'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 $p_{T}$ dependencies of $v_{1}$ within $-0.4<y<-0.1$ for $t$ in 10-40% mid-central Au+Au collisions at 3 GeV.

The rapidity and $p_{T}$ dependencies of $v_{1}$ for $^{3}$He in 10-40% mid-central Au+Au collisions at 3 GeV.

The $p_{T}$ dependencies of $v_{1}$ within $-0.1<y<0$ for $^4$He in 10-40% mid-central Au+Au collisions at 3 GeV.

The $p_{T}$ dependencies of $v_{1}$ within $-0.4<y<-0.1$ for $^{4}$He in 10-40% mid-central Au+Au collisions at 3 GeV.

The rapidity and $p_{T}$ dependencies of $v_{2}$ for $p$ in 10-40% mid-central Au+Au collisions at 3 GeV.

The rapidity and $p_{T}$ dependencies of $v_{2}$ for $d$ in 10-40% mid-central Au+Au collisions at 3 GeV.

The $p_{T}$ dependencies of $v_{2}$ within $-0.1<y<0$ for $t$ in 10-40% mid-central Au+Au collisions at 3 GeV.

The $p_{T}$ dependencies of $v_{2}$ within $-0.4<y<-0.1$ for $t$ in 10-40% mid-central Au+Au collisions at 3 GeV.

The rapidity and $p_{T}$ dependencies of $v_{2}$ for $^{3}$He in 10-40% mid-central Au+Au collisions at 3 GeV.

The $p_{T}$ dependencies of $v_{2}$ within $-0.1<y<0$ for $^4$He in 10-40% mid-central Au+Au collisions at 3 GeV.

The $p_{T}$ dependencies of $v_{2}$ within $-0.4<y<-0.1$ for $^{4}$He in 10-40% mid-central Au+Au collisions at 3 GeV.

The rapidity dependencies of $v_{1}$ for $p$, $d$, and $^{3}$He in 10-40% mid-central Au+Au collisions at 3 GeV.

The rapidity dependencies of $v_{1}$ for $t$ and $^{4}$He in 10-40% mid-central Au+Au collisions at 3 GeV.

The rapidity dependencies of $v_{1}$ from JAM plus coalescence calculations in 10-40% mid-central Au+Au collisions at 3 GeV.

The rapidity dependencies of $v_{2}$ for $p$, $d$, and $^{3}$He in 10-40% mid-central Au+Au collisions at 3 GeV.

The rapidity dependencies of $v_{2}$ for $t$ and $^{4}$He in 10-40% mid-central Au+Au collisions at 3 GeV.

The rapidity dependencies of $v_{2}$ from JAM plus coalescence calculations in 10-40% mid-central Au+Au collisions at 3 GeV.

Light nucleus scaled $v_{1}$ slopes as a function os collision energy in 10-40 mid-cantral Au+Au collisions.

Light nucleus scaled $v_{1}$ slopes from JAM plus coalescence in 10-40 mid-cantral Au+Au collisions at 3 GeV.

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

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

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

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

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

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

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

Fraction of bottom hadron decayed electrons in 0-80% Au+Au collisions at $\sqrt{s_{\rm NN}}$ = 200 GeV.

Fraction of bottom hadron decayed electrons in 0-20% and 20-40% Au+Au collisions at $\sqrt{s_{\rm NN}}$ = 200 GeV.

Fraction of bottom hadron decayed electrons in 40-80% Au+Au collisions at $\sqrt{s_{\rm NN}}$ = 200 GeV.

Nuclear modification factor $R_{\rm AA}$ of inclusive heavy flavor decayed electrons in 0-80% Au+Au collisions at $\sqrt{s_{\rm NN}}$ = 200 GeV. The 8% global uncertainty from the $p$+$p$ reference and a 8% gloabl uncertainty from $N_{\rm coll.}$ are not included in the table values.

Nuclear modification factor $R_{\rm AA}$ of bottom- and charm-decay electrons in 0-80% Au+Au collisions at $\sqrt{s_{\rm NN}}$ = 200 GeV. The 8% global uncertainty from the $p$+$p$ reference and a 8% gloabl uncertainty from $N_{\rm coll.}$ are not included in the table values.

Nuclear modification factor $R_{\rm AA}$ ratio of bottom- to charm-decay electrons in 0-80% Au+Au collisions at $\sqrt{s_{\rm NN}}$ = 200 GeV.

Null hypothesis for the nuclear modification factor $R_{\rm AA}$ ratio of bottom- to charm-decay electrons in 0-80% Au+Au collisions at $\sqrt{s_{\rm NN}}$ = 200 GeV.

Nuclear modification factor $R_{\rm CP}$ ratio of bottom- and charm-decay electrons in 0-80% Au+Au collisions at $\sqrt{s_{\rm NN}}$ = 200 GeV.

Null hypotheses for the nuclear modification factor $R_{\rm CP}$ ratio of bottom- and charm-decay electrons in 0-80% Au+Au collisions at $\sqrt{s_{\rm NN}}$ = 200 GeV.

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

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.

$K^-$ (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.

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

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

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

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.

Parton inclusive-jet $p_T$ and $A_{LL}$ values with associated uncertainties for jet-$\eta$ region $0.5<|\eta|<1$.

Parton inclusive-jet $p_T$ and $A_{LL}$ values with associated uncertainties for jet-$\eta$ region $|\eta|<0.5$.

Parton dijet invariant mass $M_{inv}$ and $A_{LL}$ values with associated uncertainties for the $\textrm{sign}(\eta_1) = \textrm{sign}(\eta_2)$ topology.

Parton dijet invariant mass $M_{inv}$ and $A_{LL}$ values with associated uncertainties for the $\textrm{sign}(\eta_1) \neq \textrm{sign}(\eta_2)$ topology.

Parton inclusive-jet $p_T$, $x_T$, and $A_{LL}$ values with associated uncertainties for jet-$\eta$ region $|\eta|<1$.

The correlation matrix for the point-to-point uncertainties for inclusive jet measurements with jets in the $0.5<|\eta|<1$ region. The $A_{LL}$ uncertainty contribution of $0.0007$ from uncertainty in the relative luminosity measurement and $6.1\%$ from the beam polarization uncertainty, which are common to all the data points, are separated from the listed values.

The correlation matrix for the point-to-point uncertainties for inclusive jet measurements with jets in the $|\eta|<0.5$ region. The $A_{LL}$ uncertainty contribution of $0.0007$ from uncertainty in the relative luminosity measurement and $6.1\%$ from the beam polarization uncertainty, which are common to all the data points, are separated from the listed values.

The correlation matrix for the point-to-point uncertainties for inclusive jet measurements with jets in the $|\eta|<1$ region. The $A_{LL}$ uncertainty contribution of $0.0007$ from uncertainty in the relative luminosity measurement and $6.1\%$ from the beam polarization uncertainty, which are common to all the data points, are separated from the listed values.

The correlation matrix for the point-to-point uncertainties coupling inclusive jet measurements with jets in the $|\eta|<0.5$ region and jets in the $0.5<|\eta|<1$ region. The $A_{LL}$ uncertainty contribution of $0.0007$ from uncertainty in the relative luminosity measurement and $6.1\%$ from the beam polarization uncertainty, which are common to all the data points, are separated from the listed values.

The correlation matrix for the point-to-point uncertainties coupling inclusive jet measurements with jets in the $0.5<|\eta|<1$ region with dijet measurements with the the $\textrm{sign}(\eta_1) = \textrm{sign}(\eta_2)$ topology. The $A_{LL}$ uncertainty contribution of $0.0007$ from uncertainty in the relative luminosity measurement and $6.1\%$ from the beam polarization uncertainty, which are common to all the data points, are separated from the listed values.

The correlation matrix for the point-to-point uncertainties coupling inclusive jet measurements with jets in the $0.5<|\eta|<1$ region with dijet measurements with the the $\textrm{sign}(\eta_1) \neq \textrm{sign}(\eta_2)$ topology. The $A_{LL}$ uncertainty contribution of $0.0007$ from uncertainty in the relative luminosity measurement and $6.1\%$ from the beam polarization uncertainty, which are common to all the data points, are separated from the listed values.

The correlation matrix for the point-to-point uncertainties coupling inclusive jet measurements with jets in the $|\eta|<0.5$ region with dijet measurements with the the $\textrm{sign}(\eta_1) = \textrm{sign}(\eta_2)$ topology. The $A_{LL}$ uncertainty contribution of $0.0007$ from uncertainty in the relative luminosity measurement and $6.1\%$ from the beam polarization uncertainty, which are common to all the data points, are separated from the listed values.

The correlation matrix for the point-to-point uncertainties coupling inclusive jet measurements with jets in the $|\eta|<0.5$ region with dijet measurements with the the $\textrm{sign}(\eta_1) \neq \textrm{sign}(\eta_2)$ topology. The $A_{LL}$ uncertainty contribution of $0.0007$ from uncertainty in the relative luminosity measurement and $6.1\%$ from the beam polarization uncertainty, which are common to all the data points, are separated from the listed values.

The correlation matrix for the point-to-point uncertainties coupling inclusive jet measurements with jets in the $|\eta|<1$ region with dijet measurements with the the $\textrm{sign}(\eta_1) = \textrm{sign}(\eta_2)$ topology. The $A_{LL}$ uncertainty contribution of $0.0007$ from uncertainty in the relative luminosity measurement and $6.1\%$ from the beam polarization uncertainty, which are common to all the data points, are separated from the listed values.

The correlation matrix for the point-to-point uncertainties coupling inclusive jet measurements with jets in the $|\eta|<1$ region with dijet measurements with the the $\textrm{sign}(\eta_1) \neq \textrm{sign}(\eta_2)$ topology. The $A_{LL}$ uncertainty contribution of $0.0007$ from uncertainty in the relative luminosity measurement and $6.1\%$ from the beam polarization uncertainty, which are common to all the data points, are separated from the listed values.

The correlation matrix for the point-to-point uncertainties for dijet measurements with the $\textrm{sign}(\eta_1) = \textrm{sign}(\eta_2)$ topology. The $A_{LL}$ uncertainty contribution of $0.0007$ from uncertainty in the relative luminosity measurement and $6.1\%$ from the beam polarization uncertainty, which are common to all the data points, are separated from the listed values.

The correlation matrix for the point-to-point uncertainties for dijet measurements with the $\textrm{sign}(\eta_1) \neq \textrm{sign}(\eta_2)$ topology. The $A_{LL}$ uncertainty contribution of $0.0007$ from uncertainty in the relative luminosity measurement and $6.1\%$ from the beam polarization uncertainty, which are common to all the data points, are separated from the listed values.

The correlation matrix for the point-to-point uncertainties coupling dijet measurements with the $\textrm{sign}(\eta_1) \neq \textrm{sign}(\eta_2)$ topology and the $\textrm{sign}(\eta_1) = \textrm{sign}(\eta_2)$ topology. The $A_{LL}$ uncertainty contribution of $0.0007$ from uncertainty in the relative luminosity measurement and $6.1\%$ from the beam polarization uncertainty, which are common to all the data points, are separated from the listed values.

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

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

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

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

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

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

FIG. 1. (Color online) Perspective views of $2 \mathrm{D}$ charge-independent angular correlations $\Delta \rho / \sqrt{\rho_{\mathrm{ref}}}$ on $\left(\eta_{\Delta}, \phi_{\Delta}\right)$ for Au-Au collisions at $\sqrt{s_{N N}}=200$ and $62 \mathrm{GeV}$ (top and bottom rows, respectively). Centrality increases left to right from most peripheral to most central. Corrected total cross-section fractions are (left to right) $84 \%-93 \%, 55 \%-64 \%, 18 \%-28 \%,$ and $0 \%-5 \%$ for the $200-\mathrm{GeV}$ data and $84 \%-95 \%, 56 \%-65 \%$ $18 \%-28 \%,$ and $0 \%-5 \%$ for the $62 \mathrm{GeV}$ data (see Tables III and IV).

FIG. 1. (Color online) Perspective views of $2 \mathrm{D}$ charge-independent angular correlations $\Delta \rho / \sqrt{\rho_{\mathrm{ref}}}$ on $\left(\eta_{\Delta}, \phi_{\Delta}\right)$ for Au-Au collisions at $\sqrt{s_{N N}}=200$ and $62 \mathrm{GeV}$ (top and bottom rows, respectively). Centrality increases left to right from most peripheral to most central. Corrected total cross-section fractions are (left to right) $84 \%-93 \%, 55 \%-64 \%, 18 \%-28 \%,$ and $0 \%-5 \%$ for the $200-\mathrm{GeV}$ data and $84 \%-95 \%, 56 \%-65 \%$ $18 \%-28 \%,$ and $0 \%-5 \%$ for the $62 \mathrm{GeV}$ data (see Tables III and IV).

FIG. 1. (Color online) Perspective views of $2 \mathrm{D}$ charge-independent angular correlations $\Delta \rho / \sqrt{\rho_{\mathrm{ref}}}$ on $\left(\eta_{\Delta}, \phi_{\Delta}\right)$ for Au-Au collisions at $\sqrt{s_{N N}}=200$ and $62 \mathrm{GeV}$ (top and bottom rows, respectively). Centrality increases left to right from most peripheral to most central. Corrected total cross-section fractions are (left to right) $84 \%-93 \%, 55 \%-64 \%, 18 \%-28 \%,$ and $0 \%-5 \%$ for the $200-\mathrm{GeV}$ data and $84 \%-95 \%, 56 \%-65 \%$ $18 \%-28 \%,$ and $0 \%-5 \%$ for the $62 \mathrm{GeV}$ data (see Tables III and IV).

FIG. 1. (Color online) Perspective views of $2 \mathrm{D}$ charge-independent angular correlations $\Delta \rho / \sqrt{\rho_{\mathrm{ref}}}$ on $\left(\eta_{\Delta}, \phi_{\Delta}\right)$ for Au-Au collisions at $\sqrt{s_{N N}}=200$ and $62 \mathrm{GeV}$ (top and bottom rows, respectively). Centrality increases left to right from most peripheral to most central. Corrected total cross-section fractions are (left to right) $84 \%-93 \%, 55 \%-64 \%, 18 \%-28 \%,$ and $0 \%-5 \%$ for the $200-\mathrm{GeV}$ data and $84 \%-95 \%, 56 \%-65 \%$ $18 \%-28 \%,$ and $0 \%-5 \%$ for the $62 \mathrm{GeV}$ data (see Tables III and IV).

FIG. 1. (Color online) Perspective views of $2 \mathrm{D}$ charge-independent angular correlations $\Delta \rho / \sqrt{\rho_{\mathrm{ref}}}$ on $\left(\eta_{\Delta}, \phi_{\Delta}\right)$ for Au-Au collisions at $\sqrt{s_{N N}}=200$ and $62 \mathrm{GeV}$ (top and bottom rows, respectively). Centrality increases left to right from most peripheral to most central. Corrected total cross-section fractions are (left to right) $84 \%-93 \%, 55 \%-64 \%, 18 \%-28 \%,$ and $0 \%-5 \%$ for the $200-\mathrm{GeV}$ data and $84 \%-95 \%, 56 \%-65 \%$ $18 \%-28 \%,$ and $0 \%-5 \%$ for the $62 \mathrm{GeV}$ data (see Tables III and IV).

FIG. 2. (Color online) Fit decomposition of the $46 \%-56 \%$ centrality data for 62 -GeV Au-Au collisions. The top panels show from left to right the corrected data, model fit, fit residuals (data - model), and same-side 2D Gaussian. The bottom panels similarly show the away-side azimuth dipole, the nonjet azimuth quadrupole, the 1D $\eta_{\Delta}$ Gaussian, and the 2D exponential. This centrality is just below the sharp transition at $v_{\text {trans }}=3$. Fit residuals (c) are scaled up eightfold relative to the data.

FIG. 3. Fit parameters for $\left(\eta_{\Delta}, \phi_{\Delta}\right)$ correlation data from Au-Au collisions at $\sqrt{s_{N N}}=62$ (open symbols) and 200 GeV (solid symbols) versus centrality measure $\nu$ computed at fixed energy $(200 \mathrm{GeV})$. The SS $2 \mathrm{D}$ Gaussian amplitudes, $\eta_{\Delta}$ widths, and $\phi_{\Delta}$ widths are shown in the left, center, and right panels, respectively of the top row. The bottom row shows from left to right the amplitudes for the dipole, quadrupole, and SS peak width aspect ratio $\sigma_{\eta_{\Delta}} / \sigma_{\phi_{\Delta}} .$ Fitting errors are indicated by error bars where larger than the symbols. Solid lines connect the points for clarity. The dotted and dashed curves indicate Glauber linear superposition estimates for 62 - and 200 -GeV peak amplitudes respectively, as discussed in the text. The quadrupole data are consistent with Ref. [60]. The hatched regions indicate the full range of systematic uncertainties listed in Appendix F. The vertical dark bands indicate estimated $v$ equivalents for $N-N$ collisions and $b=0$ Au-Au collisions.

FIG. 3. Fit parameters for $\left(\eta_{\Delta}, \phi_{\Delta}\right)$ correlation data from Au-Au collisions at $\sqrt{s_{N N}}=62$ (open symbols) and 200 GeV (solid symbols) versus centrality measure $\nu$ computed at fixed energy $(200 \mathrm{GeV})$. The SS $2 \mathrm{D}$ Gaussian amplitudes, $\eta_{\Delta}$ widths, and $\phi_{\Delta}$ widths are shown in the left, center, and right panels, respectively of the top row. The bottom row shows from left to right the amplitudes for the dipole, quadrupole, and SS peak width aspect ratio $\sigma_{\eta_{\Delta}} / \sigma_{\phi_{\Delta}} .$ Fitting errors are indicated by error bars where larger than the symbols. Solid lines connect the points for clarity. The dotted and dashed curves indicate Glauber linear superposition estimates for 62 - and 200 -GeV peak amplitudes respectively, as discussed in the text. The quadrupole data are consistent with Ref. [60]. The hatched regions indicate the full range of systematic uncertainties listed in Appendix F. The vertical dark bands indicate estimated $v$ equivalents for $N-N$ collisions and $b=0$ Au-Au collisions.

FIG. 3. Fit parameters for $\left(\eta_{\Delta}, \phi_{\Delta}\right)$ correlation data from Au-Au collisions at $\sqrt{s_{N N}}=62$ (open symbols) and 200 GeV (solid symbols) versus centrality measure $\nu$ computed at fixed energy $(200 \mathrm{GeV})$. The SS $2 \mathrm{D}$ Gaussian amplitudes, $\eta_{\Delta}$ widths, and $\phi_{\Delta}$ widths are shown in the left, center, and right panels, respectively of the top row. The bottom row shows from left to right the amplitudes for the dipole, quadrupole, and SS peak width aspect ratio $\sigma_{\eta_{\Delta}} / \sigma_{\phi_{\Delta}} .$ Fitting errors are indicated by error bars where larger than the symbols. Solid lines connect the points for clarity. The dotted and dashed curves indicate Glauber linear superposition estimates for 62 - and 200 -GeV peak amplitudes respectively, as discussed in the text. The quadrupole data are consistent with Ref. [60]. The hatched regions indicate the full range of systematic uncertainties listed in Appendix F. The vertical dark bands indicate estimated $v$ equivalents for $N-N$ collisions and $b=0$ Au-Au collisions.

FIG. 3. Fit parameters for $\left(\eta_{\Delta}, \phi_{\Delta}\right)$ correlation data from Au-Au collisions at $\sqrt{s_{N N}}=62$ (open symbols) and 200 GeV (solid symbols) versus centrality measure $\nu$ computed at fixed energy $(200 \mathrm{GeV})$. The SS $2 \mathrm{D}$ Gaussian amplitudes, $\eta_{\Delta}$ widths, and $\phi_{\Delta}$ widths are shown in the left, center, and right panels, respectively of the top row. The bottom row shows from left to right the amplitudes for the dipole, quadrupole, and SS peak width aspect ratio $\sigma_{\eta_{\Delta}} / \sigma_{\phi_{\Delta}} .$ Fitting errors are indicated by error bars where larger than the symbols. Solid lines connect the points for clarity. The dotted and dashed curves indicate Glauber linear superposition estimates for 62 - and 200 -GeV peak amplitudes respectively, as discussed in the text. The quadrupole data are consistent with Ref. [60]. The hatched regions indicate the full range of systematic uncertainties listed in Appendix F. The vertical dark bands indicate estimated $v$ equivalents for $N-N$ collisions and $b=0$ Au-Au collisions.

FIG. 3. Fit parameters for $\left(\eta_{\Delta}, \phi_{\Delta}\right)$ correlation data from Au-Au collisions at $\sqrt{s_{N N}}=62$ (open symbols) and 200 GeV (solid symbols) versus centrality measure $\nu$ computed at fixed energy $(200 \mathrm{GeV})$. The SS $2 \mathrm{D}$ Gaussian amplitudes, $\eta_{\Delta}$ widths, and $\phi_{\Delta}$ widths are shown in the left, center, and right panels, respectively of the top row. The bottom row shows from left to right the amplitudes for the dipole, quadrupole, and SS peak width aspect ratio $\sigma_{\eta_{\Delta}} / \sigma_{\phi_{\Delta}} .$ Fitting errors are indicated by error bars where larger than the symbols. Solid lines connect the points for clarity. The dotted and dashed curves indicate Glauber linear superposition estimates for 62 - and 200 -GeV peak amplitudes respectively, as discussed in the text. The quadrupole data are consistent with Ref. [60]. The hatched regions indicate the full range of systematic uncertainties listed in Appendix F. The vertical dark bands indicate estimated $v$ equivalents for $N-N$ collisions and $b=0$ Au-Au collisions.

FIG. 3. Fit parameters for $\left(\eta_{\Delta}, \phi_{\Delta}\right)$ correlation data from Au-Au collisions at $\sqrt{s_{N N}}=62$ (open symbols) and 200 GeV (solid symbols) versus centrality measure $\nu$ computed at fixed energy $(200 \mathrm{GeV})$. The SS $2 \mathrm{D}$ Gaussian amplitudes, $\eta_{\Delta}$ widths, and $\phi_{\Delta}$ widths are shown in the left, center, and right panels, respectively of the top row. The bottom row shows from left to right the amplitudes for the dipole, quadrupole, and SS peak width aspect ratio $\sigma_{\eta_{\Delta}} / \sigma_{\phi_{\Delta}} .$ Fitting errors are indicated by error bars where larger than the symbols. Solid lines connect the points for clarity. The dotted and dashed curves indicate Glauber linear superposition estimates for 62 - and 200 -GeV peak amplitudes respectively, as discussed in the text. The quadrupole data are consistent with Ref. [60]. The hatched regions indicate the full range of systematic uncertainties listed in Appendix F. The vertical dark bands indicate estimated $v$ equivalents for $N-N$ collisions and $b=0$ Au-Au collisions.

FIG. 4. (Color online) (a) 2D data histogram from $0 \%-5 \%$ central 200 GeV Au-Au collisions $[(0,0)$ bin suppressed]. (b) Additional model component fitted to the $2 \mathrm{D}$ histogram and consisting of an AS azimuth dipole modulated by function $F\left(\eta_{\Delta}\right)$ described in the text. (c) Fit residuals including the new model component. (d) Data histogram in the first panel minus the additional model component and fitted offset. Remaining structure is described accurately by an AS dipole and SS 2D Gaussian.

FIG. 9. (a) Amplitude of SS 2D peak (jet-correlated pairs per final-state hadron) for data (solid points), GLS extrapolation from $p$ - $p$ data (dashed curve) and from the HIJING Monte Carlo (open points, dotted curve). (b) Single-particle production extrapolated from $p-p$ data (dashed curve, GLS), and from more-central Au-Au data (solid line) and HIJING (dash-dotted line, open points). (c) Single-particle hard-component production per $N-N$ binary collision from $p-p$ data, from more-central Au-Au data and from HIJING (open points). (d) Jet-correlated pair production (SS 2D peak) per $N-N$ binary collision extrapolated from $p-p$ data (GLS), and from Au-Au data (solid points) and HIJING (open points).

FIG. 9. (a) Amplitude of SS 2D peak (jet-correlated pairs per final-state hadron) for data (solid points), GLS extrapolation from $p$ - $p$ data (dashed curve) and from the HIJING Monte Carlo (open points, dotted curve). (b) Single-particle production extrapolated from $p-p$ data (dashed curve, GLS), and from more-central Au-Au data (solid line) and HIJING (dash-dotted line, open points). (c) Single-particle hard-component production per $N-N$ binary collision from $p-p$ data, from more-central Au-Au data and from HIJING (open points). (d) Jet-correlated pair production (SS 2D peak) per $N-N$ binary collision extrapolated from $p-p$ data (GLS), and from Au-Au data (solid points) and HIJING (open points).

FIG. 9. (a) Amplitude of SS 2D peak (jet-correlated pairs per final-state hadron) for data (solid points), GLS extrapolation from $p$ - $p$ data (dashed curve) and from the HIJING Monte Carlo (open points, dotted curve). (b) Single-particle production extrapolated from $p-p$ data (dashed curve, GLS), and from more-central Au-Au data (solid line) and HIJING (dash-dotted line, open points). (c) Single-particle hard-component production per $N-N$ binary collision from $p-p$ data, from more-central Au-Au data and from HIJING (open points). (d) Jet-correlated pair production (SS 2D peak) per $N-N$ binary collision extrapolated from $p-p$ data (GLS), and from Au-Au data (solid points) and HIJING (open points).

FIG. 9. (a) Amplitude of SS 2D peak (jet-correlated pairs per final-state hadron) for data (solid points), GLS extrapolation from $p$ - $p$ data (dashed curve) and from the HIJING Monte Carlo (open points, dotted curve). (b) Single-particle production extrapolated from $p-p$ data (dashed curve, GLS), and from more-central Au-Au data (solid line) and HIJING (dash-dotted line, open points). (c) Single-particle hard-component production per $N-N$ binary collision from $p-p$ data, from more-central Au-Au data and from HIJING (open points). (d) Jet-correlated pair production (SS 2D peak) per $N-N$ binary collision extrapolated from $p-p$ data (GLS), and from Au-Au data (solid points) and HIJING (open points).

FIG. 11. (Color online) (Left) Uncorrected angular correlations from 62-GeV $37 \%-46 \%$ central Au-Au collisions showing pileup distortions, especially evident as the W-shaped nonuniformity of the AS ridge on $\eta_{\Delta}$. (Right) The same data with pileup correction applied.

Longitudinal single-spin asymmetry, AL, for W± events as a function of the leptonic pseudorapidity, $\eta_e$, for 25 < $E^e_T$ < 50 GeV in comparison to theory predictions

Longitudinal single-spin asymmetry, AL, for W± events as a function of the leptonic pseudorapidity, $\eta_e$, for 25 < $E^e_T$ < 50 GeV in comparison to theory predictions

Negatively charged kaon spectra from Cu+Cu collisions 62.4 GeV as a function of pT for different centralities.

Negatively charged proton spectra from Cu+Cu collisions 200 GeV as a function of pT for different centralities.

Negatively charged proton spectra from Cu+Cu collisions 62.4 GeV as a function of pT for different centralities.

Positively charged pion spectra from Cu+Cu collisions 200 GeV as a function of pT for different centralities.

Positively charged pion spectra from Cu+Cu collisions 62.4 GeV as a function of pT for different centralities.

Positively charged kaon spectra from Cu+Cu collisions 200 GeV as a function of pT for different centralities.

Positively charged kaon spectra from Cu+Cu collisions 62.4 GeV as a function of pT for different centralities.

Positively charged proton spectra from Cu+Cu collisions 200 GeV as a function of pT for different centralities.

Positively charged proton spectra from Cu+Cu collisions 62.4 GeV as a function of pT for different centralities.

Mean transverse momentum of negatively charged pions, kaons and protons as a function of charged hadron multiplicity.

Mean transverse momentum of positively charged pions, kaons and protons as a function of charged hadron multiplicity [figure not available in published paper].

Integrated yields of negatively charged pions, kaons and protons as a function of charged hadron multiplicity.

Integrated yields of positively charged pions, kaons and protons as a function of charged hadron multiplicity [figure not available in published paper].

particle Ratios -I (pbar/pi^-, k^-/pi^-) versus multiplicity.

particle ratios -II (p/pi^+, k^+/pi^+) versus multiplicity.

particle ratios -III (p+pbar/pi, k/pi) versus multiplicity.

particle Ratios -IV (pi^-/pi^+, k^-/k^+, pbar/p) versus multiplicity [only pbar/p figure available in paper].

Enhancement factors for negatively charged pions, kaons and protons as a function of Npart [Ref. Phys.Rev.C 81, 044902, 2010]. pp dNdy values are from Ref [Phys.Rev.C 79, 034909, 2009].

The kinetic freeze-out temperature (Tkin) and chemical freeze-out temperature (Tch) versus multiplicity.

flow velocity versus multiplicity.

chemical potentials versus multiplicity.

strangeness suppression factor versus multiplicity.

dNch/deta values for different centrality.

The K$\pi$ pair invariant mass distribution integrated over the $K^{*0}$ $p_T$ for minimum bias Cu+Cu collisions at $\sqrt{s_{NN}}$ =62.4 GeV after mixed-event background subtraction.

The Kπ pair invariant mass distribution for various pT bins (top left) pT = 0.4–0.6 GeV/c in Au+Au collisions at √sNN = 200 GeV after the mixed-event background subtraction.

The Kπ pair invariant mass distribution for various pT bins (top right) pT = 0.6–0.8 GeV/c in Au+Au collisions at √sNN = 62.4 GeV after the mixed-event background subtraction.

The Kπ pair invariant mass distribution for various pT bins (bottom left) pT = 0.8–1.0 GeV/c in Au+Au collisions at √sNN = 200 GeV after the mixed-event background subtraction.

The Kπ pair invariant mass distribution for various pT bins (bottom right) pT = 1.0–1.2 GeV/c in Au+Au collisions at √sNN = 62.4 GeV after the mixed-event background subtraction.

The signal-to-background ratio for $K^{*0}$ measurements as a function of $p_T$ for different collision centrality bins (0-10%, 10-40%, 40-60%, 60-80%) in Au+Au collisions at 200 GeV.

$K^{*0}$ mass as a function of $p_T$ for minimum bias Au+Au collisions at $\sqrt{s_{NN}}$ = 62.4 GeV.

$K^{*0}$ mass as a function of $p_T$ for minimum bias Au+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV.

$K^{*0}$ mass as a function of $p_T$ for minimum bias Cu+Cu collisions at $\sqrt{s_{NN}}$ = 62.4 GeV

$K^{*0}$ mass as a function of $p_T$ for minimum bias Cu+Cu collisions at $\sqrt{s_{NN}}$ = 200 GeV

$K^{*0}$ width as a function of $p_T$ for minimum bias Au+Au collisions at $\sqrt{s_{NN}}$ = 62.4 GeV

$K^{*0}$ width as a function of $p_T$ for minimum bias Au+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV

$K^{*0}$ width as a function of $p_T$ for minimum bias Cu+Cu collisions at $\sqrt{s_{NN}}$ = 62.4 GeV

$K^{*0}$ width as a function of $p_T$ for minimum bias Cu+Cu collisions at $\sqrt{s_{NN}}$ = 200 GeV

The $K^{*0}$ reconstruction efficiency multiplied by the detector acceptance as a function of $p_T$ in Au+Au (|$\eta$| < 0.8) collisions at 200 GeV for different collision centrality bins (0-20% ,20-40% , 40-60%)

The $K^{*0}$ reconstruction efficiency multiplied by the detector acceptance as a function of $p_T$ in Cu+Cu (|$\eta$| < 1.0) collisions at 200 GeV for different collision centrality bins (0-20% ,20-40% , 40-60%)

Mid-rapidity $K^{*0}$ $p_T$ spectra for various collision centrality bins (0-20%, 20-40%, 40-60%, 60-80%) in Au+Au collisions at $\sqrt{s_{NN}}$ = 62.4 GeV

Mid-rapidity $K^{*0}$ $p_T$ spectra for various collision centrality bins (0-20%, 20-40%, 40-60%) in Cu+Cu collisions at $\sqrt{s_{NN}}$ = 62.4 GeV

Mid-rapidity $K^{*0}$ $p_T$ spectra for various collision centrality bins (0-20%, 20-40%, 40-60%, 60-80%) in Au+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV

Mid-rapidity $K^{*0}$ $p_T$ spectra for various collision centrality bins (0-20%, 20-40%, 40-60%) in Cu+Cu collisions at $\sqrt{s_{NN}}$ = 200 GeV

The mid-rapidity yields dN/dy of $K^{*0}$ as a function of the average number of participating nucleons, $⟨N_{part}⟩$, for Au+Au collisions at $\sqrt{s_{NN}}$ = 62.4 GeV

The mid-rapidity yields dN/dy of $K^{*0}$ as a function of the average number of participating nucleons, $⟨N_{part}⟩$, for Cu+Cu collisions at $\sqrt{s_{NN}}$ = 62.4 GeV

The mid-rapidity yields dN/dy of $K^{*0}$ as a function of the average number of participating nucleons, $⟨N_{part}⟩$, for Au+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV

The mid-rapidity yields dN/dy of $K^{*0}$ as a function of the average number of participating nucleons, $⟨N_{part}⟩$, for Cu+Cu collisions at $\sqrt{s_{NN}}$ = 200 GeV

The mid-rapidity $K^{*0}$ $⟨p_T⟩$ as a function $⟨N_{part}⟩$ for Au+Au collisions at $\sqrt{s_{NN}}$ = 62.4 GeV

The mid-rapidity $K^{*0}$ $⟨p_T⟩$ as a function $⟨N_{part}⟩$ for Cu+Cu collisions at $\sqrt{s_{NN}}$ = 62.4 GeV

The mid-rapidity $K^{*0}$ $⟨p_T⟩$ as a function $⟨N_{part}⟩$ for Au+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV

The mid-rapidity $K^{*0}$ $⟨p_T⟩$ as a function $⟨N_{part}⟩$ for Cu+Cu collisions at $\sqrt{s_{NN}}$ = 200 GeV

The mid-rapidity $⟨p_T⟩$ of $\pi$, K, p and $K^{*0}$ as a function of $⟨N_{part}⟩$ for Au+Au collisions at $\sqrt{s_{NN}}$ = 62.4 GeV.

Mid-rapidity $N(K^{*0})/N(K^-)$ ratio for Au+Au at $\sqrt{s_{NN}}$ = 62.4 GeV as a function of $⟨N_{part}⟩$

Mid-rapidity $N(K^{*0})/N(K^-)$ ratio for Cu+Cu at $\sqrt{s_{NN}}$ = 62.4 GeV as a function of $⟨N_{part}⟩$

Mid-rapidity $N(K^{*0})/N(K^-)$ ratio for Au+Au at $\sqrt{s_{NN}}$ = 200 GeV as a function of $⟨N_{part}⟩$

Mid-rapidity $N(K^{*0})/N(K^-)$ ratio for Cu+Cu at $\sqrt{s_{NN}}$ = 200 GeV as a function of $⟨N_{part}⟩$

Mid-rapidity $N(K^{*0})N(K^-)$ in Au+Au collisions divided by $N(K^{*0})N(K^-)$ ratio in p+p collisions at $\sqrt{s_{NN}}$=200 GeV as a function of $⟨N_{part}⟩$.

Mid-rapidity $N(K^{*0})N(K^-)$ in Cu+Cu collisions divided by $N(K^{*0})N(K^-)$ ratio in p+p collisions at $\sqrt{s_{NN}}$=200 GeV as a function of $⟨N_{part}⟩$

Mid-rapidity $N(K^{*0})N(K^-)$ in d+Au collisions divided by $N(K^{*0})N(K^-)$ ratio in d+Au collisions at $\sqrt{s_{NN}}$=200 GeV as a function of $⟨N_{part}⟩$

Mid-rapidity $N(K^{*0})/N(K^-)$ ratio in minimum bias Au+Au collisions as a function of $\sqrt{s_{NN}}.

Mid-rapidity $N(K^{*0})/N(K^-)$ ratio in minimum bias Cu+Cu collisions as a function of $\sqrt{s_{NN}}.

Mid-rapidity $N(K^{*0})/N(K^-)$ ratio in minimum bias p+p collisions as a function of $\sqrt{s_{NN}}.

Mid-rapidity $N(K^{*0})/N(K^-)$ ratio in minimum bias Au+Au collisions as a function of $\sqrt{s_{NN}}.

Mid-rapidity $N(K^{*0})/N(K^-)$ ratio in minimum bias Cu+Cu collisions as a function of $\sqrt{s_{NN}}.

Mid-rapidity $N(K^{*0})/N(K^-)$ ratio in minimum bias p+p collisions as a function of $\sqrt{s_{NN}}.

Mid-rapidity $N(\phi)/N(K^{*0})$ ratio for Au+Au at $\sqrt{s_{NN}}$ = 62.4 GeV as a function of $⟨N_{part}⟩$

Mid-rapidity $N(\phi)/N(K^{*0})$ ratio for Cu+Cu at $\sqrt{s_{NN}}$ = 62.4 GeV as a function of $⟨N_{part}⟩$

Mid-rapidity $N(\phi)/N(K^{*0})$ ratio for Au+Au at $\sqrt{s_{NN}}$ = 200 GeV as a function of $⟨N_{part}⟩$

Mid-rapidity $N(\phi)/N(K^{*0})$ ratio for Cu+Cu at $\sqrt{s_{NN}}$ = 200 GeV as a function of $⟨N_{part}⟩$

Mid-rapidity $[N(\phi)/N(K^{*0})]$ in Au+Au collisions divided by $[N(\phi)/N(K^{*0})]$ ratio in p+p collisions at $\sqrt{s_{NN}}$=200 GeV as a function of $⟨N_{part}⟩$

Mid-rapidity $[N(\phi)/N(K^{*0})]$ in Cu+Cu collisions divided by $[N(\phi)/N(K^{*0})]$ ratio in p+p collisions at $\sqrt{s_{NN}}$=200 GeV as a function of $⟨N_{part}⟩$

Mid-rapidity $[N(\phi)/N(K^{*0})]$ in d+Au collisions divided by $[N(\phi)/N(K^{*0})]$ ratio in p+p collisions at $\sqrt{s_{NN}}$=200 GeV as a function of $⟨N_{part}⟩$

Mid-rapidity $N(\phi)/N(K^{*0})$ ratio in minimum bias Au+Au collisions as a function of $\sqrt{s_{NN}}$.

Mid-rapidity $N(\phi)/N(K^{*0})$ ratio in minimum bias Cu+Cu collisions as a function of $\sqrt{s_{NN}}$.

Mid-rapidity $N(\phi)/N(K^{*0})$ ratio in minimum bias p+p collisions as a function of $\sqrt{s_{NN}}$.

Mid-rapidity $N(\phi)/N(K^{*0})$ ratio in minimum bias Au+Au collisions as a function of $\sqrt{s_{NN}}$.

Mid-rapidity $N(\phi)/N(K^{*0})$ ratio in minimum bias Cu+Cu collisions as a function of $\sqrt{s_{NN}}$.

Mid-rapidity $N(\phi)/N(K^{*0})$ ratio in minimum bias p+p collisions as a function of $\sqrt{s_{NN}}$.

The $K^{*0}$ $v_2$ (Run IV) as a function of $p_T$ in minimum bias Au+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV.

The $K^{*0}$ $v_2$ (Run II) as a function of $p_T$ in minimum bias Au+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV.

The $K^{*0}$ $R_{CP}$ as a function of $p_T$ in Au+Au collisions at 62.4 and 200 GeV compared to the $R_{CP}$ of $K^0_S$ and $\Lambda$ at 200 GeV.

The $K^{*0}$ $R_{CP}$ as a function of $p_T$ in Au+Au collisions at 62.4 and 200 GeV compared to the $R_{CP}$ of $K^0_S$ and $\Lambda$ at 200 GeV.

The $K^{*0}$ $R_{CP}$ as a function of $p_T$ in Au+Au collisions at 62.4 and 200 GeV compared to the $R_{CP}$ of $K^0_S$ and $\Lambda$ at 200 GeV.

The $K^{*0}$ ~$R_{CP}$~ as a function of $p_T$ in Au+Au collisions at 62.4 and 200 GeV compared to the $R_{CP}$ of $K^0_S$ and $\Lambda$ at 200 GeV.

The balance function in terms of $\Delta y$ for identified charged pion pairs from Au+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV for nine centrality bins.

The balance function in terms of $\Delta y$ for identified charged kaon pairs from Au+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV for nine centrality bins.

The balance function for p+p collisions at $\sqrt{s_{NN}}$ = 200 GeV. The top panel shows the balance function for all charged particles in terms of $\Delta \eta$. The bottom panel gives the balance function for charged pion pairs and charged kaon pairs in terms of $\Delta y$.

The balance function for p+p collisions at $\sqrt{s_{NN}}$ = 200 GeV. The top panel shows the balance function for all charged particles in terms of $\Delta \eta$. The bottom panel gives the balance function for charged pion pairs and charged kaon pairs in terms of $\Delta y$.

The balance function in terms of $\Delta \eta$ for all charged particles from d+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV for three centrality bins.

The balance function in terms of $q_{inv}$ for charged pion pairs from Au+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV in nine centrality bins. Curves correspond to a thermal distribution (Eq. 3) plus $K^{0}_{S}$ decay.

The balance function in terms of $q_{inv}$ for charged-pion pairs in two centrality bins over the range 0 < $q_{inv}$ < 0.2 GeV/c.

The balance function in terms of $q_{inv}$ for charged kaon pairs from Au+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV in nine centrality bins. Curves correspond to a thermal (Eq. 3) distribution plus $\phi$ decay.

The balance function in terms of $q_{inv}$ for charged pion pairs [part a)] and charged kaon pairs [part b)] from p+p collisions at $\sqrt{s_{NN}}$ = 200 GeV integrated over all multiplicities. Solid curves correspond to a thermal distribution (Eq. 3) plus $K^{0}_{S}$ and $\rho^{0}$ decay for pions and φ decay for kaons. The dashed curve for pions represents a fit to a thermal distribution (Eq. 3) plus $K^{0}_{S}$ decay and $\rho^{0}$ decay, with the $\rho^{0}$ mass shifted down by 0.04 $GeV/c^{2}$.

The balance function in terms of $q_{long}$ for charged pion pairs from Au+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV in nine centrality bins.

The balance function in terms of $q_{out}$ for charged pion pairs from Au+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV in nine centrality bins.

(Color online) The balance function in terms of $q_{side}$ for charged pion pairs from Au+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV for nine centrality bins.

(Color online) The balance function in terms of $\Delta\phi$ for all charged particles with 0.2< pt<2.0 GeV/c from Au+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV in nine centrality bins.The closed circles represent the real data minus the mixed events.

(Color online) The balance function in terms of $\Delta\phi$ for all charged particles with 1.0< pt<10.0 GeV/c from Au+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV in nine centrality bins.The closed circles represent the real data minus the mixed events.

(Color online) The balance function in terms of $\Delta y$ for charged pions from central collisions of Au+Au at $\sqrt{s_{NN}}$ = 200 GeV compared with predictions from the blast-wave model from Ref.[30] and filtered HIJING calculations taking into account acceptance and efficiency.

(Color online) The balance function in terms of $\Delta y$ for charged pions from central collisions of Au+Au at $\sqrt{s_{NN}}$ = 200 GeV compared with predictions from the blast-wave model from Ref.[30] and filtered HIJING calculations taking into account acceptance and efficiency.

(Color online) The balance function in terms of $q_{inv}$ for charged pions from central collisions of Au+Au at $\sqrt{s_{NN}}$ = 200 GeV compared with predictions from the blast-wave model from Ref.[30] and predictions from filtered HIJING calculations including acceptance and efficiency. For the blast-wave calculations, HBT is not included and the decays of the $K^0_S$ and $\rho^0$ are not shown.

(Color online) The balance function in terms of $q_{inv}$ for charged pions from central collisions of Au+Au at $\sqrt{s_{NN}}$ = 200 GeV compared with predictions from the blast-wave model from Ref.[30] and predictions from filtered HIJING calculations including acceptance and efficiency. For the blast-wave calculations, HBT is not included and the decays of the $K^0_S$ and $\rho^0$ are not shown.

(Color online) The balance function width $<\Delta\eta>$ for all charged particles from Au+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV compared with the widths of balance functions calculated using shuffled events. Also shown are the balance function widths for p+p and d+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV.Filtered HIJING calculations are also shown for the widths of the balance function from p+p and Au+Au collisions. Filtered UrQMD calculations are shown for the widths of the balance function from Au+Au collisions.

(Color online) The balance function width $<\Delta\eta>$ for all charged particles from Au+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV compared with the widths of balance functions calculated using shuffled events. Also shown are the balance function widths for p+p and d+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV.Filtered HIJING calculations are also shown for the widths of the balance function from p+p and Au+Au collisions. Filtered UrQMD calculations are shown for the widths of the balance function from Au+Au collisions.

(Color online) The balance function widths for identified charged pions and charged kaons from Au+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV and p+p collisions at $\sqrt{s}$ = 200 GeV. Filtered HIJING calculations are shown for the same systems. Filtered UrQMD calculations are shown for Au+Au. Also shown is the width of the balance function for pions predicted by the blast-wave model of Ref.[30].

(Color online) The balance function width $\sigma$ extracted from $B(q_{inv})$ for identified charged pions and kaons from Au+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV and p+p collisions at $\sqrt{s}$ = 200 GeV using a thermal fit (Eq. 3) where $\sigma$ is the width. Filtered HIJING and UrQMD calculations are shown for pions and kaons from Au+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV. Values are shown for $\sqrt{2mT_{kin}}$ from Au+Au collisions, where m is the mass of a pion or a kaon, and $T_{kin}$ is calculated from identified particle spectra [45]. The width predicted by the blast-wave model of Ref. [30] is also shown for pions.

(Color online) The balance function width $\sigma$ extracted from $B(q_{inv})$ for identified charged pions and kaons from Au+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV and p+p collisions at $\sqrt{s}$ = 200 GeV using a thermal fit (Eq. 3) where $\sigma$ is the width. Filtered HIJING and UrQMD calculations are shown for pions and kaons from Au+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV. Values are shown for $\sqrt{2mT_{kin}}$ from Au+Au collisions, where m is the mass of a pion or a kaon, and $T_{kin}$ is calculated from identified particle spectra [45]. The width predicted by the blast-wave model of Ref. [30] is also shown for pions.

(Color online) The widths for the balance functions for pions in terms of $q_{long}$, $q_{out}$, and $q_{side}$ compared with UrQMD calculations.

(Color online) The weighted average cosine of the relative azimuthal angle,$<\cos(\Delta\phi)$, extracted from $B(\Delta\phi)$ for all charged particles with $0.2< p_t <2.0$ from Au+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV and from all charged particleswith $1.0< p_t <10.0$ GeV/c, compared with predictions using filtered UrQMD calculations.

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.

Fit results from a fit to data using Eq. 11 to parameterize the femtoscopic correlations and Eq. 15 for non-femtoscopic ones (EMCIC fit from Figure 6 in the paper)

Fit results from a fit to 1D correlation function using Eq. 6 to parameterize the femtoscopic correlations (standard fit from Figure 7 in the paper)

Fit results from a fit to 1D correlation function using Eq. 6 to parameterize the femtoscopic correlations and Eq. 12 for non-femtoscopic ones (delta - q fit from Figure 7 in the paper)

Fit results from a fit to 1D correlation function using Eq. 6 to parameterize the femtoscopic correlations and Eq. 15 for non-femtoscopic ones (EMCIC fit from Figure 7 in the paper). The non-femtoscopic parameters M1−4 were not varied, but kept fixed to the values in Table IV

Multiplicity dependence of fit results to 1D correlation function for different fit parameterizations (Figure 8 in the paper).

Multiplicity dependence of fit parameters to two-dimensional correlation functions using Equations 7 and 8. To consistently compare to previous measurements, Omega was set to unity (c.f. Equation 5).

The angle Delta between the away-side peaks and DeltaPhi = pi for 4 < pT_trig < 6 GeV/c in 0-12% central Au+Au collisions as a function of pT_assoc . Three different parametrisations of the away-side peak shape were used. The errors are statistical errors from the fit.

Near-side (|dphi| < 0.9) associated yield per trigger particle for various trigger particle pT selections as a function of associated pT . Results are shown for 0-12% central Au+Au collisions and for d+Au collisions.

Near-side (|dphi| < 0.9) ratios of the per-trigger associated yields in central Au+Au and d+Au collisions.

Away-side (|dphi| > 0.9) associated yield per trigger particle for various trigger particle pT selections as a function of associated pT . Results are shown for 0-12% central Au+Au collisions and for d+Au collisions.

Away-side (|dphi| > 0.9) ratios of the per-trigger associated yields in central Au+Au and d+Au collisions.

Mean transverse momentum <pT> of associated particles with 0.25 < pT,assoc < 4.0 GeV/c, for four different centrality selections.

Mean transverse momentum <pT> (DeltaPhi) of associated hadrons in the range 0.25 < pT_assoc < 4.0 GeV/c in the core (|DeltaPhi − pi| < pi/6) and cone (pi/6 < |DeltaPhi − pi| < pi/2) azimuthal regions for 3 < pT_trig < 4 GeV/c and 4 < pT_trig < 6 GeV/c as a function of number of participants. The inclusive <pT> in the same pT range for events with a trigger hadron is also indicated.

The 3ΛH (solid squares) and Λ (open circles) yield distributions versus cτ. The solid lines represent the cτ fits. The inset depicts the $\chi^2$ distribution of the best 3ΛH cτ fit. The error bars represent the statistical uncertaintiesonly.

Particle ratios as a function of center-of-mass energy per nucleon-nucleon collision. The 4ΛH/(4He × Λ/p) ratio is corrected for the spin degeneracy factor (38). The error bars represent statistical uncertainties only.

Balance functions in pseudorapidity windows -1 < eta < 1 for 0.15 < pT < 2 GEV/c.

Balance functions in pseudorapidity windows -1.3 < eta < 1.3 for 0.15 < pT < 2 GEV/c.

Balance functions observed at five different positions of pseudorapidity windows with |eta_w|=0.8 for 0.15 < pT < 2 GEV/c and -1 < eta < -0.2.

Balance functions observed at five different positions of pseudorapidity windows with |eta_w|=0.8 for 0.15 < pT < 2 GEV/c and -0.8 < eta < 0.

Balance functions observed at five different positions of pseudorapidity windows with |eta_w|=0.8 for 0.15 < pT < 2 GEV/c and -0.4 < eta < 0.4.

Balance functions observed at five different positions of pseudorapidity windows with |eta_w|=0.8 for 0.15 < pT < 2 GEV/c and 0 < eta < 0.8.

Balance functions observed at five different positions of pseudorapidity windows with |eta_w|=0.8 for 0.15 < pT < 2 GEV/c and 0.2 < eta < 1.

Scaled balance function obtained for various pseudorapidity window widths and positions for 0.15 < pT < 2 GEV/c and -0.3 < eta < 0.3.

Scaled balance function obtained for various pseudorapidity window widths and positions for 0.15 < pT < 2 GEV/c and 0 < eta < 1.

Scaled balance function obtained for various pseudorapidity window widths and positions for 0.15 < pT < 2 GEV/c and -1 < eta < 0.

Scaled balance function obtained for various pseudorapidity window widths and positions for 0.15 < pT < 2 GEV/c and -0.5 < eta < 0.5.

Scaled balance function obtained for various pseudorapidity window widths and positions for 0.15 < pT < 2 GEV/c and -1 < eta < 1.

Scaled balance function obtained for various pseudorapidity window widths and positions for 0.15 < pT < 2 GEV/c and -1.3 < eta < 1.3.

B_s(d eta) based on B(d eta|eta_w) values measured in different pseudorapidity windows for particles in 0.15 < pT < 0.4 GEV/c and -0.3 < eta < 0.3.

B_s(d eta) based on B(d eta|eta_w) values measured in different pseudorapidity windows for particles in 0.15 < pT < 0.4 GEV/c and 0 < eta < 1.

B_s(d eta) based on B(d eta|eta_w) values measured in different pseudorapidity windows for particles in 0.15 < pT < 0.4 GEV/c and -1 < eta < 0.

B_s(d eta) based on B(d eta|eta_w) values measured in different pseudorapidity windows for particles in 0.15 < pT < 0.4 GEV/c and -0.5 < eta < 0.5.

B_s(d eta) based on B(d eta|eta_w) values measured in different pseudorapidity windows for particles in 0.15 < pT < 0.4 GEV/c and -1 < eta < 1.

B_s(d eta) based on B(d eta|eta_w) values measured in different pseudorapidity windows for particles in 0.15 < pT < 0.4 GEV/c and -1.3 < eta < 1.3.

B_s(d eta) based on B(d eta|eta_w) values measured in different pseudorapidity windows for particles in 0.4 < pT < 0.7 GEV/c and -0.3 < eta < 0.3.

B_s(d eta) based on B(d eta|eta_w) values measured in different pseudorapidity windows for particles in 0.4 < pT < 0.7 GEV/c and 0 < eta < 1.

B_s(d eta) based on B(d eta|eta_w) values measured in different pseudorapidity windows for particles in 0.4 < pT < 0.7 GEV/c and -1 < eta < 0.

B_s(d eta) based on B(d eta|eta_w) values measured in different pseudorapidity windows for particles in 0.4 < pT < 0.7 GEV/c and -0.5 < eta < 0.5.

B_s(d eta) based on B(d eta|eta_w) values measured in different pseudorapidity windows for particles in 0.4 < pT < 0.7 GEV/c and -1 < eta < 1.

B_s(d eta) based on B(d eta|eta_w) values measured in different pseudorapidity windows for particles in 0.4 < pT < 0.7 GEV/c and -1.3 < eta < 1.3.

B_s(d eta) based on B(d eta|eta_w) values measured in different pseudorapidity windows for particles in 0.7 < pT < 1 GEV/c and -0.3 < eta < 0.3.

B_s(d eta) based on B(d eta|eta_w) values measured in different pseudorapidity windows for particles in 0.7 < pT < 1 GEV/c and 0 < eta < 1.

B_s(d eta) based on B(d eta|eta_w) values measured in different pseudorapidity windows for particles in 0.7 < pT < 1 GEV/c and -1 < eta < 0.

B_s(d eta) based on B(d eta|eta_w) values measured in different pseudorapidity windows for particles in 0.7 < pT < 1 GEV/c and -0.5 < eta < 0.5.

B_s(d eta) based on B(d eta|eta_w) values measured in different pseudorapidity windows for particles in 0.7 < pT < 1 GEV/c and -1 < eta < 1.

B_s(d eta) based on B(d eta|eta_w) values measured in different pseudorapidity windows for particles in 0.7 < pT < 1 GEV/c and -1.3 < eta < 1.3.

B_s(d eta) based on B(d eta|eta_w) values measured in different pseudorapidity windows for particles in 1 < pT < 2 GEV/c and -0.3 < eta < 0.3.

B_s(d eta) based on B(d eta|eta_w) values measured in different pseudorapidity windows for particles in 1 < pT < 2 GEV/c and 0 < eta < 1.

B_s(d eta) based on B(d eta|eta_w) values measured in different pseudorapidity windows for particles in 1 < pT < 2 GEV/c and -1 < eta < 0.

B_s(d eta) based on B(d eta|eta_w) values measured in different pseudorapidity windows for particles in 1 < pT < 2 GEV/c and -0.5 < eta < 0.5.

B_s(d eta) based on B(d eta|eta_w) values measured in different pseudorapidity windows for particles in 1 < pT < 2 GEV/c and -1 < eta < 1.

B_s(d eta) based on B(d eta|eta_w) values measured in different pseudorapidity windows for particles in 1 < pT < 2 GEV/c and -1.3 < eta < 1.3.

The pT dependence of the width of the BF in 60-80% centrality.

The pT dependence of the width of the BF in 30-60% centrality.

The pT dependence of the width of the BF in 10-30% centrality.

The pT dependence of the width of the BF in 0-10% centrality.

The centrality dependence of the width of the BF in 0.15 < pT < 0.4 GEV/c.

The centrality dependence of the width of the BF in 0.4 < pT < 0.7 GEV/c.

The centrality dependence of the width of the BF in 0.7 < pT < 1 GEV/c.

The centrality dependence of the width of the BF in 1 < pT < 2 GEV/c.