$ of net-proton distribution in Au+Au collisions at $\sqrt{s_{NN}}$ = 19.6 GeV as a function of $N_{part}$.

$C_{n}$ of net-proton distribution in Au+Au collisions at $\sqrt{s_{NN}}$ = 19.6 GeV as a function of $N_{part}$.

$C_{n}$ of net-proton distribution in Au+Au collisions at $\sqrt{s_{NN}}$ = 62.4 GeV as a function of $N_{part}$.

$C_{n}$ of net-proton distribution in Au+Au collisions at $\sqrt{s_{NN}}$ = 62.4 GeV as a function of $N_{part}$.

$C_{n}$ of net-proton distribution in Au+Au collisions at $\sqrt{s_{NN}}$ = 62.4 GeV as a function of $N_{part}$.

$C_{n}$ of net-proton distribution in Au+Au collisions at $\sqrt{s_{NN}}$ = 62.4 GeV as a function of $N_{part}$.

$\kappa\sigma^2$ as a function of collision energy for Au+Au collisions for 0-5% centrality.

Efficiency uncorrected $C_n$ of net-proton proton and anti-proton multiplicity distribution in Au+Au collisions at $\sqrt{s_\text{NN}}$ = 7.7 - 200 GeV as function of $\left\langle N_\text{part} \right\rangle$.

Efficiencies of proton and anti-proton as a function of $p_\mathrm{T}$ in Au+Au collisions for various $\sqrt{s_\text{NN}}$ and collision centralities.

Distribution of reconstructed protons from embedding simulations in 200 GeV top 2.5%-central Au+Au collisions.

Distribution of reconstructed protons from embedding simulations in 200 GeV top 2.5%-central Au+Au collisions.

Distribution of reconstructed protons from embedding simulations in 200 GeV top 2.5%-central Au+Au collisions.

Distribution of reconstructed protons from embedding simulations in 200 GeV top 2.5%-central Au+Au collisions.

Distribution of reconstructed protons from embedding simulations in 200 GeV top 2.5%-central Au+Au collisions.

Distribution of reconstructed protons from embedding simulations in 200 GeV top 2.5%-central Au+Au collisions.

Distribution of reconstructed protons from embedding simulations in 200 GeV top 2.5%-central Au+Au collisions.

Distribution of reconstructed protons from embedding simulations in 200 GeV top 2.5%-central Au+Au collisions.

Distribution of reconstructed protons from embedding simulations in 200 GeV top 2.5%-central Au+Au collisions.

Distribution of reconstructed protons from embedding simulations in 200 GeV top 2.5%-central Au+Au collisions.

Distribution of reconstructed protons from embedding simulations in 200 GeV top 2.5%-central Au+Au collisions.

Distribution of reconstructed protons from embedding simulations in 200 GeV top 2.5%-central Au+Au collisions.

Distribution of reconstructed protons from embedding simulations in 200 GeV top 2.5%-central Au+Au collisions.

Distribution of reconstructed protons from embedding simulations in 200 GeV top 2.5%-central Au+Au collisions.

Distribution of reconstructed protons from embedding simulations in 200 GeV top 2.5%-central Au+Au collisions.

Distribution of reconstructed protons from embedding simulations in 200 GeV top 2.5%-central Au+Au collisions.

Distribution of reconstructed protons from embedding simulations in 200 GeV top 2.5%-central Au+Au collisions.

Distribution of reconstructed protons from embedding simulations in 200 GeV top 2.5%-central Au+Au collisions.

Distribution of reconstructed protons from embedding simulations in 200 GeV top 2.5%-central Au+Au collisions.

Distribution of reconstructed protons from embedding simulations in 200 GeV top 2.5%-central Au+Au collisions.

Distribution of reconstructed protons from embedding simulations in 200 GeV top 2.5%-central Au+Au collisions.

Distribution of reconstructed protons from embedding simulations in 200 GeV top 2.5%-central Au+Au collisions.

Distribution of reconstructed protons from embedding simulations in 200 GeV top 2.5%-central Au+Au collisions.

Distribution of reconstructed protons from embedding simulations in 200 GeV top 2.5%-central Au+Au collisions.

Distribution of reconstructed protons from embedding simulations in 200 GeV top 2.5%-central Au+Au collisions.

Distribution of reconstructed protons from embedding simulations in 200 GeV top 2.5%-central Au+Au collisions.

Distribution of reconstructed protons from embedding simulations in 200 GeV top 2.5%-central Au+Au collisions.

Distribution of reconstructed protons from embedding simulations in 200 GeV top 2.5%-central Au+Au collisions.

Distribution of reconstructed protons from embedding simulations in 200 GeV top 2.5%-central Au+Au collisions.

Distribution of reconstructed protons from embedding simulations in 200 GeV top 2.5%-central Au+Au collisions.

Distribution of reconstructed protons from embedding simulations in 200 GeV top 2.5%-central Au+Au collisions.

Distribution of reconstructed protons from embedding simulations in 200 GeV top 2.5%-central Au+Au collisions.

Distribution of reconstructed protons from embedding simulations in 200 GeV top 2.5%-central Au+Au collisions.

Unfolded net-proton multiplicity distributions for $\sqrt{s_{NN}$ = 200 GeV Au+Au collisions.

Unfolded net-proton multiplicity distributions for $\sqrt{s_{NN}$ = 200 GeV Au+Au collisions.

Unfolded net-proton multiplicity distributions for $\sqrt{s_{NN}$ = 200 GeV Au+Au collisions.

Unfolded net-proton multiplicity distributions for $\sqrt{s_{NN}$ = 200 GeV Au+Au collisions.

Unfolded net-proton multiplicity distributions for $\sqrt{s_{NN}$ = 200 GeV Au+Au collisions.

Unfolded net-proton multiplicity distributions for $\sqrt{s_{NN}$ = 200 GeV Au+Au collisions.

Unfolded net-proton multiplicity distributions for $\sqrt{s_{NN}$ = 200 GeV Au+Au collisions.

Cumulant ratios as a function of $N_{part}$ for net-proton distributions in Au+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV

Cumulant ratios as a function of $N_{part}$ for net-proton distributions in Au+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV

Collision centrality dependence of proton, anti-proton and net-proton cumulants

Cumulants and their ratios as a function of $<N_{part}>$, for the net-proton distribution

Centrality dependence of normalized correlation functions $\kappa_n/$kappa_1$ for proton and anti-proton multiplicity distribution

Rapidity acceptance dependence of cumulants of proton, anti-proton and net-proton multiplicity distributions in 0-5% central Au+Au collision ...

Rapidity acceptance dependence of normalized correlation functions up to fourth order.

Rapidity-acceptance dependence of cumulant ratios of proton, anti-proton and net-proton multiplicity distributions in 0-5% central Au+Au collisions...

pT-acceptance dependence of cumulants of proton, anti-proton and net-proton multiplicity distributions for 0-5% central Au+Au collisions ...

pT-acceptance dependence of the normalized correlation functions up to fourth order ($\kappa_n/\kappa_1$, $n$ = 2, 3, 4) for proton and anti-proton multiplicity distributions in 0-5% central Au+Au collisions ...

pT-acceptance dependence of cumulant ratios of proton, anti-proton and net-proton multiplicity distributions for 0-5% central Au+Au collisions ...

Cumulant ratios from HRG model as a function of collision energy $\sqrt{s_{NN}}$

UrQMD results on pT acceptance dependence for cumulant ratios for proton and baryon

Polynomial fit of cumulant ratios as a function of collision energy $\sqrt{s_{NN}}$

Polynomial fit of cumulant ratios as a function of collision energy $\sqrt{s_{NN}}$

Polynomial fit of cumulant ratios as a function of collision energy $\sqrt{s_{NN}}$

Collision energy dependence of $C_2/C_1$, $C_3/C_2$ and $C_4/C_2$ for net-proton multiplicity distribution in 0-5% central Au+Au collisions. The expreimental net-proton measurements are compared to corresponding values from UrQMD and HRG models within the expreimental acceptances.

Collision energy dependence of $C_2/C_1$, $C_3/C_2$ and $C_4/C_2$ for net-proton multiplicity distribution in 0-5% central Au+Au collisions. The expreimental net-proton measurements are compared to corresponding values from UrQMD and HRG models within the expreimental acceptances.

Collision energy dependence of $C_2/C_1$, $C_3/C_2$ and $C_4/C_2$ for net-proton multiplicity distribution in 0-5% central Au+Au collisions. The expreimental net-proton measurements are compared to corresponding values from UrQMD and HRG models within the expreimental acceptances.

Collision energy dependence of $C_2/C_1$, $C_3/C_2$ and $C_4/C_2$ for net-proton multiplicity distribution in 0-5% central Au+Au collisions. The expreimental net-proton measurements are compared to corresponding values from UrQMD and HRG models within the expreimental acceptances.

Collision energy dependence of $C_2/C_1$, $C_3/C_2$ and $C_4/C_2$ for net-proton multiplicity distribution in 0-5% central Au+Au collisions. The expreimental net-proton measurements are compared to corresponding values from UrQMD and HRG models within the expreimental acceptances.

Collision energy dependence of $C_2/C_1$, $C_3/C_2$ and $C_4/C_2$ for net-proton multiplicity distribution in 0-5% central Au+Au collisions. The expreimental net-proton measurements are compared to corresponding values from UrQMD and HRG models within the expreimental acceptances.

Collision energy dependence of $C_2/C_1$, $C_3/C_2$ and $C_4/C_2$ for net-proton multiplicity distribution in 0-5% central Au+Au collisions. The expreimental net-proton measurements are compared to corresponding values from UrQMD and HRG models within the expreimental acceptances.

The $p_{T}$ spectra of $\pi^{-}$ measured at midrapidity (|y|<0.1) in Au+Au collisions at $\sqrt{s_{NN}}$ = 14.5 GeV. Spectra are plotted for nine centrality classes, with some spectra multiplied by a scale factor to improve clarity, as indicatedin the legend

The $p_{T}$ spectra of $K^{+}$ measured at midrapidity (|y|<0.1) in Au+Au collisions at $\sqrt{s_{NN}}$ = 14.5 GeV. Spectra are plotted for nine centrality classes, with some spectra multiplied by a scale factor to improve clarity, as indicatedin the legend

The $p_{T}$ spectra of $K^{-}$ measured at midrapidity (|y|<0.1) in Au+Au collisions at $\sqrt{s_{NN}}$ = 14.5 GeV. Spectra are plotted for nine centrality classes, with some spectra multiplied by a scale factor to improve clarity, as indicatedin the legend

Average $p_{T}$ of $\pi^{+}$ as a function of number of participant for Au+Au collisions at $\sqrt{s_{NN}}$ = 14.5 GeV.

Average $p_{T}$ of $\pi^{-}$ as a function of number of participant for Au+Au collisions at $\sqrt{s_{NN}}$ = 14.5 GeV.

Average $p_{T}$ of $K^{+}$ as a function of number of participant for Au+Au collisions at $\sqrt{s_{NN}}$ = 14.5 GeV.

Average $p_{T}$ of $K^{-}$ as a function of number of participant for Au+Au collisions at $\sqrt{s_{NN}}$= 14.5 GeV.

Average $p_{T}$ of p as a function of number of participant for Au+Au collisions at $\sqrt{s_{NN}}$ = 14.5 GeV.

Average $p_{T}$ of p-bar as a function of number of participant for Au+Au collisions at $\sqrt{s_{NN}}$ = 14.5 GeV.

dN/dy of $\pi^{+}$ scaled by 0.5*$N_{part}$ as a function of number of participant for Au+Au collisions at $\sqrt{s_{NN}}$ = 14.5 GeV.

dN/dy of $\pi^{-}$ scaled by 0.5*$N_{part}$ as a function of number of participant for Au+Au collisions at $\sqrt{s_{NN}}$ = 14.5 GeV.

dN/dy of $K^{+}$ scaled by 0.5*$N_{part}$ as a function of number of participant for Au+Au collisions at $\sqrt{s_{NN}}$ = 14.5 GeV.

dN/dy of $K^{-}$ scaled by 0.5*$N_{part}$ as a function of number of participant for Au+Au collisions at $\sqrt{s_{NN}}$ = 14.5 GeV.

dN/dy of proton scaled by 0.5*$N_{part}$ as a function of number of participant for Au+Au collisions at $\sqrt{s_{NN}}$ = 14.5 GeV.

dN/dy of p-bar scaled by 0.5*$N_{part}$ as a function of number of participant for Au+Au collisions at $\sqrt{s_{NN}}$ = 14.5 GeV.

Kinetic freeze-out temperature as a function of number of participant for Au+Au collisions at $\sqrt{s_{NN}}$ = 14.5 GeV.

Velocity as a function of number of participant for Au+Au collisions at $\sqrt{s_{NN}}$ = 14.5 GeV.

The event plane resolution calculated for Au+Au collisions at $\sqrt{s_{NN}}$ = 14.5 GeV as a function of centrality.

Inclusive charged particle elliptic flow v2 at mid-pseudorapidity (|y| <1.0) as a function of $p_{T}$ for 10-20% centrality in Au + Au collisions at $\sqrt{s_{NN}}$ = 14.5 GeV.

Inclusive charged particle elliptic flow v2 at mid-pseudorapidity (|y| <1.0) as a function of $p_{T}$ for 20-30% centrality in Au + Au collisions at $\sqrt{s_{NN}}$ = 14.5 GeV.

Inclusive charged particle elliptic flow v2 at mid-pseudorapidity (|y| <1.0) as a function of $p_{T}$ for 30-40% centrality in Au + Au collisions at $\sqrt{s_{NN}}$ = 14.5 GeV.

Inclusive charged particle elliptic flow v2 at mid-pseudorapidity (|y| <1.0) as a function of transverse momentum $p_{T}$ for six centrality classes, obtained using the $\eta$-sub event plane method in Au+Au collisions at $\sqrt{s_{NN}}$ = 14.5 GeV.

Inclusive charged particle elliptic flow v2 at mid-pseudorapidity (|y| <1.0) as a function of $p_{T}$-integrated v2($\eta$) for six centrality classes, obtained using the $\eta$-sub event plane method in Au+Au collisions at $\sqrt{s_{NN}}$ = 14.5 GeV.

The ratio inclusive charged particle elliptic flow v2 over root-mean-square participant eccentricity $Epart_{2}$ at mid-pseudorapidity as a function of $p_{T}$ for 10–20%, 30–40%, and 50–60% collision centralities in Au+Au collisions at $\sqrt{s_{NN}}$ = 14.5 GeV.

Summary of centrality bins, average number of participants $N_{part}$, number of binary collisions $N_{coll}$, reaction plane eccentricity eRP, participant eccentricity epart, root-mean-square of the participant eccentricity epart{2}, and transverse area $S_{part}$ from MC Glauber simulations at $\sqrt{s_{NN}}$ = 14.5 GeV.

The inclusive charged particle elliptic flow v2($\eta$-sub) versus pseudorapidity $\eta$ at mid-pseudorapidity for $\sqrt{s_{NN}}$ = 14.5 GeV.

Rapidity-odd charged particles directed flow v1 as a function of $p_{T}$ in Au+Au collisions at $\sqrt{s_{NN}}$ = 7.7 GeV for 0–10%, 10–40% and 40–80% centrality intervals.

Rapidity-odd charged particles directed flow v1 as a function of $p_{T}$ in Au+Au collisions at $\sqrt{s_{NN}}$ = 11.5 GeV for 0–10%, 10–40% and 40–80% centrality intervals.

Rapidity-odd charged particles directed flow v1 as a function of $p_{T}$ in Au+Au collisions at $\sqrt{s_{NN}}$ = 14.5 GeV GeV for 0–10%, 10–40% and 40–80% centrality intervals.

Rapidity-odd charged particles directed flow v1 as a function of $p_{T}$ in Au+Au collisions at $\sqrt{s_{NN}}$ = 19.6 GeV for 0–10%, 10–40% and 40–80% centrality intervals.

Rapidity-odd charged particles directed flow v1 as a function of $p_{T}$ in Au+Au collisions at $\sqrt{s_{NN}}$ = 27.0 GeV for 0–10%, 10–40% and 40–80% centrality intervals.

Rapidity-odd charged particles directed flow v1 as a function of $p_{T}$ in Au+Au collisions at $\sqrt{s_{NN}}$ = 39.0 GeV for 0–10%, 10–40% and 40–80% centrality intervals.

Rapidity-odd charged particles directed flow v1 as a function of pseudorapidity $\eta$ in Au+Au collisions at $\sqrt{s_{NN}}$ = 7.7 GeV for 0–10%, 10–40% and 40–80% centrality intervals.

Rapidity-odd charged particles directed flow v1 as a function of pseudorapidity $\eta$ in Au+Au collisions at $\sqrt{s_{NN}}$ = 11.5 GeV for 0–10%, 10–40% and 40–80% centrality intervals.

Rapidity-odd charged particles directed flow v1 as a function of pseudorapidity $\eta$ in Au+Au collisions at $\sqrt{s_{NN}}$ = 14.5 GeV for 0–10%, 10–40% and 40–80% centrality intervals.

Rapidity-odd charged particles directed flow v1 as a function of pseudorapidity $\eta$ in Au+Au collisions at $\sqrt{s_{NN}}$ = 19.6 GeV for 0–10%, 10–40% and 40–80% centrality intervals.

Rapidity-odd charged particles directed flow v1 as a function of pseudorapidity $\eta$ in Au+Au collisions at $\sqrt{s_{NN}}$ = 27.0 GeV for 0–10%, 10–40% and 40–80% centrality intervals.

Rapidity-odd charged particles directed flow v1 as a function of pseudorapidity $\eta$ in Au+Au collisions at $\sqrt{s_{NN}}$ = 39.0 GeV for 0–10%, 10–40% and 40–80% centrality intervals.

Rapidity-odd charged particles directed flow v1 as a function of pseudorapidity $\eta$ in Au+Au collisions at $\sqrt{s_{NN}}$ = 7.7 – 39 GeV for 30-60% centrality intervals.

J/psi RCP results (with respect to 40−60% peripheral) for Au+Au collisions (39, 62.4 and 200 GeV) as a function of Npart.

J/psi RCP results for Au+Au collisions (39, 62.4 and 200 GeV) as a function of Npart.

J/psi RCP results for Au+Au collisions (39, 62.4 and 200 GeV) as a function of pT.

Mid-rapidity v2(pT) for d,anti-d,t,He from minimum bias (0-80%) Au+Au collisions 27 GeV.

Mid-rapidity v2(pT) for d,anti-d,t,He from minimum bias (0-80%) Au+Au collisions 19.6 GeV.

Mid-rapidity v2(pT) for d,t,He from minimum bias (0-80%) Au+Au collisions 11.5 GeV.

Mid-rapidity v2(pT) for d,t,He from minimum bias (0-80%) Au+Au collisions 7.7 GeV.

Mid-rapidity v2(pT) difference for d-dbar in minimum bias (0-80%) Au+Au collisions 200 GeV.

Mid-rapidity v2(pT) difference for d-dbar in minimum bias (0-80%) Au+Au collisions 62.4 GeV.

Mid-rapidity v2(pT) difference for d-dbar in minimum bias (0-80%) Au+Au collisions 39 GeV.

Mid-rapidity v2(pT) difference for d-dbar in minimum bias (0-80%) Au+Au collisions 27 GeV.

Mid-rapidity v2(pT) difference for d-dbar in minimum bias (0-80%) Au+Au collisions 19.6 GeV.

Mid-rapidity v2(pT) for d and anti-d for 0-10%, 10-40% and 40-80% in Au+Au collisions 200 GeV.

Mid-rapidity v2(pT) for d and anti-d for 0-30% and 30-80% in Au+Au collisions 62.4 GeV.

Mid-rapidity v2(pT) for d and anti-d for 0-30% and 30-80% in Au+Au collisions 39 GeV.

Mid-rapidity v2(pT) for d and anti-d for 0-30% and 30-80% in Au+Au collisions 27 GeV.

Mid-rapidity v2(pT) for d 0-30% and 30-80% in Au+Au collisions 19.6 GeV.

Mid-rapidity v2(pT) for d 0-30% and 30-80% in Au+Au collisions 11.5 GeV.

Mid-rapidity v2(pT) for d 0-30% and 30-80% in Au+Au collisions 7.7 GeV.