$P_{\rm H}$ measurements are shown as a function of hyperon $p_{\rm T}$ at $\sqrt{s_{\rm NN}}$=19.6 and 27 GeV. Statistical uncertainties are represented as lines while systematic uncertainties are represented as boxes. There is no observed dependence of $P_{\rm H}$ on $p_{\rm T}$ at $\sqrt{s_{\rm NN}}$=19.6 or 27 GeV, consistent with previous observations.

$P_{\rm H}$ measurements are shown as a function of hyperon $y$ at $\sqrt{s_{\rm NN}}$=19.6 and 27 GeV. Statistical uncertainties are represented as lines while systematic uncertainties are represented as boxes. The data set at $\sqrt{s_{\rm NN}}$=19.6 GeV takes advantage of STAR upgrades to reach larger $|y|$.

\Delta v_1 between proton and anti-proton vs rapidity in Au+Au 200 GeV 50-80% centrality.

\Delta v_1 between proton and anti-proton vs rapidity in Zr+Zr and Ru+Ru (combined) 200 GeV 50-80% centrality.

\Delta v_1 between proton and anti-proton vs rapidity in Au+Au 27 GeV 50-80% centrality.

\Delta dv1/dy as a function of centrality in Au+Au 200 GeV.

\Delta dv1/dy as a function of centrality in Ru+Ru and Zr+Zr 200 GeV

\Delta dv1/dy as a function of centrality in Au+Au 27 GeV.

'Identified transverse momentum spectra of $\pi^{-}$ at midrapidity (|y| < 0.1) in U+U collisions at $\sqrt{s_{\rm NN}}$ = 193 GeV'

'Identified transverse momentum spectra of $K^{-}$ at midrapidity (|y| < 0.1) in U+U collisions at $\sqrt{s_{\rm NN}}$ = 193 GeV'

'Identified transverse momentum spectra of $\bar{p}$ at midrapidity (|y| < 0.1) in U+U collisions at $\sqrt{s_{\rm NN}}$ = 193 GeV'

'Average transverse momentum as a function of $\langle$N$_{part}$$\rangle$ for $\pi^{+}$ at midrapidity (|y| < 0.1) in U+U collisions at $\sqrt{s_{\rm NN}}$ = 193 GeV.'

'Average transverse momentum as a function of $\langle$N$_{part}$$\rangle$ for $K^{+}$ at midrapidity (|y| < 0.1) in U+U collisions at $\sqrt{s_{\rm NN}}$ = 193 GeV.'

'Average transverse momentum as a function of $\langle$N$_{part}$$\rangle$ for p at midrapidity (|y| < 0.1) in U+U collisions at $\sqrt{s_{\rm NN}}$ = 193 GeV.'

'dN/dy scaled by 0.5 × $\langle$N$_{part}$$\rangle$ as a function of $\langle$N$_{part}$$\rangle$ for $\pi^{+}$ at midrapidity (|y| < 0.1) in U+U collisions at $\sqrt{s_{\rm NN}}$ = 193 GeV.'

'dN/dy scaled by 0.5 × $\langle$N$_{part}$$\rangle$ as a function of $\langle$N$_{part}$$\rangle$ for $K^{+}$ at midrapidity (|y| < 0.1) in U+U collisions at $\sqrt{s_{\rm NN}}$ = 193 GeV.'

'dN/dy scaled by 0.5 × $\langle$N$_{part}$$\rangle$ as a function of $\langle$N$_{part}$$\rangle$ for p at midrapidity (|y| < 0.1) in U+U collisions at $\sqrt{s_{\rm NN}}$ = 193 GeV.'

'dN/dy scaled by 0.5 × $\langle$N$_{part}$$\rangle$ as a function of $\langle$N$_{part}$$\rangle$ for $\bar{p}$ at midrapidity (|y| < 0.1) in U+U collisions at $\sqrt{s_{\rm NN}}$ = 193 GeV.'

'$\pi^{−}$/$\pi^{+}$ ratio as a function of $\langle$N$_{part}$$\rangle$ at midrapidity (|y| < 0.1) in U+U collisions at $\sqrt{s_{\rm NN}}$ = 193 GeV.'

'$K^{−}$/$K^{+}$ ratio as a function of $\langle$N$_{part}$$\rangle$ at midrapidity (|y| < 0.1) in U+U collisions at $\sqrt{s_{\rm NN}}$ = 193 GeV.'

'$\bar{p}$/p ratio as a function of $\langle$N$_{part}$$\rangle$ at midrapidity (|y| < 0.1) in U+U collisions at $\sqrt{s_{\rm NN}}$ = 193 GeV.'

'$K^{+}$/$\pi^{+}$ ratio as a function of $\langle$N$_{part}$$\rangle$ at midrapidity (|y| < 0.1) in U+U collisions at $\sqrt{s_{\rm NN}}$ = 193 GeV.'

'$K^{-}$/$\pi^{-}$ ratio as a function of $\langle$N$_{part}$$\rangle$ at midrapidity (|y| < 0.1) in U+U collisions at $\sqrt{s_{\rm NN}}$ = 193 GeV.'

'p/$\pi^{+}$ ratio as a function of $\langle$N$_{part}$$\rangle$ at midrapidity (|y| < 0.1) in U+U collisions at $\sqrt{s_{\rm NN}}$ = 193 GeV.'

'$\bar{p}$/$\pi^{-}$ ratio as a function of $\langle$N$_{part}$$\rangle$ at midrapidity (|y| < 0.1) in U+U collisions at $\sqrt{s_{\rm NN}}$ = 193 GeV.'

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.

The correlation functions (corrected for nonuniform detector efficiency in $\phi$; not corrected for the absolute detection efficiency) vs. azimuthal angle difference between forward ($2.6<\eta<4.0$) $\pi^{0}$s in $p$+$p$ collisions at $\sqrt{s_{\mathrm{_{NN}}}}=200$ GeV at high $p_{T}$ ($p^{trig}_{T}$=2.5-3 GeV/c, $p^{asso}_{T}$=2-2.5 GeV/c)

The correlation functions (corrected for nonuniform detector efficiency in $\phi$; not corrected for the absolute detection efficiency) vs. azimuthal angle difference between forward ($2.6<\eta<4.0$) $\pi^{0}$s in $p$+Al collisions at $\sqrt{s_{\mathrm{_{NN}}}}=200$ GeV at high $p_{T}$ ($p^{trig}_{T}$=2.5-3 GeV/c, $p^{asso}_{T}$=2-2.5 GeV/c)

The correlation functions (corrected for nonuniform detector efficiency in $\phi$; not corrected for the absolute detection efficiency) vs. azimuthal angle difference between forward ($2.6<\eta<4.0$) $\pi^{0}$s in $p$+$Au collisions at $\sqrt{s_{\mathrm{_{NN}}}}=200$ GeV at high $p_{T}$ ($p^{trig}_{T}$=2.5-3 GeV/c, $p^{asso}_{T}$=2-2.5 GeV/c)

Relative area of MinBias $pAu/pp$ of back-to-back di-$\pi^0$ correlations at forward pseudorapidities ($2.6<\eta<4.0$) from data

Relative area of MinBias $pAl/pp$ of back-to-back di-$\pi^0$ correlations at forward pseudorapidities ($2.6<\eta<4.0$) from data

Relative area of $pAu/pp$ at b=0 of back-to-back di-$\pi^0$ correlations at forward pseudorapidities ($2.6<\eta<4.0$) from prediction

Relative width of MinBias $pAu/pp$ of back-to-back di-$\pi^0$ correlations at forward pseudorapidities ($2.6<\eta<4.0$) from data

Relative width of MinBias $pAl/pp$ of back-to-back di-$\pi^0$ correlations at forward pseudorapidities ($2.6<\eta<4.0$) from data

Relative pedestal of MinBias $pAu/pp$ of back-to-back di-$\pi^0$ correlations at forward pseudorapidities ($2.6<\eta<4.0$) from data

Relative pedestal of MinBias $pAl/pp$ of back-to-back di-$\pi^0$ correlations at forward pseudorapidities ($2.6<\eta<4.0$) from data

Relative area of MinBias $pp/pp$ of back-to-back di-$\pi^0$ correlations at forward pseudorapidities ($2.6<\eta<4.0$), the ratio is unity, error is zero

Relative area of MinBias $pA/pp$ of back-to-back di-$\pi^0$ correlations at forward pseudorapidities ($2.6<\eta<4.0$) from data

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

$z_{g}$ for Matched Trigger jets in pp$+$AuAu Data anti-kT R$=$0.4

$z_{g}$ for HardCore Recoil jets in AuAu Data anti-kT R$=$0.4

$z_{g}$ for HardCore Recoil jets in pp$+$AuAu Data anti-kT R$=$0.4

$z_{g}$ for Matched Recoil jets in AuAu Data anti-kT R$=$0.4

$z_{g}$ for Matched Recoil jets in pp$+$AuAu Data anti-kT R$=$0.4

$R_{g}$ for HardCore Trigger jets in AuAu Data anti-kT R$=$0.4

$R_{g}$ for HardCore Trigger jets in pp$+$AuAu Data anti-kT R$=$0.4

$R_{g}$ for Matched Trigger jets in AuAu Data anti-kT R$=$0.4

$R_{g}$ for Matched Trigger jets in pp$+$AuAu Data anti-kT R$=$0.4

$R_{g}$ for HardCore Recoil jets in AuAu Data anti-kT R$=$0.4

$R_{g}$ for HardCore Recoil jets in pp$+$AuAu Data anti-kT R$=$0.4

$R_{g}$ for Matched Recoil jets in AuAu Data anti-kT R$=$0.4

$R_{g}$ for Matched Recoil jets in pp$+$AuAu Data anti-kT R$=$0.4

Fully corrected two subjet $z_{sj}$ for $15 < p_{\rm{T, jet}} < 20$ GeV/c, R$=$0.4 anti-kT and R$=$0.1 subjets

Fully corrected two subjet $z_{sj}$ for $20 < p_{\rm{T, jet}} < 25$ GeV/c, R$=$0.4 anti-kT and R$=$0.1 subjets

Fully corrected two subjet $z_{sj}$ for $25 < p_{\rm{T, jet}} < 30$ GeV/c, R$=$0.4 anti-kT and R$=$0.1 subjets

Fully corrected two subjet $z_{sj}$ for $30 < p_{\rm{T, jet}} < 40$ GeV/c, R$=$0.4 anti-kT and R$=$0.1 subjets

Fully corrected two subjet $\theta_{sj}$ for $15 < p_{\rm{T, jet}} < 20$ GeV/c, R$=$0.4 anti-kT and R$=$0.1 subjets

Fully corrected two subjet $\theta_{sj}$ for $20 < p_{\rm{T, jet}} < 25$ GeV/c, R$=$0.4 anti-kT and R$=$0.1 subjets

Fully corrected two subjet $\theta_{sj}$ for $25 < p_{\rm{T, jet}} < 30$ GeV/c, R$=$0.4 anti-kT and R$=$0.1 subjets

Fully corrected two subjet $\theta_{sj}$ for $30 < p_{\rm{T, jet}} < 40$ GeV/c, R$=$0.4 anti-kT and R$=$0.1 subjets

$z_{sj}$ for HardCore Trigger jets in AuAu Data anti-kT R$=$0.4

$z_{sj}$ for HardCore Trigger jets in pp$+$AuAu Data anti-kT R$=$0.4

$z_{sj}$ for Matched Trigger jets in AuAu Data anti-kT R$=$0.4

$z_{sj}$ for Matched Trigger jets in pp$+$AuAu Data anti-kT R$=$0.4

$z_{sj}$ for HardCore Recoil jets in AuAu Data anti-kT R$=$0.4

$z_{sj}$ for HardCore Recoil jets in pp$+$AuAu Data anti-kT R$=$0.4

$z_{sj}$ for Matched Recoil jets in AuAu Data anti-kT R$=$0.4

$z_{sj}$ for Matched Recoil jets in pp$+$AuAu Data anti-kT R$=$0.4

$\theta_{sj}$ for HardCore Trigger jets in AuAu Data anti-kT R$=$0.4

$\theta_{sj}$ for HardCore Trigger jets in pp$+$AuAu Data anti-kT R$=$0.4

$\theta_{sj}$ for Matched Trigger jets in AuAu Data anti-kT R$=$0.4

$\theta_{sj}$ for Matched Trigger jets in pp$+$AuAu Data anti-kT R$=$0.4

$\theta_{sj}$ for HardCore Recoil jets in AuAu Data anti-kT R$=$0.4

$\theta_{sj}$ for HardCore Recoil jets in pp$+$AuAu Data anti-kT R$=$0.4

$\theta_{sj}$ for Matched Recoil jets in AuAu Data anti-kT R$=$0.4

$\theta_{sj}$ for Matched Recoil jets in pp$+$AuAu Data anti-kT R$=$0.4

$A_{J}$ for HardCore R=0.4 anti-kT jets with $\theta_{sj} > 0.1$ in Au$+$Au collisions

$A_{J}$ for HardCore R=0.4 anti-kT jets with $\theta_{sj} > 0.1$ in pp$+$AuAu reference

$A_{J}$ for HardCore R=0.4 anti-kT jets with $0.1 < \theta_{sj} < 0.2$ in Au$+$Au collisions

$A_{J}$ for HardCore R=0.4 anti-kT jets with $0.1 < \theta_{sj} < 0.2$ in pp$+$AuAu reference

$A_{J}$ for HardCore R=0.4 anti-kT jets with $0.2 < \theta_{sj} < 0.3$ in Au$+$Au collisions

$A_{J}$ for HardCore R=0.4 anti-kT jets with $0.2 < \theta_{sj} < 0.3$ in pp$+$AuAu reference

$A_{J}$ for Matched R=0.4 anti-kT jets with $\theta_{sj} > 0.1$ in Au$+$Au collisions

$A_{J}$ for Matched R=0.4 anti-kT jets with $\theta_{sj} > 0.1$ in pp$+$AuAu reference

$A_{J}$ for Matched R=0.4 anti-kT jets with $0.1 < \theta_{sj} < 0.2$ in Au$+$Au collisions

$A_{J}$ for Matched R=0.4 anti-kT jets with $0.1 < \theta_{sj} < 0.2$ in pp$+$AuAu reference

$A_{J}$ for Matched R=0.4 anti-kT jets with $0.2 < \theta_{sj} < 0.3$ in Au$+$Au collisions

$A_{J}$ for Matched R=0.4 anti-kT jets with $0.2 < \theta_{sj} < 0.3$ in pp$+$AuAu reference

tracking efficiency in pp collisions as a function of track momentum

tracking efficiency in AuAu collisions as a function of track momentum

$K^-$ (a), invariant yields as a function of $m_T-m_0$ for various rapidity regions in 10--40\% central Au+Au collisions at ${\sqrt{s_{\mathrm{NN}}} = \mathrm{3\,GeV}}$. Statistics and systematic uncertainties are added quadratic here for plotting. Solid and dashed black lines depict $m_T$ exponential function fits to the measured data points with arbitrate scaling factors in each rapidity windows.

$\phi$ meson (b) invariant yields as a function of $m_T-m_0$ for various rapidity regions in 10--40\% central Au+Au collisions at ${\sqrt{s_{\mathrm{NN}}} = \mathrm{3\,GeV}}$. Statistics and systematic uncertainties are added quadratic here for plotting. Solid and dashed black lines depict $m_T$ exponential function fits to the measured data points with arbitrate scaling factors in each rapidity windows.

$\Xi^-$ (c) invariant yields as a function of $m_T-m_0$ for various rapidity regions in 10--40\% central Au+Au collisions at ${\sqrt{s_{\mathrm{NN}}} = \mathrm{3\,GeV}}$. Statistics and systematic uncertainties are added quadratic here for plotting. Solid and dashed black lines depict $m_T$ exponential function fits to the measured data points with arbitrate scaling factors in each rapidity windows.

$K^-$ (a), invariant yields as a function of $m_T-m_0$ for various rapidity regions in 40--60\% central Au+Au collisions at ${\sqrt{s_{\mathrm{NN}}} = \mathrm{3\,GeV}}$. Statistics and systematic uncertainties are added quadratic here for plotting. Solid and dashed black lines depict $m_T$ exponential function fits to the measured data points with arbitrate scaling factors in each rapidity windows.

$\phi$ meson (b) invariant yields as a function of $m_T-m_0$ for various rapidity regions in 40--60\% central Au+Au collisions at ${\sqrt{s_{\mathrm{NN}}} = \mathrm{3\,GeV}}$. Statistics and systematic uncertainties are added quadratic here for plotting. Solid and dashed black lines depict $m_T$ exponential function fits to the measured data points with arbitrate scaling factors in each rapidity windows.

Rapidity density distributions of $K^-$ (squares), $p_T$-integrated yields $dN/dy$ in 0--10\% (a), 10--40\% (b) and 40--60\% central (c) Au+Au collisions at ${\sqrt{s_{\mathrm{NN}}} = \mathrm{3\,GeV}}$. %The full symbols show the measured data, while the open ones are data reflected with respect to $y=0$ in the center-of-mass frame. Solid lines depict Gaussian function fits to the data points.

Rapidity density distributions of $\phi$ meson (circles) $p_T$-integrated yields $dN/dy$ in 0--10\% (a), 10--40\% (b) and 40--60\% central (c) Au+Au collisions at ${\sqrt{s_{\mathrm{NN}}} = \mathrm{3\,GeV}}$. %The full symbols show the measured data, while the open ones are data reflected with respect to $y=0$ in the center-of-mass frame. Solid lines depict Gaussian function fits to the data points.

Rapidity density distributions of $\Xi^-$ (diamonds) $p_T$-integrated yields $dN/dy$ in 0--10\% (a), 10--40\% (b) and 40--60\% central (c) Au+Au collisions at ${\sqrt{s_{\mathrm{NN}}} = \mathrm{3\,GeV}}$. %The full symbols show the measured data, while the open ones are data reflected with respect to $y=0$ in the center-of-mass frame. Solid lines depict Gaussian function fits to the data points.

$\phi/K^-$ (a) and $\phi/\Xi^-$ (b) ratio as a function of collision energy, $\sqrt{s_{\mathrm{NN}}}$. The solid black circles show the measurements presented here in 0-10\% centrality bin, while empty markers in black or grey are used for data from various other energies and/or collision systems. The grey solid line represents a THERMUS calculation based on the Grand Canonical Ensemble (GCE) while the dotted lines depict calculations based on the Canonical Ensemble (CE) with different parameters of strangeness correlation radius ($r_c$). The green dashed line, green shaded band and the solid red line show transport model calculations from the public versions $\mathrm{UrQMD}^{1}$, modified $\mathrm{UrQMD}^{2}$ and SMASH, respectively.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

The centrality dependencies of the $\Delta\gamma\{\psi_\mathrm{ZDC}\}$ for Au+Au collision at $\sqrt{s_{\rm NN}}$=200 GeV.

The centrality dependencies of the A for Au+Au collision at $\sqrt{s_{\rm NN}}$=200 GeV.

The centrality dependencies of the a for Au+Au collision at $\sqrt{s_{\rm NN}}$=200 GeV.

The centrality dependencies of the A/a using full-event method for Au+Au collision at $\sqrt{s_{\rm NN}}$=200 GeV.

The centrality dependencies of the A/a using sub-event method for Au+Au collision at $\sqrt{s_{\rm NN}}$=200 GeV.

The centrality dependencies of the $f_\mathrm{CME}$ using full-event method for Au+Au collision at $\sqrt{s_{\rm NN}}$=200 GeV.

The centrality dependencies of the $f_\mathrm{CME}$ using sub-event method for Au+Au collision at $\sqrt{s_{\rm NN}}$=200 GeV.

The centrality dependencies of the $\Delta\gamma_\mathrm{CME}$ using full-event method for Au+Au collision at $\sqrt{s_{\rm NN}}$=200 GeV.

The centrality dependencies of the $\Delta\gamma_\mathrm{CME}$ using sub-event method for Au+Au collision at $\sqrt{s_{\rm NN}}$=200 GeV.

The $f_\mathrm{CME}$ from different methods for 20-50% centrality Au+Au collision at $\sqrt{s_{\rm NN}}$=200 GeV.

The $f_\mathrm{CME}$ from different methods for 50-80% centrality Au+Au collision at $\sqrt{s_{\rm NN}}$=200 GeV.

The $\Delta\gamma_\mathrm{CME}$ from different methods for 20-50% centrality Au+Au collision at $\sqrt{s_{\rm NN}}$=200 GeV.

The $\Delta\gamma_\mathrm{CME}$ from different methods for 50-80% centrality Au+Au collision at $\sqrt{s_{\rm NN}}$=200 GeV.