Fig. 3 bottom figure - Distributions of MC simulation compared with data for reconstructed shower energy in the 1$e$0$p$0$\pi$ signal channel, along with the LEE Signal Model 2. The signal and background event categories are summed to form the unconstrained prediction (excluding LEE). Signal events correspond to $\nu_e$ CC events. Background events include $\nu$ with $\pi^0$ events, $\nu$ other events, and cosmic ray events. In Fig. 3, the LEE component is plotted on top of the constrained prediction (excluding LEE) for illustrative purposes. In all statistical tests (results summarized in Table I), the prediction under an LEE hypothesis corresponds to a constrained prediction including LEE. The statistical uncertainties of data use a combined Neyman-Pearson (CNP) version (Eq.(19) in https://doi.org/10.1016/j.nima.2020.163677).

Fig. 4 top figure - Distributions of MC simulation compared with data for reconstructed shower cos($\theta$) in the 1$e$N$p$0$\pi$ signal channel, along with the LEE Signal Model 2. The signal and background event categories are summed to form the unconstrained prediction (excluding LEE). Signal events correspond to $\nu_e$ CC events. Background events include $\nu$ with $\pi^0$ events, $\nu$ other events, and cosmic ray events. In Fig. 4, the LEE component is plotted on top of the constrained prediction (excluding LEE) for illustrative purposes. In all statistical tests (results summarized in Table I), the prediction under an LEE hypothesis corresponds to a constrained prediction including LEE. The statistical uncertainties of data use a combined Neyman-Pearson (CNP) version (Eq.(19) in https://doi.org/10.1016/j.nima.2020.163677).

Fig. 4 bottom figure - Distributions of MC simulation compared with data for reconstructed shower cos($\theta$) in the 1$e$0$p$0$\pi$ signal channel, along with the LEE Signal Model 2. The signal and background event categories are summed to form the unconstrained prediction (excluding LEE). Signal events correspond to $\nu_e$ CC events. Background events include $\nu$ with $\pi^0$ events, $\nu$ other events, and cosmic ray events. In Fig. 4, the LEE component is plotted on top of the constrained prediction (excluding LEE) for illustrative purposes. In all statistical tests (results summarized in Table I), the prediction under an LEE hypothesis corresponds to a constrained prediction including LEE. The statistical uncertainties of data use a combined Neyman-Pearson (CNP) version (Eq.(19) in https://doi.org/10.1016/j.nima.2020.163677).

Fig. 1 top figure - Reconstructed neutrino energy distributions of the 1$\mu$N$p$0$\pi$ control sample (sideband). The signal and background event categories are summed to form the unconstrained prediction. Signal events correspond to $\nu_\mu$ CC events. Background events include $\nu_e$ CC events, NC without $\pi^0$ events, NC with $\pi^0$ events, and cosmic ray events. The statistical uncertainties of data use a combined Neyman-Pearson (CNP) version (Eq.(19) in https://doi.org/10.1016/j.nima.2020.163677).

Fig. 1 middle figure - Reconstructed neutrino energy distributions of the 1$\mu$0$p$0$\pi$ control sample (sideband). The signal and background event categories are summed to form the unconstrained prediction. Signal events correspond to $\nu_\mu$ CC events. Background events include $\nu_e$ CC events, NC without $\pi^0$ events, NC with $\pi^0$ events, and cosmic ray events. The statistical uncertainties of data use a combined Neyman-Pearson (CNP) version (Eq.(19) in https://doi.org/10.1016/j.nima.2020.163677).

Fig. 1 bottom figure - Reconstructed neutrino energy distributions of the NC$\pi^{0}$ control sample (sideband). The signal and background event categories are summed to form the unconstrained prediction. Signal events correspond to NC with $\pi^0$ events. Background events include $\nu_\mu$ CC events, $\nu_e$ CC events, NC without $\pi^0$ events, and cosmic ray events. Only bins up to 1 GeV in this sideband are released and are used in the constraint procedure due to low statistics above this energy. The statistical uncertainties of data use a combined Neyman-Pearson (CNP) version (Eq.(19) in https://doi.org/10.1016/j.nima.2020.163677).

The covariance matrix includes both signal channels and sideband channels, with the LEE component either excluded or included in the signal channels. All channels are binned in reconstructed neutrino energy. Fig. 2 in Supplemental Material shows the corresponding correlation matrix. The constraint procedure uses the correlations with sideband channels to update the prediction and its uncertainty in the signal region. The matrix accounts for uncertainties and correlations between bins due to flux, cross-section, hadron reinteraction, detector systematics, MC statistics, and cosmic ray statistics. Data statistical uncertainties are not included.

The covariance matrix includes both signal channels and sideband channels, with the LEE component either excluded or included in the signal channels. Signal channels are binned shower energy and sideband channels are binned in reconstructed neutrino energy. The constraint procedure uses the correlations with sideband channels to update the prediction and its uncertainty in the signal region. The matrix accounts for uncertainties and correlations between bins due to flux, cross-section, hadron reinteraction, detector systematics, MC statistics, and cosmic ray statistics. Data statistical uncertainties are not included.

The covariance matrix includes both signal channels and sideband channels, with the LEE component either excluded or included in the signal channels. Signal channels are binned shower cos($\theta$) and sideband channels are binned in reconstructed neutrino energy. The constraint procedure uses the correlations with sideband channels to update the prediction and its uncertainty in the signal region. The matrix accounts for uncertainties and correlations between bins due to flux, cross-section, hadron reinteraction, detector systematics, MC statistics, and cosmic ray statistics. Data statistical uncertainties are not included.

The covariance matrices of the sideband channels, binned in reconstructed neutrino energy. The systematic covariance matrix accounts for uncertainties and correlations between bins due to flux, cross-section, hadron reinteraction, detector systematics, MC statistics, and cosmic ray statistics. The total covariance matrix additionally includes data statistical uncertainties (CNP version). The $\chi^2$ values shown in Fig. 1 are calculated using this total covariance matrix, together with the data and MC predictions from the released sideband distribtions.

The unconstrained covariance matrices of the signal channels, binned in reconstructed neutrino energy, with the LEE component either excluded or included. The systematic covariance matrix accounts for uncertainties and correlations between bins due to flux, cross-section, hadron reinteraction, detector systematics, MC statistics, and cosmic ray statistics. The total covariance matrix additionally includes data statistical uncertainties (CNP version). The unconstrained systematic uncertainty in neutrino energy, shown in Supplemental Material Fig. 19, is derived from this systematic covariance matrix (excluding LEE).

The constrained covariance matrices of the signal channels, binned in reconstructed neutrino energy, with the LEE component either excluded or included. The constrained systematic uncertainty in neutrino energy, shown in Supplemental Material Fig. 19, is derived from the systematic covariance matrix (excluding LEE). The $\chi^2$ values shown in Fig. 2 and Table I are calculated using these total covariance matrices, together with the data and constrained predictions from the released signal distributions under the $H_0$ hypothesis (LEE excluded) and $H_1$ hypothesis (LEE included).

The unconstrained covariance matrices of the signal channels, binned in reconstructed shower energy, with the LEE component either excluded or included. The systematic covariance matrix accounts for uncertainties and correlations between bins due to flux, cross-section, hadron reinteraction, detector systematics, MC statistics, and cosmic ray statistics. The total covariance matrix additionally includes data statistical uncertainties (CNP version). The unconstrained systematic uncertainty in shower energy, shown in Supplemental Material Fig. 20, is derived from this systematic covariance matrix (excluding LEE).

The constrained covariance matrices of the signal channels, binned in reconstructed shower energy, with the LEE component either excluded or included. The constrained systematic uncertainty in shower energy, shown in Supplemental Material Fig. 20, is derived from the systematic covariance matrix (excluding LEE). The $\chi^2$ values shown in Fig. 3 and Table I are calculated using these total covariance matrices, together with the data and constrained predictions from the released signal distributions under the $H_0$ hypothesis (LEE excluded) and $H_1$ hypothesis (LEE included).

The unconstrained covariance matrices of the signal channels, binned in reconstructed shower cos($\theta$), with the LEE component either excluded or included. The systematic covariance matrix accounts for uncertainties and correlations between bins due to flux, cross-section, hadron reinteraction, detector systematics, MC statistics, and cosmic ray statistics. The total covariance matrix additionally includes data statistical uncertainties (CNP version). The unconstrained systematic uncertainty in shower cos($\theta$), shown in Supplemental Material Fig. 21, is derived from this systematic covariance matrix (excluding LEE).

The constrained covariance matrices of the signal channels, binned in reconstructed shower cos($\theta$), with the LEE component either excluded or included. The constrained systematic uncertainty in shower cos($\theta$), shown in Supplemental Material Fig. 21, is derived from the systematic covariance matrix (excluding LEE). The $\chi^2$ values shown in Fig. 4 and Table I are calculated using these total covariance matrices, together with the data and constrained predictions from the released signal distributions under the $H_0$ hypothesis (LEE excluded) and $H_1$ hypothesis (LEE included).

VLL "4321" cross-sections at NLO order of accuracy obtained by MadGraph.

SUSY RPV LQD higgsino cross-sections at NLO + NLL order of accuracy obtained by Resummino.

SUSY RPV LQD wino cross-sections at NLO + NLL order of accuracy obtained by Resummino.

Cutflow of the selection requirements for VLL signals with m_VLL =600, 900, and 1200 GeV. The yields correspond to an integrated luminosity of 126 fb^-1 (140 fb^-1) for the BJET (MST and MSDT) signal regions. The first row refers to unweighted event yields, while the yields presented in other rows are computed after applying event weights according to the selected object reconstruction and identification efficiency scale factors. Dashes (––) refer to requirements that are not applicable.

The expected acceptance times efficiency (including object identification and reconstruction, trigger selection, and event selection) for VLL signal as a function of m_VLL for the combined signal regions as well as for three individual signal region categories: 1τ_had ≥3b MST, 1τ_had ≥3b BJET and ≥2τ_had ≥3b MSDT. The region 1τ_had ≥3b MST refers to the combination of 1τ_had 3b MST and 1τ_had ≥4b MST signal regions, while the region 1τ_had ≥3b BJET refers to the combination of 1τ_had 3b BJET and 1τ_had ≥4b BJET signal regions.

HF Fraction at $1.2 < |\eta| < 2.0$ Top Muon Rich Data

HF Fraction at $1.2 < |\eta| < 2.0$ Bottom Ratio

Charged Hadron $v_2$; $1.2 < |\eta| < 2.0$

Charged Hadron; $1.2 < |\eta| < 2.0$

HF -> $\mu$; $1.2 < |\eta| < 2.0$

HF -> $e$; $|\eta| < 0.35$

The $\Delta\phi_{ch,Z}$ spectra for events with Z boson $p_{T}^Z > 40$ GeV and charged-hadrons with $1 <p_T < 2$ GeV in PbPb for centrality interval of 0-30% collisions.

The $\Delta\phi_{ch,Z}$ spectra for events with Z boson $p_{T}^Z > 40$ GeV and charged-hadrons with $2 <p_T < 4$ GeV in PbPb for centrality interval of 0-30% collisions.

The $\Delta\phi_{ch,Z}$ spectra for events with Z boson $p_{T}^Z > 40$ GeV and charged-hadrons with $4 <p_T < 10$ GeV in PbPb for centrality interval of 0-30% collisions.

The $\Delta\phi_{ch,Z}$ spectra for events with Z boson $p_{T}^Z > 40$ GeV and charged-hadrons with $1 <p_T < 2$ GeV in PbPb for centrality interval of 30-50% collisions.

The $\Delta\phi_{ch,Z}$ spectra for events with Z boson $p_{T}^Z > 40$ GeV and charged-hadrons with $2 <p_T < 4$ GeV in PbPb for centrality interval of 30-50% collisions.

The $\Delta\phi_{ch,Z}$ spectra for events with Z boson $p_{T}^Z > 40$ GeV and charged-hadrons with $4 <p_T < 10$ GeV in PbPb for centrality interval of 30-50% collisions.

The $\Delta\phi_{ch,Z}$ spectra for events with Z boson $p_{T}^Z > 40$ GeV and charged-hadrons with $1 <p_T < 2$ GeV in PbPb for centrality interval of 50-90% collisions.

The $\Delta\phi_{ch,Z}$ spectra for events with Z boson $p_{T}^Z > 40$ GeV and charged-hadrons with $2 <p_T < 4$ GeV in PbPb for centrality interval of 50-90% collisions.

The $\Delta\phi_{ch,Z}$ spectra for events with Z boson $p_{T}^Z > 40$ GeV and charged-hadrons with $4 <p_T < 10$ GeV in PbPb for centrality interval of 50-90% collisions.

The $\Delta\phi_{ch,Z}$ spectra for events with Z boson $p_{T}^Z > 40$ GeV and charged-hadrons with $1 <p_T < 2$ GeV in PbPb for centrality interval of 0-90% collisions.

The $\Delta\phi_{ch,Z}$ spectra for events with Z boson $p_{T}^Z > 40$ GeV and charged-hadrons with $2 <p_T < 4$ GeV in PbPb for centrality interval of 0-90% collisions.

The $\Delta\phi_{ch,Z}$ spectra for events with Z boson $p_{T}^Z > 40$ GeV and charged-hadrons with $4 <p_T < 10$ GeV in PbPb for centrality interval of 0-90% collisions.

The $\Delta y_{ch,Z}$ spectra for events with Z boson $p_{T}^Z > 40$ GeV and charged-hadrons with $1 <p_T < 2$ GeV in pp collisions.

The $\Delta y_{ch,Z}$ spectra for events with Z boson $p_{T}^Z > 40$ GeV and charged-hadrons with $2 <p_T < 4$ GeV in pp collisions.

The $\Delta y_{ch,Z}$ spectra for events with Z boson $p_{T}^Z > 40$ GeV and charged-hadrons with $4 <p_T < 10$ GeV in pp collisions.

The $\Delta y_{ch,Z}$ spectra for events with Z boson $p_{T}^Z > 40$ GeV and charged-hadrons with $1 <p_T < 2$ GeV in PbPb for centrality interval of 0-30% collisions.

The $\Delta y_{ch,Z}$ spectra for events with Z boson $p_{T}^Z > 40$ GeV and charged-hadrons with $2 <p_T < 4$ GeV in PbPb for centrality interval of 0-30% collisions.

The $\Delta y_{ch,Z}$ spectra for events with Z boson $p_{T}^Z > 40$ GeV and charged-hadrons with $4 <p_T < 10$ GeV in PbPb for centrality interval of 0-30% collisions.

The $\Delta y_{ch,Z}$ spectra for events with Z boson $p_{T}^Z > 40$ GeV and charged-hadrons with $1 <p_T < 2$ GeV in PbPb for centrality interval of 30-50% collisions.

The $\Delta y_{ch,Z}$ spectra for events with Z boson $p_{T}^Z > 40$ GeV and charged-hadrons with $2 <p_T < 4$ GeV in PbPb for centrality interval of 30-50% collisions.

The $\Delta y_{ch,Z}$ spectra for events with Z boson $p_{T}^Z > 40$ GeV and charged-hadrons with $4 <p_T < 10$ GeV in PbPb for centrality interval of 30-50% collisions.

The $\Delta y_{ch,Z}$ spectra for events with Z boson $p_{T}^Z > 40$ GeV and charged-hadrons with $1 <p_T < 2$ GeV in PbPb for centrality interval of 50-90% collisions.

The $\Delta y_{ch,Z}$ spectra for events with Z boson $p_{T}^Z > 40$ GeV and charged-hadrons with $2 <p_T < 4$ GeV in PbPb for centrality interval of 50-90% collisions.

The $\Delta y_{ch,Z}$ spectra for events with Z boson $p_{T}^Z > 40$ GeV and charged-hadrons with $4 <p_T < 10$ GeV in PbPb for centrality interval of 50-90% collisions.

The $\Delta y_{ch,Z}$ spectra for events with Z boson $p_{T}^Z > 40$ GeV and charged-hadrons with $1 <p_T < 2$ GeV in PbPb for centrality interval of 0-90% collisions.

The $\Delta y_{ch,Z}$ spectra for events with Z boson $p_{T}^Z > 40$ GeV and charged-hadrons with $2 <p_T < 4$ GeV in PbPb for centrality interval of 0-90% collisions.

The $\Delta y_{ch,Z}$ spectra for events with Z boson $p_{T}^Z > 40$ GeV and charged-hadrons with $4 <p_T < 10$ GeV in PbPb for centrality interval of 0-90% collisions.

Invariant mass of the lepton pair plus jet system, for data, background (pre- and post-reweighting) and three $H\rightarrow Za$ signal hypotheses (for $a\rightarrow q\bar{q}/gg$ inclusively). Events are required to pass the complete event selection but not the classification NN requirement. The background normalization is set equal to that of the data for events passing the preselection and being in the $m_{\ell\ell j}$ 100-180 GeV region. The signal normalization assumes the SM Higgs boson inclusive production cross-section, $\mathcal{B}(H\to Za)=100\%$, and it is scaled up by a factor of 100. The error bars (hatched regions) represent the data (MC) sample's statistical uncertainty in the histograms and the ratio plots. Vertical arrows indicate data points that fall outside the displayed $y$-axis range.

Regression NN output variable, for data, reweighted background, and three $H\rightarrow Za$ signal hypotheses ($a\rightarrow q\bar{q}/gg$ inclusively). Events are required to pass the complete event selection, including a $120<m_{\ell\ell j}<140$ GeV requirement, but not the classification NN output variable requirement. The background normalization is set equal to that of the data for events passing the preselection and being in the $m_{\ell\ell j}$ 100-180 GeV region. The signal normalization assumes the SM Higgs boson inclusive production cross-section, $\mathcal{B}(H\to Za)=100\%$, and it is scaled up by a factor of 100. The error bars (hatched regions) represent the data (MC) sample's statistical uncertainty in the histograms and the ratio plots. Vertical arrows indicate data points that fall outside the displayed $y$-axis range.

Classification NN output variable, for data, reweighted background, and three $H\rightarrow Za$ signal hypotheses ($a\rightarrow q\bar{q}/gg$ inclusively). Events are required to pass the complete event selection, including a $120<m_{\ell\ell j}<140$ GeV requirement, but not the classification NN output variable requirement. The background normalization is set equal to that of the data for events passing the preselection and being in the $m_{\ell\ell j}$ 100-180 GeV region. The signal normalization assumes the SM Higgs boson inclusive production cross-section, $\mathcal{B}(H\to Za)=100\%$, and it is scaled up by a factor of 100. The error bars (hatched regions) represent the data (MC) sample's statistical uncertainty in the histograms and the ratio plots. Vertical arrows indicate data points that fall outside the displayed $y$-axis range.

Invariant mass of the lepton pair plus jet system for data, reweighted background and its systematic uncertainties (only "up" variations are shown). Events are required to pass the complete event selection (preselection and classification NN requirement). The background normalization is set equal to that of the data for events passing this selection. The experimental uncertainty combines all the relevant jet uncertainties assuming they are completely uncorrelated. The error bars represent the data sample's statistical uncertainty and the grey bands represent the background statistical uncertainty. The lower panel shows the ratio of the data to the pre-fit background prediction.

Invariant mass of the lepton pair plus jet system for data, reweighted background, and 0.5 GeV signal hypotheses. Events are required to pass the complete event selection (preselection and classification NN requirement). The background shape and normalization come from the fit to the data. The signal includes only $gg$ decays, its shape comes from the fit, and it is normalized to $\mathcal{B}(H\rightarrow Za)=100\%$. The error bars represent the data sample's statistical uncertainty and the grey bands represent the full background model uncertainty after the fit. The lower panel shows the per-bin signal significance, $(N_\text{data}-N_\text{MC})\,\text{\Large{/}}\sqrt{\sigma_\text{data}^2+\sigma_\text{MC}^2}$. The post-fit background uncertainty is calculated from a fit under the background-only hypothesis. Vertical arrows indicate data points that fall outside the displayed $y$-axis range.

Observed 95$\%$ CL upper limits on $\mathcal{B}(H \to Za)=100\%$ for $\mathcal{B}(a \to gg)=100\%$, and the expectation under the background-only hypothesis together with its $\pm1\sigma$ and $\pm2\sigma$ intervals. The weaker limits from the previous version of the analysis (PRL 125(2020) 221802) are also shown. Linear interpolation is used to set limits between the mass points for which MC signal samples were generated.

Observed 95$\%$ confidence level upper limits on $\mathcal{B}(H \to Za)=100\%$ for $\mathcal{B}(a\rightarrow q\bar{q})=100\%$, and the expectation under the background-only hypothesis together with its $\pm1\sigma$ and $\pm2\sigma$ intervals. The weaker limits from the previous version of the analysis (PRL 125(2020) 221802) are also shown. Linear interpolation is used to set limits between the mass points for which MC signal samples were generated.

Expected and observed combined limits at 95% CL on the production cross-section of vector-like T in an $(X,T)$ doublet (50% $T\rightarrow Zt$, 50% $T\rightarrow Ht$).

Expected and observed combined limits at 95% CL on the production cross-section of vector-like T in a $T$ singlet (50% $T\rightarrow Wb$, 25% $T\rightarrow Zt$, 25% $T\rightarrow Ht$).

Expected and observed combined limits at 95% CL on the production cross-section of vector-like B for 100% $B\rightarrow Zb$.

Expected and observed combined limits at 95% CL on the production cross-section of vector-like B in a $(B,Y)$ doublet (50% $B\rightarrow Zb$, 50% $B\rightarrow Hb$).

Expected and observed combined limits at 95% CL on the production cross-section of vector-like B in a B singlet (50% $B\rightarrow Wt$, 25% $B\rightarrow Zb$, 25% $B\rightarrow Hb$).

Distribution of the final discriminant after the combined background-only fit in the 2$\ell$ 2$b$ double-tag 1 signal region. The signal contribution is the expected distribution for a singlet TT with a mass of 1.2 TeV. The last bin contains overflow.

Distribution of the final discriminant after the combined background-only fit in the 2$\ell$ 2$b$ top-tag signal region. The signal contribution is the expected distribution for a singlet TT with a mass of 1.2 TeV. The last bin contains overflow.

Distribution of the final discriminant after the combined background-only fit in the 2$\ell$ 1$b$ $V$-tag signal region. The signal contribution is the expected distribution for a singlet TT with a mass of 1.2 TeV. The last bin contains overflow.

Distribution of the final discriminant after the combined background-only fit in the 2$\ell$ 1$b$ no-tag signal region. The signal contribution is the expected distribution for a singlet TT with a mass of 1.2 TeV. The last bin contains overflow.

Distribution of the final discriminant after the combined background-only fit in the 3$\ell$ $VV$ control region. The signal contribution is the expected distribution for a singlet TT with a mass of 1.2 TeV. The last bin contains overflow.

Distribution of the final discriminant after the combined background-only fit in the 3$\ell$ $H$-tag signal region. The signal contribution is the expected distribution for a singlet TT with a mass of 1.2 TeV. The last bin contains overflow.

Distribution of the final discriminant after the combined background-only fit in the 3$\ell$ top-tag signal region. The signal contribution is the expected distribution for a singlet TT with a mass of 1.2 TeV. The last bin contains overflow.

Distribution of the final discriminant after the combined background-only fit in the 2$\ell$ 1$b$ control region. The signal contribution is the expected distribution for a singlet TT with a mass of 1.2 TeV. The last bin contains overflow.

Distribution of the final discriminant after the combined background-only fit in the 2$\ell$ 2$b$ control region. The signal contribution is the expected distribution for a singlet TT with a mass of 1.2 TeV. The last bin contains overflow.

Invariant mass $m_{J}$ of the resonance candidates in the region defined with forward photon $\eta_{\gamma} > 1.3$ and anti-tagged large-$R$ jet after the fit to data under the background-only hypothesis. The total systematic uncertainty is shown as the hatched band. Three representative $Z^{`}$ signal distributions are overlaid as red lines. The signal is shown for $g_q=0.2$ with production cross sections of 309 fb, 143 fb, and 34.2 fb for $m_{Z^{`}}=(20,~50,~\text{and}~125~\text{GeV}$), respectively.

Observed (expected) upper exclusion limits at 95$\%$ CL on the coupling strength $g_q$ of a new vector $Z^{`}$ particle decaying to a $q\bar q$ pair for a LHC DM WG benchmark signal model where decay rates for all decay modes except $Z^{`}\to q \bar q$ are set to 0, and the interference between the $Z^{`}$ and the SM $Z$ boson is neglected.

Observed (solid lines) and expected (dashed lines) upper exclusion limits at 95$\%$ CL on the product of the $Z^{`}$ production production cross section, branching ratio for $Z^{`}\to q\bar q$ and acceptance ($\sigma_{Z^{`}}\times B(Z^{`}\to q\bar q)\times A$) of a new $Z^{`}$ resonance for a LHC DM WG benchmark signal model where all decay modes except $Z^{`}\to q \bar q$ are set to 0, and the interference between the $Z^{`}$ and the SM $Z$ boson is neglected.

The measured differential cross-sections and the predictions from the GM-VFNS calculation for the $D_s^\pm$ meson in bins of $p_T$ for $|\eta| < 2.5$. The statistical, systematic (excluding branching ratio) and branching ratio uncertainties are shown separately for data, while the total theory uncertainties are shown for GM-VFNS.

Inclusive $D^\pm$ meson production cross-sections in different fiducial volumes defined by $|\eta|<2.5$ and different $p_T$ regions. For the ATLAS measurements, the statistical, systematic (excluding branching ratio) and branching ratio uncertainties are shown separately; for the theoretical predictions, the total theoretical uncertainties are shown.

Inclusive $D_s^\pm$ meson production cross-sections in different fiducial volumes defined by $|\eta|<2.5$ and different $p_T$ regions. For the ATLAS measurements, the statistical, systematic (excluding branching ratio) and branching ratio uncertainties are shown separately; for the theoretical predictions, the total theoretical uncertainties are shown.

The measured $p_{\mathrm{T}}^{\mathrm{recoil}}$ distributions in the top control region, compared with the background predictions as estimated after the simultaneous, binned background-only fit to the data in the control regions. The last bin of the distribution contains overflows.

The measured $p_{\mathrm{T}}^{\mathrm{recoil}}$ distributions in the $Z\rightarrow\mu\mu$ control region, compared with the background predictions as estimated after the simultaneous, binned background-only fit to the data in the control regions. The last bin of the distribution contains overflows.

The measured $p_{\mathrm{T}}^{\mathrm{recoil}}$ distributions in the $Z\rightarrow ee$ control region, compared with the background predictions as estimated after the simultaneous, binned background-only fit to the data in the control regions. The last bin of the distribution contains overflows.

The measured $p_{\mathrm{T}}^{\mathrm{recoil}}$ distributions in the signal region, compared with the background predictions as estimated after the simultaneous, binned background-only fit to the data in the control regions. The last bin of the distribution contains overflows.

Observed exclusion contour at 95% CL in the $m_{Z_{A}}-m_\chi$ parameter plane for the axial-vector mediator model.

1 $\sigma_{\mathrm{theory}}^{\mathrm{PDF+scale}}$ up observed exclusion contour at 95% CL in the $m_{Z_{A}}-m_\chi$ parameter plane for the axial-vector mediator model.

1 $\sigma_{\mathrm{theory}}^{\mathrm{PDF+scale}}$ down observed exclusion contour at 95% CL in the $m_{Z_{A}}-m_\chi$ parameter plane for the axial-vector mediator model.

Expected exclusion contour at 95% CL in the $m_{Z_{A}}-m_\chi$ parameter plane for the axial-vector mediator model.

1 $\sigma$ up expected exclusion contour at 95% CL in the $m_{Z_{A}}-m_\chi$ parameter plane for the axial-vector mediator model.

1 $\sigma$ down expected exclusion contour at 95% CL in the $m_{Z_{A}}-m_\chi$ parameter plane for the axial-vector mediator model.

2 $\sigma$ up expected exclusion contour at 95% CL in the $m_{Z_{A}}-m_\chi$ parameter plane for the axial-vector mediator model.

2 $\sigma$ down expected exclusion contour at 95% CL in the $m_{Z_{A}}-m_\chi$ parameter plane for the axial-vector mediator model.

Observed exclusion contour at 95% CL in the $m_{Z_{P}}-m_\chi$ parameter plane for the pseudo-scalar mediator model.

1 $\sigma_{\mathrm{theory}}^{\mathrm{PDF+scale}}$ up observed exclusion contour at 95% CL in the $m_{Z_{P}}-m_\chi$ parameter plane for the pseudo-scalar mediator model.

1 $\sigma_{\mathrm{theory}}^{\mathrm{PDF+scale}}$ down observed exclusion contour at 95% CL in the $m_{Z_{P}}-m_\chi$ parameter plane for the pseudo-scalar mediator model.

Expected exclusion contour at 95% CL in the $m_{Z_{P}}-m_\chi$ parameter plane for the pseudo-scalar mediator model.

1 $\sigma$ up expected exclusion contour at 95% CL in the $m_{Z_{P}}-m_\chi$ parameter plane for the pseudo-scalar mediator model.

1 $\sigma$ down expected exclusion contour at 95% CL in the $m_{Z_{P}}-m_\chi$ parameter plane for the pseudo-scalar mediator model.

2 $\sigma$ up expected exclusion contour at 95% CL in the $m_{Z_{P}}-m_\chi$ parameter plane for the pseudo-scalar mediator model.

2 $\sigma$ down expected exclusion contour at 95% CL in the $m_{Z_{P}}-m_\chi$ parameter plane for the pseudo-scalar mediator model.

A comparison of the inferred limits with the constraints from direct-detection experiments on the spin-dependent WIMP-neutron and WIMP-proton scattering cross section as a function of the WIMP mass, in the context of the simplified model with axial-vector couplings. Limits are shown at 90% CL.

Observed excluded regions at the 95% CL in the ($\tilde{t}_1,\tilde{\chi}^{0}_{1}$)mass plane for the decay channel $\tilde{t}_1 \to c + \tilde{\chi}^{0}_{1}$ ($\mathcal{B}=100\%$)

1 $\sigma_{\mathrm{theory}}^{\mathrm{PDF+scale}}$ up observed excluded regions at the 95% CL in the ($\tilde{t}_1,\tilde{\chi}^{0}_{1}$)mass plane for the decay channel $\tilde{t}_1 \to c + \tilde{\chi}^{0}_{1}$ ($\mathcal{B}=100\%$)

1 $\sigma_{\mathrm{theory}}^{\mathrm{PDF+scale}}$ down observed excluded regions at the 95% CL in the ($\tilde{t}_1,\tilde{\chi}^{0}_{1}$)mass plane for the decay channel $\tilde{t}_1 \to c + \tilde{\chi}^{0}_{1}$ ($\mathcal{B}=100\%$)

Expected excluded regions at the 95% CL in the ($\tilde{t}_1,\tilde{\chi}^{0}_{1}$)mass plane for the decay channel $\tilde{t}_1 \to c + \tilde{\chi}^{0}_{1}$ ($\mathcal{B}=100\%$)

1 $\sigma$ up expected excluded regions at the 95% CL in the ($\tilde{t}_1,\tilde{\chi}^{0}_{1}$)mass plane for the decay channel $\tilde{t}_1 \to c + \tilde{\chi}^{0}_{1}$ ($\mathcal{B}=100\%$)

1 $\sigma$ down expected excluded regions at the 95% CL in the ($\tilde{t}_1,\tilde{\chi}^{0}_{1}$)mass plane for the decay channel $\tilde{t}_1 \to c + \tilde{\chi}^{0}_{1}$ ($\mathcal{B}=100\%$)

2 $\sigma$ up expected excluded regions at the 95% CL in the ($\tilde{t}_1,\tilde{\chi}^{0}_{1}$)mass plane for the decay channel $\tilde{t}_1 \to c + \tilde{\chi}^{0}_{1}$ ($\mathcal{B}=100\%$)

2 $\sigma$ down expected excluded regions at the 95% CL in the ($\tilde{t}_1,\tilde{\chi}^{0}_{1}$)mass plane for the decay channel $\tilde{t}_1 \to c + \tilde{\chi}^{0}_{1}$ ($\mathcal{B}=100\%$)

Observed excluded regions at the 95% CL in the ($\tilde{t}_1,\tilde{\chi}^{0}_{1}$)mass plane for the decay channel $\tilde{t}_1 \to b + ff^{'} + \tilde{\chi}^{0}_{1}$ ($\mathcal{B}=100\%$)

1 $\sigma_{\mathrm{theory}}^{\mathrm{PDF+scale}}$ up observed excluded regions at the 95% CL in the ($\tilde{t}_1,\tilde{\chi}^{0}_{1}$)mass plane for the decay channel $\tilde{t}_1 \to b + ff^{'} + \tilde{\chi}^{0}_{1}$ ($\mathcal{B}=100\%$)

1 $\sigma_{\mathrm{theory}}^{\mathrm{PDF+scale}}$ down observed excluded regions at the 95% CL in the ($\tilde{t}_1,\tilde{\chi}^{0}_{1}$)mass plane for the decay channel $\tilde{t}_1 \to b + ff^{'} + \tilde{\chi}^{0}_{1}$ ($\mathcal{B}=100\%$)

Expected excluded regions at the 95% CL in the ($\tilde{t}_1,\tilde{\chi}^{0}_{1}$)mass plane for the decay channel $\tilde{t}_1 \to b + ff^{'} + \tilde{\chi}^{0}_{1}$ ($\mathcal{B}=100\%$)

1 $\sigma$ up expected excluded regions at the 95% CL in the ($\tilde{t}_1,\tilde{\chi}^{0}_{1}$)mass plane for the decay channel $\tilde{t}_1 \to b + ff^{'} + \tilde{\chi}^{0}_{1}$ ($\mathcal{B}=100\%$)

1 $\sigma$ down expected excluded regions at the 95% CL in the ($\tilde{t}_1,\tilde{\chi}^{0}_{1}$)mass plane for the decay channel $\tilde{t}_1 \to b + ff^{'} + \tilde{\chi}^{0}_{1}$ ($\mathcal{B}=100\%$)

2 $\sigma$ up expected excluded regions at the 95% CL in the ($\tilde{t}_1,\tilde{\chi}^{0}_{1}$)mass plane for the decay channel $\tilde{t}_1 \to b + ff^{'} + \tilde{\chi}^{0}_{1}$ ($\mathcal{B}=100\%$)

2 $\sigma$ down expected excluded regions at the 95% CL in the ($\tilde{t}_1,\tilde{\chi}^{0}_{1}$)mass plane for the decay channel $\tilde{t}_1 \to b + ff^{'} + \tilde{\chi}^{0}_{1}$ ($\mathcal{B}=100\%$)

Observed exclusion plane at 95% CL as a function of sbottom and neutralino masses for the decay channel $\tilde{b}_1 \to b + \tilde{\chi}^{0}_{1}$ ($\mathcal{B}=100\%$)

1 $\sigma_{\mathrm{theory}}^{\mathrm{PDF+scale}}$ up observed exclusion plane at 95% CL as a function of sbottom and neutralino masses for the decay channel $\tilde{b}_1 \to b + \tilde{\chi}^{0}_{1}$ ($\mathcal{B}=100\%$)

1 $\sigma_{\mathrm{theory}}^{\mathrm{PDF+scale}}$ down observed exclusion plane at 95% CL as a function of sbottom and neutralino masses for the decay channel $\tilde{b}_1 \to b + \tilde{\chi}^{0}_{1}$ ($\mathcal{B}=100\%$)

Expected exclusion plane at 95% CL as a function of sbottom and neutralino masses for the decay channel $\tilde{b}_1 \to b + \tilde{\chi}^{0}_{1}$ ($\mathcal{B}=100\%$)

1 $\sigma$ up expected exclusion plane at 95% CL as a function of sbottom and neutralino masses for the decay channel $\tilde{b}_1 \to b + \tilde{\chi}^{0}_{1}$ ($\mathcal{B}=100\%$)

1 $\sigma$ down expected exclusion plane at 95% CL as a function of sbottom and neutralino masses for the decay channel $\tilde{b}_1 \to b + \tilde{\chi}^{0}_{1}$ ($\mathcal{B}=100\%$)

2 $\sigma$ up expected exclusion plane at 95% CL as a function of sbottom and neutralino masses for the decay channel $\tilde{b}_1 \to b + \tilde{\chi}^{0}_{1}$ ($\mathcal{B}=100\%$)

2 $\sigma$ down expected exclusion plane at 95% CL as a function of sbottom and neutralino masses for the decay channel $\tilde{b}_1 \to b + \tilde{\chi}^{0}_{1}$ ($\mathcal{B}=100\%$)

Observed exclusion region at 95$\%$ CL as a function of squark mass and the squark--neutralino massdifference for $\tilde{q} \to q + \tilde{\chi}^{0}_{1}$ and $\tilde{q}_\mathrm{L} + \tilde{q}_\mathrm{R}$with ($\tilde{u},\tilde{d},\tilde{c},\tilde{s}$).

1 $\sigma_{\mathrm{theory}}^{\mathrm{PDF+scale}}$ up observed exclusion region at 95$\%$ CL as a function of squark mass and the squark--neutralino massdifference for $\tilde{q} \to q + \tilde{\chi}^{0}_{1}$ and $\tilde{q}_\mathrm{L} + \tilde{q}_\mathrm{R}$with ($\tilde{u},\tilde{d},\tilde{c},\tilde{s}$).

1 $\sigma_{\mathrm{theory}}^{\mathrm{PDF+scale}}$ down observed exclusion region at 95$\%$ CL as a function of squark mass and the squark--neutralino massdifference for $\tilde{q} \to q + \tilde{\chi}^{0}_{1}$ and $\tilde{q}_\mathrm{L} + \tilde{q}_\mathrm{R}$with ($\tilde{u},\tilde{d},\tilde{c},\tilde{s}$).

Expected exclusion region at 95$\%$ CL as a function of squark mass and the squark--neutralino massdifference for $\tilde{q} \to q + \tilde{\chi}^{0}_{1}$ and $\tilde{q}_\mathrm{L} + \tilde{q}_\mathrm{R}$with ($\tilde{u},\tilde{d},\tilde{c},\tilde{s}$).

1 $\sigma$ up expected exclusion region at 95$\%$ CL as a function of squark mass and the squark--neutralino massdifference for $\tilde{q} \to q + \tilde{\chi}^{0}_{1}$ and $\tilde{q}_\mathrm{L} + \tilde{q}_\mathrm{R}$with ($\tilde{u},\tilde{d},\tilde{c},\tilde{s}$).

1 $\sigma$ down expected exclusion region at 95$\%$ CL as a function of squark mass and the squark--neutralino massdifference for $\tilde{q} \to q + \tilde{\chi}^{0}_{1}$ and $\tilde{q}_\mathrm{L} + \tilde{q}_\mathrm{R}$with ($\tilde{u},\tilde{d},\tilde{c},\tilde{s}$).

2 $\sigma$ up expected exclusion region at 95$\%$ CL as a function of squark mass and the squark--neutralino massdifference for $\tilde{q} \to q + \tilde{\chi}^{0}_{1}$ and $\tilde{q}_\mathrm{L} + \tilde{q}_\mathrm{R}$with ($\tilde{u},\tilde{d},\tilde{c},\tilde{s}$).

2 $\sigma$ down expected exclusion region at 95$\%$ CL as a function of squark mass and the squark--neutralino massdifference for $\tilde{q} \to q + \tilde{\chi}^{0}_{1}$ and $\tilde{q}_\mathrm{L} + \tilde{q}_\mathrm{R}$with ($\tilde{u},\tilde{d},\tilde{c},\tilde{s}$).

Observed and expected exclusions at $95\%$ CL on the Horndeski dark-energy model for $m_{\phi}=0.1$ GeV and $c_{i\neq 2}=0$, $c_{2}=1$, expressed in terms of the visible cross section as a function of the suppression scale $M_{2}$.

$95\%$ CL observed and expected lower limits on the fundamental Planck scale in $4+n$ dimensions, $M_D$, as a function of the number of extra dimensions $n$, considering nominal LO signal cross sections.

Observed and expected 95$\%$ CL upper limits on the coupling $c_{\stackrel{\sim}{\smash{G}}}$ as a function of the effective scale $f_a$ for ALP mass of 1 MeV. The bands indicate the $\pm 1\sigma$ theory uncertainties in the observed limit and the $\pm 1\sigma$and $\pm 2\sigma$ ranges of the expected limit in the absence of a signal. The 95$\%$ CL limits are computed with no suppression of the events with $\hat{s} > f_a^2$.

Observed exclusion contour at 95% CL in the $m_{Z_{V}}-m_\chi$ parameter plane for the vector mediator model.

1 $\sigma_{\mathrm{theory}}^{\mathrm{PDF+scale}}$ up observed exclusion contour at 95% CL in the $m_{Z_{V}}-m_\chi$ parameter plane for the vector mediator model.

1 $\sigma_{\mathrm{theory}}^{\mathrm{PDF+scale}}$ down observed exclusion contour at 95% CL in the $m_{Z_{V}}-m_\chi$ parameter plane for the vector mediator model.

Expected exclusion contour at 95% CL in the $m_{Z_{V}}-m_\chi$ parameter plane for the vector mediator model.

1 $\sigma$ up expected exclusion contour at 95% CL in the $m_{Z_{V}}-m_\chi$ parameter plane for the vector mediator model.

1 $\sigma$ down expected exclusion contour at 95% CL in the $m_{Z_{V}}-m_\chi$ parameter plane for the vector mediator model.

2 $\sigma$ up expected exclusion contour at 95% CL in the $m_{Z_{V}}-m_\chi$ parameter plane for the vector mediator model.

2 $\sigma$ down expected exclusion contour at 95% CL in the $m_{Z_{V}}-m_\chi$ parameter plane for the vector mediator model.

A comparison of the inferred limits with the constraints from direct-detection experiments on the spin-independent WIMP-nucleon scattering cross section as a function of the WIMP mass, in the context of the simplified model with vector couplings. Limits are shown at 90% CL.

Inferred 95% CL limits on the WIMP annihilation rate as a function of WIMP mass, for the pseudoscalar mediator model. The annihilation rate is defined as the product of cross section $\sigma$ and relative velocity $v_{rel}$, averaged over the DM velocity distribution ($\langle\sigma v_{rel}\rangle$). Both the $qq$ and $gg$ annihilation channels are considered in the calculation of the annihilation rate

95% CL upper limits on the cross-section $\sigma$ in the $m_{Z_A}-m_{\chi}$ parameter plane for the axial-vector mediator model.

95% CL upper limits on the cross-section $\sigma$ in the $m_{Z_P}-m_{\chi}$ parameter plane for the pseudo-scalar mediator model.

Contribution to the total SR background uncertainty in exclusive bins of the SR, as obtained from the CR-only fit. In the table, the contribution of each source of systematic is shown as the sum in quadrature of the individual contributions represented by the corresponding nuisance parameters.

Expected and observed backgrounds, before and after a binned likelihood fit in the control regions, in the exclusive SR bin EM0.

Expected and observed backgrounds, before and after a binned likelihood fit in the control regions, in the exclusive SR bin EM1.

Expected and observed backgrounds, before and after a binned likelihood fit in the control regions, in the exclusive SR bin EM2.

Expected and observed backgrounds, before and after a binned likelihood fit in the control regions, in the exclusive SR bin EM3.

Expected and observed backgrounds, before and after a binned likelihood fit in the control regions, in the exclusive SR bin EM4.

Expected and observed backgrounds, before and after a binned likelihood fit in the control regions, in the exclusive SR bin EM5.

Expected and observed backgrounds, before and after a binned likelihood fit in the control regions, in the exclusive SR bin EM6.

Expected and observed backgrounds, before and after a binned likelihood fit in the control regions, in the exclusive SR bin EM7.

Expected and observed backgrounds, before and after a binned likelihood fit in the control regions, in the exclusive SR bin EM8.

Expected and observed backgrounds, before and after a binned likelihood fit in the control regions, in the exclusive SR bin EM9.

Expected and observed backgrounds, before and after a binned likelihood fit in the control regions, in the exclusive SR bin EM10.

Expected and observed backgrounds, before and after a binned likelihood fit in the control regions, in the exclusive SR bin EM11.

Expected and observed backgrounds, before and after a binned likelihood fit in the control regions, in the exclusive SR bin EM12.

Expected and observed backgrounds, before and after a binned likelihood fit in the control regions, in the inclusive SR IM0.

Expected and observed backgrounds, before and after a binned likelihood fit in the control regions, in the inclusive SR IM1.

Expected and observed backgrounds, before and after a binned likelihood fit in the control regions, in the inclusive SR IM2.

Expected and observed backgrounds, before and after a binned likelihood fit in the control regions, in the inclusive SR IM3.

Expected and observed backgrounds, before and after a binned likelihood fit in the control regions, in the inclusive SR IM4.

Expected and observed backgrounds, before and after a binned likelihood fit in the control regions, in the inclusive SR IM5.

Expected and observed backgrounds, before and after a binned likelihood fit in the control regions, in the inclusive SR IM6.

Expected and observed backgrounds, before and after a binned likelihood fit in the control regions, in the inclusive SR IM7.

Expected and observed backgrounds, before and after a binned likelihood fit in the control regions, in the inclusive SR IM8.

Expected and observed backgrounds, before and after a binned likelihood fit in the control regions, in the inclusive SR IM9.

Expected and observed backgrounds, before and after a binned likelihood fit in the control regions, in the inclusive SR IM10.

Expected and observed backgrounds, before and after a binned likelihood fit in the control regions, in the inclusive SR IM11.

Expected and observed backgrounds, before and after a binned likelihood fit in the control regions, in the inclusive SR IM12.

Cutflow of several signal benchmarks. A cut on the truth $E_\mathrm{T}^\mathrm{miss}$ at 150 GeV is applied.

Cutflow of several signal benchmarks. A cut on the truth $E_\mathrm{T}^\mathrm{miss}$ at 350 GeV is applied.