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.

Observed exclusion limits at the 95% CL in the $\tilde{t}_1 - \tilde\chi^0_1$ mass plane, assuming BR$(\tilde{t}_1 \rightarrow t + \tilde\chi^0_1) = 0.5$ and a $-1 \sigma$ deviation of the NNLO+NNLL theoretical cross-section of a $\tilde{t}_1$ pair-production.

Expected exclusion limits at the 95% CL in the $\tilde{t}_1 - \tilde\chi^0_1$ mass plane, assuming BR$(\tilde{t}_1 \rightarrow t + \tilde\chi^0_1) = 0.5$.

The $1\sigma$ variation of expected 95% CL exclusion contour obtained by varying MC statistical uncertainties, detector-related systematic uncertainties, and theoretical uncertainties in the $\tilde{t}_1 - \tilde\chi^0_1$ mass plane, assuming BR$(\tilde{t}_1 \rightarrow t + \tilde\chi^0_1) = 0.5$.

The $2\sigma$ variation of expected 95%CL exclusion contour obtained by varying MC statistical uncertainties, detector-related systematic uncertainties, and theoretical uncertainties in the $\tilde{t}_1 - \tilde\chi^0_1$ mass plane, assuming BR$(\tilde{t}_1 \rightarrow t + \tilde\chi^0_1) = 0.5$.

Observed exclusion limits at the 95% CL in the $m_{\tilde{t}_1} - $BR$(\tilde{t}_1 \rightarrow t + \tilde\chi^0_1)$ plane, assuming $m_{\tilde\chi^0_1} = 1 \mathrm{GeV}$.

Observed exclusion limits at the 95% CL in the $\tilde{t}_1 - \tilde\chi^0_1$ mass plane, assuming $m_{\tilde\chi^0_1} = 1 \mathrm{ GeV}$ and a $+1 \sigma$ deviation of the NNLO+NNLL theoretical cross-section of a $\tilde{t}_1$ pair-production.

Observed exclusion limits at the 95% CL in the $\tilde{t}_1 - \tilde\chi^0_1$ mass plane, assuming $m_{\tilde\chi^0_1} = 1 \mathrm{ GeV}$ and a $-1 \sigma$ deviation of the NNLO+NNLL theoretical cross-section of a $\tilde{t}_1$ pair-production.

Expected exclusion limits at the 95% CL in the $m_{\tilde{t}_1} - $BR$(\tilde{t}_1 \rightarrow t + \tilde\chi^0_1)$ plane, assuming $m_{\tilde\chi^0_1} = 1 \mathrm{GeV}$.

The $1\sigma$ variation of expected 95% CL exclusion contour obtained by varying MC statistical uncertainties, detector-related systematic uncertainties, and theoretical uncertainties in the $m_{\tilde{t}_1} - $BR$(\tilde{t}_1 \rightarrow t + \tilde\chi^0_1)$ plane, assuming $m_{\tilde\chi^0_1} = 1 \mathrm{GeV}$.

The $2\sigma$ variation of expected 95%CL exclusion contour obtained by varying MC statistical uncertainties, detector-related systematic uncertainties, and theoretical uncertainties in the $m_{\tilde{t}_1} - $BR$(\tilde{t}_1 \rightarrow t + \tilde\chi^0_1)$ plane, assuming $m_{\tilde\chi^0_1} = 1 \mathrm{GeV}$.

Observed upper limits on the top-spartner pair production cross-section in fb at the 95% CL in the $\tilde{t}_1 - \tilde\chi^0_1$ mass plane, assuming BR$(\tilde{t}_1 \rightarrow t + \tilde\chi^0_1) = 0.5$

Expected upper limits on the top-spartner pair production cross-section in fb at the 95% CL in the $\tilde{t}_1 - \tilde\chi^0_1$ mass plane, assuming BR$(\tilde{t}_1 \rightarrow t + \tilde\chi^0_1) = 0.5$

Observed upper limits on the top-spartner pair production cross-section in fb at the 95% CL in the $m_{\tilde{t}_1} - $BR$(\tilde{t}_1 \rightarrow t + \tilde\chi^0_1)$ plane, assuming $m_{\tilde\chi^0_1} = 1 \mathrm{GeV}$.

Expected upper limits on the top-spartner pair production cross-section in fb at the 95% CL in the $m_{\tilde{t}_1} - $BR$(\tilde{t}_1 \rightarrow t + \tilde\chi^0_1)$ plane, assuming $m_{\tilde\chi^0_1} = 1 \mathrm{GeV}$.

Post-fit distribution of $N_{\mathrm{tops}}^{\mathrm{DNN}} (\mathrm{R=1.0})$ in the SRA signal region presented without the associated SRA applied to the variable. For each bin yields for the data and total SM prediction are provided. The SM prediction is provided with the total uncertainty, including the MC statistical uncertainty, detector-related systematic uncertainties and theoretical uncertainties. The rightmost bin includes overflow events.

Post-fit distribution of $m_{\mathrm{T2}}(j^{b}_{R=1.0}, c)$ in the SRA signal region presented without the associated SRA applied to the variable. For each bin yields for the data and total SM prediction are provided. The SM prediction is provided with the total uncertainty, including the MC statistical uncertainty, detector-related systematic uncertainties and theoretical uncertainties. The rightmost bin includes overflow events.

Post-fit distribution of $p_{\mathrm{T}}(c_{1})$ in the SRB signal region presented without the associated SRB applied to the variable. For each bin yields for the data and total SM prediction are provided. The SM prediction is provided with the total uncertainty, including the MC statistical uncertainty, detector-related systematic uncertainties and theoretical uncertainties. The rightmost bin includes overflow events.

Post-fit distribution of $m_{\mathrm{T}}(j, \mathrm{E}_{\mathrm{T}}^{\mathrm{miss}})_{\mathrm{close}}$ in the SRB signal region presented without the associated SRB applied to the variable. For each bin yields for the data and total SM prediction are provided. The SM prediction is provided with the total uncertainty, including the MC statistical uncertainty, detector-related systematic uncertainties and theoretical uncertainties. The rightmost bin includes overflow events.

Post-fit distribution of $\mathrm{E}_{\mathrm{T}}^{\mathrm{miss}} \textrm{Significance}$ in the SRC signal region presented without the associated SRC applied to the variable. For each bin yields for the data and total SM prediction are provided. The SM prediction is provided with the total uncertainty, including the MC statistical uncertainty, detector-related systematic uncertainties and theoretical uncertainties. The rightmost bin includes overflow events.

Post-fit distribution of $m_{\mathrm{T}}(j, \mathrm{E}_{\mathrm{T}}^{\mathrm{miss}})_{\mathrm{close}}$ in the SRC signal region presented without the associated SRC applied to the variable. For each bin yields for the data and total SM prediction are provided. The SM prediction is provided with the total uncertainty, including the MC statistical uncertainty, detector-related systematic uncertainties and theoretical uncertainties. The rightmost bin includes overflow events.

Post-fit distribution of NN signal score in the SRD signal region presented without the associated SRD applied to the variable. For each bin yields for the data and total SM prediction are provided. The SM prediction is provided with the total uncertainty, including the MC statistical uncertainty, detector-related systematic uncertainties and theoretical uncertainties. The rightmost bin includes overflow events.

Post-fit distribution of $m_{\mathrm{eff}}$ in the SRD signal region. For each bin yields for the data and total SM prediction are provided. The SM prediction is provided with the total uncertainty, including the MC statistical uncertainty, detector-related systematic uncertainties and theoretical uncertainties. The rightmost bin includes overflow events.

Pull plots showing the SRA, SRB and SRC post-fit data and SM agreement using the background-only fit configuration

Pull plots showing the SRD post-fit data and SM agreement using the background-only fit configuration

Cutflow for the reference point $(m_{\tilde{t}_1}, m_{\tilde\chi^0_1})=$ (900,1) , (700,300), (550,375) in the Signal region A. Results are shown including all correction factors applied to simulation, and is normalised to 139 fb$^{-1}$.

Cutflow for the reference point $(m_{\tilde{t}_1}, m_{\tilde\chi^0_1})=$ (900,1) , (700,300), (550,375) in the Signal region B. Results are shown including all correction factors applied to simulation, and is normalised to 139 fb$^{-1}$.

Cutflow for the reference point $(m_{\tilde{t}_1}, m_{\tilde\chi^0_1})=$ (900,1) , (700,300), (550,375) in the Signal region C. Results are shown including all correction factors applied to simulation, and is normalised to 139 fb$^{-1}$.

Cutflow for the reference point $(m_{\tilde{t}_1}, m_{\tilde\chi^0_1})=$ (900,1) , (700,300), (550,375) in the Signal region D 750. Results are shown including all correction factors applied to simulation, and is normalised to 139 fb$^{-1}$.

Cutflow for the reference point $(m_{\tilde{t}_1}, m_{\tilde\chi^0_1})=$ (900,1) , (700,300), (550,375) in the Signal region D 1000. Results are shown including all correction factors applied to simulation, and is normalised to 139 fb$^{-1}$.

Cutflow for the reference point $(m_{\tilde{t}_1}, m_{\tilde\chi^0_1})=$ (900,1) , (700,300), (550,375) in the Signal region D 1250. Results are shown including all correction factors applied to simulation, and is normalised to 139 fb$^{-1}$.

Cutflow for the reference point $(m_{\tilde{t}_1}, m_{\tilde\chi^0_1})=$ (900,1) , (700,300), (550,375) in the Signal region D 1500. Results are shown including all correction factors applied to simulation, and is normalised to 139 fb$^{-1}$.

Cutflow for the reference point $(m_{\tilde{t}_1}, m_{\tilde\chi^0_1})=$ (900,1) , (700,300), (550,375) in the Signal region D 1750. Results are shown including all correction factors applied to simulation, and is normalised to 139 fb$^{-1}$.

Cutflow for the reference point $(m_{\tilde{t}_1}, m_{\tilde\chi^0_1})=$ (900,1) , (700,300), (550,375) in the Signal region D 2000. Results are shown including all correction factors applied to simulation, and is normalised to 139 fb$^{-1}$.

Signal acceptance in the SRA$^{[450,575]}$ region in the $\tilde{t}_1 - \tilde\chi^0_1$ mass plane, assuming BR$(\tilde{t}_1 \rightarrow t + \tilde\chi^0_1) = 0.5$. Please mind that the acceptance given in the table is multiplied by factor of $10^{3}$ (a factor of 10 larger than in the plots).

Signal efficiency in the SRA$^{[450,575]}$ region in the $\tilde{t}_1 - \tilde\chi^0_1$ mass plane, assuming BR$(\tilde{t}_1 \rightarrow t + \tilde\chi^0_1) = 0.5$.

Signal acceptance in the SRA$^{\geq 575}$ region in the $\tilde{t}_1 - \tilde\chi^0_1$ mass plane, assuming BR$(\tilde{t}_1 \rightarrow t + \tilde\chi^0_1) = 0.5$. Please mind that the acceptance given in the table is multiplied by factor of $10^{3}$ (a factor of 10 larger than in the plots).

Signal efficiency in the SRA$^{\geq 575}$ region in the $\tilde{t}_1 - \tilde\chi^0_1$ mass plane, assuming BR$(\tilde{t}_1 \rightarrow t + \tilde\chi^0_1) = 0.5$.

Signal acceptance in the SRB$^{[100,150]}$ region in the $\tilde{t}_1 - \tilde\chi^0_1$ mass plane, assuming BR$(\tilde{t}_1 \rightarrow t + \tilde\chi^0_1) = 0.5$. Please mind that the acceptance given in the table is multiplied by factor of $10^{3}$ (a factor of 10 larger than in the plots).

Signal efficiency in the SRB$^{[100,150]}$ region in the $\tilde{t}_1 - \tilde\chi^0_1$ mass plane, assuming BR$(\tilde{t}_1 \rightarrow t + \tilde\chi^0_1) = 0.5$.

Signal acceptance in the SRB$^{[150,400]}$ region in the $\tilde{t}_1 - \tilde\chi^0_1$ mass plane, assuming BR$(\tilde{t}_1 \rightarrow t + \tilde\chi^0_1) = 0.5$. Please mind that the acceptance given in the table is multiplied by factor of $10^{3}$ (a factor of 10 larger than in the plots).

Signal efficiency in the SRB$^{[150,400]}$ region in the $\tilde{t}_1 - \tilde\chi^0_1$ mass plane, assuming BR$(\tilde{t}_1 \rightarrow t + \tilde\chi^0_1) = 0.5$.

Signal acceptance in the SRB$^{\geq 400}$ region in the $\tilde{t}_1 - \tilde\chi^0_1$ mass plane, assuming BR$(\tilde{t}_1 \rightarrow t + \tilde\chi^0_1) = 0.5$. Please mind that the acceptance given in the table is multiplied by factor of $10^{3}$ (a factor of 10 larger than in the plots).

Signal efficiency in the SRB$^{\geq 400}$ region in the $\tilde{t}_1 - \tilde\chi^0_1$ mass plane, assuming BR$(\tilde{t}_1 \rightarrow t + \tilde\chi^0_1) = 0.5$.

Signal acceptance in the SRC$^{[100,150]}$ region in the $\tilde{t}_1 - \tilde\chi^0_1$ mass plane, assuming BR$(\tilde{t}_1 \rightarrow t + \tilde\chi^0_1) = 0.5$. Please mind that the acceptance given in the table is multiplied by factor of $10^{3}$ (a factor of 10 larger than in the plots).

Signal efficiency in the SRC$^{[100,150]}$ region in the $\tilde{t}_1 - \tilde\chi^0_1$ mass plane, assuming BR$(\tilde{t}_1 \rightarrow t + \tilde\chi^0_1) = 0.5$.

Signal acceptance in the SRC$^{[150,300]}$ region in the $\tilde{t}_1 - \tilde\chi^0_1$ mass plane, assuming BR$(\tilde{t}_1 \rightarrow t + \tilde\chi^0_1) = 0.5$. Please mind that the acceptance given in the table is multiplied by factor of $10^{3}$ (a factor of 10 larger than in the plots).

Signal efficiency in the SRC$^{[150,300]}$ region in the $\tilde{t}_1 - \tilde\chi^0_1$ mass plane, assuming BR$(\tilde{t}_1 \rightarrow t + \tilde\chi^0_1) = 0.5$.

Signal acceptance in the SRC$^{[300,500]}$ region in the $\tilde{t}_1 - \tilde\chi^0_1$ mass plane, assuming BR$(\tilde{t}_1 \rightarrow t + \tilde\chi^0_1) = 0.5$. Please mind that the acceptance given in the table is multiplied by factor of $10^{3}$ (a factor of 10 larger than in the plots).

Signal efficiency in the SRC$^{[300,500]}$ region in the $\tilde{t}_1 - \tilde\chi^0_1$ mass plane, assuming BR$(\tilde{t}_1 \rightarrow t + \tilde\chi^0_1) = 0.5$.

Signal acceptance in the SRC$^{\geq 500}$ region in the $\tilde{t}_1 - \tilde\chi^0_1$ mass plane, assuming BR$(\tilde{t}_1 \rightarrow t + \tilde\chi^0_1) = 0.5$. Please mind that the acceptance given in the table is multiplied by factor of $10^{3}$ (a factor of 10 larger than in the plots).

Signal efficiency in the SRC$^{\geq 500}$ region in the $\tilde{t}_1 - \tilde\chi^0_1$ mass plane, assuming BR$(\tilde{t}_1 \rightarrow t + \tilde\chi^0_1) = 0.5$.

Signal acceptance in the SRD750 region in the $\tilde{t}_1 - \tilde\chi^0_1$ mass plane, assuming BR$(\tilde{t}_1 \rightarrow t + \tilde\chi^0_1) = 0.5$. Please mind that the acceptance given in the table is multiplied by factor of $10^{3}$ (a factor of 10 larger than in the plots).

Signal efficiency in the SRD750 region in the $\tilde{t}_1 - \tilde\chi^0_1$ mass plane, assuming BR$(\tilde{t}_1 \rightarrow t + \tilde\chi^0_1) = 0.5$.

Signal acceptance in the SRD1000 region in the $\tilde{t}_1 - \tilde\chi^0_1$ mass plane, assuming BR$(\tilde{t}_1 \rightarrow t + \tilde\chi^0_1) = 0.5$. Please mind that the acceptance given in the table is multiplied by factor of $10^{3}$ (a factor of 10 larger than in the plots).

Signal efficiency in the SRD1000 region in the $\tilde{t}_1 - \tilde\chi^0_1$ mass plane, assuming BR$(\tilde{t}_1 \rightarrow t + \tilde\chi^0_1) = 0.5$.

Signal acceptance in the SRD1250 region in the $\tilde{t}_1 - \tilde\chi^0_1$ mass plane, assuming BR$(\tilde{t}_1 \rightarrow t + \tilde\chi^0_1) = 0.5$. Please mind that the acceptance given in the table is multiplied by factor of $10^{3}$ (a factor of 10 larger than in the plots).

Signal efficiency in the SRD1250 region in the $\tilde{t}_1 - \tilde\chi^0_1$ mass plane, assuming BR$(\tilde{t}_1 \rightarrow t + \tilde\chi^0_1) = 0.5$.

Signal acceptance in the SRD1500 region in the $\tilde{t}_1 - \tilde\chi^0_1$ mass plane, assuming BR$(\tilde{t}_1 \rightarrow t + \tilde\chi^0_1) = 0.5$. Please mind that the acceptance given in the table is multiplied by factor of $10^{3}$ (a factor of 10 larger than in the plots).

Signal efficiency in the SRD1500 region in the $\tilde{t}_1 - \tilde\chi^0_1$ mass plane, assuming BR$(\tilde{t}_1 \rightarrow t + \tilde\chi^0_1) = 0.5$.

Signal acceptance in the SRD1750 region in the $\tilde{t}_1 - \tilde\chi^0_1$ mass plane, assuming BR$(\tilde{t}_1 \rightarrow t + \tilde\chi^0_1) = 0.5$. Please mind that the acceptance given in the table is multiplied by factor of $10^{3}$ (a factor of 10 larger than in the plots).

Signal efficiency in the SRD1750 region in the $\tilde{t}_1 - \tilde\chi^0_1$ mass plane, assuming BR$(\tilde{t}_1 \rightarrow t + \tilde\chi^0_1) = 0.5$.

Signal acceptance in the SRD2000 region in the $\tilde{t}_1 - \tilde\chi^0_1$ mass plane, assuming BR$(\tilde{t}_1 \rightarrow t + \tilde\chi^0_1) = 0.5$. Please mind that the acceptance given in the table is multiplied by factor of $10^{3}$ (a factor of 10 larger than in the plots).

Signal efficiency in the SRD2000 region in the $\tilde{t}_1 - \tilde\chi^0_1$ mass plane, assuming BR$(\tilde{t}_1 \rightarrow t + \tilde\chi^0_1) = 0.5$.

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.

Distribution of $m_{\mathrm{JJ}}$ in the SR (black points) compared to the background-only expectation, where the shape is derived from the CR and the normalisation is fitted in the SR.

Observed and expected limits at 95% CL on the cross-section times branching ratio for the production of dark quarks through a $Z^\prime$ as a function of the $Z^\prime$ mass for model A (see the text for details). The darker and lighter shaded bands around the expected limits represent the $\pm 1 \sigma$ and $\pm 2 \sigma$ uncertainty range, respectively.

The predicted theory cross-section times branching ratio for the production of dark quarks through a $Z^\prime$ as a function of the $Z^\prime$ mass for model A (see the text for details). In the theory model, a universal coupling of the $Z^\prime$ to each SM quark $g_q$ is assumed and the dark quarks are all represented by one species with an effective coupling $g_{q_d}$ to the $Z^\prime$. For model A, the predicted cross-section is shown for $g_q=0.05$ and $g_{q_d} = 0.2$.

Observed and expected limits at 95% CL on the cross-section times branching ratio for the production of dark quarks through a $Z^\prime$ as a function of the $Z^\prime$ mass for model B (see the text for details). The darker and lighter shaded bands around the expected limits represent the $\pm 1 \sigma$ and $\pm 2 \sigma$ uncertainty range, respectively.

The predicted theory cross-section times branching ratio for the production of dark quarks through a $Z^\prime$ as a function of the $Z^\prime$ mass for model B (see the text for details). In the theory model, a universal coupling of the $Z^\prime$ to each SM quark $g_q$ is assumed and the dark quarks are all represented by one species with an effective coupling $g_{q_d}$ to the $Z^\prime$. For model B, the predicted cross-section is shown for $g_q=0.15$ and $g_{q_d} = 0.5$.

Observed and expected limits at 95% CL on the cross-section times branching ratio for the production of dark quarks through a $Z^\prime$ as a function of the $Z^\prime$ mass for model C (see the text for details). The darker and lighter shaded bands around the expected limits represent the $\pm 1 \sigma$ and $\pm 2 \sigma$ uncertainty range, respectively.

The predicted theory cross-section times branching ratio for the production of dark quarks through a $Z^\prime$ as a function of the $Z^\prime$ mass for model C (see the text for details). In the theory model, a universal coupling of the $Z^\prime$ to each SM quark $g_q$ is assumed and the dark quarks are all represented by one species with an effective coupling $g_{q_d}$ to the $Z^\prime$. For model C, the predicted cross-section is shown for $g_q=0.15$ and $g_{q_d}= 0.5$.

Observed and expected limits at 95% CL on the cross-section times branching ratio for the production of dark quarks through a $Z^\prime$ as a function of the $Z^\prime$ mass for model D (see the text for details). The darker and lighter shaded bands around the expected limits represent the $\pm 1 \sigma$ and $\pm 2 \sigma$ uncertainty range, respectively.

The predicted theory cross-section times branching ratio for the production of dark quarks through a $Z^\prime$ as a function of the $Z^\prime$ mass for model D (see the text for details). In the theory model, a universal coupling of the $Z^\prime$ to each SM quark $g_q$ is assumed and the dark quarks are all represented by one species with an effective coupling $g_{q_d}$ to the $Z^\prime$. For model D, the predicted cross-section is shown for $g_q=0.05$ and $g_{q_d} = 0.2$.

Relative efficiency (in %) of each stage of the analysis selection with respect to the previous one for models A through D and $m_{Z^\prime}=2.5$ TeV. Approximately 90000 events were generated per signal mass hypothesis.

Unfolded $M(l^{-}\gamma)$ distribution for $Z \to \mu\mu\gamma$ process with dressed leptons and bkg subtraction. $M_{ll}>20$ GeV. Nexp.un f. = 64822.9 $\pm$ 254.6, NPowHeg truth =634276.

Unfolded dR distribution for $Z \to ee\gamma$ process with dressed leptons and bkg subtraction. $M_{ll}>20$ GeV. Nexp.un f. = 64273.2 $\pm$ 253.5, NPowHeg truth =338671.

Unfolded dR distribution for $Z \to \mu\mu\gamma$ process with dressed leptons and bkg subtraction. $M_{ll}>20$ GeV. Nexp.un f. = 65362.4 $\pm$ 255.7 , NPowHeg truth =634214.

Unfolded $P_{T}^{\gamma}$ distribution for $Z \to ee\gamma$ process with dressed leptons and bkg subtraction. $M_{ll}>20$ GeV. Nexp.un f. = 63486.8 $\pm$ 252.0, NPowHeg truth =333348.

Unfolded $P_{T}^{\gamma}$ distribution for $Z \to \mu\mu\gamma$ process with dressed leptons and bkg subtraction. $M_{ll}>20$ GeV. Nexp.un f. = 64432.6 $\pm$ 253.8, NPowHeg truth =624059.

Unfolded $M(l^{+}\gamma)$ distribution for $Z \to ee\gamma$ process with dressed leptons and bkg subtraction. $M_{ll}>45$ GeV. Nexp.un f. = 57095.9 $\pm$ 254 , NPowHeg truth =301666, N Sherpa truth =76327.

Unfolded $M(l^{-}\gamma)$ distribution for $Z \to ee\gamma$ process with dressed leptons and bkg subtraction. $M_{ll}>45$ GeV. Nexp.un f. = 57130 $\pm$ 254 , NPowHeg truth =301666, N Sherpa truth =763273.

Unfolded $M(l^{+}\gamma)$ distribution for $Z \to \mu\mu\gamma$ process with dressed leptons and bkg subtraction. $M_{ll}>45$ GeV. Nexp.un f. = 58310.9 $\pm$ 245, NPowHeg truth =564672, N Sherpa truth =814016.

Unfolded $M(l^{-}\gamma)$ distribution for $Z \to \mu\mu\gamma$ process with dressed leptons and bkg subtraction. $M_{ll}>45$ GeV. Nexp.un f. = 58320.9 $\pm$ 245, NPowHeg truth =564672, N Sherpa truth =814016.

Unfolded dR distribution for $Z \to ee\gamma$ process with dressed leptons and bkg subtraction. $M_{ll}>45$ GeV. Nexp.un f. = 57705.4 $\pm$ 254 , NPowHeg truth =301655, N Sherpa truth =763259.

Unfolded dR distribution for $Z \to \mu\mu\gamma$ process with dressed leptons and bkg subtraction. $M_{ll}>45$ GeV. Nexp.un f. = 58869.2 $\pm$ 256, NPowHeg truth =564660, NS herpa truth =813995.

Unfolded $P_{T}^{\gamma}$ distribution for $Z \to ee\gamma$ process with dressed leptons and bkg subtraction. $M_{ll}>45$ GeV. Nexp.un f. = 57358.6 $\pm$ 254 , NPowHeg truth =298662, N Sherpa truth =756609.

Unfolded $P_{T}^{\gamma}$ distribution for $Z \to \mu\mu\gamma$ process with dressed leptons and bkg subtraction. $M_{ll}>45$ GeV. Nexp.un f. = 58226.4 $\pm$ 254, NPowHeg truth =558949, N Sherpa truth =806988.

Unfolded $M(l^{+}\gamma)$ distribution for $Z \to ee\gamma$ process with bare leptons and bkg subtraction. $M_{ll}>20$ GeV. Nexp.un f. = 63717.4 $\pm$ 252.4, NPowHeg truth =338714.

Unfolded $M(l^{-}\gamma)$ distribution for $Z \to ee\gamma$ process with bare leptons and bkg subtraction. $M_{ll}>20$ GeV. Nexp.un f. = 63855.8 $\pm$ 252.7 , NPowHeg truth =338708.

Unfolded $M(l^{+}\gamma)$ distribution for $Z \to \mu\mu\gamma$ process with bare leptons and bkg subtraction. $M_{ll}>20$ GeV. Nexp.un f. = 64809.8 $\pm$ 254.6, NPowHeg truth =634285.

Unfolded $M(l^{-}\gamma)$ distribution for $Z \to \mu\mu\gamma$ process with bare leptons and bkg subtraction. $M_{ll}>20$ GeV. Nexp.un f. = 64822.9 $\pm$ 254.6, NPowHeg truth =634276.

Unfolded dR distribution for $Z \to ee\gamma$ process with bare leptons and bkg subtraction. $M_{ll}>20$ GeV. Nexp.un f. = 64273.2 $\pm$ 253.5, NPowHeg truth =338671.

Unfolded dR distribution for $Z \to \mu\mu\gamma$ process with bare leptons and bkg subtraction. $M_{ll}>20$ GeV. Nexp.un f. = 65362.4 $\pm$ 255.7 , NPowHeg truth =634214.

Unfolded $P_{T}^{\gamma}$ distribution for $Z \to ee\gamma$ process with bare leptons and bkg subtraction. $M_{ll}>20$ GeV. Nexp.un f. = 63486.8 $\pm$ 252.0, NPowHeg truth =333348.

Unfolded $P_{T}^{\gamma}$ distribution for $Z \to \mu\mu\gamma$ process with bare leptons and bkg subtraction. $M_{ll}>20$ GeV. Nexp.un f. = 64432.6 $\pm$ 253.8, NPowHeg truth =624059.

Unfolded $M(l^{+}\gamma)$ distribution for $Z \to ee\gamma$ process with bare leptons and bkg subtraction. $M_{ll}>45$ GeV. Nexp.un f. = 57095.9 $\pm$ 254 , NPowHeg truth =301666, N Sherpa truth =76327.

Unfolded $M(l^{-}\gamma)$ distribution for $Z \to ee\gamma$ process with bare leptons and bkg subtraction. $M_{ll}>45$ GeV. Nexp.un f. = 57130 $\pm$ 254 , NPowHeg truth =301666, N Sherpa truth =763273.

Unfolded $M(l^{+}\gamma)$ distribution for $Z \to \mu\mu\gamma$ process with bare leptons and bkg subtraction. $M_{ll}>45$ GeV. Nexp.un f. = 58310.9 $\pm$ 245, NPowHeg truth =564672, N Sherpa truth =814016.

Unfolded $M(l^{-}\gamma)$ distribution for $Z \to \mu\mu\gamma$ process with bare leptons and bkg subtraction. $M_{ll}>45$ GeV. Nexp.un f. = 58320.9 $\pm$ 245, NPowHeg truth =564672, N Sherpa truth =814016.

Unfolded dR distribution for $Z \to ee\gamma$ process with bare leptons and bkg subtraction. $M_{ll}>45$ GeV. Nexp.un f. = 57705.4 $\pm$ 254 , NPowHeg truth =301655, N Sherpa truth =763259.

Unfolded dR distribution for $Z \to \mu\mu\gamma$ process with bare leptons and bkg subtraction. $M_{ll}>45$ GeV. Nexp.un f. = 58869.2 $\pm$ 256, NPowHeg truth =564660, NS herpa truth =813995.

Unfolded $P_{T}^{\gamma}$ distribution for $Z \to ee\gamma$ process with bare leptons and bkg subtraction. $M_{ll}>45$ GeV. Nexp.un f. = 57358.6 $\pm$ 254 , NPowHeg truth =298662, N Sherpa truth =756609.

Unfolded $P_{T}^{\gamma}$ distribution for $Z \to \mu\mu\gamma$ process with bare leptons and bkg subtraction. $M_{ll}>45$ GeV. Nexp.un f. = 58226.4 $\pm$ 254, NPowHeg truth =558949, N Sherpa truth =806988.

Truth $P_{T}^{Z}$ distribution after reweghting to data.

Combined Covariance Matrix for Unfolded $M(l^{+}\gamma)$ distribution for $Z \to ee\gamma$ process with dressed leptons and bkg subtraction. $M_{ll}>20$ GeV. Nexp.un f. = 63717.4 $\pm$ 252.4, NPowHeg truth =338714.

Combined Covariance Matrix for Unfolded $M(l^{-}\gamma)$ distribution for $Z \to ee\gamma$ process with dressed leptons and bkg subtraction. $M_{ll}>20$ GeV. Nexp.un f. = 63855.8 $\pm$ 252.7 , NPowHeg truth =338708.

Combined Covariance Matrix for Unfolded $M(l^{+}\gamma)$ distribution for $Z \to \mu\mu\gamma$ process with dressed leptons and bkg subtraction. $M_{ll}>20$ GeV. Nexp.un f. = 64809.8 $\pm$ 254.6, NPowHeg truth =634285.

Combined Covariance Matrix for Unfolded $M(l^{-}\gamma)$ distribution for $Z \to \mu\mu\gamma$ process with dressed leptons and bkg subtraction. $M_{ll}>20$ GeV. Nexp.un f. = 64822.9 $\pm$ 254.6, NPowHeg truth =634276.

Combined Covariance Matrix for Unfolded dR distribution for $Z \to ee\gamma$ process with dressed leptons and bkg subtraction. $M_{ll}>20$ GeV. Nexp.un f. = 64273.2 $\pm$ 253.5, NPowHeg truth =338671.

Combined Covariance Matrix for Unfolded dR distribution for $Z \to \mu\mu\gamma$ process with dressed leptons and bkg subtraction. $M_{ll}>20$ GeV. Nexp.un f. = 65362.4 $\pm$ 255.7 , NPowHeg truth =634214.

Combined Covariance Matrix for Unfolded $P_{T}^{\gamma}$ distribution for $Z \to ee\gamma$ process with dressed leptons and bkg subtraction. $M_{ll}>20$ GeV. Nexp.un f. = 63486.8 $\pm$ 252.0, NPowHeg truth =333348.

Combined Covariance Matrix for Unfolded $P_{T}^{\gamma}$ distribution for $Z \to \mu\mu\gamma$ process with dressed leptons and bkg subtraction. $M_{ll}>20$ GeV. Nexp.un f. = 64432.6 $\pm$ 253.8, NPowHeg truth =624059.

Combined Covariance Matrix for Unfolded $M(l^{+}\gamma)$ distribution for $Z \to ee\gamma$ process with dressed leptons and bkg subtraction. $M_{ll}>45$ GeV. Nexp.un f. = 57095.9 $\pm$ 254 , NPowHeg truth =301666, N Sherpa truth =76327.

Combined Covariance Matrix for Unfolded $M(l^{-}\gamma)$ distribution for $Z \to ee\gamma$ process with dressed leptons and bkg subtraction. $M_{ll}>45$ GeV. Nexp.un f. = 57130 $\pm$ 254 , NPowHeg truth =301666, N Sherpa truth =763273.

Combined Covariance Matrix for Unfolded $M(l^{+}\gamma)$ distribution for $Z \to \mu\mu\gamma$ process with dressed leptons and bkg subtraction. $M_{ll}>45$ GeV. Nexp.un f. = 58310.9 $\pm$ 245, NPowHeg truth =564672, N Sherpa truth =814016.

Combined Covariance Matrix for Unfolded $M(l^{-}\gamma)$ distribution for $Z \to \mu\mu\gamma$ process with dressed leptons and bkg subtraction. $M_{ll}>45$ GeV. Nexp.un f. = 58320.9 $\pm$ 245, NPowHeg truth =564672, N Sherpa truth =814016.

Combined Covariance Matrix for Unfolded dR distribution for $Z \to ee\gamma$ process with dressed leptons and bkg subtraction. $M_{ll}>45$ GeV. Nexp.un f. = 57705.4 $\pm$ 254 , NPowHeg truth =301655, N Sherpa truth =763259.

Combined Covariance Matrix for Unfolded dR distribution for $Z \to \mu\mu\gamma$ process with dressed leptons and bkg subtraction. $M_{ll}>45$ GeV. Nexp.un f. = 58869.2 $\pm$ 256, NPowHeg truth =564660, NS herpa truth =813995.

Combined Covariance Matrix for Unfolded $P_{T}^{\gamma}$ distribution for $Z \to ee\gamma$ process with dressed leptons and bkg subtraction. $M_{ll}>45$ GeV. Nexp.un f. = 57358.6 $\pm$ 254 , NPowHeg truth =298662, N Sherpa truth =756609.

Combined Covariance Matrix for Unfolded $P_{T}^{\gamma}$ distribution for $Z \to \mu\mu\gamma$ process with dressed leptons and bkg subtraction. $M_{ll}>45$ GeV. Nexp.un f. = 58226.4 $\pm$ 254, NPowHeg truth =558949, N Sherpa truth =806988.

Combined Covariance Matrix for Unfolded $M(l^{+}\gamma)$ distribution for $Z \to ee\gamma$ process with bare leptons and bkg subtraction. $M_{ll}>20$ GeV. Nexp.un f. = 63717.4 $\pm$ 252.4, NPowHeg truth =338714.

Combined Covariance Matrix for Unfolded $M(l^{-}\gamma)$ distribution for $Z \to ee\gamma$ process with bare leptons and bkg subtraction. $M_{ll}>20$ GeV. Nexp.un f. = 63855.8 $\pm$ 252.7 , NPowHeg truth =338708.

Combined Covariance Matrix for Unfolded $M(l^{+}\gamma)$ distribution for $Z \to \mu\mu\gamma$ process with bare leptons and bkg subtraction. $M_{ll}>20$ GeV. Nexp.un f. = 64809.8 $\pm$ 254.6, NPowHeg truth =634285.

Combined Covariance Matrix for Unfolded $M(l^{-}\gamma)$ distribution for $Z \to \mu\mu\gamma$ process with bare leptons and bkg subtraction. $M_{ll}>20$ GeV. Nexp.un f. = 64822.9 $\pm$ 254.6, NPowHeg truth =634276.

Combined Covariance Matrix for Unfolded dR distribution for $Z \to ee\gamma$ process with bare leptons and bkg subtraction. $M_{ll}>20$ GeV. Nexp.un f. = 64273.2 $\pm$ 253.5, NPowHeg truth =338671.

Combined Covariance Matrix for Unfolded dR distribution for $Z \to \mu\mu\gamma$ process with bare leptons and bkg subtraction. $M_{ll}>20$ GeV. Nexp.un f. = 65362.4 $\pm$ 255.7 , NPowHeg truth =634214.

Combined Covariance Matrix for Unfolded $P_{T}^{\gamma}$ distribution for $Z \to ee\gamma$ process with bare leptons and bkg subtraction. $M_{ll}>20$ GeV. Nexp.un f. = 63486.8 $\pm$ 252.0, NPowHeg truth =333348.

Combined Covariance Matrix for Unfolded $P_{T}^{\gamma}$ distribution for $Z \to \mu\mu\gamma$ process with bare leptons and bkg subtraction. $M_{ll}>20$ GeV. Nexp.un f. = 64432.6 $\pm$ 253.8, NPowHeg truth =624059.

Combined Covariance Matrix for Unfolded $M(l^{+}\gamma)$ distribution for $Z \to ee\gamma$ process with bare leptons and bkg subtraction. $M_{ll}>45$ GeV. Nexp.un f. = 57095.9 $\pm$ 254 , NPowHeg truth =301666, N Sherpa truth =76327.

Combined Covariance Matrix for Unfolded $M(l^{-}\gamma)$ distribution for $Z \to ee\gamma$ process with bare leptons and bkg subtraction. $M_{ll}>45$ GeV. Nexp.un f. = 57130 $\pm$ 254 , NPowHeg truth =301666, N Sherpa truth =763273.

Combined Covariance Matrix for Unfolded $M(l^{+}\gamma)$ distribution for $Z \to \mu\mu\gamma$ process with bare leptons and bkg subtraction. $M_{ll}>45$ GeV. Nexp.un f. = 58310.9 $\pm$ 245, NPowHeg truth =564672, N Sherpa truth =814016.

Combined Covariance Matrix for Unfolded $M(l^{-}\gamma)$ distribution for $Z \to \mu\mu\gamma$ process with bare leptons and bkg subtraction. $M_{ll}>45$ GeV. Nexp.un f. = 58320.9 $\pm$ 245, NPowHeg truth =564672, N Sherpa truth =814016.

Combined Covariance Matrix for Unfolded dR distribution for $Z \to ee\gamma$ process with bare leptons and bkg subtraction. $M_{ll}>45$ GeV. Nexp.un f. = 57705.4 $\pm$ 254 , NPowHeg truth =301655, N Sherpa truth =763259.

Combined Covariance Matrix for Unfolded dR distribution for $Z \to \mu\mu\gamma$ process with bare leptons and bkg subtraction. $M_{ll}>45$ GeV. Nexp.un f. = 58869.2 $\pm$ 256, NPowHeg truth =564660, NS herpa truth =813995.

Combined Covariance Matrix for Unfolded $P_{T}^{\gamma}$ distribution for $Z \to ee\gamma$ process with bare leptons and bkg subtraction. $M_{ll}>45$ GeV. Nexp.un f. = 57358.6 $\pm$ 254 , NPowHeg truth =298662, N Sherpa truth =756609.

Combined Covariance Matrix for Unfolded $P_{T}^{\gamma}$ distribution for $Z \to \mu\mu\gamma$ process with bare leptons and bkg subtraction. $M_{ll}>45$ GeV. Nexp.un f. = 58226.4 $\pm$ 254, NPowHeg truth =558949, N Sherpa truth =806988.

Unfolded $M(l^{+}\gamma\gamma)$ distribution for $Z \to ll\gamma\gamma$ process with dressed leptons.

Unfolded $M(l^{+}\gamma\gamma)$ distribution for $Z \to ll\gamma\gamma$ process with bare leptons.

Unfolded dR distribution for $Z \to ll\gamma\gamma$ process with dressed leptons for leading photon.

Unfolded dR distribution for $Z \to ll\gamma\gamma$ process with bare leptons for leading photon.

Unfolded dR distribution for $Z \to ll\gamma\gamma$ process with dressed leptons for second photon.

Unfolded dR distribution for $Z \to ll\gamma\gamma$ process with bare leptons for second photon.

Unfolded dRgg distribution for $Z \to ll\gamma\gamma$ process with dressed leptons.

Unfolded dRgg distribution for $Z \to ll\gamma\gamma$ process with bare leptons.

Unfolded $P_{T}^{\gamma 1}$ distribution for $Z \to ll\gamma\gamma$ process with dressed leptons for leading photon.

Unfolded $P_{T}^{\gamma 1}$ distribution for $Z \to ll\gamma\gamma$ process with bare leptons for leading photon.

Unfolded $P_{T}^{\gamma 2}$ distribution for $Z \to ll\gamma\gamma$ process with dressed leptons for second photon.

Unfolded $P_{T}^{\gamma 2}$ distribution for $Z \to ll\gamma\gamma$ process with bare leptons for second photon.

Summary of results for cross-section of non-prompt $\psi(2S)$ decaying to a muon pair for 13 TeV data in fb/GeV. Uncertainties are statistical and systematic, respectively.

Summary of results for non-prompt fraction of $J/\psi$ decaying to a muon pair as a percentage for 13 TeV data. Uncertainties are statistical and systematic, respectively.

Summary of results for non-prompt fraction of $\psi(2S)$ decaying to a muon pair as a percentage for 13 TeV data. Uncertainties are statistical and systematic, respectively.

Summary of results for prompt $\psi(2S)$ over $J/\psi$ ratio as a percentage for 13 TeV data. Uncertainties are statistical and systematic, respectively.

Summary of results for non-prompt $\psi(2S)$ over $J/\psi$ ratio as a percentage for 13 TeV data. Uncertainties are statistical and systematic, respectively.

Correction factors for an assumed angular dependence $\propto 1+\lambda_{\theta} \cos^2\theta $ in the helicity frame, for several values of the parameter $\lambda_{\theta}$. The correction factors were found to be the same (within 1% - 2%) for $J/\psi$ and $\psi(2S)$ mesons, for prompt and non-prompt production mechanisms, and for the three rapidity intervals considered in this paper.