Coefficients Cx and Cz for the reaction GAMMA P --> K+ LAMBDA for incident energy = 1.332 GeV and W = 1.839 GeV.

Coefficients Cx and Cz for the reaction GAMMA P --> K+ LAMBDA for incident energy = 1.433 GeV and W = 1.889 GeV.

Coefficients Cx and Cz for the reaction GAMMA P --> K+ LAMBDA for incident energy = 1.534 GeV and W = 1.939 GeV.

Coefficients Cx and Cz for the reaction GAMMA P --> K+ LAMBDA for incident energy = 1.635 GeV and W = 1.987 GeV.

Coefficients Cx and Cz for the reaction GAMMA P --> K+ LAMBDA for incident energy = 1.737 GeV and W = 2.035 GeV.

Coefficients Cx and Cz for the reaction GAMMA P --> K+ LAMBDA for incident energy = 1.838 GeV and W = 2.081 GeV.

Coefficients Cx and Cz for the reaction GAMMA P --> K+ LAMBDA for incident energy = 1.939 GeV and W = 2.126 GeV.

Coefficients Cx and Cz for the reaction GAMMA P --> K+ LAMBDA for incident energy = 2.039 GeV and W = 2.170 GeV.

Coefficients Cx and Cz for the reaction GAMMA P --> K+ LAMBDA for incident energy = 2.139 GeV and W = 2.212 GeV.

Coefficients Cx and Cz for the reaction GAMMA P --> K+ LAMBDA for incident energy = 2.240 GeV and W = 2.255 GeV.

Coefficients Cx and Cz for the reaction GAMMA P --> K+ LAMBDA for incident energy = 2.341 GeV and W = 2.296 GeV.

Coefficients Cx and Cz for the reaction GAMMA P --> K+ LAMBDA for incident energy = 2.443 GeV and W = 2.338 GeV.

Coefficients Cx and Cz for the reaction GAMMA P --> K+ LAMBDA for incident energy = 2.543 GeV and W = 2.377 GeV.

Coefficients Cx and Cz for the reaction GAMMA P --> K+ LAMBDA for incident energy = 2.642 GeV and W = 2.416 GeV.

Coefficients Cx and Cz for the reaction GAMMA P --> K+ LAMBDA for incident energy = 2.741 GeV and W = 2.454 GeV.

Coefficients Cx and Cz for the reaction GAMMA P --> K+ SIGMA0 for incident energy = 1.232 GeV and W = 1.787 GeV.

Coefficients Cx and Cz for the reaction GAMMA P --> K+ SIGMA0 for incident energy = 1.332 GeV and W = 1.839 GeV.

Coefficients Cx and Cz for the reaction GAMMA P --> K+ SIGMA0 for incident energy = 1.433 GeV and W = 1.889 GeV.

Coefficients Cx and Cz for the reaction GAMMA P --> K+ SIGMA0 for incident energy = 1.534 GeV and W = 1.939 GeV.

Coefficients Cx and Cz for the reaction GAMMA P --> K+ SIGMA0 for incident energy = 1.635 GeV and W = 1.987 GeV.

Coefficients Cx and Cz for the reaction GAMMA P --> K+ SIGMA0 for incident energy = 1.737 GeV and W = 2.035 GeV.

Coefficients Cx and Cz for the reaction GAMMA P --> K+ SIGMA0 for incident energy = 1.838 GeV and W = 2.081 GeV.

Coefficients Cx and Cz for the reaction GAMMA P --> K+ SIGMA0 for incident energy = 1.939 GeV and W = 2.126 GeV.

Coefficients Cx and Cz for the reaction GAMMA P --> K+ SIGMA0 for incident energy = 2.039 GeV and W = 2.170 GeV.

Coefficients Cx and Cz for the reaction GAMMA P --> K+ SIGMA0 for incident energy = 2.139 GeV and W = 2.212 GeV.

Coefficients Cx and Cz for the reaction GAMMA P --> K+ SIGMA0 for incident energy = 2.240 GeV and W = 2.255 GeV.

Coefficients Cx and Cz for the reaction GAMMA P --> K+ SIGMA0 for incident energy = 2.341 GeV and W = 2.296 GeV.

Coefficients Cx and Cz for the reaction GAMMA P --> K+ SIGMA0 for incident energy = 2.443 GeV and W = 2.338 GeV.

Coefficients Cx and Cz for the reaction GAMMA P --> K+ SIGMA0 for incident energy = 2.543 GeV and W = 2.377 GeV.

Coefficients Cx and Cz for the reaction GAMMA P --> K+ SIGMA0 for incident energy = 2.642 GeV and W = 2.416 GeV.

Coefficients Cx and Cz for the reaction GAMMA P --> K+ SIGMA0 for incident energy = 2.741 GeV and W = 2.454 GeV.

Photon beam asymmetry Sigma at W= 1.3147 GeV

Photon beam asymmetry Sigma at W= 1.3289 GeV

Photon beam asymmetry Sigma at W= 1.3430 GeV

Photon beam asymmetry Sigma at W= 1.3569 GeV

Photon beam asymmetry Sigma at W= 1.3707 GeV

Photon beam asymmetry Sigma at W= 1.3843 GeV

Photon beam asymmetry Sigma at W= 1.3978 GeV

Photon beam asymmetry Sigma at W= 1.4112 GeV

Photon beam asymmetry Sigma at W= 1.4244 GeV

FIG. 2: a) left side: The correlation data for the ratio of the histograms of same-event-pairs to mixed-event-pairs for unlike-sign charged pairs, shown in a two-dimensional (2-D) perspective plot $\Delta\phi$ - $\Delta\eta$. The plot was normalized to a mean of 1. b) right side: The similar correlation data for like-sign charge pairs.

FIG. 3: a) left side: Folded correlation data for unlike-sign charge pairs on $\Delta\phi$ and $\Delta\eta$ based on demonstrated symmetries in the data. This increases the statistics in a typical bin by a factor of four. Henceforth we will be dealing with folded data only. b) right side: Similar folded data for like-sign charge pairs.

FIG. 3: a) left side: Folded correlation data for unlike-sign charge pairs on $\Delta\phi$ and $\Delta\eta$ based on demonstrated symmetries in the data. This increases the statistics in a typical bin by a factor of four. Henceforth we will be dealing with folded data only. b) right side: Similar folded data for like-sign charge pairs.

FIG. 4: “(Color online)”a) left side: The 2 dimensional (2-D) approximately gaussian signal shape equation (4) from the fit to the normalized and folded unlike-sign charge pairs signal data. b) right side: The unlike-sign charge pairs signal data corresponding to the adjoining signal function on the left side.

FIG. 4: “(Color online)”a) left side: The 2 dimensional (2-D) approximately gaussian signal shape equation (4) from the fit to the normalized and folded unlike-sign charge pairs signal data. b) right side: The unlike-sign charge pairs signal data corresponding to the adjoining signal function on the left side.

FIG. 5 :“(Color online)”a) left side: A perspective plot of the fit to the 2-D like-sign charge pairs signal shape of equation (5). b) right side: Like-sign charge pairs signal data corresponding to the adjacent signal fit on the left side.

FIG. 5: “(Color online)”a) left side: A perspective plot of the fit to the 2-D like-sign charge pairs signal shape of equation (5). b) right side: Like-sign charge pairs signal data corresponding to the adjacent signal fit on the left side.

FIG. 6: “(Color online)”a) left side: The charge dependent (CD) signal shape is a 2 dimensional (2-D) approximate gaussian which is symmetrical. The average gaussian width is 27.5$^{\circ}$ $\pm$ 3.2$^{\circ}$ (0.48 $\pm$ 0.056 rad) both in $\Delta\phi$ and $\Delta\eta$. Thus we are observing a greater probability for unlike-sign charge pairs of particles than for like-sign charge pairs emitted randomly on 2-D $\eta\phi$ directions. b) right side: The CD signal data corresponding to the adjacent signal fit on the left.

FIG. 6: “(Color online)”a) left side: The charge dependent (CD) signal shape is a 2 dimensional (2-D) approximate gaussian which is symmetrical. The average gaussian width is 27.5$^{\circ}$ $\pm$ 3.2$^{\circ}$ (0.48 $\pm$ 0.056 rad) both in $\Delta\phi$ and $\Delta\eta$. Thus we are observing a greater probability for unlike-sign charge pairs of particles than for like-sign charge pairs emitted randomly on 2-D $\eta\phi$ directions. b) right side: The CD signal data corresponding to the adjacent signal fit on the left.

FIG. 7: “(Color online)”a) left side: The fit to the charge independent (CI) signal shape which is the sum of the fits of like-sign plus unlike-sign charge pairs signals. The 2-D gaussian equivalent RMS signal has a $\Delta\phi$ width of about 32$^{\circ}$ (0.52 rad), and $\Delta\eta$ width of about 66$^{\circ}$ (1.15 rad) which is about double the $\Delta\phi$ width. b) right side: The CI signal data corresponding to the adjacent fit on the left.

FIG. 7: “(Color online)”a) left side: The fit to the charge independent (CI) signal shape which is the sum of the fits of like-sign plus unlike-sign charge pairs signals. The 2-D gaussian equivalent RMS signal has a $\Delta\phi$ width of about 32$^{\circ}$ (0.52 rad), and $\Delta\eta$ width of about 66$^{\circ}$ (1.15 rad) which is about double the $\Delta\phi$ width. b) right side: The CI signal data corresponding to the adjacent fit on the left.

FIG. 8: a) left side: The charge independent (CI) signal data with the lower range of elliptic flow amplitude and the best $\chi^2$ (the same as Figure 7b) plotted as a 2-D perspective plot on $\Delta\phi$ vs. $\Delta\eta$. b) right side: The charge independent (CI) signal data with our maximum elliptic flow amplitude used in our analysis ($\chi^2$ was worse by 1$\sigma$).

FIG. 8: a) left side: The charge independent (CI) signal data with the lower range of elliptic flow amplitude and the best $\chi^2$ (the same as Figure 7b) plotted as a 2-D perspective plot on $\Delta\phi$ vs. $\Delta\eta$. b) right side: The charge independent (CI) signal data with our maximum elliptic flow amplitude used in our analysis ($\chi^2$ was worse by 1$\sigma$).

Spherical tensor analysing powers t20 and t22 for EPP 0.1 to 1.0 MeV and cos(theta) < 0.5.

Spherical tensor analysing powers t20 and t22 for EPP 1 to 3 MeV and cos(theta) > 0.5.

Spherical tensor analysing powers t20 and t22 for EPP 1 to 3 MeV and cos(theta) < 0.5.

Asymmetry results on $\vec e-^2$H parity-violating scattering from the PVDIS experiment at JLab, for RES IV settings.

Asymmetry results on $\vec e-^2$H parity-violating scattering from the PVDIS experiment at JLab, for RES III settings.

The $v_{dyn}$ and the three terms of $v_{dyn}$ vs $\sqrt{\langle N_{ch}\rangle \langle N_{\gamma}\rangle }$ for mixed events. $Corr_{\gamma\,-ch}^{real}$ is plotted.

The $v_{dyn}$ and the three terms of $v_{dyn}$ vs $\sqrt{\langle N_{ch}\rangle \langle N_{\gamma}\rangle }$ for mixed events. $Corr_{\gamma\,-ch}^{mixed}$ is plotted.

The $v_{dyn}$ and the three terms of $v_{dyn}$ vs $\sqrt{\langle N_{ch}\rangle \langle N_{\gamma}\rangle }$ for mixed events. $\omega_{\gamma}^{real}$ is plotted.

The $v_{dyn}$ and the three terms of $v_{dyn}$ vs $\sqrt{\langle N_{ch}\rangle \langle N_{\gamma}\rangle }$ for mixed events. $\omega_{\gamma}^{mixed}$ is plotted.

The $v_{dyn}$ and the three terms of $v_{dyn}$ vs $\sqrt{\langle N_{ch}\rangle \langle N_{\gamma}\rangle }$ for mixed events. $v_{dyn}^{real}$ is plotted.

The $v_{dyn}$ and the three terms of $v_{dyn}$ vs $\sqrt{\langle N_{ch}\rangle \langle N_{\gamma}\rangle }$ for mixed events. $v_{dyn}^{mixed}$ is plotted.

The values of the observable $v_{dyn}^{ch-\gamma}$ for the same side.

The values of the observable $v_{dyn}^{ch-\gamma}$ for the same side.

The values of the observable $v_{dyn}^{ch-\gamma}$ for the away-side.

The values of the observable $v_{dyn}^{ch-\gamma}$ for the away-side.

The correlation between positive and negative charged particles measured by the FTPC and photons measured by the PMD using $v_{dyn}$ for real events.

$r_{m,1}$ vs multiplicity for first order of m.

$r_{m,1}$ vs multiplicity for first order of m.

$r_{m,1}$ vs multiplicity for second order of m.

$r_{m,1}$ vs multiplicity for second order of m.

$r_{m,1}$ vs multiplicity for third order of m.

$r_{m,1}$ vs multiplicity for third order of m.

The moments $r_{m,1}$(m=1-3) for real and mixed events as a function of order m in a fixed multiplicity bin of 47$\langle \sqrt{\langle N_{ch}\rangle \langle N_{\gamma}\rangle }\langle 54$.

No description provided.

No description provided.

Reference multiplicity distributions obtained from Au+Au collisions at $\sqrt{s_{\rm NN}}$ = 3 GeV data (black markers), Glauber model (red histogram), and unfolding approach to separate single and pileup contributions. Vertical lines represent statistical uncertainties. Single, pileup, and single+pileup collisions are shown in solid blue markers, dashed green, and dashed pink lines, respectively. The 0–5% central events and 5–60% mid-central to peripheral events are indicated by black arrows. The ratio of the single+pileup to the measured multiplicity distribution is shown in the lower panel.

Reference multiplicity distributions obtained from Au+Au collisions at $\sqrt{s_{\rm NN}}$ = 3 GeV data (black markers), Glauber model (red histogram), and unfolding approach to separate single and pileup contributions. Vertical lines represent statistical uncertainties. Single, pileup, and single+pileup collisions are shown in solid blue markers, dashed green, and dashed pink lines, respectively. The 0–5% central events and 5–60% mid-central to peripheral events are indicated by black arrows. The ratio of the single+pileup to the measured multiplicity distribution is shown in the lower panel.

Proton cumulants as a function of reference multiplicity (black circles) from $\sqrt{s_{\rm NN}}$ = 3 GeV Au+Au collisions. Centrality-binned results with and without centrality bin width corrections are represented by red circles and blue squares, respectively. Vertical dashed lines indicate the centrality classes, from right to left: 0–5%, 5–10%, 10–20%. Data points in this figure are only corrected for detector efficiency but not for the pileup effect, which will be discussed in a later section.

Proton cumulants as a function of reference multiplicity (black circles) from $\sqrt{s_{\rm NN}}$ = 3 GeV Au+Au collisions. Centrality-binned results with and without centrality bin width corrections are represented by red circles and blue squares, respectively. Vertical dashed lines indicate the centrality classes, from right to left: 0–5%, 5–10%, 10–20%. Data points in this figure are only corrected for detector efficiency but not for the pileup effect, which will be discussed in a later section.

Proton cumulants as a function of reference multiplicity (black circles) from $\sqrt{s_{\rm NN}}$ = 3 GeV Au+Au collisions. Centrality-binned results with and without centrality bin width corrections are represented by red circles and blue squares, respectively. Vertical dashed lines indicate the centrality classes, from right to left: 0–5%, 5–10%, 10–20%. Data points in this figure are only corrected for detector efficiency but not for the pileup effect, which will be discussed in a later section.

Proton cumulants as a function of reference multiplicity from $\sqrt{s_{\rm NN}}$ = 3 GeV Au+Au collisions. Pileup corrected and uncorrected cumulants as a function of reference multiplicity are represented by black circles and blue open squares, respectively. Red circles and blue-filled squares represent the results of centrality binned data.

Proton cumulants as a function of reference multiplicity from $\sqrt{s_{\rm NN}}$ = 3 GeV Au+Au collisions. Pileup corrected and uncorrected cumulants as a function of reference multiplicity are represented by black circles and blue open squares, respectively. Red circles and blue-filled squares represent the results of centrality binned data.

Ratios of proton cumulants as a function of reference multiplicity from $\sqrt{s_{\rm NN}}$ = 3 GeV Au+Au collisions. Pileup corrected and uncorrected cumulants are represented by black circles and blue open squares, respectively. Red circles and blue-filled squares represent the results of centrality binned data.

Ratios of proton cumulants as a function of reference multiplicity from $\sqrt{s_{\rm NN}}$ = 3 GeV Au+Au collisions. Pileup corrected and uncorrected cumulants are represented by black circles and blue open squares, respectively. Red circles and blue-filled squares represent the results of centrality binned data.

UrQMD results of the proton cumulant ratios up to sixth order in Au+Au collisions at $\sqrt{s_{\rm NN}}$= 3 GeV. The black circles are without VF correction while blue squares and red triangles are results with VFC which used $N_{\rm part}$ distributions from UrQMD and Glauber models, respectively. The blue crosses are calculations using UrQMD events with b $\leq$ 3 fm. The above results are applied CBWC except for the one (blue crosses) using b $\leq$3 fm events.

UrQMD results of the proton cumulant ratios up to sixth order in Au+Au collisions at $\sqrt{s_{\rm NN}}$= 3 GeV. The black circles are without VF correction while blue squares and red triangles are results with VFC which used $N_{\rm part}$ distributions from UrQMD and Glauber models, respectively. The blue crosses are calculations using UrQMD events with b $\leq$ 3 fm. The above results are applied CBWC except for the one (blue crosses) using b $\leq$3 fm events.

Proton cumulants up to sixth order in $\sqrt{s_{\rm NN}}$ = 3 GeV Au+Au collisions. Data without volume fluctuation correction is shown as grey open squares while data with volume fluctuation correction using $N_{\rm part}$ distributions from Glauber and UrQMD models are shown as black circles and black open triangles, respectively. The corresponding centrality binned cumulants are shown in blue squares, red circles, and orange triangles, respectively. Similarly to Fig. 6, the vertical dashed lines indicate the centrality classes.

Proton cumulants up to sixth order in $\sqrt{s_{\rm NN}}$ = 3 GeV Au+Au collisions. Data without volume fluctuation correction is shown as grey open squares while data with volume fluctuation correction using $N_{\rm part}$ distributions from Glauber and UrQMD models are shown as black circles and black open triangles, respectively. The corresponding centrality binned cumulants are shown in blue squares, red circles, and orange triangles, respectively. Similarly to Fig. 6, the vertical dashed lines indicate the centrality classes.

Proton cumulant ratios up to sixth order in $\sqrt{s_{\rm NN}}$ = 3 GeV Au+Au collisions. Data without volume fluctuation correction are shown as grey open squares while data with volume fluctuation correction using $N_{\rm part}$ distributions from Glauber and UrQMD models are shown as black circles and black open triangles, respectively. The corresponding centrality binned cumulants are shown in blue squares, red circles, and orange triangles, respectively. Similarly to Fig. 6, the vertical dashed lines indicate the centrality classes.

Proton cumulant ratios up to sixth order in $\sqrt{s_{\rm NN}}$ = 3 GeV Au+Au collisions. Data without volume fluctuation correction are shown as grey open squares while data with volume fluctuation correction using $N_{\rm part}$ distributions from Glauber and UrQMD models are shown as black circles and black open triangles, respectively. The corresponding centrality binned cumulants are shown in blue squares, red circles, and orange triangles, respectively. Similarly to Fig. 6, the vertical dashed lines indicate the centrality classes.

UrQMD results of proton cumulant ratios up to sixth order in Au+Au collisions at $\sqrt{s_{\rm NN}}$ = 3 GeV. The vertical dashed lines indicate the centrality classes.

Experimental results on centrality dependence of cumulants (left panels) and cumulant ratios (right panels) up to sixth order of the proton multiplicity distributions in Au+Au collisions at $N_{\rm part}$ = 3 GeV. The open squares are data without VF correction while red circles and blue triangles are results with VF correction with $N_{\rm part}$ distributions from Glauber and UrQMD models, respectively.

Experimental results on centrality dependence of cumulants (left panels) and cumulant ratios (right panels) up to sixth order of the proton multiplicity distributions in Au+Au collisions at $N_{\rm part}$ = 3 GeV. The open squares are data without VF correction while red circles and blue triangles are results with VF correction with $N_{\rm part}$ distributions from Glauber and UrQMD models, respectively.

Same as Fig. 14 but for correlation function (left panels) and their normalized ratios (right panels).

Same as Fig. 14 but for correlation function (left panels) and their normalized ratios (right panels).

Cumulants and cumulant ratios of proton multiplicity distributions for Au+Au collisions at $\sqrt{s_{\rm NN}}$ = 3 GeV. The transverse momentum window is $p_{\rm T}$ from $0.4<p_{\rm T}<2.0$ GeV/$c$ and the rapidity window is $−0.5<y<0$. Statistical and systematic uncertainties are represented by black and gray bars, respectively. UrQMD predictions are depicted by gold bands.

Cumulants and cumulant ratios of proton multiplicity distributions for Au+Au collisions at $\sqrt{s_{\rm NN}}$ = 3 GeV. The transverse momentum window is $p_{\rm T}$ from $0.4<p_{\rm T}<2.0$ GeV/$c$ and the rapidity window is $−0.5<y<0$. Statistical and systematic uncertainties are represented by black and gray bars, respectively. UrQMD predictions are depicted by gold bands.

Same as Fig. 16 but for correlation functions and correlation function ratios of proton multiplicity distributions for Au+Au collisions at $\sqrt{s_{\rm NN}}$ = 3 GeV.

Same as Fig. 16 but for correlation functions and correlation function ratios of proton multiplicity distributions for Au+Au collisions at $\sqrt{s_{\rm NN}}$ = 3 GeV.

The transverse-momentum and rapidity dependence of cumulant ratios of proton multiplicity distributions for Au+Au collisions at $\sqrt{s_{\rm NN}}$ = 3 GeV. In the left column, the $p_{\rm T}$ analysis window is $0.4<p_{\rm T}<2.0$ GeV/$c$ while the rapidity window is varied in the range $y_{\rm min}<y<0$. In the right column, the rapidit$y$ analysis window is $−0.5<y<0$ while the $p_{\rm T}$ is varied in the range $0.4<p_{\rm T}<p_{\rm T}^{\rm max}$ GeV/$c$. The most central (0–5%) and peripheral (50–60%) events are depicted by black squares and blue triangles, respectively. Statistical and systematic uncertainties are represented by black and gray bars, respectively. UrQMD simulations for the top 0–5% and 50–60% are shown by gold and blue bands, respectively.

The transverse-momentum and rapidity dependence of cumulant ratios of proton multiplicity distributions for Au+Au collisions at $\sqrt{s_{\rm NN}}$ = 3 GeV. In the left column, the $p_{\rm T}$ analysis window is $0.4<p_{\rm T}<2.0$ GeV/$c$ while the rapidity window is varied in the range $y_{\rm min}<y<0$. In the right column, the rapidit$y$ analysis window is $−0.5<y<0$ while the $p_{\rm T}$ is varied in the range $0.4<p_{\rm T}<p_{\rm T}^{\rm max}$ GeV/$c$. The most central (0–5%) and peripheral (50–60%) events are depicted by black squares and blue triangles, respectively. Statistical and systematic uncertainties are represented by black and gray bars, respectively. UrQMD simulations for the top 0–5% and 50–60% are shown by gold and blue bands, respectively.

The transverse-momentum and rapidity dependence of cumulant ratios of proton multiplicity distributions for Au+Au collisions at $\sqrt{s_{\rm NN}}$ = 3 GeV. In the left column, the $p_{\rm T}$ analysis window is $0.4<p_{\rm T}<2.0$ GeV/$c$ while the rapidity window is varied in the range $y_{\rm min}<y<0$. In the right column, the rapidit$y$ analysis window is $−0.5<y<0$ while the $p_{\rm T}$ is varied in the range $0.4<p_{\rm T}<p_{\rm T}^{\rm max}$ GeV/$c$. The most central (0–5%) and peripheral (50–60%) events are depicted by black squares and blue triangles, respectively. Statistical and systematic uncertainties are represented by black and gray bars, respectively. UrQMD simulations for the top 0–5% and 50–60% are shown by gold and blue bands, respectively.

The transverse-momentum and rapidity dependence of cumulant ratios of proton multiplicity distributions for Au+Au collisions at $\sqrt{s_{\rm NN}}$ = 3 GeV. In the left column, the $p_{\rm T}$ analysis window is $0.4<p_{\rm T}<2.0$ GeV/$c$ while the rapidity window is varied in the range $y_{\rm min}<y<0$. In the right column, the rapidit$y$ analysis window is $−0.5<y<0$ while the $p_{\rm T}$ is varied in the range $0.4<p_{\rm T}<p_{\rm T}^{\rm max}$ GeV/$c$. The most central (0–5%) and peripheral (50–60%) events are depicted by black squares and blue triangles, respectively. Statistical and systematic uncertainties are represented by black and gray bars, respectively. UrQMD simulations for the top 0–5% and 50–60% are shown by gold and blue bands, respectively.

As in Fig. 18 but for transverse-momentum and rapidity dependence of correlation function ratios of proton multiplicity distributions for Au+Au collisions at $\sqrt{s_{\rm NN}}$ = 3 GeV.

As in Fig. 18 but for transverse-momentum and rapidity dependence of correlation function ratios of proton multiplicity distributions for Au+Au collisions at $\sqrt{s_{\rm NN}}$ = 3 GeV.

As in Fig. 18 but for transverse-momentum and rapidity dependence of correlation function ratios of proton multiplicity distributions for Au+Au collisions at $\sqrt{s_{\rm NN}}$ = 3 GeV.

As in Fig. 18 but for transverse-momentum and rapidity dependence of correlation function ratios of proton multiplicity distributions for Au+Au collisions at $\sqrt{s_{\rm NN}}$ = 3 GeV.

Collision energy dependence of the cumulant ratios: $C_2/C_1=\sigma/M$, $C_3/C_2=S\sigma$, and $C_4/C_2=\kappa\sigma^2$, for protons (open squares) and net protons (red circles) from top 0–5% (top panels) and 50–60% (bottom panels) Au+Au collisions at RHIC. The points for protons are shifted horizontally for clarity. The new result for protons from $\sqrt{s_{\rm NN}}$ = 3 GeV Au+Au collisions is shown as a filled square. UrQMD results with $|y|<0.5$ for protons are shown as gold bands while those for net protons are shown as green dashed lines or green bands. At 3GeV, the model results for protons (−0.5) are shown as blue crosses. UrQMD results of proton and net-proton $C_4/C_2$, see right panels, are almost totally overlapped. The open cross is the result of the model with a fixed impact parameter $b < 3$ fm. The hydrodynamic calculations, for 5% central Au+Au collisions, for protons from $|y|<0.5$ are shown as dashed red linea and the result of the 3 GeV protons from $−0.5<y<0$ is shown as an open red star.

Collision energy dependence of the cumulant ratios: $C_2/C_1=\sigma/M$, $C_3/C_2=S\sigma$, and $C_4/C_2=\kappa\sigma^2$, for protons (open squares) and net protons (red circles) from top 0–5% (top panels) and 50–60% (bottom panels) Au+Au collisions at RHIC. The points for protons are shifted horizontally for clarity. The new result for protons from $\sqrt{s_{\rm NN}}$ = 3 GeV Au+Au collisions is shown as a filled square. UrQMD results with $|y|<0.5$ for protons are shown as gold bands while those for net protons are shown as green dashed lines or green bands. At 3GeV, the model results for protons (−0.5) are shown as blue crosses. UrQMD results of proton and net-proton $C_4/C_2$, see right panels, are almost totally overlapped. The open cross is the result of the model with a fixed impact parameter $b < 3$ fm. The hydrodynamic calculations, for 5% central Au+Au collisions, for protons from $|y|<0.5$ are shown as dashed red linea and the result of the 3 GeV protons from $−0.5<y<0$ is shown as an open red star.

Collision energy dependence of the cumulant ratios: $C_2/C_1=\sigma/M$, $C_3/C_2=S\sigma$, and $C_4/C_2=\kappa\sigma^2$, for protons (open squares) and net protons (red circles) from top 0–5% (top panels) and 50–60% (bottom panels) Au+Au collisions at RHIC. The points for protons are shifted horizontally for clarity. The new result for protons from $\sqrt{s_{\rm NN}}$ = 3 GeV Au+Au collisions is shown as a filled square. UrQMD results with $|y|<0.5$ for protons are shown as gold bands while those for net protons are shown as green dashed lines or green bands. At 3GeV, the model results for protons (−0.5) are shown as blue crosses. UrQMD results of proton and net-proton $C_4/C_2$, see right panels, are almost totally overlapped. The open cross is the result of the model with a fixed impact parameter $b < 3$ fm. The hydrodynamic calculations, for 5% central Au+Au collisions, for protons from $|y|<0.5$ are shown as dashed red linea and the result of the 3 GeV protons from $−0.5<y<0$ is shown as an open red star.

Collision energy dependence of the cumulant ratios: $C_2/C_1=\sigma/M$, $C_3/C_2=S\sigma$, and $C_4/C_2=\kappa\sigma^2$, for protons (open squares) and net protons (red circles) from top 0–5% (top panels) and 50–60% (bottom panels) Au+Au collisions at RHIC. The points for protons are shifted horizontally for clarity. The new result for protons from $\sqrt{s_{\rm NN}}$ = 3 GeV Au+Au collisions is shown as a filled square. UrQMD results with $|y|<0.5$ for protons are shown as gold bands while those for net protons are shown as green dashed lines or green bands. At 3GeV, the model results for protons (−0.5) are shown as blue crosses. UrQMD results of proton and net-proton $C_4/C_2$, see right panels, are almost totally overlapped. The open cross is the result of the model with a fixed impact parameter $b < 3$ fm. The hydrodynamic calculations, for 5% central Au+Au collisions, for protons from $|y|<0.5$ are shown as dashed red linea and the result of the 3 GeV protons from $−0.5<y<0$ is shown as an open red star.

Collision energy dependence of the cumulant ratios: $C_2/C_1=\sigma/M$, $C_3/C_2=S\sigma$, and $C_4/C_2=\kappa\sigma^2$, for protons (open squares) and net protons (red circles) from top 0–5% (top panels) and 50–60% (bottom panels) Au+Au collisions at RHIC. The points for protons are shifted horizontally for clarity. The new result for protons from $\sqrt{s_{\rm NN}}$ = 3 GeV Au+Au collisions is shown as a filled square. UrQMD results with $|y|<0.5$ for protons are shown as gold bands while those for net protons are shown as green dashed lines or green bands. At 3GeV, the model results for protons (−0.5) are shown as blue crosses. UrQMD results of proton and net-proton $C_4/C_2$, see right panels, are almost totally overlapped. The open cross is the result of the model with a fixed impact parameter $b < 3$ fm. The hydrodynamic calculations, for 5% central Au+Au collisions, for protons from $|y|<0.5$ are shown as dashed red linea and the result of the 3 GeV protons from $−0.5<y<0$ is shown as an open red star.

Collision energy dependence of the cumulant ratios: $C_2/C_1=\sigma/M$, $C_3/C_2=S\sigma$, and $C_4/C_2=\kappa\sigma^2$, for protons (open squares) and net protons (red circles) from top 0–5% (top panels) and 50–60% (bottom panels) Au+Au collisions at RHIC. The points for protons are shifted horizontally for clarity. The new result for protons from $\sqrt{s_{\rm NN}}$ = 3 GeV Au+Au collisions is shown as a filled square. UrQMD results with $|y|<0.5$ for protons are shown as gold bands while those for net protons are shown as green dashed lines or green bands. At 3GeV, the model results for protons (−0.5) are shown as blue crosses. UrQMD results of proton and net-proton $C_4/C_2$, see right panels, are almost totally overlapped. The open cross is the result of the model with a fixed impact parameter $b < 3$ fm. The hydrodynamic calculations, for 5% central Au+Au collisions, for protons from $|y|<0.5$ are shown as dashed red linea and the result of the 3 GeV protons from $−0.5<y<0$ is shown as an open red star.