Expected and observed upper limits at 95% CL on the cross section of vector-like quark pair production for $B\bar{B}$ in the singlet model.

Expected and observed upper limits at 95% CL on the cross section of vector-like quark pair production for $T\bar{T}$ in the doublet model.

Expected and observed upper limits at 95% CL on the cross section of vector-like quark pair production, considereing both $T\bar{T}$ and $B\bar{B}$, in the $(T,B)$ doublet model.

Expected 95% CL lower limits on the vector-like top quark mass as a function of the branching ratios into $Wb$ and $Ht$.

Observed 95% CL lower limits on the vector-like top quark mass as a function of the branching ratios into $Wb$ and $Ht$.

Expected 95% CL lower limits on the vector-like bottom quark mass as a function of the branching ratios into $Hb$ and $Wt$.

Observed 95% CL lower limits on the vector-like top quark mass as a function of the branching ratios into $Hb$ and $Wt$.

Measured unfolded differential cross-section as a function of the dilepton transverse momentum $p^{ll}_{\mathrm{T}}$. NLO predictions from Sherpa 2.2.10 and MadGraph5_aMC@NLO 2.7.3 are also shown. The uncertainty in the predictions is divided into statistical and theoretical uncertainties (scale and PDF+$\alpha_{s}$).

Measured unfolded differential cross-section as a function of the the four-body transverse momentum $p^{ll\gamma\gamma}_{\mathrm{T}}$. NLO predictions from Sherpa 2.2.10 and MadGraph5_aMC@NLO 2.7.3 are also shown. The uncertainty in the predictions is divided into statistical and theoretical uncertainties (scale and PDF+$\alpha_{s}$).

Measured unfolded differential cross-section as a function of the diphoton invariant mass $m_{\gamma\gamma}$. NLO predictions from Sherpa 2.2.10 and MadGraph5_aMC@NLO 2.7.3 are also shown. The uncertainty in the predictions is divided into statistical and theoretical uncertainties (scale and PDF+$\alpha_{s}$).

Measured unfolded differential cross-section as a function of the four-body invariant mass $m_{ll\gamma\gamma}$. NLO predictions from Sherpa 2.2.10 and MadGraph5_aMC@NLO 2.7.3 are also shown. The uncertainty in the predictions is divided into statistical and theoretical uncertainties (scale and PDF+$\alpha_{s}$).

Expected and observed $95\%$ confidence intervals for the coupling parameters $f_{T,j}/\Lambda^{4}$ of transverse dimension-8 operators. All parameter values outside of the stated range are excluded at the chosen confidence level. No unitarity constraints are applied.

Expected and observed unitarised $95\%$ confidence intervals for the coupling parameter $f_{T,8}/\Lambda^{4}$ in the clipping energy range between 1.1 and 5 TeV. The non-unitarised limits ($E_c = \infty$) are also shown. All parameter values outside of the stated range are excluded at the chosen confidence level.

Expected and observed unitarised $95\%$ confidence intervals for the coupling parameter $f_{T,0}/\Lambda^{4}$ in the clipping energy range between 1.1 and 5 TeV. The non-unitarised limits ($E_c = \infty$) are also shown. All parameter values outside of the stated range are excluded at the chosen confidence level.

Expected and observed unitarised $95\%$ confidence intervals for the coupling parameter $f_{T,1}/\Lambda^{4}$ in the clipping energy range between 1.1 and 5 TeV. The non-unitarised limits ($E_c = \infty$) are also shown. All parameter values outside of the stated range are excluded at the chosen confidence level.

Expected and observed unitarised $95\%$ confidence intervals for the coupling parameter $f_{T,2}/\Lambda^{4}$ in the clipping energy range between 1.1 and 5 TeV. The non-unitarised limits ($E_c = \infty$) are also shown. All parameter values outside of the stated range are excluded at the chosen confidence level.

Expected and observed unitarised $95\%$ confidence intervals for the coupling parameter $f_{T,5}/\Lambda^{4}$ in the clipping energy range between 1.1 and 5 TeV. The non-unitarised limits ($E_c = \infty$) are also shown. All parameter values outside of the stated range are excluded at the chosen confidence level.

Expected and observed unitarised $95\%$ confidence intervals for the coupling parameter $f_{T,6}/\Lambda^{4}$ in the clipping energy range between 1.1 and 5 TeV. The non-unitarised limits ($E_c = \infty$) are also shown. All parameter values outside of the stated range are excluded at the chosen confidence level.

Expected and observed unitarised $95\%$ confidence intervals for the coupling parameter $f_{T,7}/\Lambda^{4}$ in the clipping energy range between 1.1 and 5 TeV. The non-unitarised limits ($E_c = \infty$) are also shown. All parameter values outside of the stated range are excluded at the chosen confidence level.

Expected and observed unitarised $95\%$ confidence intervals for the coupling parameter $f_{T,9}/\Lambda^{4}$ in the clipping energy range between 1.1 and 5 TeV. The non-unitarised limits ($E_c = \infty$) are also shown. All parameter values outside of the stated range are excluded at the chosen confidence level.

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

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

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

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

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

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

The observed and expected 95% CL upper limits on the minimal coupling vector LQ pair production cross-sections assuming B = 1 as a function of m$_\text{LQ}$.

The observed and expected 95% CL upper limits on the Yang-Mills coupling vector LQ pair production cross-sections assuming B = 1 as a function of m$_\text{LQ}$.

The observed and expected 95% CL upper limits on the branching ratio into charged leptons as a function of m$_\text{LQ}$ for the scalar LQ.

The observed and expected 95% CL upper limits on the branching ratio into charged leptons as a function of m$_\text{LQ}$ for the vector LQ minimal coupling scenario.

The observed and expected 95% CL upper limits on the branching ratio into charged leptons as a function of m$_\text{LQ}$ for the vector LQ Yang-Mills coupling scenario.

Measured $p_T$ cross sections in full-lepton phase space for 1.2 < |y| < 1.6.

Measured $p_T$ cross sections in full-lepton phase space for 1.6 < |y| < 2.0.

Measured $p_T$ cross sections in full-lepton phase space for 2.0 < |y| < 2.4.

Measured $p_T$ cross sections in full-lepton phase space for 2.4 < |y| < 2.8.

Measured $p_T$ cross sections in full-lepton phase space for 2.8 < |y| < 3.2.

Measured cross sections in full-lepton phase space as a function of |y|.

Normalised measured $p_T$ cross sections in full-lepton phase space for |y| < 1.6.

The +1 $\sigma$ band of the observed exclusion contor for the $Z^{\prime}_{B}$ model in the $m_{\chi}$-$m_{Z^{\prime}_{B}}$ plane.

The -1 $\sigma$ band of the observed exclusion contor for the $Z^{\prime}_{B}$ model in the $m_{\chi}$-$m_{Z^{\prime}_{B}}$ plane.

A comparison of the inferred limits to the constraints from direct detection experiments on the spin-independent DM--nucleon cross section in the context of the $Z'_B$ simplified model with vector couplings. Limits are shown at 90% CL.

The observed exclusion contor for the $Z^{\prime}$-2HDM model in the $m_{A}$-$m_{Z^{\prime}}$ plane.

The expected exclusion contor for the $Z^{\prime}$-2HDM model in the $m_{A}$-$m_{Z^{\prime}}$ plane.

The +1 $\sigma$ band of the observed exclusion contor for the $m_{A}$-$Z^{\prime}$-2HDM model in the $m_{Z^{\prime}}$ plane.

The -1 $\sigma$ band of the observed exclusion contor for the $m_{A}$-$Z^{\prime}$-2HDM model in the $m_{Z^{\prime}}$ plane.

The observed exclusion contor for the 2HDM-a model in the $m_{A}$-$m_{a}$ plane.

The expected exclusion contor for the 2HDM-a model in the $m_{A}$-$m_{a}$ plane.

The +1 $\sigma$ band of the observed exclusion contor for the 2HDM-a model in the $m_{A}$-$m_{a}$ plane.

The -1 $\sigma$ band of the observed exclusion contor for the 2HDM-a model in the $m_{A}$-$m_{a}$ plane.

The observed exclusion contor for the 2HDM-a model in the $tan\beta$-$m_{a}$ plane.

The expected exclusion contor for the 2HDM-a model in the $tan\beta$-$m_{a}$ plane.

The +1 $\sigma$ band of the observed exclusion contor for the 2HDM-a model in the $tan\beta$-$m_{a}$ plane.

The -1 $\sigma$ band of the observed exclusion contor for the 2HDM-a model in the $tan\beta$-$m_{a}$ plane.

The exclusion limits at 95% CL for the 2HDM+a model as a function of $\sin \theta$ for $m_{A,H^{\pm},H}$= 600GeV, $m_a$ = 200GeV, $\tan \beta$ = 1.0$.

The exclusion limits at 95% CL for the 2HDM+a model as a function of $\sin \theta$ for $m_{A,H^{\pm},H}$= 1000GeV, $m_a$ = 350GeV, $\tan \beta$ = 1.0$.

Breakdown of the dominant systematic uncertainties.

Event yields in the range of 120 $<m_{\gamma\gamma}<$ 130 GeV for data, signal models, the SM Higgs boson background and non-resonant background in each analysis category, for an integrated luminosity of $139$fb$^{-1}$.

Detailed background contributions from the SM Higgs boson and continuum background for each cut

Detailed contributions from the signals for each cut.

Acceptance times efficiency for several signals in each category.

Distribution of $S$, which is one of the discriminating variables used to define the $2\ell^{sc}$ SRs. The events are selected with the preselection requirements listed in Table 4 in the paper. The data (dots) are compared with the expected contributions from the relevant background sources (histograms). The expected signal distributions for $m_{H^{\pm\pm}} = 300~GeV$ are also shown, scaled to the observed number of events. The last bin includes overflows.

Distribution of $E_{T}^{miss}$, which is one of the discriminating variables used to define the $3\ell$ SRs. The events are selected with the preselection requirements listed in Table 4 in the paper. The data (dots) are compared with the expected contributions from the relevant background sources (histograms). The expected signal distributions for $m_{H^{\pm\pm}} = 300~GeV$ are also shown, scaled to the observed number of events. The last bin includes overflows.

Distribution of $\Delta R_{\ell^{\pm}\ell^{\pm}}$, which is one of the discriminating variables used to define the $3\ell$ SRs. The events are selected with the preselection requirements listed in Table 4 in the paper. The data (dots) are compared with the expected contributions from the relevant background sources (histograms). The expected signal distributions for $m_{H^{\pm\pm}} = 300~GeV$ are also shown, scaled to the observed number of events. The last bin includes overflows.

Distribution of $m_{x\ell}$ ($x$=3), which is one of the discriminating variables used to define the $3\ell$ SRs. The events are selected with the preselection requirements listed in Table 4 in the paper. The data (dots) are compared with the expected contributions from the relevant background sources (histograms). The expected signal distributions for $m_{H^{\pm\pm}} = 300~GeV$ are also shown, scaled to the observed number of events. The last bin includes overflows.

Distribution of $p_{T}^{leading jet}$, which is one of the discriminating variables used to define the $3\ell$ SRs. The events are selected with the preselection requirements listed in Table 4 in the paper. The data (dots) are compared with the expected contributions from the relevant background sources (histograms). The expected signal distributions for $m_{H^{\pm\pm}} = 300~GeV$ are also shown, scaled to the observed number of events. The last bin includes overflows.

Distribution of $E_{T}^{miss}$, which is one of the discriminating variables used to define the $4\ell$ SRs. The events are selected with the preselection requirements listed in Table 4 in the paper. The data (dots) are compared with the expected contributions from the relevant background sources (histograms). The expected signal distributions for $m_{H^{\pm\pm}} = 300~GeV$ are also shown, scaled to the observed number of events. The last bin includes overflows.

Distribution of $\Delta R_{\ell^{\pm}\ell^{\pm}}^{min}$, which is one of the discriminating variables used to define the $4\ell$ SRs. The events are selected with the preselection requirements listed in Table 4 in the paper. The data (dots) are compared with the expected contributions from the relevant background sources (histograms). The expected signal distributions for $m_{H^{\pm\pm}} = 300~GeV$ are also shown, scaled to the observed number of events. The last bin includes overflows.

Distribution of $m_{x\ell}$ ($x$=4), which is one of the discriminating variables used to define the $4\ell$ SRs. The events are selected with the preselection requirements listed in Table 4 in the paper. The data (dots) are compared with the expected contributions from the relevant background sources (histograms). The expected signal distributions for $m_{H^{\pm\pm}} = 300~GeV$ are also shown, scaled to the observed number of events. The last bin includes overflows.

Distribution of $p_{T}^{\ell_{1}}$, which is one of the discriminating variables used to define the $4\ell$ SRs. The events are selected with the preselection requirements listed in Table 4 in the paper. The data (dots) are compared with the expected contributions from the relevant background sources (histograms). The expected signal distributions for $m_{H^{\pm\pm}} = 300~GeV$ are also shown, scaled to the observed number of events. The last bin includes overflows.

Contributions from different categories of uncertainties relative to the expected background yields in the defined SRs, as obtained after performing the likelihood ratio test discussed in Section 9 in the paper. The uncertainties are shown for the combination of the individual channels of the $2\ell^{sc}$, $3\ell$ and $4\ell$ SRs. The SRs are indicated along the horizontal axis. In the HEPData entry, the x-axis is simplified for easier visualisation. The first number indicates the sub channel (2:$2\ell^{sc}$, 3:$3\ell$, 4:$4\ell$), while the second number indicates the mass point (2:200, 3:300, 4:400, 5:500).

Data event yields compared with the expected contributions from relevant background sources, for the combination of the individual channels of the $2\ell^{sc}$, $3\ell$ and $4\ell$ SRs. The total uncertainties in the expected event yields are shown as the hatched bands. The SRs are indicated along the horizontal axis. In the HEPData entry, the x-axis is simplified for easier visualisation. The first number indicates the sub channel (2:$2\ell^{sc}$, 3:$3\ell$, 4:$4\ell$), while the second number indicates the mass point (2:200, 3:300, 4:400, 5:500).

The $E_{T}^{miss}$ distribution for the SRs of the $m_{H^{\pm\pm}} = 300~GeV$ signal mass hypothesis, where the selection requirement on $E_{T}^{miss}$ has been removed. In the attached plot, the signals are stacked on top of the backgrounds while individuals contributions of the $2\ell^{sc}$ channel are shown in HEPData. The last bin, isolated by a vertical red dashed line, is inclusive and corresponds to the SR.

The $E_{T}^{miss}$ distribution for the SRs of the $m_{H^{\pm\pm}} = 300~GeV$ signal mass hypothesis, where the selection requirement on $E_{T}^{miss}$ has been removed. In the attached plot, the signals are stacked on top of the backgrounds while individuals contributions of the $3\ell$ channel are shown in HEPData. The last bin, isolated by a vertical red dashed line, is inclusive and corresponds to the SR.

The $E_{T}^{miss}$ distribution for the SRs of the $m_{H^{\pm\pm}} = 300~GeV$ signal mass hypothesis, where the selection requirement on $E_{T}^{miss}$ has been removed. In the attached plot, the signals are stacked on top of the backgrounds while individuals contributions of the $4\ell$ channel are shown in HEPData. The last bin, isolated by a vertical red dashed line, is inclusive and corresponds to the SR.

Observed and expected upper limits of the $H^{\pm\pm}$ pair production cross section times branching fraction at 95% CL obtained from the combination of 2$\ell^{sc}$, 3$\ell$ and 4$\ell$ channels. The region above the observed limit is excluded by the measurement. The bands represent the expected exclusion curves within one and two standard deviations.

The theoretical prediction of Figure 9(a) in the paper.

Observed and expected upper limits of the $H^{\pm\pm}$ and $H^{\pm}$ production cross section times branching fraction at 95% CL obtained from the combination of 2$\ell^{sc}$, 3$\ell$ and 4$\ell$ channels. The region above the observed limit is excluded by the measurement. The bands represent the expected exclusion curves within one and two standard deviations.

The theoretical prediction of Figure 9(b) in the paper.

Data event yields compared with the estimated background in the $m_{H^{\pm\pm}} = 200~GeV$ or $m_{H^{\pm\pm}} = 220~GeV$ SRs. SFOC 0 and SFOC 1,2 refer to the number of same-flavour opposite charge lepton pairs. The total uncertainties in the estimated background yields are shown as the hashed bands. In the HEPData entry, the x-axis is simplified for easier visualisation (1:$e^{\pm}e^{\pm}$, 2:$e^{\pm}\mu^{\pm}$, 3:$\mu^{\pm}\mu^{\pm}$, 4:SFOC 0, 5:SFOC 1,2, 6:$4\ell$).

Data event yields compared with the estimated background in the $m_{H^{\pm\pm}} = 300~GeV$ or $m_{H^{\pm\pm}} = 350~GeV$ SRs. SFOC 0 and SFOC 1,2 refer to the number of same-flavour opposite charge lepton pairs. The total uncertainties in the estimated background yields are shown as the hashed bands. In the HEPData entry, the x-axis is simplified for easier visualisation (1:$e^{\pm}e^{\pm}$, 2:$e^{\pm}\mu^{\pm}$, 3:$\mu^{\pm}\mu^{\pm}$, 4:SFOC 0, 5:SFOC 1,2, 6:$4\ell$).

Data event yields compared with the estimated background in the $m_{H^{\pm\pm}} = 400~GeV$ or $m_{H^{\pm\pm}} = 450~GeV$ SRs. SFOC 0 and SFOC 1,2 refer to the number of same-flavour opposite charge lepton pairs. The total uncertainties in the estimated background yields are shown as the hashed bands. In the HEPData entry, the x-axis is simplified for easier visualisation (1:$e^{\pm}e^{\pm}$, 2:$e^{\pm}\mu^{\pm}$, 3:$\mu^{\pm}\mu^{\pm}$, 4:SFOC 0, 5:SFOC 1,2, 6:$4\ell$).

Data event yields compared with the estimated background in the $m_{H^{\pm\pm}} = 500~GeV$ or $m_{H^{\pm\pm}} = 550~GeV$ or $m_{H^{\pm\pm}} = 600~GeV$ SRs. SFOC 0 and SFOC 1,2 refer to the number of same-flavour opposite charge lepton pairs. The total uncertainties in the estimated background yields are shown as the hashed bands. In the HEPData entry, the x-axis is simplified for easier visualisation (1:$e^{\pm}e^{\pm}$, 2:$e^{\pm}\mu^{\pm}$, 3:$\mu^{\pm}\mu^{\pm}$, 4:SFOC 0, 5:SFOC 1,2, 6:$4\ell$).

Summary of the observed and expected 95% CL upper limits on the cross section for $\mathrm{LQ}_{3}^{\mathrm{d}}$ pair production as a function of $m_{\mathrm{LQ}_{3}^{\mathrm{d}}}$ under the assumptions of B=1.

Summary of the observed and expected 95% CL upper limits on B as a function of $m_{\mathrm{LQ}_{3}^{\mathrm{d}}}$.

Summary of the observed and expected 95% CL upper limits on B as a function of $m_{\mathrm{LQ}_{3}^{\mathrm{d}}}$.

Cutflow of the preselection requirements (see Section 5) for $\mathrm{LQ}_{3}^{\mathrm{d}}$ signals with $m_{\mathrm{LQ}_{3}^{\mathrm{d}}}$=0.9, 1.1, and 1.3 TeV, assuming B=1. The yields correspond to an integrated luminosity of 139 fb$^{-1}$.

Cutflow of the preselection requirements (see Section 5) for $\mathrm{LQ}_{3}^{\mathrm{d}}$ signals with $m_{\mathrm{LQ}_{3}^{\mathrm{d}}}$=0.9, 1.1, and 1.3 TeV, assuming B=1. The yields correspond to an integrated luminosity of 139 fb$^{-1}$.

Cutflow of the signal region requirements in 1$\ell+\geq 1\tau$ channel (see Table 3) for $\mathrm{LQ}_{3}^{\mathrm{d}}$ signals with $m_{\mathrm{LQ}_{3}^{\mathrm{d}}}$=0.9, 1.1, and 1.3 TeV, assuming B=1. Events that satisfy the preselection requirements are considered. The yields correspond to an integrated luminosity of 139 fb$^{-1}$.

Cutflow of the signal region requirements in 1$\ell+\geq 1\tau$ channel (see Table 3) for $\mathrm{LQ}_{3}^{\mathrm{d}}$ signals with $m_{\mathrm{LQ}_{3}^{\mathrm{d}}}$=0.9, 1.1, and 1.3 TeV, assuming B=1. Events that satisfy the preselection requirements are considered. The yields correspond to an integrated luminosity of 139 fb$^{-1}$.

Cutflow of the signal region requirements in the 2$\ell$OS+$\geq 1\tau$ channel (see Table 4) for $\mathrm{LQ}_{3}^{\mathrm{d}}$ signals with $m_{\mathrm{LQ}_{3}^{\mathrm{d}}}$=0.9, 1.1, and 1.3 TeV, assuming B=1. Events that satisfy the preselection requirements are considered. The yields correspond to an integrated luminosity of 139 fb$^{-1}$.

Cutflow of the signal region requirements in the 2$\ell$OS+$\geq 1\tau$ channel (see Table 4) for $\mathrm{LQ}_{3}^{\mathrm{d}}$ signals with $m_{\mathrm{LQ}_{3}^{\mathrm{d}}}$=0.9, 1.1, and 1.3 TeV, assuming B=1. Events that satisfy the preselection requirements are considered. The yields correspond to an integrated luminosity of 139 fb$^{-1}$.

Cutflow of the signal region requirements in the $2\ell$SS/$3\ell+\geq 1\tau$ channel (see Table 5) for $\mathrm{LQ}_{3}^{\mathrm{d}}$ signals with $m_{\mathrm{LQ}_{3}^{\mathrm{d}}}$=0.9, 1.1, and 1.3 TeV, assuming B=1. Events that satisfy the preselection requirements are considered. In this channel, two signal regions (SR-L and SR-H) are defined based on $p_{\mathrm{T}, 1}^{\tau}$, with SR-L and SR-H requiring $125< p_{\mathrm{T}, 1}^{\tau} < 225$ GeV and $p_{\mathrm{T}, 1}^{\tau}>225$ GeV, respectively. The yields correspond to an integrated luminosity of 139 fb$^{-1}$.

Cutflow of the signal region requirements in the $2\ell$SS/$3\ell+\geq 1\tau$ channel (see Table 5) for $\mathrm{LQ}_{3}^{\mathrm{d}}$ signals with $m_{\mathrm{LQ}_{3}^{\mathrm{d}}}$=0.9, 1.1, and 1.3 TeV, assuming B=1. Events that satisfy the preselection requirements are considered. In this channel, two signal regions (SR-L and SR-H) are defined based on $p_{\mathrm{T}, 1}^{\tau}$, with SR-L and SR-H requiring $125< p_{\mathrm{T}, 1}^{\tau} < 225$ GeV and $p_{\mathrm{T}, 1}^{\tau}>225$ GeV, respectively. The yields correspond to an integrated luminosity of 139 fb$^{-1}$.