Probability of finding at least one TAR jet, where the p_T-leading TAR jet passes the m_Wcand and D₂^β=1 requirements, as a function of m_s. The probability is determined in a sample of signal events with m_Z'=2100 GeV, with the preselections applied.

Probability of finding a W_had candidate reconstructed as a pair of R=0.4 PFlow jets, as a function of m_s. The probability is determined in a sample of signal events with m_Z'=500 GeV, with the preselections applied that do not pass the requirements of the merged category.

Probability of finding a W_had candidate reconstructed as a pair of R=0.4 PFlow jets, as a function of m_s. The probability is determined in a sample of signal events with m_Z'=1000 GeV, with the preselections applied that do not pass the requirements of the merged category.

Probability of finding a W_had candidate reconstructed as a pair of R=0.4 PFlow jets, as a function of m_s. The probability is determined in a sample of signal events with m_Z'=1700 GeV, with the preselections applied that do not pass the requirements of the merged category.

Probability of finding a W_had candidate reconstructed as a pair of R=0.4 PFlow jets, as a function of m_s. The probability is determined in a sample of signal events with m_Z'=2100 GeV, with the preselections applied that do not pass the requirements of the merged category.

Observed exclusion contour at 95% C.L. for the dark Higgs model in the (m_Z', m_s) plane for g_q=0.25, g_χ=1, m_χ=200 GeV, and sinθ=0.01.

Expected exclusion contour at 95% C.L. for the dark Higgs model in the (m_Z', m_s) plane for g_q=0.25, g_χ=1, m_χ=200 GeV, and sinθ=0.01.

Expected+1σ exclusion contour at 95% C.L. for the dark Higgs model in the (m_Z', m_s) plane for g_q=0.25, g_χ=1, m_χ=200 GeV, and sinθ=0.01.

Expected-1σ exclusion contour at 95% C.L. for the dark Higgs model in the (m_Z', m_s) plane for g_q=0.25, g_χ=1, m_χ=200 GeV, and sinθ=0.01.

Expected+2σ exclusion contour at 95% C.L. for the dark Higgs model in the (m_Z', m_s) plane for g_q=0.25, g_χ=1, m_χ=200 GeV, and sinθ=0.01.

Expected-2σ exclusion contour at 95% C.L. for the dark Higgs model in the (m_Z', m_s) plane for g_q=0.25, g_χ=1, m_χ=200 GeV, and sinθ=0.01.

Observed upper limits at 95% C.L. on σ(pp → s χχ) × B(s → W^± W^∓) for m_Z'=0.5 TeV as a function of m_s. The expected limits, varied up and down by one and two standard deviations, are shown as green and yellow bands, respectively. The observed and expected limits are compared to the theoretical LO cross section for the σ(pp → s χχ) × B(s → W^± W^∓) process for m_Z'=0.5 TeV, shown in dashed blue.

Observed upper limits at 95% C.L. on σ(pp → s χχ) × B(s → W^± W^∓) for m_Z'=1 TeV as a function of m_s. The expected limits, varied up and down by one and two standard deviations, are shown as green and yellow bands, respectively. The observed and expected limits are compared to the theoretical LO cross section for the σ(pp → s χχ) × B(s → W^± W^∓) process for m_Z'=1 TeV, shown in dashed blue.

Observed upper limits at 95% C.L. on σ(pp → s χχ) × B(s → W^± W^∓) for m_Z'=1.7 TeV as a function of m_s. The expected limits, varied up and down by one and two standard deviations, are shown as green and yellow bands, respectively. The observed and expected limits are compared to the theoretical LO cross section for the σ(pp → s χχ) × B(s → W^± W^∓) process for m_Z'=1.7 TeV, shown in dashed blue.

Observed upper limits at 95% C.L. on σ(pp → s χχ) × B(s → W^± W^∓) for m_Z'=2.1 TeV as a function of m_s. The expected limits, varied up and down by one and two standard deviations, are shown as green and yellow bands, respectively. The observed and expected limits are compared to the theoretical LO cross section for the σ(pp → s χχ) × B(s → W^± W^∓) process for m_Z'=2.1 TeV, shown in dashed blue.

Data overlaid on SM background yields stacked in each SR and CR category after the fit to data ('Post-fit'). The yields in the SR are broken down into their contributions to the individual bins. The maximum-likelihood estimators are set to the conditional values of the CR-only fit, and propagated to SR and CRs.

Dominant sources of uncertainty for three dark Higgs scenarios after the fit to data. The uncertainties are quantified in terms of their contribution to the fitted signal uncertainty that is expressed relative to the theory prediction. Three representative dark Higgs signal scenarios with g_q=0.25, g_χ=1.0, sinθ=0.01 and m_χ=200 GeV are considered, which are indicated using the (m_Z', m_s) format in units of GeV in the table columns.

Cumulative efficiencies in the merged category for three representative dark Higgs signal scenarios with g_q=0.25, g_χ=1.0, sinθ=0.01, m_Z' = 1 TeV, and m_χ=200 GeV considering s→W(ℓν)W(qq) decays only.

Cumulative efficiencies in the resolved category for three representative dark Higgs signal scenarios with g_q=0.25, g_χ=1.0, sinθ=0.01, m_Z' = 1 TeV, and m_χ=200 GeV considering s→W(ℓν)W(qq) decays only.

Theoretical cross section for &sigma;(pp &rarr; s&chi;&chi;) &times; B(s &rarr; W^&plusmn;W^&#8723;) for each of the dark Higgs signal points at m_Z′ ={300, 350, 400, 500, 750} GeV, with g_q = 0.25, g<sub>&chi; = 1.0, sin&theta; = 0.01, m_Z′ = 1 TeV , and m_&chi; = 200 GeV. Also shown are experimentally excluded cross sections of &sigma;(pp &rarr; s&chi;&chi;) &times; B(s &rarr; W^&plusmn;W^&#8723;) (Obs.) together with the expectations (Exp.) varied up and down by one standard deviation (&plusmn;1&sigma;).

Theoretical cross section for &sigma;(pp &rarr; s&chi;&chi;) &times; B(s &rarr; W^&plusmn;W^&#8723;) for each of the dark Higgs signal points at m_Z′ ={1000, 1700} GeV, with g_q = 0.25, g<sub>&chi; = 1.0, sin&theta; = 0.01, m_Z′ = 1 TeV , and m_&chi; = 200 GeV. Also shown are experimentally excluded cross sections of &sigma;(pp &rarr; s&chi;&chi;) &times; B(s &rarr; W^&plusmn;W^&#8723;) (Obs.) together with the expectations (Exp.) varied up and down by one standard deviation (&plusmn;1&sigma;).

Theoretical cross section for &sigma;(pp &rarr; s&chi;&chi;) &times; B(s &rarr; W^&plusmn;W^&#8723;) for each of the dark Higgs signal points at m_Z′ ={2100, 2500, 2900, 3300} GeV, with g_q = 0.25, g<sub>&chi; = 1.0, sin&theta; = 0.01, m_Z′ = 1 TeV , and m_&chi; = 200 GeV. Also shown are experimentally excluded cross sections of &sigma;(pp &rarr; s&chi;&chi;) &times; B(s &rarr; W^&plusmn;W^&#8723;) (Obs.) together with the expectations (Exp.) varied up and down by one standard deviation (&plusmn;1&sigma;).

The unfolded differential charge asymmetry as a function of the transverse momentum of the top pair system. The measured values are given with statistical and systematic uncertainties. The SM theory predictions calculated at NNLO in QCD and NLO in EW theory are listed. The scale uncertainty is obtained by varying renormalisation and factorisation scales independently by a factor of 2 or 0.5 around $\mu_0$ to calculate the maximum and minimum value of the asymmetry, respectively. The nominal value $\mu_0$ is chosen as $H_T/4$. The variations in which one scale is multiplied by 2 while the other scale is divided by 2 are excluded. Finally, the scale and MC integration uncertainties are added in quadrature.

The unfolded differential charge asymmetry as a function of the longitudinal boost of the top pair system. The measured values are given with statistical and systematic uncertainties. The SM theory predictions calculated at NNLO in QCD and NLO in EW theory are listed. The scale uncertainty is obtained by varying renormalisation and factorisation scales independently by a factor of 2 or 0.5 around $\mu_0$ to calculate the maximum and minimum value of the asymmetry, respectively. The nominal value $\mu_0$ is chosen as $H_T/4$. The variations in which one scale is multiplied by 2 while the other scale is divided by 2 are excluded. Finally, the scale and MC integration uncertainties are added in quadrature.

The unfolded inclusive leptonic asymmetry. The unfolded $A_C^{\ell\bar{\ell}}$ is obtained in the reduced phase-space defined by the requirement $|\Delta |\eta_{\ell\bar{\ell}}||<2.5$. The measured values are given with statistical and systematic uncertainties. The SM theory predictions calculated at NLO in QCD and NLO in EW theory are listed. The theory uncertainty is obtained by varying both scales by a factor of 0.5 or 2.0 to calculate the minimum and maximum value of the asymmetry, respectively.

The unfolded differential leptonic asymmetry as a function of the invariant mass of the di-lepton pair. The unfolded $A_C^{\ell\bar{\ell}}$ is obtained in the reduced phase-space defined by the requirement $|\Delta |\eta_{\ell\bar{\ell}}||<2.5$. The measured values are given with statistical and systematic uncertainties. The SM theory predictions calculated at NLO in QCD and NLO in EW theory are listed. The theory uncertainty is obtained by varying both scales by a factor of 0.5 or 2.0 to calculate the minimum and maximum value of the asymmetry, respectively.

The unfolded differential leptonic asymmetry as a function of the transverse momentum of the di-lepton pair. The unfolded $A_C^{\ell\bar{\ell}}$ is obtained in the reduced phase-space defined by the requirement $|\Delta |\eta_{\ell\bar{\ell}}||<2.5$. The measured values are given with statistical and systematic uncertainties. The SM theory predictions calculated at NLO in QCD and NLO in EW theory are listed. The theory uncertainty is obtained by varying both scales by a factor of 0.5 or 2.0 to calculate the minimum and maximum value of the asymmetry, respectively.

The unfolded differential leptonic asymmetry as a function of the longitudinal boost of the di-lepton pair. The unfolded $A_C^{\ell\bar{\ell}}$ is obtained in the reduced phase-space defined by the requirement $|\Delta |\eta_{\ell\bar{\ell}}||<2.5$. The measured values are given with statistical and systematic uncertainties. The SM theory predictions calculated at NLO in QCD and NLO in EW theory are listed. The theory uncertainty is obtained by varying both scales by a factor of 0.5 or 2.0 to calculate the minimum and maximum value of the asymmetry, respectively.

Individual 68% and 95% CL bounds on the relevant Wilson coefficients of the SM Effective Field Theory in units of $\text{TeV}^{-2}$. The bounds are derived from the $A_C^{t\bar{t}}$ inclusive measurement. The experimental uncertainties are accounted for, in the form of the complete covariance matrix that keeps track of correlations between bins for the differential measurement. The theory uncertainty from the NNLO QCD + NLO EW calculation is included by explicitly varying the renormalization and factorization scales, or the parton density functions, in the calculation and registering the variations in the intervals.

Individual 68% and 95% CL bounds on the relevant Wilson coefficients of the SM Effective Field Theory in units of $\text{TeV}^{-2}$. The bounds are derived from the $A_C^{t\bar{t}}$ vs $m_{t\bar{t}}$ measurement. The experimental uncertainties are accounted for, in the form of the complete covariance matrix that keeps track of correlations between bins for the differential measurement. The theory uncertainty from the NNLO QCD + NLO EW calculation is included by explicitly varying the renormalization and factorization scales, or the parton density functions, in the calculation and registering the variations in the intervals.

Ranking of the systematic uncertainties with marginalisation for the $A_C^{t\bar{t}}$ inclusive measurement. The effect on unfolded $A_C$ for down and up variation of the systematic uncertainty is shown, respectively. The pulls and constraints of the ranked NPs are obtained from data.

Ranking of the systematic uncertainties with marginalisation for the $A_C^{t\bar{t}}$ vs $\beta_{z,t\bar{t}}$ measurement for $\beta_{z,t\bar{t}}$ $\in$ [0,0.3]. The effect on unfolded $A_C$ for down and up variation of the systematic uncertainty is shown, respectively. The pulls and constraints of the ranked NPs are obtained from data.

Ranking of the systematic uncertainties with marginalisation for the $A_C^{t\bar{t}}$ vs $\beta_{z,t\bar{t}}$ measurement for $\beta_{z,t\bar{t}}$ $\in$ [0.3,0.6]. The effect on unfolded $A_C$ for down and up variation of the systematic uncertainty is shown, respectively. The pulls and constraints of the ranked NPs are obtained from data.

Ranking of the systematic uncertainties with marginalisation for the $A_C^{t\bar{t}}$ vs $\beta_{z,t\bar{t}}$ measurement for $\beta_{z,t\bar{t}}$ $\in$ [0.6,0.8]. The effect on unfolded $A_C$ for down and up variation of the systematic uncertainty is shown, respectively. The pulls and constraints of the ranked NPs are obtained from data.

Ranking of the systematic uncertainties with marginalisation for the $A_C^{t\bar{t}}$ vs $\beta_{z,t\bar{t}}$ measurement for $\beta_{z,t\bar{t}}$ $\in$ [0.8,1]. The effect on unfolded $A_C$ for down and up variation of the systematic uncertainty is shown, respectively. The pulls and constraints of the ranked NPs are obtained from data.

Ranking of the systematic uncertainties with marginalisation for the $A_C^{t\bar{t}}$ vs $m_{t\bar{t}}$ measurement for $m_{t\bar{t}}$ < 500 GeV. The effect on unfolded $A_C$ for down and up variation of the systematic uncertainty is shown, respectively. The pulls and constraints of the ranked NPs are obtained from data.

Ranking of the systematic uncertainties with marginalisation for the $A_C^{t\bar{t}}$ vs $m_{t\bar{t}}$ measurement for $m_{t\bar{t}}$ $\in$ [500,750] GeV. The effect on unfolded $A_C$ for down and up variation of the systematic uncertainty is shown, respectively. The pulls and constraints of the ranked NPs are obtained from data.

Ranking of the systematic uncertainties with marginalisation for the $A_C^{t\bar{t}}$ vs $m_{t\bar{t}}$ measurement for $m_{t\bar{t}}$ $\in$ [750,1000] GeV. The effect on unfolded $A_C$ for down and up variation of the systematic uncertainty is shown, respectively. The pulls and constraints of the ranked NPs are obtained from data.

Ranking of the systematic uncertainties with marginalisation for the $A_C^{t\bar{t}}$ vs $m_{t\bar{t}}$ measurement for $m_{t\bar{t}}$ $\in$ [1000,1500] GeV. The effect on unfolded $A_C$ for down and up variation of the systematic uncertainty is shown, respectively. The pulls and constraints of the ranked NPs are obtained from data.

Ranking of the systematic uncertainties with marginalisation for the $A_C^{t\bar{t}}$ vs $m_{t\bar{t}}$ measurement for $m_{t\bar{t}}$ > 1500 GeV. The effect on unfolded $A_C$ for down and up variation of the systematic uncertainty is shown, respectively. The pulls and constraints of the ranked NPs are obtained from data.

Ranking of the systematic uncertainties with marginalisation for the $A_C^{t\bar{t}}$ vs $p_{T,t\bar{t}}$ measurement for $p_{T,t\bar{t}}$ < 30 GeV. The effect on unfolded $A_C$ for down and up variation of the systematic uncertainty is shown, respectively. The pulls and constraints of the ranked NPs are obtained from data.

Ranking of the systematic uncertainties with marginalisation for the $A_C^{t\bar{t}}$ vs $p_{T,t\bar{t}}$ measurement for $p_{T,t\bar{t}}$ $\in$ [30,120] GeV. The effect on unfolded $A_C$ for down and up variation of the systematic uncertainty is shown, respectively. The pulls and constraints of the ranked NPs are obtained from data.

Ranking of the systematic uncertainties with marginalisation for the $A_C^{t\bar{t}}$ vs $p_{T,t\bar{t}}$ measurement for $p_{T,t\bar{t}}$ > 120 GeV. The effect on unfolded $A_C$ for down and up variation of the systematic uncertainty is shown, respectively. The pulls and constraints of the ranked NPs are obtained from data.

Ranking of the systematic uncertainties with marginalisation for the $A_C^{\ell\ell}$ inclusive measurement. The effect on unfolded $A_C$ for down and up variation of the systematic uncertainty is shown, respectively. The pulls and constraints of the ranked NPs are obtained from data.

Ranking of the systematic uncertainties with marginalisation for the $A_C^{\ell\ell}$ vs $\beta_{z,\ell\bar{\ell}}$ measurement for $\beta_{z,\ell\bar{\ell}}$ $\in$[0,0.3]. The effect on unfolded $A_C$ for down and up variation of the systematic uncertainty is shown, respectively. The pulls and constraints of the ranked NPs are obtained from data.

Ranking of the systematic uncertainties with marginalisation for the $A_C^{\ell\ell}$ vs $\beta_{z,\ell\bar{\ell}}$ measurement for $\beta_{z,\ell\bar{\ell}}$ $\in$[0.3,0.6]. The effect on unfolded $A_C$ for down and up variation of the systematic uncertainty is shown, respectively. The pulls and constraints of the ranked NPs are obtained from data.

Ranking of the systematic uncertainties with marginalisation for the $A_C^{\ell\ell}$ vs $\beta_{z,\ell\bar{\ell}}$ measurement for $\beta_{z,\ell\bar{\ell}}$ $\in$[0.6,0.8]. The effect on unfolded $A_C$ for down and up variation of the systematic uncertainty is shown, respectively. The pulls and constraints of the ranked NPs are obtained from data.

Ranking of the systematic uncertainties with marginalisation for the $A_C^{\ell\ell}$ vs $\beta_{z,\ell\bar{\ell}}$ measurement for $\beta_{z,\ell\bar{\ell}}$ $\in$[0.8,1]. The effect on unfolded $A_C$ for down and up variation of the systematic uncertainty is shown, respectively. The pulls and constraints of the ranked NPs are obtained from data.

Ranking of the systematic uncertainties with marginalisation for the $A_C^{\ell\ell}$ vs $m_{\ell\bar{\ell}}$ measurement for $m_{\ell\bar{\ell}}$ < 200 GeV. The effect on unfolded $A_C$ for down and up variation of the systematic uncertainty is shown, respectively. The pulls and constraints of the ranked NPs are obtained from data.

Ranking of the systematic uncertainties with marginalisation for the $A_C^{\ell\ell}$ vs $m_{\ell\bar{\ell}}$ measurement for $m_{\ell\bar{\ell}}$ $\in$ [200,300] GeV. The effect on unfolded $A_C$ for down and up variation of the systematic uncertainty is shown, respectively. The pulls and constraints of the ranked NPs are obtained from data.

Ranking of the systematic uncertainties with marginalisation for the $A_C^{\ell\ell}$ vs $m_{\ell\bar{\ell}}$ measurement for $m_{\ell\bar{\ell}}$ $\in$ [300,400] GeV. The effect on unfolded $A_C$ for down and up variation of the systematic uncertainty is shown, respectively. The pulls and constraints of the ranked NPs are obtained from data.

Ranking of the systematic uncertainties with marginalisation for the $A_C^{\ell\ell}$ vs $m_{\ell\bar{\ell}}$ measurement for $m_{\ell\bar{\ell}}$ > 400 GeV. The effect on unfolded $A_C$ for down and up variation of the systematic uncertainty is shown, respectively. The pulls and constraints of the ranked NPs are obtained from data.

Ranking of the systematic uncertainties with marginalisation for the $A_C^{\ell\ell}$ vs $p_{T,\ell\bar{\ell}}$ measurement for $p_{T,\ell\bar{\ell}}$ < 20 GeV. The effect on unfolded $A_C$ for down and up variation of the systematic uncertainty is shown, respectively. The pulls and constraints of the ranked NPs are obtained from data.

Ranking of the systematic uncertainties with marginalisation for the $A_C^{\ell\ell}$ vs $p_{T,\ell\bar{\ell}}$ measurement for $p_{T,\ell\bar{\ell}}$ $\in$ [20, 70] GeV. The effect on unfolded $A_C$ for down and up variation of the systematic uncertainty is shown, respectively. The pulls and constraints of the ranked NPs are obtained from data.

Ranking of the systematic uncertainties with marginalisation for the $A_C^{\ell\ell}$ vs $p_{T,\ell\bar{\ell}}$ measurement for $p_{T,\ell\bar{\ell}}$ > 70 GeV. The effect on unfolded $A_C$ for down and up variation of the systematic uncertainty is shown, respectively. The pulls and constraints of the ranked NPs are obtained from data.

Post-marginalisation correlation coefficients $\rho_{ij}$ of nuisance parameters for the $A_C^{t\bar{t}}$ inclusive measurement. Only $|\rho_{ij}| > 0.05$ values are included.

Post-marginalisation correlation coefficients $\rho_{ij}$ of nuisance parameters for the $A_C^{t\bar{t}}$ vs $m_{t\bar{t}}$ measurement. Only $|\rho_{ij}| > 0.05$ values are included.

Post-marginalisation correlation coefficients $\rho_{ij}$ of nuisance parameters for the $A_C^{t\bar{t}}$ vs $p_{T,t\bar{t}}$ measurement. Only $|\rho_{ij}| > 0.05$ values are included.

Post-marginalisation correlation coefficients $\rho_{ij}$ of nuisance parameters for the $A_C^{t\bar{t}}$ vs $\beta_{z,t\bar{t}}$ measurement. Only $|\rho_{ij}| > 0.05$ values are included.

Post-marginalisation correlation coefficients $\rho_{ij}$ of nuisance parameters for the $A_C^{\ell\ell}$ inclusive measurement. Only $|\rho_{ij}| > 0.05$ values are included.

Post-marginalisation correlation coefficients $\rho_{ij}$ of nuisance parameters for the $A_C^{\ell\ell}$ vs $m_{\ell\bar{\ell}}$ measurement. Only $|\rho_{ij}| > 0.05$ values are included.

Post-marginalisation correlation coefficients $\rho_{ij}$ of nuisance parameters for the $A_C^{\ell\ell}$ vs $p_{T,\ell\bar{\ell}}$ measurement. Only $|\rho_{ij}| > 0.05$ values are included.

Post-marginalisation correlation coefficients $\rho_{ij}$ of nuisance parameters for the $A_C^{\ell\ell}$ vs $\beta_{z,\ell\bar{\ell}}$ measurement. Only $|\rho_{ij}| > 0.05$ values are included.

Covariance matrix for the $A_C^{t\bar{t}}$ vs $m_{t\bar{t}}$ measurement.

Covariance matrix for the $A_C^{t\bar{t}}$ vs $p_{T,t\bar{t}}$ measurement.

Covariance matrix for the $A_C^{t\bar{t}}$ vs $\beta_{z,t\bar{t}}$ measurement.

Covariance matrix for the $A_C^{\ell\ell}$ vs $m_{\ell\bar{\ell}}$ measurement.

Covariance matrix for the $A_C^{\ell\ell}$ vs $p_{T,\ell\bar{\ell}}$ measurement.

Covariance matrix for the $A_C^{\ell\ell}$ vs $\beta_{z,\ell\bar{\ell}}$ measurement.

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.

The best-fit predicted and observed distributions of the combined NN output in the high-$p_\text{T}$-SR for the $\mu\tau_e$ channel. The first and last bin include underflow and overflow events, respectively.

The best-fit predicted and observed distributions of the collinear mass $m_\text{coll}$ in the high-$p_\text{T}$-SR for the $e\tau_\mu$ channel. The first and last bin include underflow and overflow events, respectively.

The best-fit predicted and observed distributions of the collinear mass $m_\text{coll}$ in the high-$p_\text{T}$-SR for the $\mu\tau_e$ channel. The first and last bin include underflow and overflow events, respectively.

Observed and expected upper limits on $\mathcal{B}(Z\rightarrow\ell\tau)$ with leptonically decaying $\tau$ at 95% confidence level.

Observed and expected upper limits on $\mathcal{B}(Z\rightarrow\ell\tau)$ at 95% confidence level, combination of hadronically and leptonically decaying $\tau$ channels.

The best-fit predicted and observed distributions of the collinear mass $m_\text{coll}$ in the CRZ$\tau\tau$ for the $e\tau_\mu$ channel. The first and last bin include underflow and overflow events, respectively.

The best-fit predicted and observed distributions of the collinear mass $m_\text{coll}$ in the CRZ$\tau\tau$ for the $\mu\tau_e$ channel. The first and last bin include underflow and overflow events, respectively.

The best-fit predicted and observed distributions of the combined NN output in the CRZ$\tau\tau$ for the $e\tau_\mu$ channel. The first and last bin include underflow and overflow events, respectively.

The best-fit predicted and observed distributions of the combined NN output in the CRZ$\tau\tau$ for the $\mu\tau_e$ channel. The first and last bin include underflow and overflow events, respectively.

The best-fit predicted and observed distributions of the leading lepton transverse momentum $p_\text{T}(e)$ in the high-$p_\text{T}$-SR for the $e\tau_\mu$ channel. The first and last bin include underflow and overflow events, respectively.

The best-fit predicted and observed distributions of the leading lepton transverse momentum $p_\text{T}(\mu)$ in the high-$p_\text{T}$-SR for the $\mu\tau_e$ channel. The first and last bin include underflow and overflow events, respectively.

The best-fit predicted and observed distributions of the missing transverse momentum $E^\text{miss}_\text{T}$ in the low-$p_\text{T}$-SR for the $e\tau_\mu$ channel. The first and last bin include underflow and overflow events, respectively.

The best-fit predicted and observed distributions of the missing transverse momentum $E^\text{miss}_\text{T}$ in the low-$p_\text{T}$-SR for the $\mu\tau_e$ channel. The first and last bin include underflow and overflow events, respectively.

Event yields of the signal and SM background processes in the six analysis regions after the fit to the data under the $t \rightarrow uX$ hypothesis assuming $m_X = 30$ GeV. Total includes signal and background.The quoted uncertainties take into account correlations and constraints of the nuisance parameters and include both the statistical and systematic uncertainties. Negative correlations between the $t\bar{t} +$ light, $t\bar{t} + \geq1b$ and $t\bar{t} + \geq1c$ modelling uncertainties can make the uncertainty in the total yields smaller than in the individual components.

Event yields of the signal and SM background processes in the six analysis regions after the fit to the data under the $t \rightarrow cX$ hypothesis assuming $m_X = 30$ GeV. Total includes signal and background.The quoted uncertainties take into account correlations and constraints of the nuisance parameters and include both the statistical and systematic uncertainties. Negative correlations between the $t\bar{t} +$ light, $t\bar{t} + \geq1b$ and $t\bar{t} + \geq1c$ modelling uncertainties can make the uncertainty in the total yields smaller than in the individual components.

Event acceptance times efficiency in percent for every $t\rightarrow uX$ and $t\rightarrow cX$ mass signal sample.

Cut flow for the scalar signal in the $t\rightarrow uX$ decay combining both quark and anti-quark samples. Shown for each signal are the corresponding mass, the number of generated events, the number of reconstructed ("Reco") events, the events that pass the lepton triggers, the events that have only one electron ("el") or only one muon ("mu") with p$_{\text{T}}$ larger than 27 GeV, the number of events with at least four jets with p$_{\text{T}}$ larger than 25 GeV, the number of events with at least three $b$-tagged jets at the 70% efficiency working point, and the number of events with at least two $b$-tagged jets at the 60% efficiency working point and at least another one at the 70%. The quoted yields do not include reweighting.

Cut flow for the scalar signal in the $t\rightarrow cX$ decay combining both quark and anti-quark samples. Shown for each signal are the corresponding mass, the number of generated events, the number of reconstructed ("Reco") events, the events that pass the lepton triggers, the events that have only one electron ("el") or only one muon ("mu") with p$_{\text{T}}$ larger than 27 GeV, the number of events with at least four jets with p$_{\text{T}}$ larger than 25 GeV, the number of events with at least three $b$-tagged jets at the 70% efficiency working point, and the number of events with at least two $b$-tagged jets at the 60% efficiency working point and at least another one at the 70%. The quoted yields do not include reweighting.

The $m_{jj}$ distributions for the CRs and the BDT classifier response distribution for the SR after the fit in all regions. The dashed line shows the total background distribution before the fit. The vertical error bars on the data points correspond to the data's statistical uncertainty. Overflows are included in the last bin. The uncertainty band corresponds to the combination of the MC statistical uncertainty and systematic uncertainties obtained in the fit.

The $m_{jj}$ distributions for the CRs and the BDT classifier response distribution for the SR after the fit in all regions. The dashed line shows the total background distribution before the fit. The vertical error bars on the data points correspond to the data's statistical uncertainty. Overflows are included in the last bin. The uncertainty band corresponds to the combination of the MC statistical uncertainty and systematic uncertainties obtained in the fit.

The $m_{jj}$ distributions for the CRs and the BDT classifier response distribution for the SR after the fit in all regions. The dashed line shows the total background distribution before the fit. The vertical error bars on the data points correspond to the data's statistical uncertainty. Overflows are included in the last bin. The uncertainty band corresponds to the combination of the MC statistical uncertainty and systematic uncertainties obtained in the fit.

Observed and expected event yields for the signal and all of the background processes considered in this analysis after the fit to the data in all of the regions. The uncertainty on the expected yield is the combination of statistical and systematic uncertainties obtained in the fit. The individual uncertainties can be correlated and do not necessarily add in quadrature to equal the total background uncertainty.

Summary of the event yield for processes in all regions, after the fit over all regions. The dashed line shows the total background distribution before the fit. The vertical error bars on the data points correspond to the data's statistical uncertainty. The uncertainty band corresponds to the combination of the MC statistical uncertainty and systematic uncertainties obtained in the fit.

Impact of different components of systematic uncertainty on the measured cross section, without taking into account the correlations. The impact is calculated by fixing the value of the corresponding nuisance parameters to the values obtained in the fit used to measure the cross section, performing the fit, estimating the signal strength uncertainty and subtracting it from the nominal uncertainty in quadrature.

Fitted POI values for this analysis, the previous ATLAS analysis, and their combination. The first and second columns present the values obtained in the individual analyses. The third column presents the values obtained in the combination.

Observed and expected one-dimensional limits on dimension 8 aQGC parameters. Limits are obtained by setting all aQGCs parameters except one to zero. Unitarity is not preserved.

Observed and expected one-dimensional limits on dimension 8 aQGC parameters in the region, where unitarity is preserved. Cutoff scales in MC, $E_{c}$, are given for each parameter. Limits are obtained by setting all aQGCs parameters except one to zero.

The $E_{T}^{\gamma}$ distribution in the SR after the fit in the control regions. The red (green) line shows the expected number of events in the case of non-zero EFT coefficient $f_{T0}/\Lambda^4$ ($f_{M0}/\Lambda^4$) with the value shown in the legend. The vertical error bars on the data points correspond to the data statistical uncertainty. Overflows are included in the last bin. The uncertainty band corresponds to the combination of the MC statistical uncertainty and systematic uncertainties obtained in the fit.

Evolution of the expected (red line) and observed (blue line) limits versus $E_{c}$ values for $f_{T0}/\Lambda^4$. The unitarity bound is shown by the black line. The $E_{c}<4$ TeV regime was obtained with $E_{T}^{\gamma} > 600$ GeV. The $E_{c} \geq 4$ TeV regime was obtained with $E_{T}^{\gamma} > 900$ GeV.

Evolution of the expected (red line) and observed (blue line) limits versus $E_{c}$ values for $f_{T5}/\Lambda^4$. The unitarity bound is shown by the black line. The $E_{c}<4$ TeV regime was obtained with $E_{T}^{\gamma} > 600$ GeV. The $E_{c} \geq 4$ TeV regime was obtained with $E_{T}^{\gamma} > 900$ GeV.

Evolution of the expected (red line) and observed (blue line) limits versus $E_{c}$ values for $f_{T8}/\Lambda^4$. The unitarity bound is shown by the black line. The $E_{c}<4$ TeV regime was obtained with $E_{T}^{\gamma} > 600$ GeV. The $E_{c} \geq 4$ TeV regime was obtained with $E_{T}^{\gamma} > 900$ GeV.

Evolution of the expected (red line) and observed (blue line) limits versus $E_{c}$ values for $f_{T9}/\Lambda^4$. The unitarity bound is shown by the black line. The $E_{c}<4$ TeV regime was obtained with $E_{T}^{\gamma} > 600$ GeV. The $E_{c} \geq 4$ TeV regime was obtained with $E_{T}^{\gamma} > 900$ GeV.

Evolution of the expected (red line) and observed (blue line) limits versus $E_{c}$ values for $f_{M0}/\Lambda^4$. The unitarity bound is shown by the black line. The $E_{c}<4$ TeV regime was obtained with $E_{T}^{\gamma} > 400$ GeV. The $E_{c} \geq 4$ TeV regime was obtained with $E_{T}^{\gamma} > 900$ GeV.

Evolution of the expected (red line) and observed (blue line) limits versus $E_{c}$ values for $f_{M1}/\Lambda^4$. The unitarity bound is shown by the black line. The $E_{c}<4$ TeV regime was obtained with $E_{T}^{\gamma} > 400$ GeV. The $E_{c} \geq 4$ TeV regime was obtained with $E_{T}^{\gamma} > 900$ GeV.

Evolution of the expected (red line) and observed (blue line) limits versus $E_{c}$ values for $f_{M2}/\Lambda^4$. The unitarity bound is shown by the black line. The $E_{c}<4$ TeV regime was obtained with $E_{T}^{\gamma} > 400$ GeV. The $E_{c} \geq 4$ TeV regime was obtained with $E_{T}^{\gamma} > 900$ GeV.

Correlation matrix of the parameters for the fit in all regions. Only parameters with absolute value of the correlation coefficient larger than 10 are shown.

The $Z'$ signal event selection efficiencies compared to the events passing the previous cut level for several representative mass points. The overall signal efficiencies are the products of the 4$\mu$ MC filter and the combined event selection efficiencies.

The selected 4$\mu$ events in data and the estimated backgrounds and their combined statistical and systematic uncertainties.

The selected 4$\mu$ events in data and the estimated backgrounds and their combined statistical and systematic uncertainties.

Distributions of $p_{T}^{Z_1}$. Small background contributions are denoted as "other backgrounds", including 4$\mu$ events containing non-prompt muons estimated from data and from $ttV$, $VVV$, and Higgs boson production processes.

Distributions of $p_{T}^{Z_1}$. Small background contributions are denoted as "other backgrounds", including 4$\mu$ events containing non-prompt muons estimated from data and from $ttV$, $VVV$, and Higgs boson production processes.

Distributions of $p_{T}^{Z_2}$. Small background contributions are denoted as "other backgrounds", including 4$\mu$ events containing non-prompt muons estimated from data and from $ttV$, $VVV$, and Higgs boson production processes.

Distributions of $p_{T}^{Z_2}$. Small background contributions are denoted as "other backgrounds", including 4$\mu$ events containing non-prompt muons estimated from data and from $ttV$, $VVV$, and Higgs boson production processes.

Distributions of the mass difference of the $Z_1$ and $Z_2$ candidates. Small background contributions are denoted as "other backgrounds", including 4$\mu$ events containing non-prompt muons estimated from data and from $ttV$, $VVV$, and Higgs boson production processes.

Distributions of the mass difference of the $Z_1$ and $Z_2$ candidates. Small background contributions are denoted as "other backgrounds", including 4$\mu$ events containing non-prompt muons estimated from data and from $ttV$, $VVV$, and Higgs boson production processes.

The pDNN output discriminant variable distributions for low mass with a signal sample at 35 GeV and 51 GeV, respectively.

The pDNN output discriminant variable distributions for low mass with a signal sample at 35 GeV and 51 GeV, respectively.

The pDNN output discriminant variable distributions for high mass with a signal sample at 35 GeV and 51 GeV, respectively.

The pDNN output discriminant variable distributions for high mass with a signal sample at 35 GeV and 51 GeV, respectively.

Mass spectra of $m_{Z2}$ for the pDNN-selected events with a signal sample at 15 GeV.

Mass spectra of $m_{Z2}$ for the pDNN-selected events with a signal sample at 15 GeV.

Mass spectra of $m_{Z1}$ for the pDNN-selected events with a signal sample at 51 GeV.

Mass spectra of $m_{Z1}$ for the pDNN-selected events with a signal sample at 51 GeV.

The $p_0$-value scan across the Z' mass signal regions.

The $p_0$-value scan across the Z' mass signal regions.

95% CL upper limits (expected and observed) on the cross-sections times branching fraction. The discontinuity at 42 GeV represents the border of the low/high mass classifiers.

95% CL upper limits (expected and observed) on the cross-sections times branching fraction. The discontinuity at 42 GeV represents the border of the low/high mass classifiers.

95% CL upper limits (expected and observed) on the coupling parameter. The discontinuity at 42 GeV represents the border of the low/high mass classifiers.

95% CL upper limits (expected and observed) on the coupling parameter. The discontinuity at 42 GeV represents the border of the low/high mass classifiers.

The parameterized mass resolution $\sigma_{m_{\mu\mu}}$ as a function of $m_{Z'}$ using fully simulated $Z' \rightarrow \mu^+\mu^-$ events.

The parameterized mass resolution $\sigma_{m_{\mu\mu}}$ as a function of $m_{Z'}$ using fully simulated $Z' \rightarrow \mu^+\mu^-$ events.

The transverse momentum $p_{T}$ distributions for each muon (ordered with $p_{T}$ from (a) to (d)). In addition to the major background from the SM $Z(Z^*)\rightarrow 4\mu$ production, other backgrounds, including 4$\mu$ events containing non-prompt muons estimated from data, and from $ttV$, $VVV$, and Higgs boson production processes, are included in the plots. Examples of the Z' signal from $pp\rightarrow Z'\mu^+\mu^- \rightarrow 4\mu$ process with masses of 15 and 51 GeV are also shown in the plots.

The transverse momentum $p_{T}$ distributions for each muon (ordered with $p_{T}$ from (a) to (d)). In addition to the major background from the SM $Z(Z^*)\rightarrow 4\mu$ production, other backgrounds, including 4$\mu$ events containing non-prompt muons estimated from data, and from $ttV$, $VVV$, and Higgs boson production processes, are included in the plots. Examples of the Z' signal from $pp\rightarrow Z'\mu^+\mu^- \rightarrow 4\mu$ process with masses of 15 and 51 GeV are also shown in the plots.

The transverse momentum $p_{T}$ distributions for each muon (ordered with $p_{T}$ from (a) to (d)). In addition to the major background from the SM $Z(Z^*)\rightarrow 4\mu$ production, other backgrounds, including 4$\mu$ events containing non-prompt muons estimated from data, and from $ttV$, $VVV$, and Higgs boson production processes, are included in the plots. Examples of the Z' signal from $pp\rightarrow Z'\mu^+\mu^- \rightarrow 4\mu$ process with masses of 15 and 51 GeV are also shown in the plots.

The transverse momentum $p_{T}$ distributions for each muon (ordered with $p_{T}$ from (a) to (d)). In addition to the major background from the SM $Z(Z^*)\rightarrow 4\mu$ production, other backgrounds, including 4$\mu$ events containing non-prompt muons estimated from data, and from $ttV$, $VVV$, and Higgs boson production processes, are included in the plots. Examples of the Z' signal from $pp\rightarrow Z'\mu^+\mu^- \rightarrow 4\mu$ process with masses of 15 and 51 GeV are also shown in the plots.

The transverse momentum $p_{T}$ distributions for each muon (ordered with $p_{T}$ from (a) to (d)). In addition to the major background from the SM $Z(Z^*)\rightarrow 4\mu$ production, other backgrounds, including 4$\mu$ events containing non-prompt muons estimated from data, and from $ttV$, $VVV$, and Higgs boson production processes, are included in the plots. Examples of the Z' signal from $pp\rightarrow Z'\mu^+\mu^- \rightarrow 4\mu$ process with masses of 15 and 51 GeV are also shown in the plots.

The transverse momentum $p_{T}$ distributions for each muon (ordered with $p_{T}$ from (a) to (d)). In addition to the major background from the SM $Z(Z^*)\rightarrow 4\mu$ production, other backgrounds, including 4$\mu$ events containing non-prompt muons estimated from data, and from $ttV$, $VVV$, and Higgs boson production processes, are included in the plots. Examples of the Z' signal from $pp\rightarrow Z'\mu^+\mu^- \rightarrow 4\mu$ process with masses of 15 and 51 GeV are also shown in the plots.

The transverse momentum $p_{T}$ distributions for each muon (ordered with $p_{T}$ from (a) to (d)). In addition to the major background from the SM $Z(Z^*)\rightarrow 4\mu$ production, other backgrounds, including 4$\mu$ events containing non-prompt muons estimated from data, and from $ttV$, $VVV$, and Higgs boson production processes, are included in the plots. Examples of the Z' signal from $pp\rightarrow Z'\mu^+\mu^- \rightarrow 4\mu$ process with masses of 15 and 51 GeV are also shown in the plots.

The transverse momentum $p_{T}$ distributions for each muon (ordered with $p_{T}$ from (a) to (d)). In addition to the major background from the SM $Z(Z^*)\rightarrow 4\mu$ production, other backgrounds, including 4$\mu$ events containing non-prompt muons estimated from data, and from $ttV$, $VVV$, and Higgs boson production processes, are included in the plots. Examples of the Z' signal from $pp\rightarrow Z'\mu^+\mu^- \rightarrow 4\mu$ process with masses of 15 and 51 GeV are also shown in the plots.

Kinematic distributions of the pre-selected $4\mu$ events. The plots (a) to (d) are the $\eta$ distributions of the 4 muons ($p_{T}$ ordered). In addition to the major background from the SM $Z(Z^*)\rightarrow 4\mu$ production, other backgrounds, including 4$\mu$ events containing non-prompt muons estimated from data, and from $ttV$, $VVV$, and Higgs boson production processes, are included in the plots. Examples of the Z' signal from $pp\rightarrow Z'\mu^+\mu^- \rightarrow 4\mu$ process with masses of 15 and 51 GeV are also shown in the plots.

Kinematic distributions of the pre-selected $4\mu$ events. The plots (a) to (d) are the $\eta$ distributions of the 4 muons ($p_{T}$ ordered). In addition to the major background from the SM $Z(Z^*)\rightarrow 4\mu$ production, other backgrounds, including 4$\mu$ events containing non-prompt muons estimated from data, and from $ttV$, $VVV$, and Higgs boson production processes, are included in the plots. Examples of the Z' signal from $pp\rightarrow Z'\mu^+\mu^- \rightarrow 4\mu$ process with masses of 15 and 51 GeV are also shown in the plots.

Kinematic distributions of the pre-selected $4\mu$ events. The plots (a) to (d) are the $\eta$ distributions of the 4 muons ($p_{T}$ ordered). In addition to the major background from the SM $Z(Z^*)\rightarrow 4\mu$ production, other backgrounds, including 4$\mu$ events containing non-prompt muons estimated from data, and from $ttV$, $VVV$, and Higgs boson production processes, are included in the plots. Examples of the Z' signal from $pp\rightarrow Z'\mu^+\mu^- \rightarrow 4\mu$ process with masses of 15 and 51 GeV are also shown in the plots.

Kinematic distributions of the pre-selected $4\mu$ events. The plots (a) to (d) are the $\eta$ distributions of the 4 muons ($p_{T}$ ordered). In addition to the major background from the SM $Z(Z^*)\rightarrow 4\mu$ production, other backgrounds, including 4$\mu$ events containing non-prompt muons estimated from data, and from $ttV$, $VVV$, and Higgs boson production processes, are included in the plots. Examples of the Z' signal from $pp\rightarrow Z'\mu^+\mu^- \rightarrow 4\mu$ process with masses of 15 and 51 GeV are also shown in the plots.

Kinematic distributions of the pre-selected $4\mu$ events. The plots (a) to (d) are the $\eta$ distributions of the 4 muons ($p_{T}$ ordered). In addition to the major background from the SM $Z(Z^*)\rightarrow 4\mu$ production, other backgrounds, including 4$\mu$ events containing non-prompt muons estimated from data, and from $ttV$, $VVV$, and Higgs boson production processes, are included in the plots. Examples of the Z' signal from $pp\rightarrow Z'\mu^+\mu^- \rightarrow 4\mu$ process with masses of 15 and 51 GeV are also shown in the plots.

Kinematic distributions of the pre-selected $4\mu$ events. The plots (a) to (d) are the $\eta$ distributions of the 4 muons ($p_{T}$ ordered). In addition to the major background from the SM $Z(Z^*)\rightarrow 4\mu$ production, other backgrounds, including 4$\mu$ events containing non-prompt muons estimated from data, and from $ttV$, $VVV$, and Higgs boson production processes, are included in the plots. Examples of the Z' signal from $pp\rightarrow Z'\mu^+\mu^- \rightarrow 4\mu$ process with masses of 15 and 51 GeV are also shown in the plots.

Kinematic distributions of the pre-selected $4\mu$ events. The plots (a) to (d) are the $\eta$ distributions of the 4 muons ($p_{T}$ ordered). In addition to the major background from the SM $Z(Z^*)\rightarrow 4\mu$ production, other backgrounds, including 4$\mu$ events containing non-prompt muons estimated from data, and from $ttV$, $VVV$, and Higgs boson production processes, are included in the plots. Examples of the Z' signal from $pp\rightarrow Z'\mu^+\mu^- \rightarrow 4\mu$ process with masses of 15 and 51 GeV are also shown in the plots.

Kinematic distributions of the pre-selected $4\mu$ events. The plots (a) to (d) are the $\eta$ distributions of the 4 muons ($p_{T}$ ordered). In addition to the major background from the SM $Z(Z^*)\rightarrow 4\mu$ production, other backgrounds, including 4$\mu$ events containing non-prompt muons estimated from data, and from $ttV$, $VVV$, and Higgs boson production processes, are included in the plots. Examples of the Z' signal from $pp\rightarrow Z'\mu^+\mu^- \rightarrow 4\mu$ process with masses of 15 and 51 GeV are also shown in the plots.

Kinematic distributions of the pre-selected $4\mu$ events. Plots (a) to (d) are the angular separations, $\Delta R$ of the two muons that formed $Z_1$ and $Z_2$, and the mass distributions of $Z_1$ and $Z_2$. In addition to the major backgrounds from the SM $Z(Z^*)\rightarrow 4\mu$ production, other background, including 4$\mu$ events containing non-prompt muons estimated from data, and from $ttV$, $VVV$, and Higgs boson production processes, are included in the plots. Examples of the Z' signal from $pp\rightarrow Z'\mu^+\mu^- \rightarrow 4\mu$ process with masses of 15 and 51 GeV are also shown in the plots.

Kinematic distributions of the pre-selected $4\mu$ events. Plots (a) to (d) are the angular separations, $\Delta R$ of the two muons that formed $Z_1$ and $Z_2$, and the mass distributions of $Z_1$ and $Z_2$. In addition to the major backgrounds from the SM $Z(Z^*)\rightarrow 4\mu$ production, other background, including 4$\mu$ events containing non-prompt muons estimated from data, and from $ttV$, $VVV$, and Higgs boson production processes, are included in the plots. Examples of the Z' signal from $pp\rightarrow Z'\mu^+\mu^- \rightarrow 4\mu$ process with masses of 15 and 51 GeV are also shown in the plots.

Kinematic distributions of the pre-selected $4\mu$ events. Plots (a) to (d) are the angular separations, $\Delta R$ of the two muons that formed $Z_1$ and $Z_2$, and the mass distributions of $Z_1$ and $Z_2$. In addition to the major backgrounds from the SM $Z(Z^*)\rightarrow 4\mu$ production, other background, including 4$\mu$ events containing non-prompt muons estimated from data, and from $ttV$, $VVV$, and Higgs boson production processes, are included in the plots. Examples of the Z' signal from $pp\rightarrow Z'\mu^+\mu^- \rightarrow 4\mu$ process with masses of 15 and 51 GeV are also shown in the plots.

Kinematic distributions of the pre-selected $4\mu$ events. Plots (a) to (d) are the angular separations, $\Delta R$ of the two muons that formed $Z_1$ and $Z_2$, and the mass distributions of $Z_1$ and $Z_2$. In addition to the major backgrounds from the SM $Z(Z^*)\rightarrow 4\mu$ production, other background, including 4$\mu$ events containing non-prompt muons estimated from data, and from $ttV$, $VVV$, and Higgs boson production processes, are included in the plots. Examples of the Z' signal from $pp\rightarrow Z'\mu^+\mu^- \rightarrow 4\mu$ process with masses of 15 and 51 GeV are also shown in the plots.

Kinematic distributions of the pre-selected $4\mu$ events. Plots (a) to (d) are the angular separations, $\Delta R$ of the two muons that formed $Z_1$ and $Z_2$, and the mass distributions of $Z_1$ and $Z_2$. In addition to the major backgrounds from the SM $Z(Z^*)\rightarrow 4\mu$ production, other background, including 4$\mu$ events containing non-prompt muons estimated from data, and from $ttV$, $VVV$, and Higgs boson production processes, are included in the plots. Examples of the Z' signal from $pp\rightarrow Z'\mu^+\mu^- \rightarrow 4\mu$ process with masses of 15 and 51 GeV are also shown in the plots.

Kinematic distributions of the pre-selected $4\mu$ events. Plots (a) to (d) are the angular separations, $\Delta R$ of the two muons that formed $Z_1$ and $Z_2$, and the mass distributions of $Z_1$ and $Z_2$. In addition to the major backgrounds from the SM $Z(Z^*)\rightarrow 4\mu$ production, other background, including 4$\mu$ events containing non-prompt muons estimated from data, and from $ttV$, $VVV$, and Higgs boson production processes, are included in the plots. Examples of the Z' signal from $pp\rightarrow Z'\mu^+\mu^- \rightarrow 4\mu$ process with masses of 15 and 51 GeV are also shown in the plots.

Kinematic distributions of the pre-selected $4\mu$ events. Plots (a) to (d) are the angular separations, $\Delta R$ of the two muons that formed $Z_1$ and $Z_2$, and the mass distributions of $Z_1$ and $Z_2$. In addition to the major backgrounds from the SM $Z(Z^*)\rightarrow 4\mu$ production, other background, including 4$\mu$ events containing non-prompt muons estimated from data, and from $ttV$, $VVV$, and Higgs boson production processes, are included in the plots. Examples of the Z' signal from $pp\rightarrow Z'\mu^+\mu^- \rightarrow 4\mu$ process with masses of 15 and 51 GeV are also shown in the plots.

Kinematic distributions of the pre-selected $4\mu$ events. Plots (a) to (d) are the angular separations, $\Delta R$ of the two muons that formed $Z_1$ and $Z_2$, and the mass distributions of $Z_1$ and $Z_2$. In addition to the major backgrounds from the SM $Z(Z^*)\rightarrow 4\mu$ production, other background, including 4$\mu$ events containing non-prompt muons estimated from data, and from $ttV$, $VVV$, and Higgs boson production processes, are included in the plots. Examples of the Z' signal from $pp\rightarrow Z'\mu^+\mu^- \rightarrow 4\mu$ process with masses of 15 and 51 GeV are also shown in the plots.

Data and MC comparison of the $Z \to 4\mu$ invariant mass using pre-selected 4$\mu$ events. Figure (b) shows the distribution between 80 GeV~and 110 GeV~in Figure (a). Figure (c) shows the distribution of transverse momentum of $4\mu$ system. In addition to the major background from the SM $Z(Z^*)\rightarrow 4\mu$ production, other backgrounds, including 4$\mu$ events containing non-prompt muons estimated from data, and from $ttV$, $VVV$, and Higgs boson production processes, are included in the plots. Examples of the Z' signal from $pp\rightarrow Z'\mu^+\mu^- \rightarrow 4\mu$ process with masses of 15 and 51 GeV are also shown in the plots.

Data and MC comparison of the $Z \to 4\mu$ invariant mass using pre-selected 4$\mu$ events. Figure (b) shows the distribution between 80 GeV~and 110 GeV~in Figure (a). Figure (c) shows the distribution of transverse momentum of $4\mu$ system. In addition to the major background from the SM $Z(Z^*)\rightarrow 4\mu$ production, other backgrounds, including 4$\mu$ events containing non-prompt muons estimated from data, and from $ttV$, $VVV$, and Higgs boson production processes, are included in the plots. Examples of the Z' signal from $pp\rightarrow Z'\mu^+\mu^- \rightarrow 4\mu$ process with masses of 15 and 51 GeV are also shown in the plots.

Data and MC comparison of the $Z \to 4\mu$ invariant mass using pre-selected 4$\mu$ events. Figure (b) shows the distribution between 80 GeV~and 110 GeV~in Figure (a). Figure (c) shows the distribution of transverse momentum of $4\mu$ system. In addition to the major background from the SM $Z(Z^*)\rightarrow 4\mu$ production, other backgrounds, including 4$\mu$ events containing non-prompt muons estimated from data, and from $ttV$, $VVV$, and Higgs boson production processes, are included in the plots. Examples of the Z' signal from $pp\rightarrow Z'\mu^+\mu^- \rightarrow 4\mu$ process with masses of 15 and 51 GeV are also shown in the plots.

Data and MC comparison of the $Z \to 4\mu$ invariant mass using pre-selected 4$\mu$ events. Figure (b) shows the distribution between 80 GeV~and 110 GeV~in Figure (a). Figure (c) shows the distribution of transverse momentum of $4\mu$ system. In addition to the major background from the SM $Z(Z^*)\rightarrow 4\mu$ production, other backgrounds, including 4$\mu$ events containing non-prompt muons estimated from data, and from $ttV$, $VVV$, and Higgs boson production processes, are included in the plots. Examples of the Z' signal from $pp\rightarrow Z'\mu^+\mu^- \rightarrow 4\mu$ process with masses of 15 and 51 GeV are also shown in the plots.

Data and MC comparison of the $Z \to 4\mu$ invariant mass using pre-selected 4$\mu$ events. Figure (b) shows the distribution between 80 GeV~and 110 GeV~in Figure (a). Figure (c) shows the distribution of transverse momentum of $4\mu$ system. In addition to the major background from the SM $Z(Z^*)\rightarrow 4\mu$ production, other backgrounds, including 4$\mu$ events containing non-prompt muons estimated from data, and from $ttV$, $VVV$, and Higgs boson production processes, are included in the plots. Examples of the Z' signal from $pp\rightarrow Z'\mu^+\mu^- \rightarrow 4\mu$ process with masses of 15 and 51 GeV are also shown in the plots.

Data and MC comparison of the $Z \to 4\mu$ invariant mass using pre-selected 4$\mu$ events. Figure (b) shows the distribution between 80 GeV~and 110 GeV~in Figure (a). Figure (c) shows the distribution of transverse momentum of $4\mu$ system. In addition to the major background from the SM $Z(Z^*)\rightarrow 4\mu$ production, other backgrounds, including 4$\mu$ events containing non-prompt muons estimated from data, and from $ttV$, $VVV$, and Higgs boson production processes, are included in the plots. Examples of the Z' signal from $pp\rightarrow Z'\mu^+\mu^- \rightarrow 4\mu$ process with masses of 15 and 51 GeV are also shown in the plots.

Fit results of the simultaneous measurements of the $H\to e\tau$ and $H\to \mu\tau$ signals (2POI) showing best-fit values of the LFV branching ratios of the Higgs boson $\hat{B}$($H\to e\tau$). The results from standalone channel/categories fits are compared with the results of the combined fit.

Fit results of the simultaneous measurements of the $H\to e\tau$ and $H\to \mu\tau$ signals (2POI) showing upper limits at 95% C.L. on the LFV branching ratios of the Higgs boson $H\to \mu\tau$. The results from standalone channel/categories fits are compared with the results of the combined fit.

Fit results of the simultaneous measurements of the $H\to e\tau$ and $H\to \mu\tau$ signals (2POI) showing upper limits at 95% C.L. on the LFV branching ratios of the Higgs boson $H\to \mu\tau$. The results from standalone channel/categories fits are compared with the results of the combined fit.

Fit results of the simultaneous measurements of the $H\to e\tau$ and $H\to \mu\tau$ signals (2POI) showing best-fit values of the LFV branching ratios of the Higgs boson $\hat{B}$($H\to \mu\tau$). The results from standalone channel/categories fits are compared with the results of the combined fit.

Fit results of the simultaneous measurements of the $H\to e\tau$ and $H\to \mu\tau$ signals (2POI) showing best-fit values of the LFV branching ratios of the Higgs boson $\hat{B}$($H\to \mu\tau$). The results from standalone channel/categories fits are compared with the results of the combined fit.

Fit results of the independent searches (1 POI) showing upper limits at 95% C.L. on the LFV branching ratios of the Higgs boson $H\to e\tau$. The results from standalone channel/categories fits are compared with the results of the combined fit.

Fit results of the independent searches (1 POI) showing upper limits at 95% C.L. on the LFV branching ratios of the Higgs boson $H\to e\tau$. The results from standalone channel/categories fits are compared with the results of the combined fit.

Fit results of the independent searches (1 POI) showing best-fit values of the LFV branching ratios of the Higgs boson $\hat{B}$($H\to e\tau$). The results from standalone channel/categories fits are compared with the results of the combined fit.

Fit results of the independent searches (1 POI) showing best-fit values of the LFV branching ratios of the Higgs boson $\hat{B}$($H\to e\tau$). The results from standalone channel/categories fits are compared with the results of the combined fit.

Fit results of the independent searches (1 POI) showing upper limits at 95% C.L. on the LFV branching ratios of the Higgs boson $H\to \mu\tau$. The results from standalone channel/categories fits are compared with the results of the combined fit.

Fit results of the independent searches (1 POI) showing upper limits at 95% C.L. on the LFV branching ratios of the Higgs boson $H\to \mu\tau$. The results from standalone channel/categories fits are compared with the results of the combined fit.

Fit results of the independent searches (1 POI) showing best-fit values of the LFV branching ratios of the Higgs boson $\hat{B}$($H\to \mu\tau$). The results from standalone channel/categories fits are compared with the results of the combined fit.

Fit results of the independent searches (1 POI) showing best-fit values of the LFV branching ratios of the Higgs boson $\hat{B}$($H\to \mu\tau$). The results from standalone channel/categories fits are compared with the results of the combined fit.

BDT score distribution, after the simultaneous fit of the $H\to e\tau$ and $H\to \mu\tau$ signals, obtained by fitting the data of the MC-template $\ell\tau_{\ell'}$ channel for $e\tau_{\mu}$ final state in the non-VBF category.

BDT score distribution, after the simultaneous fit of the $H\to e\tau$ and $H\to \mu\tau$ signals, obtained by fitting the data of the MC-template $\ell\tau_{\ell'}$ channel for $e\tau_{\mu}$ final state in the non-VBF category.

BDT score distribution, after the simultaneous fit of the $H\to e\tau$ and $H\to \mu\tau$ signals, obtained by fitting the data of the MC-template $\ell\tau_{\ell'}$ channel for $\mu\tau_{e}$ final state in the non-VBF category.

BDT score distribution, after the simultaneous fit of the $H\to e\tau$ and $H\to \mu\tau$ signals, obtained by fitting the data of the MC-template $\ell\tau_{\ell'}$ channel for $\mu\tau_{e}$ final state in the non-VBF category.

BDT score distribution, after the simultaneous fit of the $H\to e\tau$ and $H\to \mu\tau$ signals, obtained by fitting the data of the MC-template $\ell\tau_{\ell'}$ channel for $e\tau_{\mu}$ final state in the VBF category.

BDT score distribution, after the simultaneous fit of the $H\to e\tau$ and $H\to \mu\tau$ signals, obtained by fitting the data of the MC-template $\ell\tau_{\ell'}$ channel for $e\tau_{\mu}$ final state in the VBF category.

BDT score distribution, after the simultaneous fit of the $H\to e\tau$ and $H\to \mu\tau$ signals, obtained by fitting the data of the MC-template $\ell\tau_{\ell'}$ channel for $\mu\tau_{e}$ final state in the VBF category.

BDT score distribution, after the simultaneous fit of the $H\to e\tau$ and $H\to \mu\tau$ signals, obtained by fitting the data of the MC-template $\ell\tau_{\ell'}$ channel for $\mu\tau_{e}$ final state in the VBF category.

BDT score distribution, after the simultaneous fit of the $H\to e\tau$ and $H\to \mu\tau$ signals, obtained by fitting the data of the MC-template $\ell\tau_{had}$ channel for $e\tau_{had}$ final state in the non-VBF category.

BDT score distribution, after the simultaneous fit of the $H\to e\tau$ and $H\to \mu\tau$ signals, obtained by fitting the data of the MC-template $\ell\tau_{had}$ channel for $e\tau_{had}$ final state in the non-VBF category.

BDT score distribution, after the simultaneous fit of the $H\to e\tau$ and $H\to \mu\tau$ signals, obtained by fitting the data of the MC-template $\ell\tau_{had}$ channel for $\mu\tau_{had}$ final state in the non-VBF category.

BDT score distribution, after the simultaneous fit of the $H\to e\tau$ and $H\to \mu\tau$ signals, obtained by fitting the data of the MC-template $\ell\tau_{had}$ channel for $\mu\tau_{had}$ final state in the non-VBF category.

BDT score distribution, after the simultaneous fit of the $H\to e\tau$ and $H\to \mu\tau$ signals, obtained by fitting the data of the MC-template $\ell\tau_{had}$ channel for $e\tau_{had}$ final state in the VBF category.

BDT score distribution, after the simultaneous fit of the $H\to e\tau$ and $H\to \mu\tau$ signals, obtained by fitting the data of the MC-template $\ell\tau_{had}$ channel for $e\tau_{had}$ final state in the VBF category.

BDT score distribution, after the simultaneous fit of the $H\to e\tau$ and $H\to \mu\tau$ signals, obtained by fitting the data of the MC-template $\ell\tau_{had}$ channel for $\mu\tau_{had}$ final state in the VBF category.

BDT score distribution, after the simultaneous fit of the $H\to e\tau$ and $H\to \mu\tau$ signals, obtained by fitting the data of the MC-template $\ell\tau_{had}$ channel for $\mu\tau_{had}$ final state in the VBF category.

NN score distribution, after an independent fit of the $H\to \mu\tau$ signal, obtained by fitting the data of the Symmetry $\ell\tau_{\ell'}$ channel, for the $\mu\tau_{e}$ final state in the non-VBF category.

NN score distribution, after an independent fit of the $H\to \mu\tau$ signal, obtained by fitting the data of the Symmetry $\ell\tau_{\ell'}$ channel, for the $\mu\tau_{e}$ final state in the non-VBF category.

NN score distribution, after an independent fit of the $H\to \mu\tau$ signal, obtained by fitting the data of the Symmetry $\ell\tau_{\ell'}$ channel, for the $\mu\tau_{e}$ final state in the VBF category.

NN score distribution, after an independent fit of the $H\to \mu\tau$ signal, obtained by fitting the data of the Symmetry $\ell\tau_{\ell'}$ channel, for the $\mu\tau_{e}$ final state in the VBF category.

Best-fit $\mathcal{B}(H\to \mu\tau)- \mathcal{B}(H\to e\tau)$ values, given in %, obtained from the standalone fits of the $\ell\tau_\ell'$ final state with either background estimation method. For the MC-template method, the correlated uncertainties are fixed to their best-fit values and the uncertainties are re-derived considering only the uncorrelated sources. For the Symmetry method, the full uncertainty is considered.

Best-fit $\mathcal{B}(H\to \mu\tau)- \mathcal{B}(H\to e\tau)$ values, given in %, obtained from the standalone fits of the $\ell\tau_\ell'$ final state with either background estimation method. For the MC-template method, the correlated uncertainties are fixed to their best-fit values and the uncertainties are re-derived considering only the uncorrelated sources. For the Symmetry method, the full uncertainty is considered.

Best-fit value of the branching ratios $\mathcal{B}(H\to e\tau)$ and $\mathcal{B}(H\to \mu\tau)$, given in %, and likelihood contours at 68% and 95% C.L. Obtained from the simultaneous fit of $H\to e\tau$ and $H\to \mu\tau$ signals based on the MC-template method, compared to the SM expectation.

Best-fit value of the branching ratios $\mathcal{B}(H\to e\tau)$ and $\mathcal{B}(H\to \mu\tau)$, given in %, and likelihood contours at 68% and 95% C.L. Obtained from the simultaneous fit of $H\to e\tau$ and $H\to \mu\tau$ signals based on the MC-template method, compared to the SM expectation.

Distribution (events/100 GeV) of the reconstructed $m_{tb}$ for data and backgrounds in the 0-lepton channel's the signal region 3 after the background-only fit to data. The systematics uncertainty is shown for the post-fit background sum, including the background statistical uncertainty. The individual background components are obtained after the fit, too. There are also the pre-fit background sum and the expected signal distribution. The distribution of the $W^{\prime}$ boson signal for a mass of 3 TeV is normalised to the predicted cross-section. The last bin in each distribution includes overflow.

Distribution (events/100 GeV) of the reconstructed $m_{tb}$ for data and backgrounds in the 0-lepton channel's validation region before the fit to data. The systematics uncertainty is shown for the pre-fit background sum, including the background statistical uncertainty. The individual background components are obtained before the fit, too. There is also the expected signal distribution. The distribution of the $W^{\prime}$ boson signal for a mass of 3 TeV is normalised to the predicted cross-section. The last bin in each distribution includes overflow.

Reconstructed $m_{tb}$ distributions (events/50 GeV) for data and backgrounds in the 1-lepton channel's 2j1b signal region after the background-only fit to data. The systematics uncertainty is shown for the post-fit background sum, including the background statistical uncertainty. The individual background components are obtained after the fit, too. There are also the pre-fit background sum and the expected signal distribution. The distribution of the $W^{\prime}$ boson signal for a mass of 3 TeV is normalised to the predicted cross-section. The last bin in each distribution includes overflow.

Reconstructed $m_{tb}$ distributions (events/50 GeV) for data and backgrounds in the 1-lepton channel's 3j1b signal region after the background-only fit to data. The systematics uncertainty is shown for the post-fit background sum, including the background statistical uncertainty. The individual background components are obtained after the fit, too. There are also the pre-fit background sum and the expected signal distribution. The distribution of the $W^{\prime}$ boson signal for a mass of 3 TeV is normalised to the predicted cross-section. The last bin in each distribution includes overflow.

Reconstructed $m_{tb}$ distributions (events/50 GeV) for data and backgrounds in the 1-lepton channel's 2j2b signal region after the background-only fit to data. The systematics uncertainty is shown for the post-fit background sum, including the background statistical uncertainty. The individual background components are obtained after the fit, too. There are also the pre-fit background sum and the expected signal distribution. The distribution of the $W^{\prime}$ boson signal for a mass of 3 TeV is normalised to the predicted cross-section. The last bin in each distribution includes overflow.

Reconstructed $m_{tb}$ distributions (events/50 GeV) for data and backgrounds in the 1-lepton channel's 3j2b signal region after the background-only fit to data. The systematics uncertainty is shown for the post-fit background sum, including the background statistical uncertainty. The individual background components are obtained after the fit, too. There are also the pre-fit background sum and the expected signal distribution. The distribution of the $W^{\prime}$ boson signal for a mass of 3 TeV is normalised to the predicted cross-section. The last bin in each distribution includes overflow.

Reconstructed $m_{tb}$ distributions (events/50 GeV) for data and backgrounds in the 1-lepton channel's 2j1b control region after the background-only fit to data. The systematics uncertainty is shown for the post-fit background sum, including the background statistical uncertainty. The individual background components are obtained after the fit, too. There are also the pre-fit background sum and the expected signal distribution. The distribution of the $W^{\prime}$ boson signal for a mass of 3 TeV is normalised to the predicted cross-section. The last bin in each distribution includes overflow.

Reconstructed $m_{tb}$ distributions (events/50 GeV) for data and backgrounds in the 1-lepton channel's 3j1b control region after the background-only fit to data. The systematics uncertainty is shown for the post-fit background sum, including the background statistical uncertainty. The individual background components are obtained after the fit, too. There are also the pre-fit background sum and the expected signal distribution. The distribution of the $W^{\prime}$ boson signal for a mass of 3 TeV is normalised to the predicted cross-section. The last bin in each distribution includes overflow.

Reconstructed $m_{tb}$ distributions (events/50 GeV) for data and backgrounds in the 1-lepton channel's 2j1b validation region after the background-only fit to data. The systematics uncertainty is shown for the post-fit background sum, including the background statistical uncertainty. The individual background components are obtained after the fit, too. There are also the pre-fit background sum and the expected signal distribution. The distribution of the $W^{\prime}$ boson signal for a mass of 3 TeV is normalised to the predicted cross-section. The last bin in each distribution includes overflow.

Reconstructed $m_{tb}$ distributions (events/50 GeV) for data and backgrounds in the 1-lepton channel's 3j1b validation region after the background-only fit to data. The systematics uncertainty is shown for the post-fit background sum, including the background statistical uncertainty. The individual background components are obtained after the fit, too. There are also the pre-fit background sum and the expected signal distribution. The distribution of the $W^{\prime}$ boson signal for a mass of 3 TeV is normalised to the predicted cross-section. The last bin in each distribution includes overflow.

Observed and expected 95% CL limits on the cross-section times branching ratio for the production of a $W^{\prime}$ boson with decay to tb and left-handed couplings as a function of the mass of the $W^{\prime}$ boson and a coupling value of $g^{\prime}/g$=0.5. The observed and expected limits are derived using a linear interpolation between simulated signal mass hypotheses. The uncertainty on the theory prediction includes components from factorisation and renormalisation scales, PDFs, the strong coupling constant, and the top-quark mass.

Observed and expected 95% CL limits on the cross-section times branching ratio for the production of a $W^{\prime}$ boson with decay to tb and left-handed couplings as a function of the mass of the $W^{\prime}$ boson and a coupling value of $g^{\prime}/g$=1.0. The observed and expected limits are derived using a linear interpolation between simulated signal mass hypotheses. The uncertainty on the theory prediction includes components from factorisation and renormalisation scales, PDFs, the strong coupling constant, and the top-quark mass.

Observed and expected 95% CL limits on the cross-section times branching ratio for the production of a $W^{\prime}$ boson with decay to tb and left-handed couplings as a function of the mass of the $W^{\prime}$ boson and a coupling value of $g^{\prime}/g$=2.0. The observed and expected limits are derived using a linear interpolation between simulated signal mass hypotheses. The uncertainty on the theory prediction includes components from factorisation and renormalisation scales, PDFs, the strong coupling constant, and the top-quark mass.

Observed and expected 95% CL limits on the cross-section times branching ratio for the production of a $W^{\prime}$ boson with decay to tb and right-handed couplings as a function of the mass of the $W^{\prime}$ boson and a coupling value of $g^{\prime}/g$=0.5. The observed and expected limits are derived using a linear interpolation between simulated signal mass hypotheses. The uncertainty on the theory prediction includes components from factorisation and renormalisation scales, PDFs, the strong coupling constant, and the top-quark mass.

Observed and expected 95% CL limits on the cross-section times branching ratio for the production of a $W^{\prime}$ boson with decay to tb and right-handed couplings as a function of the mass of the $W^{\prime}$ boson and a coupling value of $g^{\prime}/g$=1.0. The observed and expected limits are derived using a linear interpolation between simulated signal mass hypotheses. The uncertainty on the theory prediction includes components from factorisation and renormalisation scales, PDFs, the strong coupling constant, and the top-quark mass.

Observed and expected 95% CL limits on the cross-section times branching ratio for the production of a $W^{\prime}$ boson with decay to tb and right-handed couplings as a function of the mass of the $W^{\prime}$ boson and a coupling value of $g^{\prime}/g$=2.0. The observed and expected limits are derived using a linear interpolation between simulated signal mass hypotheses. The uncertainty on the theory prediction includes components from factorisation and renormalisation scales, PDFs, the strong coupling constant, and the top-quark mass.

95% CL limits on the coupling value ($g^{\prime}/g$) and the $W^{\prime}$-boson mass for left-handed $W^{\prime}$-boson couplings. The area above the line is excluded.

95% CL limits on the coupling value ($g^{\prime}/g$) and the $W^{\prime}$-boson mass for right-handed $W^{\prime}$-boson couplings. The area above the line is excluded.

The product of fiducial acceptance and selection efficiency for the three signal regions of the 0-lepton channel as a function of the mass of the $W^{\prime}$ boson with left-handed chirality. The $W^{\prime}$ boson coupling strength is set to $g^{\prime}/g=1$.

The product of fiducial acceptance and selection efficiency for the three signal regions of the 0-lepton channel as a function of the mass of the $W^{\prime}$ boson with left-handed chirality. The $W^{\prime}$ boson coupling strength is set to $g^{\prime}/g=0.5$.

The product of fiducial acceptance and selection efficiency for the three signal regions of the 0-lepton channel as a function of the mass of the $W^{\prime}$ boson with left-handed chirality. The $W^{\prime}$ boson coupling strength is set to $g^{\prime}/g=2$.

The product of fiducial acceptance and selection efficiency for the four signal regions of the 1-lepton channel as a function of the mass of the $W^{\prime}$ boson with left-handed chirality. The $W^{\prime}$ boson coupling strength is set to $g^{\prime}/g=1$.

The product of fiducial acceptance and selection efficiency for the four signal regions of the 1-lepton channel as a function of the mass of the $W^{\prime}$ boson with left-handed chirality. The $W^{\prime}$ boson coupling strength is set to $g^{\prime}/g=0.5$.

The product of fiducial acceptance and selection efficiency for the four signal regions of the 1-lepton channel as a function of the mass of the $W^{\prime}$ boson with left-handed chirality. The $W^{\prime}$ boson coupling strength is set to $g^{\prime}/g=2$.

The product of fiducial acceptance and selection efficiency for the three signal regions of the 0-lepton channel as a function of the mass of the $W^{\prime}$ boson with right-handed chirality. The $W^{\prime}$ boson coupling strength is set to $g^{\prime}/g=1$.

The product of fiducial acceptance and selection efficiency for the three signal regions of the 0-lepton channel as a function of the mass of the $W^{\prime}$ boson with right-handed chirality. The $W^{\prime}$ boson coupling strength is set to $g^{\prime}/g=0.5$.

The product of fiducial acceptance and selection efficiency for the three signal regions of the 0-lepton channel as a function of the mass of the $W^{\prime}$ boson with right-handed chirality. The $W^{\prime}$ boson coupling strength is set to $g^{\prime}/g=2$.

The product of fiducial acceptance and selection efficiency for the four signal regions of the 1-lepton channel as a function of the mass of the $W^{\prime}$ boson with right-handed chirality. The $W^{\prime}$ boson coupling strength is set to $g^{\prime}/g=1$.

The product of fiducial acceptance and selection efficiency for the four signal regions of the 1-lepton channel as a function of the mass of the $W^{\prime}$ boson with right-handed chirality. The $W^{\prime}$ boson coupling strength is set to $g^{\prime}/g=0.5$.

The product of fiducial acceptance and selection efficiency for the four signal regions of the 1-lepton channel as a function of the mass of the $W^{\prime}$ boson with right-handed chirality. The $W^{\prime}$ boson coupling strength is set to $g^{\prime}/g=2$.