Expected and observed 95% CL upper limits on the branching ratio of the Higgs boson decay to $Za$ times the branching ratio $a $->$ \gamma \gamma$ as a function of the $a$ particle mass in the merged ($m_a \le 2$ GeV) and the resolved ($m_a > 2$ GeV) categories. The figure uses $pp$ collision data at $\sqrt{s}=13$ TeV corresponding to 139 fb$^{-1}$.

ATLAS observed 95% CL exclusion contours limits in terms of the ALP mass and its effective coupling to photons, $|C_{\gamma\gamma}|/\Lambda$, for different values of the Higgs coupling to $Za$, $|C_{Zh}|/\Lambda$. The figure uses $pp$ collision data at $\sqrt{s}=13$ TeV corresponding to 139 fb$^{-1}$. The value 100 in the tables is presentational, denoting the upper edge of the plot.

Upper limits on $\mathcal{B}(H\rightarrow aa\rightarrow 4\gamma)$ at 95% CL as a function of the axion mass and for ALP-photon coupling $C_{a\gamma\gamma}=0.01$.

Upper limits on $\mathcal{B}(H\rightarrow aa\rightarrow 4\gamma)$ at 95% CL as a function of the axion mass and for ALP-photon coupling $C_{a\gamma\gamma}=5\times10^{-4}$

Upper limits on $\mathcal{B}(H\rightarrow aa\rightarrow 4\gamma)$ at 95% CL as a function of the axion mass and for ALP-photon coupling $C_{a\gamma\gamma}=10^{-5}$

Upper limits on $B(H\rightarrow 4\gamma)$ at 95% CL as a function of the signal mass hypothesis and for the assumption of promptly decaying ALPs.

Identification efficiency for isolated photons that pass the tight photon ID requirements in dependence of the opening angle in $\Delta R$ of both decay photons of the axion and the decay radius of the originating axion from the primary vertex for axions with masses between 100 MeV and 300 MeV. All four axion decay photons on MC truth level are required to fulfil $|\eta|<2.5$ and $p_T>5$ GeV. Only a mild dependency on the decay radius can be seen, since the distance between the two photons is small and hence the combined decay signature in the calorimeter still points to the primary vertex.

Efficiency for classified merged isolated photons in dependence of the opening angle in $\Delta R$ of both decay photons of the axion and the decay radius of the originating axion from the primary vertex for axions with masses between 100 MeV and 300 MeV. All four axion decay photons on MC truth level are required to fulfil $|\eta|<2.5$ and $p_T>5$ GeV. Only a mild dependency on the decay radius can be seen, since the distance between the two photons is small and hence the combined decay signature in the calorimeter still points to the primary vertex.

Limits on the ALP mass and coupling to photons at 95\%~CL, assuming $\mathcal{B}(a\rightarrow\gamma\gamma) = 1$, $\Lambda = 1\,TeV$ with $|C_{aH}^{\text{eff}}|$ = $1$ (solid line) and $|C_{aH}^{\text{eff}}|$ = $0.1$.

The number of data and estimated background events in the signal region of the most sensitive categories..

Bayesian upper exclusion limits on the ratio $g_{W'}/g_{W}$ for an SSM-like W$\prime$ boson are shown. The unity coupling ratio (blue dotted curve) corresponds to the SSM common benchmark. The 68 and 95% quantiles of the limits are represented by the green and yellow bands, respectively.

Bayesian lower exclusion limits on the NUGIM G(221) mixing angle $\cot(\theta_{E})$ are shown as a function of the W$\prime$ boson mass. The theoretically excluded region is shaded in grey. The 68 and 95% quantiles of the limits are represented by the green and yellow bands, respectively.

Bayesian upper exclusion limits at 95% CL on the product of the production cross section and branching fraction of a QBH in an associated $ au$ lepton and neutrino final state. Minimum threshold masses $m_{th}$ of up to 6.6 TeV are excluded at 95% CL. The observed limit (solid line) is obtained from the intersection with the LO QBH cross section (blue dotted curve). The 68 and 95% quantiles of the limits are represented by the green and yellow bands, respectively.

Bayesian upper limits at 95% CL on the cross section of the process $pp\rightarrow\tau\nu$ mediated via LQ exchange in the t-channel. The inner (green) band and the outer (yellow) band indicate the regions containing 68 and 95%, respectively, of the distribution of limits expected under the background-only hypothesis. The predicted LQ cross section at LO in the three coupling benchmark scenarios is depicted in different colors for $g_{U}=1$. The uncertainty bandy correspond to the sum in quadrature of PDF and scale variations. The first benchmark scenario considers only couplings to left-handed SM fermions (i.e. $\beta_{\text{R}}^{ij}=0$) and is referred to as "best fit LH". The second benchmark, referred to as "best fit LH+RH", considers $|\beta_{\text{R}}^{\text{b}\tau}|=1$ and all other $\beta_{\text{R}}^{ij}=0$. In the third "democratic" benchmark, equal couplings only to LH fermions are assumed, i.e. $\beta_{\text{L}}^{ij}=1$ and $\beta_{\text{R}}^{ij}=0$ for all $i$ and $j$.

Expected and observed lower limits of the LQ mass as a function of the coupling $g_{U}$ in the LH scenario. The blue band shows the 68% and 95% regions of $g_{U}$ preferred by the fit to the b anomalies data.

Expected and observed lower limits of the LQ mass as a function of the coupling $g_{U}$ in the LH+RH scenario. The blue band shows the 68% and 95% regions of $g_{U}$ preferred by the fit to the b anomalies data.

Expected and observed lower limits of the LQ mass as a function of the coupling $g_{U}$ in the democratic scenario. The blue band shows the 68% and 95% regions of $g_{U}$ preferred by the fit to the b anomalies data.

Bayesian upper exclusion limits at 95% CL on each of the Wilson coefficients described by the EFT model based on 2016-2018 data. The three different coupling types represent a left-handed vector coupling ($\epsilon^{cb}_{L}$), tensor-like coupling ($\epsilon^{cb}_{T}$), and scalar-tensor-like coupling ($\epsilon^{cb}_{S_{L}}$). The 68 and 95% quantiles of the limits are represented by the green and yellow bands, respectively.

Summary of exclusion limits (expected and observed) calculated at 95% CL for full Run-2 CMS data.

Background prediction and observed data yields in the signal region bins. The background yields are obtained from the background-only fit and serve as input to the simplified likelihood reinterpretation scheme. The naming of the bins is "year_binnumber", following the binning from Figure 4.

Matrix of covariance coefficients between signal region bins. The coefficients are obtained from the background-only fit and serve as input to the simplified likelihood reinterpretation scheme. The naming of the bins is "year_binnumber", following the binning used in Figure 4.

Predicted signal yields for the 2017 data-taking period, corresponding to 41.3 fb$^{-1}$, after the application of each search requirement (cumulative) for various signal hypothesis. The requirements listed are presented as total efficiencies w.r.t. the previous selection step.

Expected (dashed line) value of $-2\ln\Lambda$ as a function of $\kappa_{2V}$, when all other coupling modifiers are fixed to their SM predictions.

Likelihood observed contours at 68% CL (solid line) and 95% CL (dashed line) in the $\kappa_{\lambda}$, $\kappa_{2V}$ parameter space, when all other coupling modifiers are fixed to their SM predictions. The best-fit value, denoted by a cross in the plot, corresponds to the very first entry in the table.

Likelihood expected contours at 68% CL (teal shaded region) and 95% CL (yellow shaded region) in the $\kappa_{\lambda}$, $\kappa_{2V}$ parameter space, when all other coupling modifiers are fixed to their SM predictions.In the plot, the SM prediction is indicated by the star.

Likelihood observed contours at 68% CL (solid line) and 95% CL (dashed line) in the $c_{gghh}$ versus $c_{hhh}$ HEFT parameter space, with the remaining coefficient fixed to its SM value. The best-fit value, denoted by a cross in the plot, corresponds to the very first entry in the table.

Likelihood expected contours at 68% CL (teal shaded region) 95% CL (yellow shaded region) in the $c_{gghh}$ versus $c_{hhh}$ HEFT parameter space, with the remaining coefficient fixed to its SM value. In the plot, the SM prediction is indicated by the star.

Likelihood observed contours at 68% CL (solid line) and 95% CL (dashed line) in the $c_{tthh}$ versus $c_{hhh}$ HEFT parameter space, with the remaining coefficient fixed to its SM value. The best-fit value, denoted by a cross in the plot, corresponds to the very first entry in the table.

Likelihood exptected contours at 68% CL (teal shaded region) and 95% CL (yellow shaded region) in the $c_{tthh}$ versus $c_{hhh}$ HEFT parameter space, with the remaining coefficient fixed to its SM value. In the plot, the SM prediction is indicated by the star.

The observed (filled circles) and expected (hollow circles) 95% CL upper limits on the $HH$ ggF production cross-section in the Standard Model and for seven HEFT benchmark points. The teal and yellow colored bands indicate the $\pm 1\sigma$ and $\pm 2\sigma$ variations on the expected limit due to statistical and systematic uncertainties. The predicted cross-sections of each of the models under consideration are shown by the red crosses. The contribution from VBF production to the total $HH$ production cross-section is neglected.

Likelihood observed contours at 68% CL (solid line) and 95% CL (dashed line) in the $c_{{H}\boxed{}}$ versus $c_{H}$ SMEFT parameter space, with the remaining coefficient fixed to its SM value. The best-fit value, denoted by a cross in the plot, corresponds to the very first entry in the table.

Likelihood expected contours at 68% CL (teal shaded region) 95% CL (yellow shaded region) in the $c_{{H}\boxed{}}$ versus $c_{H}$ SMEFT parameter space, with the remaining coefficient fixed to its SM value. In the plot, the SM prediction is indicated by the star.

The acceptance times efficiency for the signal ggF $HH$ process as a function of the coupling modifier $\kappa_{\lambda}$ in each analysis category. The other coupling modifiers affecting ggF $HH$ production are fixed to their SM predictions. The bands indicate the simulation statistical uncertainty.

The acceptance times efficiency for the signal VBF $HH$ process as a function of the coupling modifier $\kappa_{\lambda}$ in each analysis category. When varying $\kappa_{\lambda}$, the other coupling modifiers affecting the VBF $HH$ production mode are set to their SM predictions. The bands indicate the simulation statistical uncertainty.

The acceptance times efficiency for the signal VBF $HH$ process as a function of the coupling modifier $\kappa_{2V}$ in each analysis category. When varying $\kappa_{2V}$, the other coupling modifiers affecting the VBF $HH$ production mode are set to their SM predictions. The bands indicate the simulation statistical uncertainty.

Expected yields of the signal $HH$ process as a function of the coupling modifier $\kappa_{\lambda}$ after applying the analysis preselection and in each analysis category after the final selection. The $HH$ yield is obtained considering both the $ggF$ and $VBF$ contributions. The other coupling modifiers affecting $HH$ production are fixed to their SM predictions. The bands indicate the simulation statistical uncertainty.

The acceptance times efficiency for the signal ggF $HH$ process in each analysis category as a function of the $c_{hhh}$ HEFT coefficients. The dashed lines denote values that are excluded at 95% CL. The bottom panels show the efficiency of the sum of all analysis categories.

The acceptance times efficiency for the signal ggF $HH$ process in each analysis category as a function of the $c_{tthh}$ HEFT coefficients. The dashed lines denote values that are excluded at 95% CL. The bottom panels show the efficiency of the sum of all analysis categories.

The acceptance times efficiency for the signal ggF $HH$ process in each analysis category as a function of the $c_{gghh}$ HEFT coefficients. The dashed lines denote values that are excluded at 95% CL. The bottom panels show the efficiency of the sum of all analysis categories.

The acceptance times efficiency for the signal ggF $HH$ process in each analysis category as a function of the $c_{H}$ SMEFT coefficients. The dashed lines denote values that are excluded at 95% CL. The bottom panels show the efficiency of the sum of all analysis categories.

The acceptance times efficiency for the signal ggF $HH$ process in each analysis category as a function of the $c_{{H}\boxed{}}$ SMEFT coefficients. The dashed lines denote values that are excluded at 95% CL. The bottom panels show the efficiency of the sum of all analysis categories.

The yield of the signal ggF $HH$ process in each analysis category as a function of the $c_{hhh}$ HEFT coefficients. The dashed lines denote values that are excluded at 95% CL. The bottom panels show the efficiency of the sum of all analysis categories.

The yield of the signal ggF $HH$ process in each analysis category as a function of the $c_{tthh}$ HEFT coefficients. The dashed lines denote values that are excluded at 95% CL. The bottom panels show the efficiency of the sum of all analysis categories.

The yield of the signal ggF $HH$ process in each analysis category as a function of the $c_{gghh}$ HEFT coefficients. The dashed lines denote values that are excluded at 95% CL. The bottom panels show the efficiency of the sum of all analysis categories.

The yield of the signal ggF $HH$ process in each analysis category as a function of the $c_{H}$ SMEFT coefficients. The dashed lines denote values that are excluded at 95% CL. The bottom panels show the efficiency of the sum of all analysis categories.

The yield of the signal ggF $HH$ process in each analysis category as a function of the $c_{{H}\boxed{}}$ SMEFT coefficients. The dashed lines denote values that are excluded at 95% CL. The bottom panels show the efficiency of the sum of all analysis categories.

Distributions of the diphoton invariant mass for events in data (black dots with error bars) compared to the sum of the expected signal and backgrounds (histograms) in the low mass 1 region.

Distributions of the diphoton invariant mass for events in data (black dots with error bars) compared to the sum of the expected signal and backgrounds (histograms) in the low mass 2 region.

Distributions of the diphoton invariant mass for events in data (black dots with error bars) compared to the sum of the expected signal and backgrounds (histograms) in the low mass 3 region.

Distributions of the diphoton invariant mass for events in data (black dots with error bars) compared to the sum of the expected signal and backgrounds (histograms) in the low mass 4 region.

Distributions of the diphoton invariant mass for events in data (black dots with error bars) compared to the sum of the expected signal and backgrounds (histograms) in the high mass 1 region.

Distributions of the diphoton invariant mass for events in data (black dots with error bars) compared to the sum of the expected signal and backgrounds (histograms) in the high mass 2 region.

Distributions of the diphoton invariant mass for events in data (black dots with error bars) compared to the sum of the expected signal and backgrounds (histograms) in the high mass 3 region.

Observed (solid line) value of $-2\ln\Lambda$ as a function of the $c_{hhh}$ HEFT coefficients when all other coupling modifiers are fixed to the SM value

Expected (dashed line) value of $-2\ln\Lambda$ as a function of the $c_{hhh}$ HEFT coefficients when all other coupling modifiers are fixed to the SM value

Observed (solid line) value of $-2\ln\Lambda$ as a function of the $c_{gghh}$ HEFT coefficients when all other coupling modifiers are fixed to the SM value

Expected (dashed line) value of $-2\ln\Lambda$ as a function of the $c_{gghh}$ HEFT coefficients when all other coupling modifiers are fixed to the SM value

Observed (solid line) value of $-2\ln\Lambda$ as a function of the $c_{tthh}$ HEFT coefficients when all other coupling modifiers are fixed to the SM value

Expected (dashed line) value of $-2\ln\Lambda$ as a function of the $c_{tthh}$ HEFT coefficients when all other coupling modifiers are fixed to the SM value

Observed (solid line) value of $-2\ln\Lambda$ as a function of the $c_{H}$ SMEFT coefficients when all other coupling modifiers are fixed to the SM value.

Expected (dashed line) value of $-2\ln\Lambda$ as a function of the $c_{H}$ SMEFT coefficients when all other coupling modifiers are fixed to the SM value.

Observed (solid line) value of $-2\ln\Lambda$ as a function of the $c_{{H}\boxed{}}$ SMEFT coefficients when all other coupling modifiers are fixed to the SM value.

Expected (dashed line) value of $-2\ln\Lambda$ as a function of the $c_{{H}\boxed{}}$ SMEFT coefficients when all other coupling modifiers are fixed to the SM value.

Summary of the expected (blue) and observed (orange) one-dimensional constraints at 68% (solid error bars) and 95% (dashed error bars) CL on the coefficients of selected HEFT (top) and SMEFT (bottom) operators describing Higgs boson interactions affecting $HH$ production through gluon--gluon fusion. The results are obtained from one dimensional scans of the profile log-likelihood assuming that all other Wilson coefficients are fixed to their SM values. The contribution from VBF $HH$ production is neglected.

Covariance matrix for the extrapolation uncertainty for the measurement of the absolute differential cross section as a function of the rho observable at parton level.

Normalized differential cross section as a function of the rho observable at parton level.

Covariance matrix for the total uncertainty (i.e. fit including stat., not extrapolation) for the measurement of the normalized differential cross section as a function of the rho observable at parton level.

Covariance matrix for the statistical uncertainty for the measurement of the normalized differential cross section as a function of the rho observable at parton level.

Covariance matrix for the extrapolation uncertainty for the measurement of the normalized differential cross section as a function of the rho observable at parton level.

Correlation matrix for all nuisance parameters and parameters of interest of the Likelihood fit.

This table is a numerical representation of Fig. 8 for all nuisance parameters.

Summary of observed and expected background yields in the SR after the likelihood fit under the background-only hypothesis.

Centrality dependence of (a) $v_2${2} and (b) $v_2${4}. (a) The red points indicate no pseudorapidity gap whereas the magenta points indicate a pseudorapidity gap of |$\Delta\eta$| > 2.0. (b) The black points indicate $v_2${4} with no pseudorapidity gap, the blue points indicate a two-subevent method with |$\Delta\eta$| > 2.0 but where some short-range pairs are allowed, and the red points indicate a two-subevent method with |$\Delta\eta$| > 2.0 where no short-range pairs are allowed.

Centrality dependence of (a) $v_2${2} and (b) $v_2${4}. (a) The red points indicate no pseudorapidity gap whereas the magenta points indicate a pseudorapidity gap of |$\Delta\eta$| > 2.0. (b) The black points indicate $v_2${4} with no pseudorapidity gap, the blue points indicate a two-subevent method with |$\Delta\eta$| > 2.0 but where some short-range pairs are allowed, and the red points indicate a two-subevent method with |$\Delta\eta$| > 2.0 where no short-range pairs are allowed.

Multi-particle $v_2$ as a function of centrality in Au+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV. The magenta open diamonds indicate the $v_2${SP }, the blue open squares indicate $v_2${4}, the black open circles indicate $v_2${6}, and the green filled diamonds indicate $v_2${8}.

Multi-particle $v_2$ as a function of centrality in Au+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV. The magenta open diamonds indicate the $v_2${SP }, the blue open squares indicate $v_2${4}, the black open circles indicate $v_2${6}, and the green filled diamonds indicate $v_2${8}.

Multi-particle $v_2$ as a function of centrality in Au+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV. The magenta open diamonds indicate the $v_2${SP }, the blue open squares indicate $v_2${4}, the black open circles indicate $v_2${6}, and the green filled diamonds indicate $v_2${8}.

Multi-particle $v_2$ as a function of centrality in Au+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV. The magenta open diamonds indicate the $v_2${SP }, the blue open squares indicate $v_2${4}, the black open circles indicate $v_2${6}, and the green filled diamonds indicate $v_2${8}.

Cumulant method estimate of $\sigma_{v_{2}}$ / $\langle v_{2} \rangle$ as a function of centrality in Au+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV. The data are shown as black open squares. The same calculation as done in data is done in ampt, shown as a solid green line. Calculations of $\sigma_{\epsilon_{2}}$ /$ \langle\epsilon_{2}\rangle$ performed in the Monte Carlo Glauber model are shown as blue lines. The solid blue line is the Monte Carlo Glauber calculation done using the same estimate as the data, the dashed blue line is the direct calculation of the moments of the MC Glauber $\epsilon_{2}$ distribution.

Centrality dependence of $v_3${2, |$\Delta\eta$| > 2} in Au+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV, shown as magenta diamonds. The systematic uncertainty is indicated as a shaded magenta band. Also shown as black squares are $\sqrt{\langle v^{2}_{3}\rangle}$ as determined from the folding analysis, which is shown in the next section.

Centrality dependence of $v_3${2, |$\Delta\eta$| > 2} in Au+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV, shown as magenta diamonds. The systematic uncertainty is indicated as a shaded magenta band. Also shown as black squares are $\sqrt{\langle v^{2}_{3}\rangle}$ as determined from the folding analysis, which is shown in the next section.

Centrality dependence of $c_3${4} for Au+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV. (a) Calculations using both arms: $c_3${4} (black circles), $c_3${4}$_{ab|ab}$ (blue diamonds), $c_3${4}$_{aa|bb}$ (red squares), and comparison to STAR [36] (black stars). (b) Comparison of $c_3${4} determined using both arms (open symbols) and a single arm (closed symbols). Note that the open black circles are the same in (a) and (b).

Centrality dependence of $c_3${4} for Au+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV. (a) Calculations using both arms: $c_3${4} (black circles), $c_3${4}$_{ab|ab}$ (blue diamonds), $c_3${4}$_{aa|bb}$ (red squares), and comparison to STAR [36] (black stars). (b) Comparison of $c_3${4} determined using both arms (open symbols) and a single arm (closed symbols). Note that the open black circles are the same in (a) and (b).

Centrality dependence of $c_3${4} for Au+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV. (a) Calculations using both arms: $c_3${4} (black circles), $c_3${4}$_{ab|ab}$ (blue diamonds), $c_3${4}$_{aa|bb}$ (red squares), and comparison to STAR [36] (black stars). (b) Comparison of $c_3${4} determined using both arms (open symbols) and a single arm (closed symbols). Note that the open black circles are the same in (a) and (b).

Folding results for (a) $v_2$, (b) $\sigma_{v_{2}}$ , and (c) $\sigma_{v_{2}}$ / $\langle v_{2}\rangle$. The black lines above and below the points indicate the systematic uncertainties. The red (green) boxes indicate the statistical uncertainties at the 68.27% (95.45%) confidence level. In the case of $\langle v_{2}\rangle$, the statistical uncertainties at the 68.27% confidence level are too small to be seen, and the uncertainties at the 95.45% confidence level are visible but noticeably smaller than the marker size. Shown as blue squares are the same quantities as determined using the cumulant based calculation—these points are slightly offset in the x-coordinate to improve visibility.

Folding results for (a) $v_2$, (b) $\sigma_{v_{2}}$ , and (c) $\sigma_{v_{2}}$ / $\langle v_{2}\rangle$. The black lines above and below the points indicate the systematic uncertainties. The red (green) boxes indicate the statistical uncertainties at the 68.27% (95.45%) confidence level. In the case of $\langle v_{2}\rangle$, the statistical uncertainties at the 68.27% confidence level are too small to be seen, and the uncertainties at the 95.45% confidence level are visible but noticeably smaller than the marker size. Shown as blue squares are the same quantities as determined using the cumulant based calculation—these points are slightly offset in the x-coordinate to improve visibility.

Folding results for (a) $v_2$, (b) $\sigma_{v_{2}}$ , and (c) $\sigma_{v_{2}}$ / $\langle v_{2}\rangle$. The black lines above and below the points indicate the systematic uncertainties. The red (green) boxes indicate the statistical uncertainties at the 68.27% (95.45%) confidence level. In the case of $\langle v_{2}\rangle$, the statistical uncertainties at the 68.27% confidence level are too small to be seen, and the uncertainties at the 95.45% confidence level are visible but noticeably smaller than the marker size. Shown as blue squares are the same quantities as determined using the cumulant based calculation—these points are slightly offset in the x-coordinate to improve visibility.

Folding results for (a) $\langle v_{3}\rangle$, (b) $\sigma_{v_{3}}$ , and (c) $\sigma_{v_{3}}$ /$\langle v_{3}\rangle$. The black lines above and below the points indicate the systematic uncertainties. The red (green) boxes indicate the statistical uncertainties at the 68.27% (95.45%) confidence level. The $\sigma_{v_{3}}$ /$\langle v_{3}\rangle$ values are all ≈ 0.52, the apparent limiting value of this quantity for the Bessel-Gaussian distribution.

Folding results for (a) $\langle v_{3}\rangle$, (b) $\sigma_{v_{3}}$ , and (c) $\sigma_{v_{3}}$ /$\langle v_{3}\rangle$. The black lines above and below the points indicate the systematic uncertainties. The red (green) boxes indicate the statistical uncertainties at the 68.27% (95.45%) confidence level. The $\sigma_{v_{3}}$ /$\langle v_{3}\rangle$ values are all ≈ 0.52, the apparent limiting value of this quantity for the Bessel-Gaussian distribution.

Folding results for (a) $\langle v_{3}\rangle$, (b) $\sigma_{v_{3}}$ , and (c) $\sigma_{v_{3}}$ /$\langle v_{3}\rangle$. The black lines above and below the points indicate the systematic uncertainties. The red (green) boxes indicate the statistical uncertainties at the 68.27% (95.45%) confidence level. The $\sigma_{v_{3}}$ /$\langle v_{3}\rangle$ values are all ≈ 0.52, the apparent limiting value of this quantity for the Bessel-Gaussian distribution.

$v_2$ for inclusive charged hadrons in Au+Au at $\sqrt{s_{NN}}$ = 200 GeV.

$v_2$ for inclusive charged hadrons in Au+Au at $\sqrt{s_{NN}}$ = 200 GeV.

$v_2$ for inclusive charged hadrons in Au+Au at $\sqrt{s_{NN}}$ = 200 GeV.

$v_2$ for inclusive charged hadrons in Au+Au at $\sqrt{s_{NN}}$ = 200 GeV.

$v_2$ for inclusive charged hadrons in Au+Au at $\sqrt{s_{NN}}$ = 200 GeV.

$v_2$ for inclusive charged hadrons in Au+Au at $\sqrt{s_{NN}}$ = 62.4 GeV.

$v_2$ for inclusive charged hadrons in Au+Au at $\sqrt{s_{NN}}$ = 62.4 GeV.

$v_2$ for inclusive charged hadrons in Cu+Cu at $\sqrt{s_{NN}}$ = 62.4 GeV compared with 200 GeV.

$v_2$ for inclusive charged hadrons in Cu+Cu at $\sqrt{s_{NN}}$ = 62.4 GeV compared with 200 GeV.

$v_2$ for inclusive charged hadrons in Cu+Cu at $\sqrt{s_{NN}}$ = 62.4 GeV compared with 200 GeV.

Comparison of integrated $v_2$ at $\sqrt{s_{NN}}$ = 62.4 and 200 GeV. Au+Au reaction.

Comparison of integrated $v_2$ at $\sqrt{s_{NN}}$ = 62.4 and 200 GeV. Au+Au reaction.

Comparison of integrated $v_2$ at $\sqrt{s_{NN}}$ = 62.4 and 200 GeV. Cu+Cu reaction.

Comparison of integrated $v_2$ at $\sqrt{s_{NN}}$ = 62.4 and 200 GeV. Cu+Cu reaction.

The comparison of integrated $v_2$ as a function of centrality.

The comparison of the normalized $v_2$/$\epsilon$ vs. centrality.

The comparison of integrated $v_2$ as a function of centrality.

The comparison of the normalized $v_2$/$\epsilon$ vs. centrality.

The comparison of integrated $v_2$ as a function of centrality.

The comparison of the normalized $v_2$/$\epsilon$ vs. centrality.

The comparison of integrated $v_2$ as a function of centrality.

The comparison of the normalized $v_2$/$\epsilon$ vs. centrality.

Comparison of $v_2$ ($p_T$) at 200 GeV for two example systems with different collision size.

Comparison of $v_2$ ($p_T$) at 200 GeV for two example systems with different collision size.

Comparison of $v_2$ ($p_T$) at 200 GeV for two example systems with different collision size.

$v_2$ vs. $p_T$ for $\pi$/$K$/$p$ emitted from Au+Au at 62.4 and 200 GeV and Cu+Cu at 62.4 and 200 GeV for centralities given.

$v_2$ vs. $p_T$ for $\pi$/$K$/$p$ emitted from Au+Au at 62.4 and 200 GeV and Cu+Cu at 62.4 and 200 GeV for centralities given.

$v_2$ vs. $p_T$ for $\pi$/$K$/$p$ emitted from Au+Au at 62.4 and 200 GeV and Cu+Cu at 62.4 and 200 GeV for centralities given.

$v_2$ vs. $p_T$ for $\pi$/$K$/$p$ emitted from Au+Au at 62.4 and 200 GeV and Cu+Cu at 62.4 and 200 GeV for centralities given.

$v_2$ vs. $p_T$ for $\pi$/$K$/$p$ emitted from Au+Au at 62.4 and 200 GeV and Cu+Cu at 62.4 and 200 GeV for centralities given.

$v_2$ vs. $p_T$ for $\pi$/$K$/$p$ emitted from Au+Au at 62.4 and 200 GeV and Cu+Cu at 62.4 and 200 GeV for centralities given.

$v_2$ vs. $p_T$ for $\pi$/$K$/$p$ emitted from Au+Au at 62.4 and 200 GeV and Cu+Cu at 62.4 and 200 GeV for centralities given.

$v_2$ vs. $p_T$ for $\pi$/$K$/$p$ emitted from Au+Au at 62.4 and 200 GeV and Cu+Cu at 62.4 and 200 GeV for centralities given.

$v_2$ vs. $p_T$ for $\pi$/$K$/$p$ emitted from Au+Au at 62.4 and 200 GeV and Cu+Cu at 62.4 and 200 GeV for centralities given.

$v_2$ vs. $p_T$ for $\pi$/$K$/$p$ emitted from Au+Au at 62.4 and 200 GeV and Cu+Cu at 62.4 and 200 GeV for centralities given.

Comparison of $v_2$ between $\sqrt{s_{NN}}$ = 62.4 GeV and 200 GeV for $\pi$/$K$/$p$ emitted from central Au+Au collisions.

Comparison of $v_2$ between $\sqrt{s_{NN}}$ = 62.4 GeV and 200 GeV for $\pi$/$K$/$p$ emitted from central Au+Au collisions.

Comparison of $v_2$ between $\sqrt{s_{NN}}$ = 62.4 GeV and 200 GeV for $\pi$/$K$/$p$ emitted from central Au+Au collisions.

Comparison of $v_2$ between $\sqrt{s_{NN}}$ = 62.4 GeV and 200 GeV for $\pi$/$K$/$p$ emitted from central Au+Au collisions.

Comparison of $v_2$ between $\sqrt{s_{NN}}$ = 62.4 GeV and 200 GeV for $\pi$/$K$/$p$ emitted from central Au+Au collisions.

Comparison of $v_2$ between $\sqrt{s_{NN}}$ = 62.4 GeV and 200 GeV for $\pi$/$K$/$p$ emitted from central Au+Au collisions.

Comparison of $v_2$ between $\sqrt{s_{NN}}$ = 62.4 GeV and 200 GeV for $\pi$/$K$/$p$ emitted from central Au+Au collisions.

Comparison of the $v_2$ of particles, antiparticles, for a minimum bias sample at 200 GeV and central 62.4 GeV Au+Au collisions.

Comparison of the $v_2$ of particles, antiparticles, for a minimum bias sample at 200 GeV and central 62.4 GeV Au+Au collisions.

Comparison of the $v_2$ of particles, antiparticles, for a minimum bias sample at 200 GeV and central 62.4 GeV Au+Au collisions.

Comparison of the $v_2$ of particles, antiparticles, for a minimum bias sample at 200 GeV and central 62.4 GeV Au+Au collisions.

Comparison of the $v_2$ of particles, antiparticles, for a minimum bias sample at 200 GeV and central 62.4 GeV Au+Au collisions.

Comparison of the $v_2$ of particles, antiparticles, for a minimum bias sample at 200 GeV and central 62.4 GeV Au+Au collisions.

The ratio $v_2$/$n_q$ vs. $p_T$/$n_q$ for $\pi$/$K$/$p$ emitted from Au+Au at 62.4 and 200 GeV and Cu+Cu at 200 GeV collisions.

The ratio $v_2$/$n_q$ vs. $p_T$/$n_q$ for $\pi$/$K$/$p$ emitted from Au+Au at 62.4 and 200 GeV and Cu+Cu at 200 GeV collisions.

The ratio $v_2$/$n_q$ vs. $p_T$/$n_q$ for $\pi$/$K$/$p$ emitted from Au+Au at 62.4 and 200 GeV and Cu+Cu at 200 GeV collisions.

The ratio $v_2$/$n_q$ vs. $p_T$/$n_q$ for $\pi$/$K$/$p$ emitted from Au+Au at 62.4 and 200 GeV and Cu+Cu at 200 GeV collisions.

The ratio $v_2$/$n_q$ vs. $p_T$/$n_q$ for $\pi$/$K$/$p$ emitted from Au+Au at 62.4 and 200 GeV and Cu+Cu at 200 GeV collisions.

The ratio $v_2$/$n_q$ vs. $p_T$/$n_q$ for $\pi$/$K$/$p$ emitted from Au+Au at 62.4 and 200 GeV and Cu+Cu at 200 GeV collisions.

The ratio $v_2$/$n_q$ vs. $p_T$/$n_q$ for $\pi$/$K$/$p$ emitted from Au+Au at 62.4 and 200 GeV and Cu+Cu at 200 GeV collisions.

The ratio $v_2$/$n_q$ vs. $p_T$/$n_q$ for $\pi$/$K$/$p$ emitted from Au+Au at 62.4 and 200 GeV and Cu+Cu at 200 GeV collisions.

The ratio $v_2$/$n_q$ vs. $p_T$/$n_q$ for $\pi$/$K$/$p$ emitted from Au+Au at 62.4 and 200 GeV and Cu+Cu at 200 GeV collisions.

The ratio $v_2$/$n_q$ vs. $p_T$/$n_q$ for $\pi$/$K$/$p$ emitted from Au+Au at 62.4 and 200 GeV and Cu+Cu at 200 GeV collisions.

The ratio $v_2$/$n_q$ vs. ${KE}_T$/$n_q$ for $\pi$/$K$/$p$ emitted from Au+Au at 62.4 and 200 GeV and Cu+Cu at 200 GeV collisions.

The ratio $v_2$/$n_q$ vs. ${KE}_T$/$n_q$ for $\pi$/$K$/$p$ emitted from Au+Au at 62.4 and 200 GeV and Cu+Cu at 200 GeV collisions.

The ratio $v_2$/$n_q$ vs. ${KE}_T$/$n_q$ for $\pi$/$K$/$p$ emitted from Au+Au at 62.4 and 200 GeV and Cu+Cu at 200 GeV collisions.

The ratio $v_2$/$n_q$ vs. ${KE}_T$/$n_q$ for $\pi$/$K$/$p$ emitted from Au+Au at 62.4 and 200 GeV and Cu+Cu at 200 GeV collisions.

The ratio $v_2$/$n_q$ vs. ${KE}_T$/$n_q$ for $\pi$/$K$/$p$ emitted from Au+Au at 62.4 and 200 GeV and Cu+Cu at 200 GeV collisions.

The ratio $v_2$/$n_q$ vs. ${KE}_T$/$n_q$ for $\pi$/$K$/$p$ emitted from Au+Au at 62.4 and 200 GeV and Cu+Cu at 200 GeV collisions.

The ratio $v_2$/$n_q$ vs. ${KE}_T$/$n_q$ for $\pi$/$K$/$p$ emitted from Au+Au at 62.4 and 200 GeV and Cu+Cu at 200 GeV collisions.

The ratio $v_2$/$n_q$ vs. ${KE}_T$/$n_q$ for $\pi$/$K$/$p$ emitted from Au+Au at 62.4 and 200 GeV and Cu+Cu at 200 GeV collisions.

The ratio $v_2$/$n_q$ vs. ${KE}_T$/$n_q$ for $\pi$/$K$/$p$ emitted from Au+Au at 62.4 and 200 GeV and Cu+Cu at 200 GeV collisions.

The ratio $v_2$/$n_q$ vs. ${KE}_T$/$n_q$ for $\pi$/$K$/$p$ emitted from Au+Au at 62.4 and 200 GeV and Cu+Cu at 200 GeV collisions.

The ratio $v_2$/$n_q$ vs. ${KE}_T$/$n_q$ for the indicated hadrons emitted from central Au+Au collisions at 62.4 GeV.

The ratio $v_2$/$n_q$ vs. ${KE}_T$/$n_q$ for the indicated hadrons emitted from central Au+Au collisions at 62.4 GeV.

The ratio $v_2$/$n_q$ vs. ${KE}_T$/$n_q$ for the indicated hadrons emitted from central Au+Au collisions at 62.4 GeV.

$v_2$ vs. $p_T$ and $v_2$/($\epsilon * N^{1/3}_{part} * n_q$) vs. ${KE}_T$/$n_q$ for $\pi$/$K$/$p$ in Au+Au at 200 GeV, in Au+Au at 62.4 GeV, and in Cu+Cu at 200 GeV. The values of $v_2$ and $p_T$ in Au+Au at 200 GeV, in Au+Au at 62.4 GeV, and in Cu+Cu at 200 GeV are the same for as figure 14, and the values of $v_2$, $n_q$, and $KE_T$ in Au+Au at 200 GeV, in Au+Au at 62.4 GeV, and in Cu+Cu at 200 GeV are the same for as figure 18.