The figure shows the post-fit distribution of events as a function of $H_{\mathrm{T}}^{\ell,j} = \sum_{\ell,j} p_{T}^{\ell,j}$, scalar sum of $p_T$ for all jets and leptons in the $\ell+$jets channel, in proton-lead (p+Pb) collisions at a center-of-mass energy of $\sqrt{s_{\mathrm{NN}}} = 8.16$ TeV, with an integrated luminosity of 165 nb$^{-1}$. The data correspond to the $1\ell 1b$ $\mu$+jets channel in a pre-fit configuration. The stacked histograms represent different processes contributing to the event yield, including top quark pair production ($t\bar{t}$), single top, $W$ boson production with $b$, $c$, and light quarks, $Z$ boson production with $b$, $c$, and light quarks, diboson, and fake lepton backgrounds.

The figure shows the pre-fit distribution of events as a function of $H_{\mathrm{T}}^{\ell,j} = \sum_{\ell,j} p_{T}^{\ell,j}$, scalar sum of $p_T$ for all jets and leptons in the $\ell+$jets channel, in proton-lead (p+Pb) collisions at a center-of-mass energy of $\sqrt{s_{\mathrm{NN}}} = 8.16$ TeV, with an integrated luminosity of 165 nb$^{-1}$. The data correspond to the $1\ell 2bincl$ $e$+jets channel in a pre-fit configuration. The stacked histograms represent different processes contributing to the event yield, including top quark pair production ($t\bar{t}$), single top, $W$ boson production with $b$, $c$, and light quarks, $Z$ boson production with $b$, $c$, and light quarks, diboson, and fake lepton backgrounds.

The figure shows the post-fit distribution of events as a function of $H_{\mathrm{T}}^{\ell,j} = \sum_{\ell,j} p_{T}^{\ell,j}$, scalar sum of $p_T$ for all jets and leptons in the $\ell+$jets channel, in proton-lead (p+Pb) collisions at a center-of-mass energy of $\sqrt{s_{\mathrm{NN}}} = 8.16$ TeV, with an integrated luminosity of 165 nb$^{-1}$. The data correspond to the $1\ell 2bincl$ $e$+jets channel in a pre-fit configuration. The stacked histograms represent different processes contributing to the event yield, including top quark pair production ($t\bar{t}$), single top, $W$ boson production with $b$, $c$, and light quarks, $Z$ boson production with $b$, $c$, and light quarks, diboson, and fake lepton backgrounds.

The figure shows the pre-fit distribution of events as a function of $H_{\mathrm{T}}^{\ell,j} = \sum_{\ell,j} p_{T}^{\ell,j}$, scalar sum of $p_T$ for all jets and leptons in the $\ell+$jets channel, in proton-lead (p+Pb) collisions at a center-of-mass energy of $\sqrt{s_{\mathrm{NN}}} = 8.16$ TeV, with an integrated luminosity of 165 nb$^{-1}$. The data correspond to the $1\ell 2bincl$ $\mu$+jets channel in a pre-fit configuration. The stacked histograms represent different processes contributing to the event yield, including top quark pair production ($t\bar{t}$), single top, $W$ boson production with $b$, $c$, and light quarks, $Z$ boson production with $b$, $c$, and light quarks, diboson, and fake lepton backgrounds.

The figure shows the post-fit distribution of events as a function of $H_{\mathrm{T}}^{\ell,j} = \sum_{\ell,j} p_{T}^{\ell,j}$, scalar sum of $p_T$ for all jets and leptons in the $\ell+$jets channel, in proton-lead (p+Pb) collisions at a center-of-mass energy of $\sqrt{s_{\mathrm{NN}}} = 8.16$ TeV, with an integrated luminosity of 165 nb$^{-1}$. The data correspond to the $1\ell 2bincl$ $\mu$+jets channel in a pre-fit configuration. The stacked histograms represent different processes contributing to the event yield, including top quark pair production ($t\bar{t}$), single top, $W$ boson production with $b$, $c$, and light quarks, $Z$ boson production with $b$, $c$, and light quarks, diboson, and fake lepton backgrounds.

The figure shows the pre-fit distribution of events as a function of $H_{\mathrm{T}}^{\ell,j} = \sum_{\ell,j} p_{T}^{\ell,j}$, scalar sum of $p_T$ for all jets and leptons in the $\ell+$jets channel, in proton-lead (p+Pb) collisions at a center-of-mass energy of $\sqrt{s_{\mathrm{NN}}} = 8.16$ TeV, with an integrated luminosity of 165 nb\(^{-1}\) in the 2\(\ell\)1b signal region. The histogram represents the number of events per GeV, with the data points shown as black dots and their associated uncertainties. The stacked colored histograms indicate different processes: \(t\bar{t}\) (red), single top (orange), \(Z+b\) (dark blue), \(Z+c\) (medium blue), \(Z+\)light (light blue), diboson (gray), and fake lepton (purple). The hatched area represents the uncertainty in the predictions.

The figure shows the post-fit distribution of events as a function of $H_{\mathrm{T}}^{\ell,j} = \sum_{\ell,j} p_{T}^{\ell,j}$, scalar sum of $p_T$ for all jets and leptons in the $\ell+$jets channel, in proton-lead (p+Pb) collisions at a center-of-mass energy of $\sqrt{s_{\mathrm{NN}}} = 8.16$ TeV, with an integrated luminosity of 165 nb\(^{-1}\) in the 2\(\ell\)1b signal region. The histogram represents the number of events per GeV, with the data points shown as black dots and their associated uncertainties. The stacked colored histograms indicate different processes: \(t\bar{t}\) (red), single top (orange), \(Z+b\) (dark blue), \(Z+c\) (medium blue), \(Z+\)light (light blue), diboson (gray), and fake lepton (purple). The hatched area represents the uncertainty in the predictions.

The figure shows the pre-fit distribution of events as a function of $H_{\mathrm{T}}^{\ell,j} = \sum_{\ell,j} p_{T}^{\ell,j}$, scalar sum of $p_T$ for all jets and leptons in the $\ell+$jets channel, in proton-lead (p+Pb) collisions at a center-of-mass energy of $\sqrt{s_{\mathrm{NN}}} = 8.16$ TeV, with an integrated luminosity of 165 nb\(^{-1}\) in the 2\(\ell\)2bincl signal region. The histogram represents the number of events per GeV, with the data points shown as black dots and their associated uncertainties. The stacked colored histograms indicate different processes: \(t\bar{t}\) (red), single top (orange), \(Z+b\) (dark blue), \(Z+c\) (medium blue), \(Z+\)light (light blue), diboson (gray), and fake lepton (purple). The hatched area represents the uncertainty in the predictions.

The figure shows the post-fit distribution of events as a function of $H_{\mathrm{T}}^{\ell,j} = \sum_{\ell,j} p_{T}^{\ell,j}$, scalar sum of $p_T$ for all jets and leptons in the $\ell+$jets channel, in proton-lead (p+Pb) collisions at a center-of-mass energy of $\sqrt{s_{\mathrm{NN}}} = 8.16$ TeV, with an integrated luminosity of 165 nb\(^{-1}\) in the 2\(\ell\)2bincl signal region. The histogram represents the number of events per GeV, with the data points shown as black dots and their associated uncertainties. The stacked colored histograms indicate different processes: \(t\bar{t}\) (red), single top (orange), \(Z+b\) (dark blue), \(Z+c\) (medium blue), \(Z+\)light (light blue), diboson (gray), and fake lepton (purple). The hatched area represents the uncertainty in the predictions.

The correlation matrix of the fit parameters for the six combined regions, including the signal regions (electron+jets: 1-lepton 1-bjet and 1-lepton 2-bjet inclusive, muon+jets: 1-lepton 1-bjet and 1-lepton 2-bjet inclusive, dilepton: 2-lepton 1-bjet and 2-lepton 2-bjet inclusive) is shown.

The impact of systematic uncertainties on the fitted signal-strength parameter $\hat{\mu}$ for the combined (six signal regions ($e+$jets: $1\ell1b$ and $1\ell2b\mathrm{incl}$, $\mu+$jets: $1\ell1b$ and $1\ell2b\mathrm{incl}$, dilepton: $2\ell1b$ and $2\ell2b\mathrm{incl}$) fit of all channels. Only the 15 most significant systematic uncertainties are shown and listed in decreasing order of their impact on $\mu$ on the $y$-axis. The empty (filled) blue/cyan boxes correspond to the pre-fit (post-fit) impact on $\mu$, referring to the upper $x$-axis. The impact of each systematic uncertainty, $\Delta \mu$, is calculated by comparing the nominal best-fit value of $\mu$ with the result of the fit when fixing the corresponding nuisance parameter $\theta$ to its best-fit value $\hat{\theta}$ shifted by its pre-fit (post-fit) uncertainties $\hat{\theta} \pm \Delta \theta(\hat{\theta} \pm \Delta \hat{\theta})$. The black points, which refer to the lower $x$-axis, show the pulls of the fitted nuisance parameters, i.e., the deviations of the fitted parameters $\hat{\theta}$ from their nominal values $\theta_0$, normalized to their nominal uncertainties $\Delta \theta$. The black lines show the post-fit uncertainties of the nuisance parameters, relative to their nominal uncertainties, which are indicated by the dashed lines.

Breakdown of relative systematic uncertainties in the measured ${t\bar{t}}$ cross-section. The quoted uncertainties are obtained by repeating the fit with a group of nuisance parameters fixed to their fitted values and subtracting in quadrature the resulting total uncertainty from the uncertainty of the complete fit. However, the total uncertainty is not the quadratic sum of the grouped impacts, as this approach neglects the correlation among the different groups.

The signal strength $\mu_{t\bar{t}}$, defined as the ratio of the observed signal for the combined six signal regions ($e+$jets: $1\ell1b$ and $1\ell2b\mathrm{incl}$, $\mu+$jets: $1\ell1b$ and $1\ell2b\mathrm{incl}$, dilepton: $2\ell1b$ and $2\ell2b\mathrm{incl}$.) to the SM expectation with no nPDF effects included, is measured using a binned profile-likelihood method. The parameter $\mu_{t\bar{t}}$ is determined by the fit to the $H_{T}^{\ell,j}$ data distributions in the six signal regions, where the $H_{T}^{\ell,j}$ variable is defined as the scalar sum of the transverse momenta of the leptons and HI jets. Over all 9% uncertainties is observed

The figure shows the measurement of the top quark pair production cross-section, $\sigma_{t\bar{t}}$, in proton-lead (p+Pb) collisions at a center-of-mass energy of $\sqrt{s_{\mathrm{NN}}} = 8.16$ TeV, based on 165 nb$^{-1}$ of data. The central measured value is shown alongside theoretical predictions using various parton distribution functions (PDFs): MCFM TUJU21, MCFM nNNPDF30, MCFM nCTEQ15HQ, and MCFM EPPS21. The green and yellow bands represent the total and statistical uncertainties of the data, respectively. Additional measurements for comparison include the CMS result at 8.16 TeV for p+Pb collisions and an extrapolated ATLAS+CMS result for pp collisions at 8 TeV. Relevant references are indicated: PRL 119 (2017) 242001 and JHEP 07 (2023) 213.

The ATLAS measurement of \( R_{p\text{Pb}} \) as a function of the nuclear modification factor in proton-lead (\( p\) + Pb) collisions at a center-of-mass energy per nucleon pair \( \sqrt{s_{NN}} = 8.16 \) TeV, with an integrated luminosity of 165 nb\(^{-1}\). The black points represent theoretical predictions from various MCFM parton distribution functions (PDFs): TUJU21, nNNPDF30, nCTEQ15HQ, and EPPS21. The green band indicates the total uncertainty of the data, while the yellow band represents the statistical uncertainty. The dashed line at \( R_{p\text{Pb}} = 1 \) shows the expected value in the absence of nuclear modifications.

Fiducial differential cross section of the electroweak $W^\pm W^\pm jj$ production as a function of $N_{\mathrm{gap}\,\mathrm{jets}}$. The correlation of uncertainties of the measured cross section across bins is presented in Table 14.

Fiducial differential cross section of the electroweak $W^\pm W^\pm jj$ production as a function of $\xi_{\mathrm{j}3}$. The correlation of uncertainties of the measured cross section across bins is presented in Table 15.

Fiducial differential cross section of the inclusive $W^\pm W^\pm jj$ production as a function of $m_{\ell\ell}$. The correlation of uncertainties of the measured cross section across bins is presented in Table 16.

Fiducial differential cross section of the inclusive $W^\pm W^\pm jj$ production as a function of $m_{\mathrm{T}}$. The correlation of uncertainties of the measured cross section across bins is presented in Table 17.

Fiducial differential cross section of the inclusive $W^\pm W^\pm jj$ production as a function of $m_{\mathrm{jj}}$. The correlation of uncertainties of the measured cross section across bins is presented in Table 18.

Fiducial differential cross section of the inclusive $W^\pm W^\pm jj$ production as a function of $N_{\mathrm{gap}\,\mathrm{jets}}$. The correlation of uncertainties of the measured cross section across bins is presented in Table 19.

Fiducial differential cross section of the inclusive $W^\pm W^\pm jj$ production as a function of $\xi_{\mathrm{j}3}$. The correlation of uncertainties of the measured cross section across bins is presented in Table 20.

Observed correlations between the bins of the LH-unfolded cross section of the electroweak $W^\pm W^\pm jj$ production as a function of $m_{\ell\ell}$. See Table 1.

Observed correlations between the bins of the LH-unfolded cross section of the electroweak $W^\pm W^\pm jj$ production as a function of $m_{\mathrm{T}}$. See Table 2.

Observed correlations between the bins of the LH-unfolded cross section of the electroweak $W^\pm W^\pm jj$ production as a function of $m_{\mathrm{jj}}$. See Table 3.

Observed correlations between the bins of the LH-unfolded cross section of the electroweak $W^\pm W^\pm jj$ production as a function of $N_{\mathrm{gap}\,\mathrm{jets}}$. See Table 4.

Observed correlations between the bins of the LH-unfolded cross section of the electroweak $W^\pm W^\pm jj$ production as a function of $\xi_{\mathrm{j}3}$. See Table 5.

Observed correlations between the bins of the LH-unfolded cross section of the inclusive $W^\pm W^\pm jj$ production as a function of $m_{\ell\ell}$. See Table 6.

Observed correlations between the bins of the LH-unfolded cross section of the inclusive $W^\pm W^\pm jj$ production as a function of $m_{\mathrm{T}}$. See Table 7.

Observed correlations between the bins of the LH-unfolded cross section of the inclusive $W^\pm W^\pm jj$ production as a function of $m_{\mathrm{jj}}$. See Table 8.

Observed correlations between the bins of the LH-unfolded cross section of the inclusive $W^\pm W^\pm jj$ production as a function of $N_{\mathrm{gap}\,\mathrm{jets}}$. See Table 9.

Observed correlations between the bins of the LH-unfolded cross section of the inclusive $W^\pm W^\pm jj$ production as a function of $\xi_{\mathrm{j}3}$. See Table 10.

Evolution of the one-dimensional expected and observed limits at 95% CL on the parameters corresponding to the quartic operators with label M0 as a function of the cut-off scale. The unitarity bounds as a function of the cut-off scale are defined for one non-zero Wilson coefficient.

Evolution of the one-dimensional expected and observed limits at 95% CL on the parameters corresponding to the quartic operators with label M1 as a function of the cut-off scale. The unitarity bounds as a function of the cut-off scale are defined for one non-zero Wilson coefficient.

Evolution of the one-dimensional expected and observed limits at 95% CL on the parameters corresponding to the quartic operators with label M7 as a function of the cut-off scale. The unitarity bounds as a function of the cut-off scale are defined for one non-zero Wilson coefficient. The limits on M7 were obtained without taking into account the SM-EFT interference for the EW W$^\pm$Zjj final state.

Evolution of the one-dimensional expected and observed limits at 95% CL on the parameters corresponding to the quartic operators with label S02 as a function of the cut-off scale. The unitarity bounds as a function of the cut-off scale are defined for one non-zero Wilson coefficient.

Evolution of the one-dimensional expected and observed limits at 95% CL on the parameters corresponding to the quartic operators with label S1 as a function of the cut-off scale. The unitarity bounds as a function of the cut-off scale are defined for one non-zero Wilson coefficient.

Evolution of the one-dimensional expected and observed limits at 95% CL on the parameters corresponding to the quartic operators with label T0 as a function of the cut-off scale. The unitarity bounds as a function of the cut-off scale are defined for one non-zero Wilson coefficient.

Evolution of the one-dimensional expected and observed limits at 95% CL on the parameters corresponding to the quartic operators with label T1 as a function of the cut-off scale. The unitarity bounds as a function of the cut-off scale are defined for one non-zero Wilson coefficient.

Evolution of the one-dimensional expected and observed limits at 95% CL on the parameters corresponding to the quartic operators with label T2 as a function of the cut-off scale. The unitarity bounds as a function of the cut-off scale are defined for one non-zero Wilson coefficient.

Expected and observed exclusion limits at 95% CL for $\sigma_{\mathrm{VBF}}(\mathrm{H}^{\pm\pm}_5) \times \mathcal{B}(\mathrm{H}^{\pm\pm}_5 \rightarrow W^{\pm}W^{\pm})$ as a function of the doubly-charged Higgs mass.

Expected and observed exclusion limits at 95% CL for $\sin\theta_{\mathrm{H}}$ as a function of the doubly-charged Higgs mass in the Georgi-Machacek model.

Predicted and observed yields as a function of $m_{4\ell}$ in the VBS-Suppressed region. Overflow events are included in the last bin of the distribution.

Relative systematic uncertainties in the unfolded differential cross section for 4ljj production in the VBS-Enhanced region as a function of m_{jj}

Relative systematic uncertainties in the unfolded differential cross section for 4ljj production in the VBS-Enhanced region as a function of m_{4\ell}

Differential cross-sections for inclusive 4ljj production in the VBS-Enhanced region as a function of $m_{jj}$. Overflow events are included in the last bin of the distribution.

Differential cross-sections for inclusive 4ljj production in the VBS-Suppressed region as a function of $m_{jj}$. Overflow events are included in the last bin of the distribution.

Differential cross-sections for inclusive 4ljj production in the VBS-Enhanced region as a function of $m_{4\ell}$. Overflow events are included in the last bin of the distribution.

Differential cross-sections for inclusive 4ljj production in the VBS-Suppressed region as a function of $m_{4\ell}$. Overflow events are included in the last bin of the distribution.

Differential cross-sections for inclusive 4ljj production in the VBS-Enhanced region as a function of $ p_{T,4l}$. Overflow events are included in the last bin of the distribution.

Differential cross-sections for inclusive 4ljj production in the VBS-Suppressed region as a function of $ p_{T,4l}$. Overflow events are included in the last bin of the distribution.

Differential cross-sections for inclusive 4ljj production in the VBS-Enhanced region as a function of $\Delta\phi_{jj}$. Overflow events are included in the last bin of the distribution.

Differential cross-sections for inclusive 4ljj production in the VBS-Suppressed region as a function of $\Delta\phi_{jj}$. Overflow events are included in the last bin of the distribution.

Differential cross-sections for inclusive 4ljj production in the VBS-Enhanced region as a function of $|\Delta y_{jj}|$. Overflow events are included in the last bin of the distribution.

Differential cross-sections for inclusive 4ljj production in the VBS-Suppressed region as a function of $|\Delta y_{jj}|$. Overflow events are included in the last bin of the distribution.

Differential cross-sections for inclusive 4ljj production in the VBS-Enhanced region as a function of $cos(\theta^{*}_{12})$. Overflow events are included in the last bin of the distribution.

Differential cross-sections for inclusive 4ljj production in the VBS-Suppressed region as a function of $cos(\theta^{*}_{12})$. Overflow events are included in the last bin of the distribution.

Differential cross-sections for inclusive 4ljj production in the VBS-Enhanced region as a function of $cos(\theta^{*}_{34})$. Overflow events are included in the last bin of the distribution.

Differential cross-sections for inclusive 4ljj production in the VBS-Suppressed region as a function of $cos(\theta^{*}_{34})$. Overflow events are included in the last bin of the distribution.

Differential cross-sections for inclusive 4ljj production in the VBS-Enhanced region as a function of $p_{T,jj}$. Overflow events are included in the last bin of the distribution.

Differential cross-sections for inclusive 4ljj production in the VBS-Suppressed region as a function of $p_{T,jj}$. Overflow events are included in the last bin of the distribution.

Differential cross-sections for inclusive 4ljj production in the VBS-Enhanced region as a function of $p_{T,4ljj}$. Overflow events are included in the last bin of the distribution.

Differential cross-sections for inclusive 4ljj production in the VBS-Suppressed region as a function of $p_{T,4ljj}$. Overflow events are included in the last bin of the distribution.

Differential cross-sections for inclusive 4ljj production in the VBS-Enhanced region as a function of $S_{T,4ljj}$. Overflow events are included in the last bin of the distribution.

Differential cross-sections for inclusive 4ljj production in the VBS-Suppressed region as a function of $S_{T,4ljj}$. Overflow events are included in the last bin of the distribution.

Statistical correlation between different bins of the unfolded cross-section for all the measured observables in the VBS-Enhanced region.

Statistical correlation between different bins of the unfolded cross-section for all the measured observables in the VBS-Suppressed region.

Distribution of ${E}_{T}^{miss}$ after the fit of the multijet backgrounds, in the electron channel, in the $t\bar{t}$ 3-jets VR, without applying the cut on ${E}_{T}^{miss}$. Simulated events are normalised to the expected number of events given the integrated luminosity, after applying the normalisation factors obtained in the multijet fit. The last bin includes the overflow. The uncertainty band indicates the simulation's statistical uncertainty, the normalisation uncertainties for different processes ($40$ % for $W$+jets production, $30$ % for multijet background and $6$ % for top-quark processes) and the multijet background shape uncertainty in each bin, summed in quadrature. The lower panel of the figure shows the ratio of the data to the prediction.

Distribution of ${E}_{T}^{miss}$ after the fit of the multijet backgrounds, in the electron channel, in the $t\bar{t}$ 4-jets VR, without applying the cut on ${E}_{T}^{miss}$. Simulated events are normalised to the expected number of events given the integrated luminosity, after applying the normalisation factors obtained in the multijet fit. The last bin includes the overflow. The uncertainty band indicates the simulation's statistical uncertainty, the normalisation uncertainties for different processes ($40$ % for $W$+jets production, $30$ % for multijet background and $6$ % for top-quark processes) and the multijet background shape uncertainty in each bin, summed in quadrature. The lower panel of the figure shows the ratio of the data to the prediction.

Distribution of $m_{T}^{W}$ after the fit of the multijet backgrounds, in the muon channel, in the signal region, without applying the cut on $m_{T}^{W}$. Simulated events are normalised to the expected number of events given the integrated luminosity, after applying the normalisation factors obtained in the multijet fit. The last bin includes the overflow. The uncertainty band indicates the simulation's statistical uncertainty, the normalisation uncertainties for different processes ($40$ % for $W$+jets production, $30$ % for multijet background and $6$ % for top-quark processes) and the multijet background shape uncertainty in each bin, summed in quadrature. The lower panel of the figure shows the ratio of the data to the prediction.

Distribution of $m_{T}^{W}$ after the fit of the multijet backgrounds, in the muon channel, in the $W$+jets VR, without applying the cut on $m_{T}^{W}$. Simulated events are normalised to the expected number of events given the integrated luminosity, after applying the normalisation factors obtained in the multijet fit. The last bin includes the overflow. The uncertainty band indicates the simulation's statistical uncertainty, the normalisation uncertainties for different processes ($40$ % for $W$+jets production, $30$ % for multijet background and $6$ % for top-quark processes) and the multijet background shape uncertainty in each bin, summed in quadrature. The lower panel of the figure shows the ratio of the data to the prediction.

Distribution of $m_{T}^{W}$ after the fit of the multijet backgrounds, in the muon channel, in the $t\bar{t}$ 3-jets VR, without applying the cut on $m_{T}^{W}$. Simulated events are normalised to the expected number of events given the integrated luminosity, after applying the normalisation factors obtained in the multijet fit. The last bin includes the overflow. The uncertainty band indicates the simulation's statistical uncertainty, the normalisation uncertainties for different processes ($40$ % for $W$+jets production, $30$ % for multijet background and $6$ % for top-quark processes) and the multijet background shape uncertainty in each bin, summed in quadrature. The lower panel of the figure shows the ratio of the data to the prediction.

Distribution of $m_{T}^{W}$ after the fit of the multijet backgrounds, in the muon channel, in the $t\bar{t}$ 4-jets VR, without applying the cut on $m_{T}^{W}$. Simulated events are normalised to the expected number of events given the integrated luminosity, after applying the normalisation factors obtained in the multijet fit. The last bin includes the overflow. The uncertainty band indicates the simulation's statistical uncertainty, the normalisation uncertainties for different processes ($40$ % for $W$+jets production, $30$ % for multijet background and $6$ % for top-quark processes) and the multijet background shape uncertainty in each bin, summed in quadrature. The lower panel of the figure shows the ratio of the data to the prediction.

Expected distributions of the MEM discriminant $P(S|X)$ in the SR, for the s-channel single-top signal, and for the $t\bar{t}$ and $W$+jets backgrounds, for MEM discriminant values larger than $2.0\times10^{-4}$. Each distribution is normalised to unity. The binning is the same as the optimised binning used in the signal extraction fit, resulting in a non-linear horizontal scale.

Distribution of the MEM discriminant $P(S|X)$ in the $W$+jets VR. Simulated events are normalised to the expected number of events given the integrated luminosity, after applying the normalisation factors obtained in the multijet fit presented in Section 5 in the paper. The uncertainty band indicates the simulation's statistical uncertainty and the normalisation uncertainties for the various processes in each bin, summed in quadrature. The ratio of the observed number to the predicted number of events in each bin is shown in the lower panel of the figure, with different vertical axis ranges. The binning is the same as the optimised binning used in the signal extraction fit described in Section 8 in the paper, resulting in a non-linear horizontal scale.

Distribution of the MEM discriminant $P(S|X)$ in the $t\bar{t}$ 3-jets VR. Simulated events are normalised to the expected number of events given the integrated luminosity, after applying the normalisation factors obtained in the multijet fit presented in Section 5 in the paper. The uncertainty band indicates the simulation's statistical uncertainty and the normalisation uncertainties for the various processes in each bin, summed in quadrature. The ratio of the observed number to the predicted number of events in each bin is shown in the lower panel of the figure, with different vertical axis ranges. The binning is the same as the optimised binning used in the signal extraction fit described in Section 8 in the paper, resulting in a non-linear horizontal scale.

Distribution of the MEM discriminant $P(S|X)$ in the $t\bar{t}$ 4-jets VR. Simulated events are normalised to the expected number of events given the integrated luminosity, after applying the normalisation factors obtained in the multijet fit presented in Section 5 in the paper. The uncertainty bands indicate the simulation's statistical uncertainty and the normalisation uncertainties for the various processes in each bin, summed in quadrature. The ratio of the observed number to the predicted number of events in each bin is shown in the lower panel of the figure, with different vertical axis ranges. The binning is the same as the optimised binning used in the signal extraction fit described in Section 8 in the paper, resulting in a non-linear horizontal scale.

Distribution of the MEM discriminant $P(S|X)$ in the SR before the fit to data, for MEM discriminant values larger than $2.0\times10^{-4}$. The lower panel of the figure shows the ratio of the data to the prediction, with different vertical axis ranges. The uncertainty band indicates the total uncertainties and their correlations in each bin. The uncertainties in the $t\bar{t}$ and $W$+jets normalisation factors, as well as in the s-channel signal cross-section, are not defined pre-fit and therefore not included. The binning is the same as the optimised binning used in the fit, resulting in a non-linear horizontal scale.

Distribution of the MEM discriminant $P(S|X)$ in the SR after the fit to data, for MEM discriminant values larger than $2.0\times10^{-4}$. The lower panel of the figure shows the ratio of the data to the prediction, with different vertical axis ranges. The uncertainty band indicates the total uncertainties and their correlations in each bin. The binning is the same as the optimised binning used in the fit, resulting in a non-linear horizontal scale.

Distribution of the MEM discriminant $P(S|X)$ in the SR after the fit to data, for MEM discriminant values larger than $2.0\times10^{-4}$, after subtraction of all backgrounds. The fitted distribution for the simulation of the signal is shown together with the post-fit uncertainty in the backgrounds. The binning is the same as the optimised binning used in the fit, resulting in a non-linear horizontal scale.

Pre-fit and post-fit event yields in the SR, for MEM discriminant values larger than $2.0\times10^{-4}$. The central value of the event yield for each process is calculated by summing the values of the discriminant bin contents, using the nominal expected yield for the pre-fit value, and the best-fit estimate for the post-fit value. The error includes statistical and systematic uncertainties summed in quadrature. All sources of systematic uncertainties are included, taking into account correlations and anti-correlations in the post-fit case. The uncertainties in the $t\bar{t}$ and $W$+jets normalisation factors, as well as in the s-channel signal cross-section, are not defined pre-fit and therefore only included in the post-fit uncertainties.

Observed impact of the different sources of uncertainty on the measured s-channel signal cross-section, grouped by categories. The impact of each category is obtained by repeating the fit after having fixed the set of nuisance parameters corresponding to that category, subtracting the square of the resulting uncertainty from the square of the uncertainty found in the full fit, and calculating the square root. The 'Systematic uncertainties' category combines all sources of systematic uncertainties. The statistical uncertainty is obtained by repeating the fit after having fixed all nuisance parameters, including the $t\bar{t}$ and $W$+jets normalisation factors. 'Total' gives the total uncertainty on the measurement.

Observed impact of the different sources of $t\bar{t}$ modelling uncertainty on the measured s-channel signal cross-section. The impact of each category is obtained by repeating the fit after having fixed the set of nuisance parameters corresponding to that category, subtracting the square of the resulting uncertainty from the square of the uncertainty found in the full fit, and calculating the square root. 'PS & had.' refers to the parton shower and hadronisation model, and 'ME/PS matching' to the matching of the ME to the parton shower.

Observed impact of the different sources of s-channel modelling uncertainty on the measured s-channel signal cross-section. The impact of each category is obtained by repeating the fit after having fixed the set of nuisance parameters corresponding to that category, subtracting the square of the resulting uncertainty from the square of the uncertainty found in the full fit, and calculating the square root. 'PS & had.' refers to the parton shower and hadronisation model, as described in Section 7 in the paper.

Observed impact of the different sources of t-channel modelling uncertainty on the measured s-channel signal cross-section. The impact of each category is obtained by repeating the fit after having fixed the set of nuisance parameters corresponding to that category, subtracting the square of the resulting uncertainty from the square of the uncertainty found in the full fit, and calculating the square root. 'PS & had.' refers to the parton shower and hadronisation model, as described in Section 7 in the paper.

Observed impact of the different sources of $tW$ modelling uncertainty on the measured s-channel signal cross-section, grouped by categories. The impact of each category is obtained by repeating the fit after having fixed the set of nuisance parameters corresponding to that category, subtracting the square of the resulting uncertainty from the square of the uncertainty found in the full fit, and calculating the square root. 'PS & had.' refers to the parton shower and hadronisation model, and '$t\bar{t}$ overlap' to the algorithm removing the overlap between $tW$ and $t\bar{t}$ production at NLO, as described in Section 7 in the paper.

Observed impact of the different sources of PDF uncertainties on the measured s-channel signal cross-section, grouped by categories. The impact of each category is obtained by repeating the fit after having fixed the set of nuisance parameters corresponding to that category, subtracting the square of the resulting uncertainty from the square of the uncertainty found in the full fit, and calculating the square root.

Comparison between data and prediction after the fit to data in the signal region for the leading-jet $p_{T}$. The last bin includes the overflow. The uncertainty band includes all uncertainties and their correlations. The lower panel of the figure shows the ratio of the data to the prediction.

Comparison between data and prediction after the fit to data in the signal region for the leading-jet $\eta$. The uncertainty band includes all uncertainties and their correlations. The lower panel of the figure shows the ratio of the data to the prediction.

Comparison between data and prediction after the fit to data in the signal region for the subleading-jet $p_{T}$. The last bin includes the overflow. The uncertainty band includes all uncertainties and their correlations. The lower panel of the figure shows the ratio of the data to the prediction.

Comparison between data and prediction after the fit to data in the signal region for the subleading-jet $\eta$. The uncertainty band includes all uncertainties and their correlations. The lower panel of the figure shows the ratio of the data to the prediction.

Comparison between data and prediction after the fit to data in the signal region for the lepton $p_{T}$. The last bin includes the overflow. The uncertainty band includes all uncertainties and their correlations. The lower panel of the figure shows the ratio of the data to the prediction.

Comparison between data and prediction after the fit to data in the signal region for the lepton $\eta$. The uncertainty band includes all uncertainties and their correlations. The lower panel of the figure shows the ratio of the data to the prediction.

Comparison between data and prediction after the fit to data in the signal region for the ${E}_{T}^{miss}$. The last bin includes the overflow. The uncertainty band includes all uncertainties and their correlations. The lower panel of the figure shows the ratio of the data to the prediction.

Comparison between data and prediction after the fit to data in the signal region for the $m_{T}^{W}$. The last bin includes the overflow. The uncertainty band includes all uncertainties and their correlations. The lower panel of the figure shows the ratio of the data to the prediction.

Nuisance parameters ranked according to their post-fit impacts on the best-fit value of the ratio $\mu$ of the measured cross-section to the predicted cross-section. In the figure, only the 20 nuisance parameters with the largest post-fit impacts are shown. The empty (solid) blue rectangles illustrate the pre-fit (post-fit) impact on $\mu$, corresponding to the upper axis. The pre-fit (post-fit) impact of each nuisance parameter, $\Delta\mu$, is calculated as the difference in the fitted value of $\mu$ between the nominal fit and the fit when fixing the corresponding nuisance parameter to $\hat{\theta}\pm\Delta\theta$ ($\hat{\theta}\pm\Delta\hat{\theta}$), where $\hat{\theta}$ is the best-fit value of the nuisance parameter and $\Delta\theta$ ($\Delta\hat{\theta}$) is its pre-fit (post-fit) uncertainty. Several systematic uncertainties are split into different nuisance parameters, which are indicated by NP. JES (JER) indicates jet energy scale (resolution), and $\gamma$ indicates a nuisance parameter associated to the MC statistics in one of the 18 bins numbered from 0 to 17. The black points show the best-fit values of the nuisance parameters, with the error bars representing the post-fit uncertainties. Each nuisance parameter is shown wrt. its nominal value, $\theta_0$, and in units of its pre-fit uncertainty, except the free-floating normalisation factors of the $t\bar{t}$ and $W$+jets backgrounds, and the parameters associated to the MC statistics in each bin, for which the post-fit values and uncertainties are shown.

Correlation matrix of the nuisance parameters and of the ratio $\mu$ of the measured cross-section to the predicted cross-section. The correlations are given after the fit to data. In the figure, only the parameters which have a correlation of at least 0.2 with any other parameter are shown.

Distribution of the MEM discriminant $P(S|X)$ in the SR for MEM discriminant values larger than $2.0\times10^{-4}$, for the collision data used for the measurement, and for 1000 pseudo-data replicas, generated using a bootstrapping technique, in order to assess the statistical correlations between this measurement and others, for the purpose of combinations. The replicas are obtained by reweighting each observed data event by a random integer generated according to Poisson statistics, using the <a href="https://zenodo.org/record/5361038">BootstrapGenerator</a> software package , which implements a technique described in <a href="https://cds.cern.ch/record/2759945/">ATL-PHYS-PUB-2021-011</a>. The ATLAS event number and run number of each event are used as seed to uniquely but reproducibly initialise the random number generator for each event. Each pseudo-data replica is assigned an index, ranging from 0 to 999, corresponding to the random number index used consistently for each observed data event.

Measured values of the signal cross-section and of the $t\bar{t}$ and $W$+jets normalisation factors, obtained by statistical-only fits to the collision data used for the measurement, and to 1000 pseudo-data replicas, generated using a bootstrapping technique, in order to assess the statistical correlations between this measurement and others, for the purpose of combinations. The central values and their statistical uncertainties are obtained by repeating the fit after having fixed all nuisance parameters, except the $t\bar{t}$ and $W$+jets normalisation factors, which are let free-floating (unlike for the statistical uncertainty on the cross-section quoted in the paper). The replicas are obtained by reweighting each observed data event by a random integer generated according to Poisson statistics, using the <a href="https://zenodo.org/record/5361038">BootstrapGenerator</a> software package , which implements a technique described in <a href="https://cds.cern.ch/record/2759945/">ATL-PHYS-PUB-2021-011</a>. The ATLAS event number and run number of each event are used as seed to uniquely but reproducibly initialise the random number generator for each event. Each pseudo-data replica is assigned an index, ranging from 0 to 999, corresponding to the random number index used consistently for each observed data event.

Signal region detector-level distribution for the observable $p_{\mathrm{T}}^{\mathrm{lead}\, \ell}$.

Signal region detector-level distribution for the observable $m_{e\mu}$.

Signal region detector-level distribution for the observable $p_{\mathrm{T}}^{e\mu}$.

Measured fiducial differential cross-section of $WW \rightarrow e^{\pm}\nu\mu^{\mp}\nu$ production for the observable $|y_{e\mu}|$

Relative systematic uncertainties for the fiducial differential cross-section of $WW \rightarrow e^{\pm}\nu\mu^{\mp}\nu$ production for the observable $|y_{e\mu}|$

Measured fiducial differential cross-section of $WW \rightarrow e^{\pm}\nu\mu^{\mp}\nu$ production for the observable $|\Delta \phi(e \mu)|$

Relative systematic uncertainties for the fiducial differential cross-section of $WW \rightarrow e^{\pm}\nu\mu^{\mp}\nu$ production for the observable $|\Delta \phi(e \mu)|$

Measured fiducial differential cross-section of $WW \rightarrow e^{\pm}\nu\mu^{\mp}\nu$ production for the observable $ \cos\theta^{\ast}$

Relative systematic uncertainties for the fiducial differential cross-section of $WW \rightarrow e^{\pm}\nu\mu^{\mp}\nu$ production for the observable $ \cos\theta^{\ast}$

Measured fiducial differential cross-section of $WW \rightarrow e^{\pm}\nu\mu^{\mp}\nu$ production for the observable $p_{\mathrm{T}}^{\mathrm{lead}\, \ell}$

Relative systematic uncertainties for the fiducial differential cross-section of $WW \rightarrow e^{\pm}\nu\mu^{\mp}\nu$ production for the observable $p_{\mathrm{T}}^{\mathrm{lead}\, \ell}$

Measured fiducial differential cross-section of $WW \rightarrow e^{\pm}\nu\mu^{\mp}\nu$ production for the observable $m_{e\mu}$

Relative systematic uncertainties for the fiducial differential cross-section of $WW \rightarrow e^{\pm}\nu\mu^{\mp}\nu$ production for the observable $m_{e\mu}$

Measured fiducial differential cross-section of $WW \rightarrow e^{\pm}\nu\mu^{\mp}\nu$ production for the observable $p_{\mathrm{T}}^{e\mu}$

Relative systematic uncertainties for the fiducial differential cross-section of $WW \rightarrow e^{\pm}\nu\mu^{\mp}\nu$ production for the observable $p_{\mathrm{T}}^{e\mu}$

The statistical correlation coefficients (in percentage) between bins for the measured fiducial differential cross-section of $WW \rightarrow e^{\pm}\nu\mu^{\mp}\nu$ production for the observable $|y_{e\mu}|$

The total correlation coefficients (in percentage) between bins for the measured fiducial differential cross-section of $WW \rightarrow e^{\pm}\nu\mu^{\mp}\nu$ production for the observable $|y_{e\mu}|$

The statistical correlation coefficients (in percentage) between bins for the measured fiducial differential cross-section of $WW \rightarrow e^{\pm}\nu\mu^{\mp}\nu$ production for the observable $|\Delta \phi(e \mu)|$

The total correlation coefficients (in percentage) between bins for the measured fiducial differential cross-section of $WW \rightarrow e^{\pm}\nu\mu^{\mp}\nu$ production for the observable $|\Delta \phi(e \mu)|$

The statistical correlation coefficients (in percentage) between bins for the measured fiducial differential cross-section of $WW \rightarrow e^{\pm}\nu\mu^{\mp}\nu$ production for the observable $ \cos\theta^{\ast}$

The total correlation coefficients (in percentage) between bins for the measured fiducial differential cross-section of $WW \rightarrow e^{\pm}\nu\mu^{\mp}\nu$ production for the observable $ \cos\theta^{\ast}$

The statistical correlation coefficients (in percentage) between bins for the measured fiducial differential cross-section of $WW \rightarrow e^{\pm}\nu\mu^{\mp}\nu$ production for the observable $p_{\mathrm{T}}^{\mathrm{lead}\, \ell}$

The total correlation coefficients (in percentage) between bins for the measured fiducial differential cross-section of $WW \rightarrow e^{\pm}\nu\mu^{\mp}\nu$ production for the observable $p_{\mathrm{T}}^{\mathrm{lead}\, \ell}$

The statistical correlation coefficients (in percentage) between bins for the measured fiducial differential cross-section of $WW \rightarrow e^{\pm}\nu\mu^{\mp}\nu$ production for the observable $m_{e\mu}$

The total correlation coefficients (in percentage) between bins for the measured fiducial differential cross-section of $WW \rightarrow e^{\pm}\nu\mu^{\mp}\nu$ production for the observable $m_{e\mu}$

The statistical correlation coefficients (in percentage) between bins for the measured fiducial differential cross-section of $WW \rightarrow e^{\pm}\nu\mu^{\mp}\nu$ production for the observable $p_{\mathrm{T}}^{e\mu}$

The total correlation coefficients (in percentage) between bins for the measured fiducial differential cross-section of $WW \rightarrow e^{\pm}\nu\mu^{\mp}\nu$ production for the observable $p_{\mathrm{T}}^{e\mu}$

Sample correlations in $\Delta\phi$ ($|\Delta\eta|<$ 1.78) for 3 $<$ $p_T^{trigger}$ $<$ 6 GeV/$c$ and 1.5 GeV/$c$ $<$ $p_T^{associated}$ $<$ $p_T^{trigger}$ for 0-60% Cu+Cu at $\sqrt{s_{NN}}$ = 62.4 GeV, 0-80% Au+Au at $\sqrt{s_{NN}}$ = 62.4 GeV, 0-95% $d$+Au at $\sqrt{s_{NN}}$ = 200 GeV, 0-60% Cu+Cu at $\sqrt{s_{NN}}$ = 200 GeV, 40-80% Au+Au at $\sqrt{s_{NN}}$ = 200 GeV, and 0-12% central Au+Au at $\sqrt{s_{NN}}$ = 200 GeV. The data are averaged between positive and negative $\Delta\phi$ and reflected in the plot.

Background subtracted sample correlations for 3 $<$ $p_T^{trigger}$ $<$ 6 GeV/$c$ and 1.5 GeV/$c$ $<$ $p_T^{associated}$ $<$ $p_T^{trigger}$ on the near-side for 0-60% Cu+Cu at $\sqrt{s_{NN}}$ = 62.4 GeV, 0-80% Au+Au at $\sqrt{s_{NN}}$ = 62.4 GeV, 0-95% $d$+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV, 0-60% Cu+Cu at $\sqrt{s_{NN}}$ = 200 GeV, 40-80% Au+Au at $\sqrt{s_{NN}}$ = 200 GeV and 0-12% central Au+Au at $\sqrt{s_{NN}}$ = 200 GeV. The dependence of the jet-like correlation is shown as a function of $\Delta\eta$ ($|\Delta\phi|<$ 0.78). The data are averaged between positive and negative $\Delta\eta$.

Background subtracted sample correlations for 3 $<$ $p_T^{trigger}$ $<$ 6 GeV/$c$ and 1.5 GeV/$c$ $<$ $p_T^{associated}$ $<$ $p_T^{trigger}$ on the near-side for 0-60% Cu+Cu at $\sqrt{s_{NN}}$ = 62.4 GeV, 0-80% Au+Au at $\sqrt{s_{NN}}$ = 62.4 GeV, 0-95% $d$+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV, 0-60% Cu+Cu at $\sqrt{s_{NN}}$ = 200 GeV, 40-80% Au+Au at $\sqrt{s_{NN}}$ = 200 GeV and 0-12% central Au+Au at $\sqrt{s_{NN}}$ = 200 GeV. The dependence of the jet-like correlation is shown as a function of $\Delta\phi$ ($|\Delta\eta|<$ 1.78). The data are averaged between positive and negative $\Delta\phi$.

Dependence of jet-like yield on $N_{part}$ for 3 $<$ $p_T^{trigger}$ $<$ 6 GeV/$c$ and 1.5 GeV/$c$ $<$ $p_T^{associated}$ $<$ $p_T^{trigger}$ for Cu+Cu at $\sqrt{s_{NN}}$ = 62.4 GeV. 5% systematic error due to the uncertainty on the associated particle's efficiency is not shown.

Dependence of jet-like yield on $N_{part}$ for 3 $<$ $p_T^{trigger}$ $<$ 6 GeV/$c$ and 1.5 GeV/$c$ $<$ $p_T^{associated}$ $<$ $p_T^{trigger}$ for Au+Au at $\sqrt{s_{NN}}$ = 62.4 GeV. 5% systematic error due to the uncertainty on the associated particle's efficiency is not shown.

Dependence of jet-like yield on $N_{part}$ for 3 $<$ $p_T^{trigger}$ $<$ 6 GeV/$c$ and 1.5 GeV/$c$ $<$ $p_T^{associated}$ $<$ $p_T^{trigger}$ for $d$+Au at $\sqrt{s_{NN}}$ = 200 GeV. 5% systematic error due to the uncertainty on the associated particle's efficiency is not shown.

Dependence of jet-like yield on $N_{part}$ for 3 $<$ $p_T^{trigger}$ $<$ 6 GeV/$c$ and 1.5 GeV/$c$ $<$ $p_T^{associated}$ $<$ $p_T^{trigger}$ for Cu+Cu at $\sqrt{s_{NN}}$ = 200 GeV. 5% systematic error due to the uncertainty on the associated particle's efficiency is not shown.

Dependence of jet-like yield on $N_{part}$ for 3 $<$ $p_T^{trigger}$ $<$ 6 GeV/$c$ and 1.5 GeV/$c$ $<$ $p_T^{associated}$ $<$ $p_T^{trigger}$ for Au+Au at $\sqrt{s_{NN}}$ = 200 GeV. 5% systematic error due to the uncertainty on the associated particle's efficiency is not shown.

Dependence of jet-like yield on $p_T^{\mathrm{trigger}}$ for 0-60% Cu+Cu at $\sqrt{s_{NN}}$ = 62.4 GeV, 0-80% Au+Au at $\sqrt{s_{NN}}$ = 62.4 GeV, 0-95% $d$+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV, 0-60% Cu+Cu at $\sqrt{s_{NN}}$ = 200 GeV, 40-80% Au+Au at $\sqrt{s_{NN}}$ = 200 GeV and 0-12% central Au+Au at $\sqrt{s_{NN}}$ = 200 GeV. The 5% systematic error due to the uncertainty on the associated particle's efficiency is not shown.

Dependence of jet-like yield on $p_T^{\mathrm{associated}}$ for 3 $<$ $p_T^{trigger}$ $<$ 6 GeV/$c$ for 0-60% Cu+Cu and 0-80% Au+Au collisions at $\sqrt{s_{NN}}$ = 62.4 GeV and 0-95% $d$+Au, 0-60% Cu+Cu, 0-12% Au+Au and 40-80% Au+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV. The 5% systematic error due to the uncertainty on the associated particle's efficiency is not shown.

Dependence of the widths in $\Delta\phi$ on $p_T^{\mathrm{trigger}}$ for 1.5 GeV/$c$ $<$ $p_T^{associated}$ $<$ $p_T^{trigger}$ for 0-95% $d$+Au, 0-60% Cu+Cu at $\sqrt{s_{NN}}$ = 62.4 GeV and $\sqrt{s_{NN}}$ = 200 GeV, 0-80% Au+Au at $\sqrt{s_{NN}}$ = 62.4 GeV, and 0-12% and 40-80% Au+Au at $\sqrt{s_{NN}}$ = 200 GeV.

Dependence of the widths in $\Delta\phi$ on $p_T^{\mathrm{associated}}$ for 3 $<$ $p_T^{trigger}$ $<$ 6 GeV/$c$ for 0-95% $d$+Au, 0-60% Cu+Cu at $\sqrt{s_{NN}}$ = 62.4 GeV and $\sqrt{s_{NN}}$ = 200 GeV, 0-80% Au+Au at $\sqrt{s_{NN}}$ = 62.4 GeV, and 0-12% and 40-80% Au+Au at $\sqrt{s_{NN}}$ = 200 GeV.

Dependence of the widths in $\Delta\phi$ on $N_{part}$ for 3 $<$ $p_T^{trigger}$ $<$ 6 GeV/$c$ and 1.5 GeV/$c$ $<$ $p_T^{associated}$ $<$ $p_T^{trigger}$ for 0-60% Cu+Cu at $\sqrt{s_{NN}}$ = 62.4 GeV.

Dependence of the widths in $\Delta\phi$ on $N_{part}$ for 3 $<$ $p_T^{trigger}$ $<$ 6 GeV/$c$ and 1.5 GeV/$c$ $<$ $p_T^{associated}$ $<$ $p_T^{trigger}$ for 0-80% Au+Au at $\sqrt{s_{NN}}$ = 62.4 GeV.

Dependence of the widths in $\Delta\phi$ on $N_{part}$ for 3 $<$ $p_T^{trigger}$ $<$ 6 GeV/$c$ and 1.5 GeV/$c$ $<$ $p_T^{associated}$ $<$ $p_T^{trigger}$ for 0-95% $d$+Au at $\sqrt{s_{NN}}$ = 200 GeV.

Dependence of the widths in $\Delta\phi$ on $N_{part}$ for 3 $<$ $p_T^{trigger}$ $<$ 6 GeV/$c$ and 1.5 GeV/$c$ $<$ $p_T^{associated}$ $<$ $p_T^{trigger}$ for 0-60% Cu+Cu at $\sqrt{s_{NN}}$ = 200 GeV.

Dependence of the widths in $\Delta\phi$ on $N_{part}$ for 3 $<$ $p_T^{trigger}$ $<$ 6 GeV/$c$ and 1.5 GeV/$c$ $<$ $p_T^{associated}$ $<$ $p_T^{trigger}$ for Au+Au at $\sqrt{s_{NN}}$ = 200 GeV.

Dependence of the widths in $\Delta\eta$ on $p_T^{\mathrm{trigger}}$ for 1.5 GeV/$c$ $<$ $p_T^{associated}$ $<$ $p_T^{trigger}$ for 0-95% $d$+Au, 0-60% Cu+Cu at $\sqrt{s_{NN}}$ = 62.4 GeV and $\sqrt{s_{NN}}$ = 200 GeV, 0-80% Au+Au at $\sqrt{s_{NN}}$ = 62.4 GeV, and 0-12% and 40-80% Au+Au at $\sqrt{s_{NN}}$ = 200 GeV.

Dependence of the widths in $\Delta\eta$ on $p_T^{\mathrm{associated}}$ for 3 $<$ $p_T^{trigger}$ $<$ 6 GeV/$c$ for 0-95% $d$+Au, 0-60% Cu+Cu at $\sqrt{s_{NN}}$ = 62.4 GeV and $\sqrt{s_{NN}}$ = 200 GeV, 0-80% Au+Au at $\sqrt{s_{NN}}$ = 62.4 GeV, and 0-12% and 40-80% Au+Au at $\sqrt{s_{NN}}$ = 200 GeV.

Dependence of the widths in $\Delta\eta$ on $N_{part}$ for 3 $<$ $p_T^{trigger}$ $<$ 6 GeV/$c$ and 1.5 GeV/$c$ $<$ $p_T^{associated}$ $<$ $p_T^{trigger}$ for 0-60% Cu+Cu at $\sqrt{s_{NN}}$ = 62.4 GeV.

Dependence of the widths in $\Delta\eta$ on $N_{part}$ for 3 $<$ $p_T^{trigger}$ $<$ 6 GeV/$c$ and 1.5 GeV/$c$ $<$ $p_T^{associated}$ $<$ $p_T^{trigger}$ for 0-80% Au+Au at $\sqrt{s_{NN}}$ = 62.4 GeV.

Dependence of the widths in $\Delta\eta$ on $N_{part}$ for 3 $<$ $p_T^{trigger}$ $<$ 6 GeV/$c$ and 1.5 GeV/$c$ $<$ $p_T^{associated}$ $<$ $p_T^{trigger}$ for 0-95% $d$+Au at $\sqrt{s_{NN}}$ = 200 GeV.

Dependence of the widths in $\Delta\eta$ on $N_{part}$ for 3 $<$ $p_T^{trigger}$ $<$ 6 GeV/$c$ and 1.5 GeV/$c$ $<$ $p_T^{associated}$ $<$ $p_T^{trigger}$ for 0-60% Cu+Cu at $\sqrt{s_{NN}}$ = 200 GeV.

Dependence of the widths in $\Delta\eta$ on $N_{part}$ for 3 $<$ $p_T^{trigger}$ $<$ 6 GeV/$c$ and 1.5 GeV/$c$ $<$ $p_T^{associated}$ $<$ $p_T^{trigger}$ for Au+Au at $\sqrt{s_{NN}}$ = 200 GeV.

Dependence of ridge yield on $N_{part}$ for 3 $<$ $p_T^{trigger}$ $<$ 6 GeV/$c$ and 1.5 GeV/$c$ $<$ $p_T^{associated}$ $<$ $p_T^{trigger}$ for Cu+Cu at $\sqrt{s_{NN}}$ = 62.4 GeV.

Dependence of ridge yield on $N_{part}$ for 3 $<$ $p_T^{trigger}$ $<$ 6 GeV/$c$ and 1.5 GeV/$c$ $<$ $p_T^{associated}$ $<$ $p_T^{trigger}$ for Au+Au at $\sqrt{s_{NN}}$ = 62.4 GeV.

Dependence of ridge yield on $N_{part}$ for 3 $<$ $p_T^{trigger}$ $<$ 6 GeV/$c$ and 1.5 GeV/$c$ $<$ $p_T^{associated}$ $<$ $p_T^{trigger}$ for Cu+Cu at $\sqrt{s_{NN}}$ = 200 GeV.

Dependence of ridge yield on $N_{part}$ for 3 $<$ $p_T^{trigger}$ $<$ 6 GeV/$c$ and 1.5 GeV/$c$ $<$ $p_T^{associated}$ $<$ $p_T^{trigger}$ for Au+Au at $\sqrt{s_{NN}}$ = 200 GeV.

Ratio of the ridge and jet-like yields on $N_{part}$ for 3 $<$ $p_T^{trigger}$ $<$ 6 GeV/$c$ and 1.5 GeV/$c$ $<$ $p_T^{associated}$ $<$ $p_T^{trigger}$ for Cu+Cu at $\sqrt{s_{NN}}$ = 62.4 GeV.

Ratio of the ridge and jet-like yields on $N_{part}$ for 3 $<$ $p_T^{trigger}$ $<$ 6 GeV/$c$ and 1.5 GeV/$c$ $<$ $p_T^{associated}$ $<$ $p_T^{trigger}$ for Au+Au at $\sqrt{s_{NN}}$ = 62.4 GeV.

Ratio of the ridge and jet-like yields on $N_{part}$ for 3 $<$ $p_T^{trigger}$ $<$ 6 GeV/$c$ and 1.5 GeV/$c$ $<$ $p_T^{associated}$ $<$ $p_T^{trigger}$ for Cu+Cu at $\sqrt{s_{NN}}$ = 200 GeV.

Ratio of the ridge and jet-like yields on $N_{part}$ for 3 $<$ $p_T^{trigger}$ $<$ 6 GeV/$c$ and 1.5 GeV/$c$ $<$ $p_T^{associated}$ $<$ $p_T^{trigger}$ for Au+Au at $\sqrt{s_{NN}}$ = 200 GeV.

Dependence of $V_{3\Delta}/V_{2\Delta}$ on $N_{part}$ for 3 $<$ $p_T^{trigger}$ $<$ 6 GeV/$c$ and 1.5 GeV/$c$ $<$ $p_T^{associated}$ $<$ $p_T^{trigger}$ for Cu+Cu at $\sqrt{s_{NN}}$ = 62.4 GeV.

Dependence of $V_{3\Delta}/V_{2\Delta}$ on $N_{part}$ for 3 $<$ $p_T^{trigger}$ $<$ 6 GeV/$c$ and 1.5 GeV/$c$ $<$ $p_T^{associated}$ $<$ $p_T^{trigger}$ for Au+Au at $\sqrt{s_{NN}}$ = 62.4 GeV.

Dependence of $V_{3\Delta}/V_{2\Delta}$ on $N_{part}$ for 3 $<$ $p_T^{trigger}$ $<$ 6 GeV/$c$ and 1.5 GeV/$c$ $<$ $p_T^{associated}$ $<$ $p_T^{trigger}$ for $d$+Au at $\sqrt{s_{NN}}$ = 200 GeV.

Dependence of $V_{3\Delta}/V_{2\Delta}$ on $N_{part}$ for 3 $<$ $p_T^{trigger}$ $<$ 6 GeV/$c$ and 1.5 GeV/$c$ $<$ $p_T^{associated}$ $<$ $p_T^{trigger}$ for Cu+Cu at $\sqrt{s_{NN}}$ = 200 GeV.

Dependence of $V_{3\Delta}/V_{2\Delta}$ on $N_{part}$ for 3 $<$ $p_T^{trigger}$ $<$ 6 GeV/$c$ and 1.5 GeV/$c$ $<$ $p_T^{associated}$ $<$ $p_T^{trigger}$ for Au+Au at $\sqrt{s_{NN}}$ = 200 GeV.

V1Delta coefficients as a function of the trigger particle PT for events in the centrality class 0-2% having the associated particle PT in the range 0.25-0.5 GeV. Note that in the paper the data are plotted multiplied by 100.

V1Delta coefficients as a function of the trigger particle PT for events in the centrality class 0-2% having the associated particle PT in the range 1-1.5 GeV. Note that in the paper the data are plotted multiplied by 100.

V1Delta coefficients as a function of the trigger particle PT for events in the centrality class 0-10% having the associated particle PT in the range 0.25-0.5 GeV. Note that in the paper the data are plotted multiplied by 100.

V1Delta coefficients as a function of the trigger particle PT for events in the centrality class 0-10% having the associated particle PT in the range 1-1.5 GeV. Note that in the paper the data are plotted multiplied by 100.

V1Delta coefficients as a function of the trigger particle PT for events in the centrality class 0-10% having the associated particle PT in the range 2-2.5 GeV. Note that in the paper the data are plotted multiplied by 100.

V1Delta coefficients as a function of the trigger particle PT for events in the centrality class 40-50% having the associated particle PT in the range 0.25-0.5 GeV. Note that in the paper the data are plotted multiplied by 100.

V1Delta coefficients as a function of the trigger particle PT for events in the centrality class 40-50% having the associated particle PT in the range 1-1.5 GeV. Note that in the paper the data are plotted multiplied by 100.

V1Delta coefficients as a function of the trigger particle PT for events in the centrality class 40-50% having the associated particle PT in the range 2-2.5 GeV. Note that in the paper the data are plotted multiplied by 100.

V2Delta coefficients as a function of the trigger particle PT for events in the centrality class 0-2% having the associated particle PT in the range 0.25-0.5 GeV. Note that in the paper the data are plotted multiplied by 100.

V2Delta coefficients as a function of the trigger particle PT for events in the centrality class 0-2% having the associated particle PT in the range 1-1.5 GeV. Note that in the paper the data are plotted multiplied by 100.

V2Delta coefficients as a function of the trigger particle PT for events in the centrality class 0-10% having the associated particle PT in the range 0.25-0.5 GeV. Note that in the paper the data are plotted multiplied by 100.

V2Delta coefficients as a function of the trigger particle PT for events in the centrality class 0-10% having the associated particle PT in the range 1-1.5 GeV. Note that in the paper the data are plotted multiplied by 100.

V2Delta coefficients as a function of the trigger particle PT for events in the centrality class 0-10% having the associated particle PT in the range 2-2.5 GeV. Note that in the paper the data are plotted multiplied by 100.

V2Delta coefficients as a function of the trigger particle PT for events in the centrality class 40-50% having the associated particle PT in the range 0.25-0.5 GeV. Note that in the paper the data are plotted multiplied by 100.

V2Delta coefficients as a function of the trigger particle PT for events in the centrality class 40-50% having the associated particle PT in the range 1-1.5 GeV. Note that in the paper the data are plotted multiplied by 100.

V2Delta coefficients as a function of the trigger particle PT for events in the centrality class 40-50% having the associated particle PT in the range 2-2.5 GeV. Note that in the paper the data are plotted multiplied by 100.

V3Delta coefficients as a function of the trigger particle PT for events in the centrality class 0-2% having the associated particle PT in the range 0.25-0.5 GeV. Note that in the paper the data are plotted multiplied by 100.

V3Delta coefficients as a function of the trigger particle PT for events in the centrality class 0-2% having the associated particle PT in the range 1-1.5 GeV. Note that in the paper the data are plotted multiplied by 100.

V3Delta coefficients as a function of the trigger particle PT for events in the centrality class 0-10% having the associated particle PT in the range 0.25-0.5 GeV. Note that in the paper the data are plotted multiplied by 100.

V3Delta coefficients as a function of the trigger particle PT for events in the centrality class 0-10% having the associated particle PT in the range 1-1.5 GeV. Note that in the paper the data are plotted multiplied by 100.

V3Delta coefficients as a function of the trigger particle PT for events in the centrality class 0-10% having the associated particle PT in the range 2-2.5 GeV. Note that in the paper the data are plotted multiplied by 100.

V3Delta coefficients as a function of the trigger particle PT for events in the centrality class 40-50% having the associated particle PT in the range 0.25-0.5 GeV. Note that in the paper the data are plotted multiplied by 100.

V3Delta coefficients as a function of the trigger particle PT for events in the centrality class 40-50% having the associated particle PT in the range 1-1.5 GeV. Note that in the paper the data are plotted multiplied by 100.

V3Delta coefficients as a function of the trigger particle PT for events in the centrality class 40-50% having the associated particle PT in the range 2-2.5 GeV. Note that in the paper the data are plotted multiplied by 100.

V4Delta coefficients as a function of the trigger particle PT for events in the centrality class 0-2% having the associated particle PT in the range 0.25-0.5 GeV. Note that in the paper the data are plotted multiplied by 100.

V4Delta coefficients as a function of the trigger particle PT for events in the centrality class 0-2% having the associated particle PT in the range 1-1.5 GeV. Note that in the paper the data are plotted multiplied by 100.

V4Delta coefficients as a function of the trigger particle PT for events in the centrality class 0-10% having the associated particle PT in the range 0.25-0.5 GeV. Note that in the paper the data are plotted multiplied by 100.

V4Delta coefficients as a function of the trigger particle PT for events in the centrality class 0-10% having the associated particle PT in the range 1-1.5 GeV. Note that in the paper the data are plotted multiplied by 100.

V4Delta coefficients as a function of the trigger particle PT for events in the centrality class 0-10% having the associated particle PT in the range 2-2.5 GeV. Note that in the paper the data are plotted multiplied by 100.

V4Delta coefficients as a function of the trigger particle PT for events in the centrality class 40-50% having the associated particle PT in the range 0.25-0.5 GeV. Note that in the paper the data are plotted multiplied by 100.

V4Delta coefficients as a function of the trigger particle PT for events in the centrality class 40-50% having the associated particle PT in the range 1-1.5 GeV. Note that in the paper the data are plotted multiplied by 100.

V4Delta coefficients as a function of the trigger particle PT for events in the centrality class 40-50% having the associated particle PT in the range 2-2.5 GeV. Note that in the paper the data are plotted multiplied by 100.

V5Delta coefficients as a function of the trigger particle PT for events in the centrality class 0-2% having the associated particle PT in the range 0.25-0.5 GeV. Note that in the paper the data are plotted multiplied by 100.

V5Delta coefficients as a function of the trigger particle PT for events in the centrality class 0-2% having the associated particle PT in the range 1-1.5 GeV. Note that in the paper the data are plotted multiplied by 100.

V5Delta coefficients as a function of the trigger particle PT for events in the centrality class 0-10% having the associated particle PT in the range 0.25-0.5 GeV. Note that in the paper the data are plotted multiplied by 100.

V5Delta coefficients as a function of the trigger particle PT for events in the centrality class 0-10% having the associated particle PT in the range 1-1.5 GeV. Note that in the paper the data are plotted multiplied by 100.

V5Delta coefficients as a function of the trigger particle PT for events in the centrality class 0-10% having the associated particle PT in the range 2-2.5 GeV. Note that in the paper the data are plotted multiplied by 100.

V5Delta coefficients as a function of the trigger particle PT for events in the centrality class 40-50% having the associated particle PT in the range 0.25-0.5 GeV. Note that in the paper the data are plotted multiplied by 100.

V5Delta coefficients as a function of the trigger particle PT for events in the centrality class 40-50% having the associated particle PT in the range 1-1.5 GeV. Note that in the paper the data are plotted multiplied by 100.

V5Delta coefficients as a function of the trigger particle PT for events in the centrality class 40-50% having the associated particle PT in the range 2-2.5 GeV. Note that in the paper the data are plotted multiplied by 100.

V1Delta for all pt combinations for the centrality classes 0-10% and 40-50%.

V2Delta for all pt combinations for the centrality classes 0-10% and 40-50%.

V3Delta for all pt combinations for the centrality classes 0-10% and 40-50%.

V4Delta for all pt combinations for the centrality classes 0-10% and 40-50%.

V5Delta for all pt combinations for the centrality classes 0-10% and 40-50%.

The global fit paramter v_2{GF} vs. the trigger particle PT for fit range of 0.25-15 GeV/c for the centrality class 0-2%.

The global fit paramter v_2{GF} vs. the trigger particle PT for fit range of 0.25-15 GeV/c for the centrality class 2-10%.

The global fit paramter v_2{GF} vs. the trigger particle PT for fit range of 0.25-15 GeV/c for the centrality class 10-20%.

The global fit paramter v_2{GF} vs. the trigger particle PT for fit range of 0.25-15 GeV/c for the centrality class 20-30%.

The global fit paramter v_2{GF} vs. the trigger particle PT for fit range of 0.25-15 GeV/c for the centrality class 30-40%.

The global fit paramter v_2{GF} vs. the trigger particle PT for fit range of 0.25-15 GeV/c for the centrality class 40-50%.

The global fit paramter v_3{GF} vs. the trigger particle PT for fit range of 0.25-15 GeV/c for the centrality class 0-2%.

The global fit paramter v_3{GF} vs. the trigger particle PT for fit range of 0.25-15 GeV/c for the centrality class 2-10%.

The global fit paramter v_3{GF} vs. the trigger particle PT for fit range of 0.25-15 GeV/c for the centrality class 10-20%.

The global fit paramter v_3{GF} vs. the trigger particle PT for fit range of 0.25-15 GeV/c for the centrality class 20-30%.

The global fit paramter v_3{GF} vs. the trigger particle PT for fit range of 0.25-15 GeV/c for the centrality class 30-40%.

The global fit paramter v_3{GF} vs. the trigger particle PT for fit range of 0.25-15 GeV/c for the centrality class 40-50%.

The global fit paramter v_4{GF} vs. the trigger particle PT for fit range of 0.25-15 GeV/c for the centrality class 0-2%.

The global fit paramter v_4{GF} vs. the trigger particle PT for fit range of 0.25-15 GeV/c for the centrality class 2-10%.

The global fit paramter v_4{GF} vs. the trigger particle PT for fit range of 0.25-15 GeV/c for the centrality class 10-20%.

The global fit paramter v_4{GF} vs. the trigger particle PT for fit range of 0.25-15 GeV/c for the centrality class 20-30%.

The global fit paramter v_4{GF} vs. the trigger particle PT for fit range of 0.25-15 GeV/c for the centrality class 30-40%.

The global fit paramter v_4{GF} vs. the trigger particle PT for fit range of 0.25-15 GeV/c for the centrality class 40-50%.

The global fit paramter v_5{GF} vs. the trigger particle PT for fit range of 0.25-15 GeV/c for the centrality class 0-2%.

The global fit paramter v_5{GF} vs. the trigger particle PT for fit range of 0.25-15 GeV/c for the centrality class 2-10%.

The global fit paramter v_5{GF} vs. the trigger particle PT for fit range of 0.25-15 GeV/c for the centrality class 10-20%.

The global fit paramter v_5{GF} vs. the trigger particle PT for fit range of 0.25-15 GeV/c for the centrality class 20-30%.

The global fit paramter v_5{GF} vs. the trigger particle PT for fit range of 0.25-15 GeV/c for the centrality class 30-40%.

The global fit paramter v_5{GF} vs. the trigger particle PT for fit range of 0.25-15 GeV/c for the centrality class 40-50%.

The global fit paramter v_1{GF} vs. the trigger particle PT for fit range of 0.25-5 GeV/c for the centrality class 0-20%.

The global fit paramter v_1{GF} vs. the trigger particle PT for fit range of 0.25-5 GeV/c for the centrality class 40-50%.

The global fit paramter v_2{GF} vs. the trigger particle PT for fit range of 0.25-5 GeV/c for the centrality class 0-20%.

The global fit paramter v_2{GF} vs. the trigger particle PT for fit range of 0.25-5 GeV/c for the centrality class 40-50%.

The global fit paramter v_3{GF} vs. the trigger particle PT for fit range of 0.25-5 GeV/c for the centrality class 0-20%.

The global fit paramter v_3{GF} vs. the trigger particle PT for fit range of 0.25-5 GeV/c for the centrality class 40-50%.

The global fit paramter v_4{GF} vs. the trigger particle PT for fit range of 0.25-5 GeV/c for the centrality class 0-20%.

The global fit paramter v_4{GF} vs. the trigger particle PT for fit range of 0.25-5 GeV/c for the centrality class 40-50%.

The global fit paramter v_5{GF} vs. the trigger particle PT for fit range of 0.25-5 GeV/c for the centrality class 0-20%.

The global fit paramter v_5{GF} vs. the trigger particle PT for fit range of 0.25-5 GeV/c for the centrality class 40-50%.

The global fit paramter v_1{GF} vs. the trigger particle PT for fit range of 5-15 GeV/c for the centrality class 0-20%.

The global fit paramter v_1{GF} vs. the trigger particle PT for fit range of 5-15 GeV/c for the centrality class 40-50%.

The global fit paramter v_2{GF} vs. the trigger particle PT for fit range of 5-15 GeV/c for the centrality class 0-20%.

The global fit paramter v_2{GF} vs. the trigger particle PT for fit range of 5-15 GeV/c for the centrality class 40-50%.

The global fit paramter v_3{GF} vs. the trigger particle PT for fit range of 5-15 GeV/c for the centrality class 0-20%.

The global fit paramter v_3{GF} vs. the trigger particle PT for fit range of 5-15 GeV/c for the centrality class 40-50%.

The global fit paramter v_4{GF} vs. the trigger particle PT for fit range of 5-15 GeV/c for the centrality class 0-20%.

The global fit paramter v_4{GF} vs. the trigger particle PT for fit range of 5-15 GeV/c for the centrality class 40-50%.

The global fit paramter v_5{GF} vs. the trigger particle PT for fit range of 5-15 GeV/c for the centrality class 0-20%.

The global fit paramter v_5{GF} vs. the trigger particle PT for fit range of 5-15 GeV/c for the centrality class 40-50%.

The global fit paramter v_1{GF} vs. the trigger particle PT for fit range of 0.25-1 GeV/c for the centrality class 0-10%.

The global fit paramter v_1{GF} vs. the trigger particle PT for fit range of 0.25-1 GeV/c for the centrality class 40-50%.

The global fit paramter v_2{GF} vs. the trigger particle PT for fit range of 0.25-1 GeV/c for the centrality class 0-10%.

The global fit paramter v_2{GF} vs. the trigger particle PT for fit range of 0.25-1 GeV/c for the centrality class 40-50%.

The global fit paramter v_1{GF} vs. the trigger particle PT for fit range of 2-4 GeV/c for the centrality class 0-10%.

The global fit paramter v_1{GF} vs. the trigger particle PT for fit range of 2-4 GeV/c for the centrality class 40-50%.

The global fit paramter v_2{GF} vs. the trigger particle PT for fit range of 2-4 GeV/c for the centrality class 0-10%.

The global fit paramter v_2{GF} vs. the trigger particle PT for fit range of 2-4 GeV/c for the centrality class 40-50%.

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.

Projections of the correlation function C.

Projections of the correlation function C.

Projections of the correlation function C.

Projections of the correlation function C.

Pion HBT radii for the 5% most central collisions.

Pion HBT radii for the 5% most central collisions from the STAR experiment at 200 GeV taken from Adams et al. PR C71(2005)044906.

Ratio of Pion HBT radii for the OUT projection to that for the SIDE projection for the 5% most central collisions.

Ratio of Pion HBT radii for the OUT projection to that for the SIDE projection for the 5% most central collisions from the STAR experiment at 200 GeV taken from Adams et al. PR C71(2005)044906.;.

Pion HBT radii at KT=0.3 for the 5% most central collisions as a function of the central charged multiplicity. Data from other experiments is shown for comparison.

Product of the three HBT radii at KT=0.3 for the 5% most central collisions as a function of the central charged multiplicity. Data from other experiments is shown for comparison.

The decoupling time extracted from R_long(KT) as a function of the central charged multiplicity. Data from other experiments is shown for comparison.

The measured strange quark helicity distribution as a funxtion of X.