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.

Raw $\Delta N_k$ distributions in Au+Au collisions at 19.6 GeV for 0–5%, 30–40%, and 70–80% collision centralities at midrapidity. The distributions are not corrected for the finite centrality bin width effect nor the reconstruction efficiency.

Raw $\Delta N_k$ distributions in Au+Au collisions at 27 GeV for 0–5%, 30–40%, and 70–80% collision centralities at midrapidity. The distributions are not corrected for the finite centrality bin width effect nor the reconstruction efficiency.

Raw $\Delta N_k$ distributions in Au+Au collisions at 39 GeV for 0–5%, 30–40%, and 70–80% collision centralities at midrapidity. The distributions are not corrected for the finite centrality bin width effect nor the reconstruction efficiency.

Raw $\Delta N_k$ distributions in Au+Au collisions at 62.4 GeV for 0–5%, 30–40%, and 70–80% collision centralities at midrapidity. The distributions are not corrected for the finite centrality bin width effect nor the reconstruction efficiency.

Raw $\Delta N_k$ distributions in Au+Au collisions at 200 GeV for 0–5%, 30–40%, and 70–80% collision centralities at midrapidity. The distributions are not corrected for the finite centrality bin width effect nor the reconstruction efficiency.

Collision centrality dependence of cumulants (C1, C2, C3, and C4) of $\Delta N_k$ distributions in Au+Au collisions at 7.7 GeV. The error bars are statistical uncertainties and the caps represent systematic uncertainties.

Collision centrality dependence of cumulants (C1, C2, C3, and C4) of $\Delta N_k$ distributions in Au+Au collisions at 11.5 GeV. The error bars are statistical uncertainties and the caps represent systematic uncertainties.

Collision centrality dependence of cumulants (C1, C2, C3, and C4) of $\Delta N_k$ distributions in Au+Au collisions at 14.5 GeV. The error bars are statistical uncertainties and the caps represent systematic uncertainties.

Collision centrality dependence of cumulants (C1, C2, C3, and C4) of $\Delta N_k$ distributions in Au+Au collisions at 19.6 GeV. The error bars are statistical uncertainties and the caps represent systematic uncertainties.

Collision centrality dependence of cumulants (C1, C2, C3, and C4) of $\Delta N_k$ distributions in Au+Au collisions at 27 GeV. The error bars are statistical uncertainties and the caps represent systematic uncertainties.

Collision centrality dependence of cumulants (C1, C2, C3, and C4) of $\Delta N_k$ distributions in Au+Au collisions at 39 GeV. The error bars are statistical uncertainties and the caps represent systematic uncertainties.

Collision centrality dependence of cumulants (C1, C2, C3, and C4) of $\Delta N_k$ distributions in Au+Au collisions at 62.4 GeV. The error bars are statistical uncertainties and the caps represent systematic uncertainties.

Collision centrality dependence of cumulants (C1, C2, C3, and C4) of $\Delta N_k$ distributions in Au+Au collisions at 200 GeV. The error bars are statistical uncertainties and the caps represent systematic uncertainties.

Collision centrality dependence of the $M/\sigma^2$ for $\Delta N_k$ distributions in Au+Au collisions at 7.7 GeV. The error bars are statistical uncertainties and the caps represent systematic uncertainties.

Collision centrality dependence of the $M/\sigma^2$ for $\Delta N_k$ distributions in Au+Au collisions at 11.5 GeV. The error bars are statistical uncertainties and the caps represent systematic uncertainties.

Collision centrality dependence of the $M/\sigma^2$ for $\Delta N_k$ distributions in Au+Au collisions at 14.5 GeV. The error bars are statistical uncertainties and the caps represent systematic uncertainties.

Collision centrality dependence of the $M/\sigma^2$ for $\Delta N_k$ distributions in Au+Au collisions at 19.6 GeV. The error bars are statistical uncertainties and the caps represent systematic uncertainties.

Collision centrality dependence of the $M/\sigma^2$ for $\Delta N_k$ distributions in Au+Au collisions at 27 GeV. The error bars are statistical uncertainties and the caps represent systematic uncertainties.

Collision centrality dependence of the $M/\sigma^2$ for $\Delta N_k$ distributions in Au+Au collisions at 39 GeV. The error bars are statistical uncertainties and the caps represent systematic uncertainties.

Collision centrality dependence of the $M/\sigma^2$ for $\Delta N_k$ distributions in Au+Au collisions at 62.4 GeV. The error bars are statistical uncertainties and the caps represent systematic uncertainties.

Collision centrality dependence of the $M/\sigma^2$ for $\Delta N_k$ distributions in Au+Au collisions at 200 GeV. The error bars are statistical uncertainties and the caps represent systematic uncertainties.

Collision centrality dependence of the $S\sigma$ for $\Delta N_k$ distributions in Au+Au collisions at 7.7 GeV. The error bars are statistical uncertainties and the caps represent systematic uncertainties.

Collision centrality dependence of the $S\sigma$ for $\Delta N_k$ distributions in Au+Au collisions at 11.5 GeV. The error bars are statistical uncertainties and the caps represent systematic uncertainties.

Collision centrality dependence of the $S\sigma$ for $\Delta N_k$ distributions in Au+Au collisions at 14.5 GeV. The error bars are statistical uncertainties and the caps represent systematic uncertainties.

Collision centrality dependence of the $S\sigma$ for $\Delta N_k$ distributions in Au+Au collisions at 19.6 GeV. The error bars are statistical uncertainties and the caps represent systematic uncertainties.

Collision centrality dependence of the $S\sigma$ for $\Delta N_k$ distributions in Au+Au collisions at 27 GeV. The error bars are statistical uncertainties and the caps represent systematic uncertainties.

Collision centrality dependence of the $S\sigma$ for $\Delta N_k$ distributions in Au+Au collisions at 39 GeV. The error bars are statistical uncertainties and the caps represent systematic uncertainties.

Collision centrality dependence of the $S\sigma$ for $\Delta N_k$ distributions in Au+Au collisions at 62.4 GeV. The error bars are statistical uncertainties and the caps represent systematic uncertainties.

Collision centrality dependence of the $S\sigma$ for $\Delta N_k$ distributions in Au+Au collisions at 200 GeV. The error bars are statistical uncertainties and the caps represent systematic uncertainties.

Collision centrality dependence of the $\kappa\sigma^2$ for $\Delta N_k$ distributions in Au+Au collisions at 7.7 GeV. The error bars are statistical uncertainties and the caps represent systematic uncertainties.

Collision centrality dependence of the $\kappa\sigma^2$ for $\Delta N_k$ distributions in Au+Au collisions at 11.5 GeV. The error bars are statistical uncertainties and the caps represent systematic uncertainties.

Collision centrality dependence of the $\kappa\sigma^2$ for $\Delta N_k$ distributions in Au+Au collisions at 14.5 GeV. The error bars are statistical uncertainties and the caps represent systematic uncertainties.

Collision centrality dependence of the $\kappa\sigma^2$ for $\Delta N_k$ distributions in Au+Au collisions at 19.6 GeV. The error bars are statistical uncertainties and the caps represent systematic uncertainties.

Collision centrality dependence of the $\kappa\sigma^2$ for $\Delta N_k$ distributions in Au+Au collisions at 27 GeV. The error bars are statistical uncertainties and the caps represent systematic uncertainties.

Collision centrality dependence of the $\kappa\sigma^2$ for $\Delta N_k$ distributions in Au+Au collisions at 39 GeV. The error bars are statistical uncertainties and the caps represent systematic uncertainties.

Collision centrality dependence of the $\kappa\sigma^2$ for $\Delta N_k$ distributions in Au+Au collisions at 62.4 GeV. The error bars are statistical uncertainties and the caps represent systematic uncertainties.

Collision centrality dependence of the $\kappa\sigma^2$ for $\Delta N_k$ distributions in Au+Au collisions at 200 GeV. The error bars are statistical uncertainties and the caps represent systematic uncertainties.

Collisions energy dependence of $M/\sigma^2$ for $\Delta N_k$ multiplicity distributions from 0–5% most central and 70–80% peripheral collisions in Au+Au collisions at \sqrt{s_{NN}} = 7.7, 11.5, 14.5, 19.6, 27, 39, 62.4 and 200 GeV. The error bars are statistical uncertainties and the caps represent systematic uncertainties.

Collisions energy dependence of $S\sigma$ for $\Delta N_k$ multiplicity distributions from 0–5% most central and 70–80% peripheral collisions in Au+Au collisions at \sqrt{s_{NN}} = 7.7, 11.5, 14.5, 19.6, 27, 39, 62.4 and 200 GeV. The error bars are statistical uncertainties and the caps represent systematic uncertainties.

Collisions energy dependence of $\kappa\sigma^2$ for $\Delta N_k$ multiplicity distributions from 0–5% most central and 70–80% peripheral collisions in Au+Au collisions at \sqrt{s_{NN}} = 7.7, 11.5, 14.5, 19.6, 27, 39, 62.4 and 200 GeV. The error bars are statistical uncertainties and the caps represent systematic uncertainties.

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.

$\Delta N_p$ multiplicity distributions in Au+Au collisions at $\sqrt{S_{NN}}=27$ GeV for 0-5 percent, 30-40 percent and 70-80 percent collision centralities at midrapidity.

$\Delta N_p$ multiplicity distributions in Au+Au collisions at $\sqrt{S_{NN}}=39$ GeV for 0-5 percent, 30-40 percent and 70-80 percent collision centralities at midrapidity.

$\Delta N_p$ multiplicity distributions in Au+Au collisions at $\sqrt{S_{NN}}=62.4$ GeV for 0-5 percent, 30-40 percent and 70-80 percent collision centralities at midrapidity.

$\Delta N_p$ multiplicity distributions in Au+Au collisions at $\sqrt{S_{NN}}=200$ GeV for 0-5 percent, 30-40 percent and 70-80 percent collision centralities at midrapidity.

Centrality dependence of the cumulants of $\Delta N_p$ distributions for Au+Au collisions at $\sqrt{S_{NN}}=7.7$ GeV.

Centrality dependence of the cumulants of $\Delta N_p$ distributions for Au+Au collisions at $\sqrt{S_{NN}}=11.5$ GeV.

Centrality dependence of the cumulants of $\Delta N_p$ distributions for Au+Au collisions at $\sqrt{S_{NN}}=19.6$ GeV.

Centrality dependence of the cumulants of $\Delta N_p$ distributions for Au+Au collisions at $\sqrt{S_{NN}}=27$ GeV.

Centrality dependence of the cumulants of $\Delta N_p$ distributions for Au+Au collisions at $\sqrt{S_{NN}}=39$ GeV.

Centrality dependence of the cumulants of $\Delta N_p$ distributions for Au+Au collisions at $\sqrt{S_{NN}}=62.4$ GeV.

Centrality dependence of the cumulants of $\Delta N_p$ distributions for Au+Au collisions at $\sqrt{S_{NN}}=200$ GeV.

Centrality dependence of $S\sigma$/Skellam and $\kappa\sigma^2$ for $\Delta N_p$ in Au+Au collisions at $\sqrt{S_{NN}}=7.7$ GeV.

Centrality dependence of $S\sigma$/Skellam and $\kappa\sigma^2$ for $\Delta N_p$ in Au+Au collisions at $\sqrt{S_{NN}}=11.5$ GeV.

Centrality dependence of $S\sigma$/Skellam and $\kappa\sigma^2$ for $\Delta N_p$ in Au+Au collisions at $\sqrt{S_{NN}}=19.6$ GeV.

Centrality dependence of $S\sigma$/Skellam and $\kappa\sigma^2$ for $\Delta N_p$ in Au+Au collisions at $\sqrt{S_{NN}}=27$ GeV.

Centrality dependence of $S\sigma$/Skellam and $\kappa\sigma^2$ for $\Delta N_p$ in Au+Au collisions at $\sqrt{S_{NN}}=39$ GeV.

Centrality dependence of $S\sigma$/Skellam and $\kappa\sigma^2$ for $\Delta N_p$ in Au+Au collisions at $\sqrt{S_{NN}}=62.4$ GeV.

Centrality dependence of $S\sigma$/Skellam and $\kappa\sigma^2$ for $\Delta N_p$ in Au+Au collisions at $\sqrt{S_{NN}}=200$ GeV.

Collision energy and centrality dependence of the net-proton $S\sigma$ and $\kappa\sigma^2$ from Au+Au and p+p collisions at RHIC.

Collision energy and centrality dependence of the net-proton $S\sigma$ and $\kappa\sigma^2$ from Au+Au and p+p collisions at RHIC.

Collision energy and centrality dependence of the net-proton $S\sigma$ and $\kappa\sigma^2$ from Au+Au and p+p collisions at RHIC.

Collision energy and centrality dependence of the net-proton $S\sigma$ and $\kappa\sigma^2$ from Au+Au and p+p collisions at RHIC.

Cumulants of net-proton distribution at $\sqrt{S_{NN}}=7.7$ GeV. (efficiency corrected).

Cumulants of net-proton distribution at $\sqrt{S_{NN}}=11.5$ GeV. (efficiency corrected).

Cumulants of net-proton distribution at $\sqrt{S_{NN}}=19.6$ GeV. (efficiency corrected).

Cumulants of net-proton distribution at $\sqrt{S_{NN}}=27$ GeV. (efficiency corrected).

Cumulants of net-proton distribution at $\sqrt{S_{NN}}=39$ GeV. (efficiency corrected).

Cumulants of net-proton distribution at $\sqrt{S_{NN}}=62.4$ GeV. (efficiency corrected).

Cumulants of net-proton distribution at $\sqrt{S_{NN}}=200$ GeV. (efficiency corrected).

Cumulants of proton distribution at $\sqrt{S_{NN}}=7.7$ GeV. (efficiency corrected).

Cumulants of proton distribution at $\sqrt{S_{NN}}=11.5$ GeV. (efficiency corrected).

Cumulants of proton distribution at $\sqrt{S_{NN}}=19.6$ GeV. (efficiency corrected).

Cumulants of proton distribution at $\sqrt{S_{NN}}=27$ GeV. (efficiency corrected).

Cumulants of proton distribution at $\sqrt{S_{NN}}=39$ GeV. (efficiency corrected).

Cumulants of proton distribution at $\sqrt{S_{NN}}=62.4$ GeV. (efficiency corrected).

Cumulants of proton distribution at $\sqrt{S_{NN}}=200$ GeV. (efficiency corrected).

Cumulants of anti-proton distribution at $\sqrt{S_{NN}}=7.7$ GeV. (efficiency corrected).

Cumulants of anti-proton distribution at $\sqrt{S_{NN}}=11.5$ GeV. (efficiency corrected).

Cumulants of anti-proton distribution at $\sqrt{S_{NN}}=19.6$ GeV. (efficiency corrected).

Cumulants of anti-proton distribution at $\sqrt{S_{NN}}=27$ GeV. (efficiency corrected).

Cumulants of anti-proton distribution at $\sqrt{S_{NN}}=39$ GeV. (efficiency corrected).

Cumulants of anti-proton distribution at $\sqrt{S_{NN}}=62.4$ GeV. (efficiency corrected).

Cumulants of anti-proton distribution at $\sqrt{S_{NN}}=200$ GeV. (efficiency corrected).

Centrality dependence of moments of $\Delta N_p$ distributions for Au+Au collisions at $\sqrt{s_{NN}}$ = 19.6 GeV.

Centrality dependence of moments of $\Delta N_p$ distributions for Au+Au collisions at $\sqrt{s_{NN}}$ = 19.6 GeV.

Centrality dependence of moments of $\Delta N_p$ distributions for Au+Au collisions at $\sqrt{s_{NN}}$ = 19.6 GeV.

Centrality dependence of moments of $\Delta N_p$ distributions for Au+Au collisions at $\sqrt{s_{NN}}$ = 19.6 GeV.

Centrality dependence of moments of $\Delta N_p$ distributions for Au+Au collisions at $\sqrt{s_{NN}}$ = 62.4 GeV.

Centrality dependence of moments of $\Delta N_p$ distributions for Au+Au collisions at $\sqrt{s_{NN}}$ = 62.4 GeV.

Centrality dependence of moments of $\Delta N_p$ distributions for Au+Au collisions at $\sqrt{s_{NN}}$ = 62.4 GeV.

Centrality dependence of moments of $\Delta N_p$ distributions for Au+Au collisions at $\sqrt{s_{NN}}$ = 62.4 GeV.

Centrality dependence of moments of $\Delta N_p$ distributions for Au+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV.

Centrality dependence of moments of $\Delta N_p$ distributions for Au+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV.

Centrality dependence of moments of $\Delta N_p$ distributions for Au+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV.

Centrality dependence of moments of $\Delta N_p$ distributions for Au+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV.

Centrality dependence of $S\sigma$ for $\Delta N_p$ in Au+Au collisions at $\sqrt{s_{NN}}$ = 19.6 GeV.

Centrality dependence of $\kappa\sigma^2$ for $\Delta N_p$ in Au+Au collisions at $\sqrt{s_{NN}}$ = 19.6 GeV.

Centrality dependence of $S\sigma$ for $\Delta N_p$ in Au+Au collisions at $\sqrt{s_{NN}}$ = 62.4 GeV.

Centrality dependence of $\kappa\sigma^2$ for $\Delta N_p$ in Au+Au collisions at $\sqrt{s_{NN}}$ = 62.4 GeV.

Centrality dependence of $S\sigma$ for $\Delta N_p$ in Au+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV.

Centrality dependence of $\kappa\sigma^2$ for $\Delta N_p$ in Au+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV.

Centrality dependence of $S\sigma$ for $\Delta N_p$ in Au+Au collisions from Lattice QCD Calculations.

Centrality dependence of $S\sigma$ for $\Delta N_p$ in Au+Au collisions at $\sqrt{s_{NN}}$ = 19.6 GeV from Transport Model Calculations.

Centrality dependence of $S\sigma$ for $\Delta N_p$ in Au+Au collisions at $\sqrt{s_{NN}}$ = 62.4 GeV from Transport Model Calculations.

Centrality dependence of $S\sigma$ for $\Delta N_p$ in Au+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV from Transport Model Calculations.

Centrality dependence of $\kappa\sigma^2$ for $\Delta N_p$ in Au+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV from Transport Model Calculations.

Centrality dependence of $\kappa\sigma^2$ for $\Delta N_p$ in Au+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV from Transport Model Calculations for net-baryon.

Centrality dependence of $\kappa\sigma^2$ for $\Delta N_p$ in Au+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV from Transport Model Calculations for net-proton (No Decay).

Centrality dependence of $\kappa\sigma^2$ for $\Delta N_p$ in Au+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV from Transport Model Calculations.

Centrality dependence of $\kappa\sigma^2$ for $\Delta N_p$ in Au+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV from Transport Model Calculations.

Centrality dependence of $\kappa\sigma^2$ for $\Delta N_p$ in Au+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV from Transport Model Calculations.

Centrality dependence of $\kappa\sigma^2$ for $\Delta N_p$ in Au+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV from Transport Model Calculations.

Centrality dependence of $\kappa\sigma^2$ for $\Delta N_p$ in Au+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV from Transport Model Calculations.

Centrality dependence of $\kappa\sigma^2$ for $\Delta N_p$ in Au+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV from Transport Model Calculations.

$\sqrt{s_{NN}}$ dependence of $\kappa\sigma^2$ for net proton distributions measured at RHIC. The results are STAR data.

$\sqrt{s_{NN}}$ dependence of $\kappa\sigma^2$ for net proton distributions measured at RHIC. The results are from UrQMD net-proton.

$\sqrt{s_{NN}}$ dependence of $\kappa\sigma^2$ for net proton distributions measured at RHIC. The results are from AMPT default net-proton.

$\sqrt{s_{NN}}$ dependence of $\kappa\sigma^2$ for net proton distributions measured at RHIC. The results are from AMPT String Melting net-proton.

$\sqrt{s_{NN}}$ dependence of $\kappa\sigma^2$ for net proton distributions measured at RHIC. The results are from Therminator net-proton.

$\sqrt{s_{NN}}$ dependence of $\kappa\sigma^2$ for net proton distributions measured at RHIC. The results are from Hijing net-proton.