Correlation between the Wilson coefficients (in %), after the 5D fit to data.

Differential signal yields for various signal hypotheses.

Differential signal yields for various signal hypotheses.

Differential signal yields for various signal hypotheses.

Differential signal yields for various signal hypotheses.

Differential signal yields for various signal hypotheses.

Differential signal yields for various signal hypotheses.

Differential signal yields for various signal hypotheses.

Differential signal yields for various signal hypotheses.

Differential signal yields for various signal hypotheses.

Differential signal yields for various signal hypotheses.

Differential signal yields for various signal hypotheses.

Differential signal yields for various signal hypotheses.

Differential signal yields for various signal hypotheses.

Background and data yields in the control and signal region bins. The prediction before ("prefit") and after the background only fit ("b-only") are given separately.

Background and data yields in the control and signal region bins. The prediction before ("prefit") and after the background only fit ("b-only") are given separately.

Background and data yields in the control and signal region bins. The prediction before ("prefit") and after the background only fit ("b-only") are given separately.

Background and data yields in the control and signal region bins. The prediction before ("prefit") and after the background only fit ("b-only") are given separately.

Background and data yields in the control and signal region bins. The prediction before ("prefit") and after the background only fit ("b-only") are given separately.

Background and data yields in the control and signal region bins. The prediction before ("prefit") and after the background only fit ("b-only") are given separately.

Matrix of covariance coefficients between signal region bins. The coefficients are obtained from the background-only fit to the control regions, and serve as input to the simplified likelihood reinterpretation scheme.

Matrix of covariance coefficients between signal region bins. The coefficients are obtained from the background-only fit to the control regions, and serve as input to the simplified likelihood reinterpretation scheme.

Background prediction and observed data yields in the signal region bins. The background yields are obtained from the background-only fit to the corresponding control regions, and serve as input to the simplified likelihood reinterpretation scheme.

Background prediction and observed data yields in the signal region bins. The background yields are obtained from the background-only fit to the corresponding control regions, and serve as input to the simplified likelihood reinterpretation scheme.

Matrix of covariance coefficients between signal region bins. The coefficients are obtained from the background-only fit to the control regions, and serve as input to the simplified likelihood reinterpretation scheme.

Matrix of covariance coefficients between signal region bins. The coefficients are obtained from the background-only fit to the control regions, and serve as input to the simplified likelihood reinterpretation scheme.

Background prediction and observed data yields in the signal region bins. The background yields are obtained from the background-only fit to the corresponding control regions, and serve as input to the simplified likelihood reinterpretation scheme.

Background prediction and observed data yields in the signal region bins. The background yields are obtained from the background-only fit to the corresponding control regions, and serve as input to the simplified likelihood reinterpretation scheme.

Matrix of covariance coefficients between signal region bins. The coefficients are obtained from the background-only fit to the control regions, and serve as input to the simplified likelihood reinterpretation scheme.

Matrix of covariance coefficients between signal region bins. The coefficients are obtained from the background-only fit to the control regions, and serve as input to the simplified likelihood reinterpretation scheme.

Background prediction and observed data yields in the signal region bins. The background yields are obtained from the background-only fit to the corresponding control regions, and serve as input to the simplified likelihood reinterpretation scheme.

Background prediction and observed data yields in the signal region bins. The background yields are obtained from the background-only fit to the corresponding control regions, and serve as input to the simplified likelihood reinterpretation scheme.

Unweighted signal acceptance times efficiency at every cut stage. The requirements called "HCAL mitigation" refer to the requirements imposed in the 2018 data set in order to mitigate the localized failure of the HCAL detector.

Unweighted signal acceptance times efficiency at every cut stage. The requirements called "HCAL mitigation" refer to the requirements imposed in the 2018 data set in order to mitigate the localized failure of the HCAL detector.

Unweighted signal acceptance times efficiency at every cut stage. The requirements called "HCAL mitigation" refer to the requirements imposed in the 2018 data set in order to mitigate the localized failure of the HCAL detector.

Unweighted signal acceptance times efficiency at every cut stage. The requirements called "HCAL mitigation" refer to the requirements imposed in the 2018 data set in order to mitigate the localized failure of the HCAL detector.

Unweighted signal acceptance times efficiency at every cut stage. The requirements called "HCAL mitigation" refer to the requirements imposed in the 2018 data set in order to mitigate the localized failure of the HCAL detector.

Unweighted signal acceptance times efficiency at every cut stage. The requirements called "HCAL mitigation" refer to the requirements imposed in the 2018 data set in order to mitigate the localized failure of the HCAL detector.

Unweighted signal acceptance times efficiency at every cut stage. The requirements called "HCAL mitigation" refer to the requirements imposed in the 2018 data set in order to mitigate the localized failure of the HCAL detector.

Unweighted signal acceptance times efficiency at every cut stage. The requirements called "HCAL mitigation" refer to the requirements imposed in the 2018 data set in order to mitigate the localized failure of the HCAL detector.

Unweighted signal acceptance times efficiency at every cut stage. The requirements called "HCAL mitigation" refer to the requirements imposed in the 2018 data set in order to mitigate the localized failure of the HCAL detector.

Unweighted signal acceptance times efficiency at every cut stage. The requirements called "HCAL mitigation" refer to the requirements imposed in the 2018 data set in order to mitigate the localized failure of the HCAL detector.

Unweighted signal acceptance times efficiency at every cut stage. The requirements called "HCAL mitigation" refer to the requirements imposed in the 2018 data set in order to mitigate the localized failure of the HCAL detector.

Unweighted signal acceptance times efficiency at every cut stage. The requirements called "HCAL mitigation" refer to the requirements imposed in the 2018 data set in order to mitigate the localized failure of the HCAL detector.

Unweighted signal acceptance times efficiency at every cut stage. The requirements called "HCAL mitigation" refer to the requirements imposed in the 2018 data set in order to mitigate the localized failure of the HCAL detector.

Unweighted signal acceptance times efficiency at every cut stage. The requirements called "HCAL mitigation" refer to the requirements imposed in the 2018 data set in order to mitigate the localized failure of the HCAL detector.

Unweighted signal acceptance times efficiency at every cut stage. The requirements called "HCAL mitigation" refer to the requirements imposed in the 2018 data set in order to mitigate the localized failure of the HCAL detector.

Unweighted signal acceptance times efficiency at every cut stage. The requirements called "HCAL mitigation" refer to the requirements imposed in the 2018 data set in order to mitigate the localized failure of the HCAL detector.

Unweighted signal acceptance times efficiency at every cut stage. The requirements called "HCAL mitigation" refer to the requirements imposed in the 2018 data set in order to mitigate the localized failure of the HCAL detector.

Unweighted signal acceptance times efficiency at every cut stage. The requirements called "HCAL mitigation" refer to the requirements imposed in the 2018 data set in order to mitigate the localized failure of the HCAL detector.

Unweighted signal acceptance times efficiency at every cut stage. The requirements called "HCAL mitigation" refer to the requirements imposed in the 2018 data set in order to mitigate the localized failure of the HCAL detector.

Unweighted signal acceptance times efficiency at every cut stage. The requirements called "HCAL mitigation" refer to the requirements imposed in the 2018 data set in order to mitigate the localized failure of the HCAL detector.

Unweighted signal acceptance times efficiency at every cut stage. The requirements called "HCAL mitigation" refer to the requirements imposed in the 2018 data set in order to mitigate the localized failure of the HCAL detector.

Unweighted signal acceptance times efficiency at every cut stage. The requirements called "HCAL mitigation" refer to the requirements imposed in the 2018 data set in order to mitigate the localized failure of the HCAL detector.

Unweighted signal acceptance times efficiency at every cut stage. The requirements called "HCAL mitigation" refer to the requirements imposed in the 2018 data set in order to mitigate the localized failure of the HCAL detector.

Unweighted signal acceptance times efficiency at every cut stage. The requirements called "HCAL mitigation" refer to the requirements imposed in the 2018 data set in order to mitigate the localized failure of the HCAL detector.

Unweighted signal acceptance times efficiency at every cut stage. The requirements called "HCAL mitigation" refer to the requirements imposed in the 2018 data set in order to mitigate the localized failure of the HCAL detector.

Unweighted signal acceptance times efficiency at every cut stage. The requirements called "HCAL mitigation" refer to the requirements imposed in the 2018 data set in order to mitigate the localized failure of the HCAL detector.

Unweighted signal acceptance times efficiency at every cut stage. The requirements called "HCAL mitigation" refer to the requirements imposed in the 2018 data set in order to mitigate the localized failure of the HCAL detector.

Unweighted signal acceptance times efficiency at every cut stage. The requirements called "HCAL mitigation" refer to the requirements imposed in the 2018 data set in order to mitigate the localized failure of the HCAL detector.

Unweighted signal acceptance times efficiency at every cut stage. The requirements called "HCAL mitigation" refer to the requirements imposed in the 2018 data set in order to mitigate the localized failure of the HCAL detector.

Unweighted signal acceptance times efficiency at every cut stage. The requirements called "HCAL mitigation" refer to the requirements imposed in the 2018 data set in order to mitigate the localized failure of the HCAL detector.

Unweighted signal acceptance times efficiency at every cut stage. The requirements called "HCAL mitigation" refer to the requirements imposed in the 2018 data set in order to mitigate the localized failure of the HCAL detector.

Unweighted signal acceptance times efficiency at every cut stage. The requirements called "HCAL mitigation" refer to the requirements imposed in the 2018 data set in order to mitigate the localized failure of the HCAL detector.

Unweighted signal acceptance times efficiency at every cut stage. The requirements called "HCAL mitigation" refer to the requirements imposed in the 2018 data set in order to mitigate the localized failure of the HCAL detector.

Unweighted signal acceptance times efficiency at every cut stage. The requirements called "HCAL mitigation" refer to the requirements imposed in the 2018 data set in order to mitigate the localized failure of the HCAL detector.

Unweighted signal acceptance times efficiency at every cut stage. The requirements called "HCAL mitigation" refer to the requirements imposed in the 2018 data set in order to mitigate the localized failure of the HCAL detector.

Unweighted signal acceptance times efficiency at every cut stage. The requirements called "HCAL mitigation" refer to the requirements imposed in the 2018 data set in order to mitigate the localized failure of the HCAL detector.

Median Expected exclusion contour in the $m_{med}$-$m_{\chi}$ plane in the simplified model with axial couplings.

Median Expected exclusion contour in the $m_{med}$-$m_{\chi}$ plane in the simplified model with axial couplings.

Observed exclusion contour in the $m_{med}$-$m_{\chi}$ plane in the simplified model with axial couplings.

Observed exclusion contour in the $m_{med}$-$m_{\chi}$ plane in the simplified model with axial couplings.

Expected plus 1 s.d. exclusion contour in the $m_{med}$-$m_{\chi}$ plane in the simplified model with axial couplings.

Expected plus 1 s.d. exclusion contour in the $m_{med}$-$m_{\chi}$ plane in the simplified model with axial couplings.

Expected minus 1 s.d. exclusion contour in the $m_{med}$-$m_{\chi}$ plane in the simplified model with axial couplings.

Expected minus 1 s.d. exclusion contour in the $m_{med}$-$m_{\chi}$ plane in the simplified model with axial couplings.

Median Expected exclusion contour in the $m_{med}$-$m_{\chi}$ plane in the simplified model with vector couplings.

Median Expected exclusion contour in the $m_{med}$-$m_{\chi}$ plane in the simplified model with vector couplings.

Observed exclusion contour in the $m_{med}$-$m_{\chi}$ plane in the simplified model with vector couplings.

Observed exclusion contour in the $m_{med}$-$m_{\chi}$ plane in the simplified model with vector couplings.

Expected plus 1 s.d. exclusion contour in the $m_{med}$-$m_{\chi}$ plane in the simplified model with vector couplings.

Expected plus 1 s.d. exclusion contour in the $m_{med}$-$m_{\chi}$ plane in the simplified model with vector couplings.

Expected minus 1 s.d. exclusion contour in the $m_{med}$-$m_{\chi}$ plane in the simplified model with vector couplings.

Expected minus 1 s.d. exclusion contour in the $m_{med}$-$m_{\chi}$ plane in the simplified model with vector couplings.

Upper limits on the coupling $g_{\chi}$ in the simplified model with a axial mediator.

Upper limits on the coupling $g_{\chi}$ in the simplified model with a axial mediator.

Upper limits on the coupling $g_{q}$ in the simplified model with a axial mediator.

Upper limits on the coupling $g_{q}$ in the simplified model with a axial mediator.

Upper limits on the coupling $g_{\chi}$ in the simplified model with a vector mediator.

Upper limits on the coupling $g_{\chi}$ in the simplified model with a vector mediator.

Upper limits on the coupling $g_{q}$ in the simplified model with a vector mediator.

Upper limits on the coupling $g_{q}$ in the simplified model with a vector mediator.

Exclusion limits on the signal strength in the simplified model with scalar couplings.

Exclusion limits on the signal strength in the simplified model with scalar couplings.

Exclusion limits on the signal strength in the simplified model with pseudoscalar couplings.

Exclusion limits on the signal strength in the simplified model with pseudoscalar couplings.

Exclusion limits on the fundamental Planck scale $M_{D}$ as a function of the number of extra dimensions $d$.

Exclusion limits on the fundamental Planck scale $M_{D}$ as a function of the number of extra dimensions $d$.

Median Expected exclusion contour in the $m_{med}$-$m_{\chi}$ plane in the fermion portal model.

Median Expected exclusion contour in the $m_{med}$-$m_{\chi}$ plane in the fermion portal model.

Observed exclusion contour in the $m_{med}$-$m_{\chi}$ plane in the fermion portal model.

Observed exclusion contour in the $m_{med}$-$m_{\chi}$ plane in the fermion portal model.

Expected plus 1 s.d. exclusion contour in the $m_{med}$-$m_{\chi}$ plane in the fermion portal model.

Expected plus 1 s.d. exclusion contour in the $m_{med}$-$m_{\chi}$ plane in the fermion portal model.

Expected minus 1 s.d. exclusion contour in the $m_{med}$-$m_{\chi}$ plane in the fermion portal model.

Expected minus 1 s.d. exclusion contour in the $m_{med}$-$m_{\chi}$ plane in the fermion portal model.

Tagging efficiency for AK8 jets. The efficiency includes the effect of the machine-learning based DeepAK8 tagger, as well as the application of the mass window requirement on the jet. The efficiency is split depending on the matching generator-level object. For reinterpretation purposes, this efficiency can directly be applied to any AK8 jet that is matched to a given type of generator-level object, with no prior selection on the jet mass. Other acceptance requirements on jet $\p_{T}$ and $\eta$ should still be applied.

Tagging efficiency for AK8 jets. The efficiency includes the effect of the machine-learning based DeepAK8 tagger, as well as the application of the mass window requirement on the jet. The efficiency is split depending on the matching generator-level object. For reinterpretation purposes, this efficiency can directly be applied to any AK8 jet that is matched to a given type of generator-level object, with no prior selection on the jet mass. Other acceptance requirements on jet $\p_{T}$ and $\eta$ should still be applied.

The correlation matrix for the Higgs pT measurements, both for the unregularized and regularized fits. The last bin is inclusive.

The correlation matrix for the jet multiplicity measurements, both for the unregularized and regularized fits. The last bin is inclusive.

The correlation matrix for the leading jet pT measurements, both for the unregularized and regularized fits. The last bin is inclusive.

The fiducial integrated signal strength and cross section.

The 95% CL observed and expected limits on the branching fraction B(H $\rightarrow$ SS) for 15 GeV mass and $ S \rightarrow d\bar{d}$ decay mode.

The 95% CL observed and expected limits on the branching fraction B(H $\rightarrow$ SS) for 40 GeV mass and $ S \rightarrow d\bar{d}$ decay mode.

The 95% CL observed and expected limits on the branching fraction B(H $\rightarrow$ SS) for 40 GeV mass and $ S \rightarrow d\bar{d}$ decay mode.

The 95% CL observed and expected limits on the branching fraction B(H $\rightarrow$ SS) for 55 GeV mass and $ S \rightarrow d\bar{d}$ decay mode.

The 95% CL observed and expected limits on the branching fraction B(H $\rightarrow$ SS) for 55 GeV mass and $ S \rightarrow d\bar{d}$ decay mode.

The 95% CL observed and expected limits on the branching fraction B(H $\rightarrow$ SS) for 7 GeV mass and $ S \rightarrow \tau^{+} \tau^{-}$ decay mode.

The 95% CL observed and expected limits on the branching fraction B(H $\rightarrow$ SS) for 7 GeV mass and $ S \rightarrow \tau^{+} \tau^{-}$ decay mode.

The 95% CL observed and expected limits on the branching fraction B(H $\rightarrow$ SS) for 15 GeV mass and $ S \rightarrow \tau^{+} \tau^{-}$ decay mode.

The 95% CL observed and expected limits on the branching fraction B(H $\rightarrow$ SS) for 15 GeV mass and $ S \rightarrow \tau^{+} \tau^{-}$ decay mode.

The 95% CL observed and expected limits on the branching fraction B(H $\rightarrow$ SS) for 40 GeV mass and $ S \rightarrow \tau^{+} \tau^{-}$ decay mode.

The 95% CL observed and expected limits on the branching fraction B(H $\rightarrow$ SS) for 40 GeV mass and $ S \rightarrow \tau^{+} \tau^{-}$ decay mode.

The 95% CL observed and expected limits on the branching fraction B(H $\rightarrow$ SS) for 55 GeV mass and $ S \rightarrow \tau^{+} \tau^{-}$ decay mode.

The 95% CL observed and expected limits on the branching fraction B(H $\rightarrow$ SS) for 55 GeV mass and $ S \rightarrow \tau^{+} \tau^{-}$ decay mode.

The 95% CL observed and expected limits on the branching fraction B(H $\rightarrow$ SS) for 15 GeV mass and $ S \rightarrow b\bar{b}$ decay mode.

The 95% CL observed and expected limits on the branching fraction B(H $\rightarrow$ SS) for 15 GeV mass and $ S \rightarrow b\bar{b}$ decay mode.

The 95% CL observed and expected limits on the branching fraction B(H $\rightarrow$ SS) for 40 GeV mass and $ S \rightarrow b\bar{b}$ decay mode.

The 95% CL observed and expected limits on the branching fraction B(H $\rightarrow$ SS) for 40 GeV mass and $ S \rightarrow b\bar{b}$ decay mode.

The 95% CL observed and expected limits on the branching fraction B(H $\rightarrow$ SS) for 55 GeV mass and $ S \rightarrow b\bar{b}$ decay mode.

The 95% CL observed and expected limits on the branching fraction B(H $\rightarrow$ SS) for 55 GeV mass and $ S \rightarrow b\bar{b}$ decay mode.

The cluster efficiency in bins of hadronic and EM energy in region A. Region A is defined as 391 cm $< r <$ 695.5 cm and 400 cm $< |z| <$ 671 cm. The cluster efficiency is estimated with LLPs decaying to $\tau^{+} \tau^{-}$. The sample contains equal fractions of events with LLP mass of 7, 15, 40, and 55 GeV and LLP lifetime of 0.1, 1, 10, and 100m. The first hadronic energy bins correspond to LLPs that decayed leptonically with 0 hadronic energy. The cluster efficiency includes all cluster-level selections described in the paper, except for the jet veto, time cut, and $\Delta\phi$ cut. The full simulation signal yield prediction for samples with various LLP mass between 7 - 55 GeV, lifetime between 0.1 - 100 m, and decay mode to $d\bar{d}$ and $\tau^{+} \tau^{-}$ can be reproduced using this parameterization to within 35% and 20% for region A and B, respectively.

The cluster efficiency in bins of hadronic and EM energy in region A. Region A is defined as 391 cm $< r <$ 695.5 cm and 400 cm $< |z| <$ 671 cm. The cluster efficiency is estimated with LLPs decaying to $\tau^{+} \tau^{-}$. The sample contains equal fractions of events with LLP mass of 7, 15, 40, and 55 GeV and LLP lifetime of 0.1, 1, 10, and 100m. The first hadronic energy bins correspond to LLPs that decayed leptonically with 0 hadronic energy. The cluster efficiency includes all cluster-level selections described in the paper, except for the jet veto, time cut, and $\Delta\phi$ cut. The full simulation signal yield prediction for samples with various LLP mass between 7 - 55 GeV, lifetime between 0.1 - 100 m, and decay mode to $d\bar{d}$ and $\tau^{+} \tau^{-}$ can be reproduced using this parameterization to within 35% and 20% for region A and B, respectively.

The cluster efficiency in bins of hadronic and EM energy in region B. Region B is defined as 671 cm $< |z| <$ 1100 cm, $r <$ 695.5 cm, and $|\eta| <$ 2. The cluster efficiency is estimated with LLPs decaying to $\tau^{+} \tau^{-}$. The sample contains equal fractions of events with LLP mass of 7, 15, 40, and 55 GeV and LLP lifetime of 0.1, 1, 10, and 100m. The first hadronic energy bins correspond to LLPs that decayed leptonically with 0 hadronic energy. The cluster efficiency includes all cluster-level selections described in the paper, except for the jet veto, time cut, and $\Delta\phi$ cut. The full simulation signal yield prediction for samples with various LLP mass between 7 - 55 GeV, lifetime between 0.1 - 100 m, and decay mode to $d\bar{d}$ and $\tau^{+} \tau^{-}$ can be reproduced using this parameterization to within 35% and 20% for region A and B, respectively.

The cluster efficiency in bins of hadronic and EM energy in region B. Region B is defined as 671 cm $< |z| <$ 1100 cm, $r <$ 695.5 cm, and $|\eta| <$ 2. The cluster efficiency is estimated with LLPs decaying to $\tau^{+} \tau^{-}$. The sample contains equal fractions of events with LLP mass of 7, 15, 40, and 55 GeV and LLP lifetime of 0.1, 1, 10, and 100m. The first hadronic energy bins correspond to LLPs that decayed leptonically with 0 hadronic energy. The cluster efficiency includes all cluster-level selections described in the paper, except for the jet veto, time cut, and $\Delta\phi$ cut. The full simulation signal yield prediction for samples with various LLP mass between 7 - 55 GeV, lifetime between 0.1 - 100 m, and decay mode to $d\bar{d}$ and $\tau^{+} \tau^{-}$ can be reproduced using this parameterization to within 35% and 20% for region A and B, respectively.

The efficiency of $N_{station} > 1$ requirement in bins of hadronic energy in region B. Region B is defined as 671 cm $< |z| <$ 1100 cm, $r <$ 695.5 cm, and $|\eta| <$ 2. The cluster efficiency is estimated with LLPs decaying to $\tau^{+} \tau^{-}$. The sample contains equal fractions of events with LLP mass of 7, 15, 40, and 55 GeV and LLP lifetime of 0.1, 1, 10, and 100m. The first hadronic energy bin corresponds to LLPs that decayed leptonically with 0 hadronic energy. The efficiency is calculated with respect to clusters that pass all cluster-level cuts described in the paper, except for the jet veto, time cut, and $\Delta\phi$ cut. The full simulation signal yield prediction for samples with various LLP mass between 7 - 55 GeV, lifetime between 0.1 - 100 m, and decay mode to $d\bar{d}$ and $\tau^{+} \tau^{-}$ can be reproduced using this parameterization to within 10%.

The efficiency of $N_{station} > 1$ requirement in bins of hadronic energy in region B. Region B is defined as 671 cm $< |z| <$ 1100 cm, $r <$ 695.5 cm, and $|\eta| <$ 2. The cluster efficiency is estimated with LLPs decaying to $\tau^{+} \tau^{-}$. The sample contains equal fractions of events with LLP mass of 7, 15, 40, and 55 GeV and LLP lifetime of 0.1, 1, 10, and 100m. The first hadronic energy bin corresponds to LLPs that decayed leptonically with 0 hadronic energy. The efficiency is calculated with respect to clusters that pass all cluster-level cuts described in the paper, except for the jet veto, time cut, and $\Delta\phi$ cut. The full simulation signal yield prediction for samples with various LLP mass between 7 - 55 GeV, lifetime between 0.1 - 100 m, and decay mode to $d\bar{d}$ and $\tau^{+} \tau^{-}$ can be reproduced using this parameterization to within 10%.

The geometric signal acceptance as a function of $c\tau$. The acceptance is shown for four different LLP mass hypotheses: 7, 15, 40, and 55 GeV. The acceptance is defined by requiring at least 1 LLP to decay in the region defined as 400 cm $< |z| <$ 1100 cm, $r < $ 695.5 cm, and $|\eta| <$ 2.4.

Distribution of $m_{T}(W)$ in the $N_{jet}\geq 3$ signal region.

Distribution of $M_{3}$ in the $N_{jet}\geq 3$ signal region.

Distribution of $M_{3}$ in the $N_{jet}\geq 3$ signal region.

Distribution of $m(l,\gamma)$ in the $N_{jet}\geq 3$ signal region.

Distribution of $m(l,\gamma)$ in the $N_{jet}\geq 3$ signal region.

Distribution of $\Delta R(l,\gamma)$ in the $N_{jet}\geq 3$ signal region.

Distribution of $\Delta R(l,\gamma)$ in the $N_{jet}\geq 3$ signal region.

Distribution of $\Delta R(j,\gamma)$ in the $N_{jet}\geq 3$ signal region.

Distribution of $\Delta R(j,\gamma)$ in the $N_{jet}\geq 3$ signal region.

Fit result of the multijet template obtained with loosely isolated leptons and the electroweak background to the measured $m_{T}(W)$ distribution with isolated leptons in the $N_{jet}=2$, $N_{b jet}=0$ selection for electrons.

Fit result of the multijet template obtained with loosely isolated leptons and the electroweak background to the measured $m_{T}(W)$ distribution with isolated leptons in the $N_{jet}=2$, $N_{b jet}=0$ selection for electrons.

Fit result of the multijet template obtained with loosely isolated leptons and the electroweak background to the measured $m_{T}(W)$ distribution with isolated leptons in the $N_{jet}=2$, $N_{b jet}=0$ selection for muons.

Fit result of the multijet template obtained with loosely isolated leptons and the electroweak background to the measured $m_{T}(W)$ distribution with isolated leptons in the $N_{jet}=2$, $N_{b jet}=0$ selection for muons.

Distribution of the invariant mass of the lepton and the photon ($m(l,\gamma)$) in the $N_{jet}\geq 3$, $N_{b jet}=0$ selection for the e channel.

Distribution of the invariant mass of the lepton and the photon ($m(l,\gamma)$) in the $N_{jet}\geq 3$, $N_{b jet}=0$ selection for the e channel.

Distribution of the invariant mass of the lepton and the photon ($m(l,\gamma)$) in the $N_{jet}\geq 3$, $N_{b jet}=0$ selection for the $\mu$ channel.

Distribution of the invariant mass of the lepton and the photon ($m(l,\gamma)$) in the $N_{jet}\geq 3$, $N_{b jet}=0$ selection for the $\mu$ channel.

Extracted scale factors for the contribution from misidentified electrons for the three data-taking periods, and the Z$\gamma$, W$\gamma$ simulations.

Extracted scale factors for the contribution from misidentified electrons for the three data-taking periods, and the Z$\gamma$, W$\gamma$ simulations.

Predicted and observed yields in the control regions in the $N_{jet}= 3$ and $\geq 4$ seletions using the post-fit values of the nuisance parameters.

Predicted and observed yields in the control regions in the $N_{jet}= 3$ and $\geq 4$ seletions using the post-fit values of the nuisance parameters.

Predicted and observed yields in the signal regions in the $N_{jet}= 3$ and $\geq 4$ seletions using the post-fit values of the nuisance parameters.

Predicted and observed yields in the signal regions in the $N_{jet}= 3$ and $\geq 4$ seletions using the post-fit values of the nuisance parameters.

The measured inclusive ttgamma cross section in the fiducial phase space compared to the prediction from simulation using Madgraph_aMC@NLO at a center-of-mass energy of 13 TeV.

The measured inclusive ttgamma cross section in the fiducial phase space compared to the prediction from simulation using Madgraph_aMC@NLO at a center-of-mass energy of 13 TeV.

Summary of the measured cross section ratios with respect to the NLO cross section prediction for signal regions binned in the electron channel, muon channel and the combined single lepton measurement.

Summary of the measured cross section ratios with respect to the NLO cross section prediction for signal regions binned in the electron channel, muon channel and the combined single lepton measurement.

The unfolded differential cross sections for $p_{T}(\gamma)$ and the comparison to simulations.

The unfolded differential cross sections for $p_{T}(\gamma)$ and the comparison to simulations.

The unfolded differential cross sections for $|\eta(\gamma)|$ and the comparison to simulations.

The unfolded differential cross sections for $|\eta(\gamma)|$ and the comparison to simulations.

The unfolded differential cross sections for $\Delta R(l,\gamma)$ and the comparison to simulations.

The unfolded differential cross sections for $\Delta R(l,\gamma)$ and the comparison to simulations.

The covariance matrix of systematic uncertainties for the unfolded differential measurement for $p_{T}(\gamma)$.

The covariance matrix of systematic uncertainties for the unfolded differential measurement for $p_{T}(\gamma)$.

The covariance matrix of systematic uncertainties for the unfolded differential measurement for $|\eta(\gamma)|$.

The covariance matrix of systematic uncertainties for the unfolded differential measurement for $|\eta(\gamma)|$.

The covariance matrix of systematic uncertainties for the unfolded differential measurement for $\Delta R(l,\gamma)$.

The covariance matrix of systematic uncertainties for the unfolded differential measurement for $\Delta R(l,\gamma)$.

The covariance matrix of statistic uncertainties for the unfolded differential measurement for $p_{T}(\gamma)$.

The covariance matrix of statistic uncertainties for the unfolded differential measurement for $p_{T}(\gamma)$.

The covariance matrix of statistic uncertainties for the unfolded differential measurement for $|\eta(\gamma)|$.

The covariance matrix of statistic uncertainties for the unfolded differential measurement for $|\eta(\gamma)|$.

The covariance matrix of statistic uncertainties for the unfolded differential measurement for $\Delta R(l,\gamma)$.

The covariance matrix of statistic uncertainties for the unfolded differential measurement for $\Delta R(l,\gamma)$.

The correlation matrix of statistical uncertainties for the unfolded differential measurement for $p_{T}(\gamma)$.

The correlation matrix of statistical uncertainties for the unfolded differential measurement for $p_{T}(\gamma)$.

The correlation matrix of statistical uncertainties for the unfolded differential measurement for $|\eta(\gamma)|$.

The correlation matrix of statistical uncertainties for the unfolded differential measurement for $|\eta(\gamma)|$.

The correlation matrix of statistical uncertainties for the unfolded differential measurement for $\Delta R(l,\gamma)$.

The correlation matrix of statistical uncertainties for the unfolded differential measurement for $\Delta R(l,\gamma)$.

The correlation matrix of systematic uncertainties for the unfolded differential measurement for $p_{T}(\gamma)$.

The correlation matrix of systematic uncertainties for the unfolded differential measurement for $p_{T}(\gamma)$.

The correlation matrix of systematic uncertainties for the unfolded differential measurement for $|\eta(\gamma)|$.

The correlation matrix of systematic uncertainties for the unfolded differential measurement for $|\eta(\gamma)|$.

The correlation matrix of systematic uncertainties for the unfolded differential measurement for $\Delta R(l,\gamma)$.

The correlation matrix of systematic uncertainties for the unfolded differential measurement for $\Delta R(l,\gamma)$.

Summary of the one-dimensional intervals at 68 and 95% CL.

Summary of the one-dimensional intervals at 68 and 95% CL.

The observed and predicted post-fit yields for the combined Run 2 data set in the SR3 signal region for the electron channel.

The observed and predicted post-fit yields for the combined Run 2 data set in the SR3 signal region for the electron channel.

The observed and predicted post-fit yields for the combined Run 2 data set in the SR3 signal region for the muon channel.

The observed and predicted post-fit yields for the combined Run 2 data set in the SR3 signal region for the muon channel.

The observed and predicted post-fit yields for the combined Run 2 data set in the SR4p signal region for the electron channel.

The observed and predicted post-fit yields for the combined Run 2 data set in the SR4p signal region for the electron channel.

The observed and predicted post-fit yields for the combined Run 2 data set in the SR4p signal region for the muon channel.

The observed and predicted post-fit yields for the combined Run 2 data set in the SR4p signal region for the muon channel.

Negative log-likelihood ratio values with respect to the best fit value of the one-dimensional profiled scan for the Wilson coefficient $c_{tZ}$.

Negative log-likelihood ratio values with respect to the best fit value of the one-dimensional profiled scan for the Wilson coefficient $c_{tZ}$.

Negative log-likelihood ratio values with respect to the best fit value of the one-dimensional profiled scan for the Wilson coefficient $c^{I}_{tZ}$.

Negative log-likelihood ratio values with respect to the best fit value of the one-dimensional profiled scan for the Wilson coefficient $c^{I}_{tZ}$.

Negative log-likelihood ratio values with respect to the best fit value of the one-dimensional scan for the Wilson coefficient $c_{tZ}$.

Negative log-likelihood ratio values with respect to the best fit value of the one-dimensional scan for the Wilson coefficient $c_{tZ}$.

Negative log-likelihood ratio values with respect to the best fit value of the one-dimensional scan for the Wilson coefficient $c^{I}_{tZ}$.

Negative log-likelihood ratio values with respect to the best fit value of the one-dimensional scan for the Wilson coefficient $c^{I}_{tZ}$.

Negative log-likelihood ratio values with respect to the best fit value of the two-dimensional scan for the Wilson coefficients $c_{tZ}$ and $c^{I}_{tZ}$.

Negative log-likelihood ratio values with respect to the best fit value of the two-dimensional scan for the Wilson coefficients $c_{tZ}$ and $c^{I}_{tZ}$.

The measured single-differential cross sections in leading jet transverse momenta for the pure electroweak Z$\gamma$jj production. The total uncertainty includes the stastical uncertianty and the systematic uncertainty, while the uncertainty of the predicted results is the theoretical uncertainty from the MadGraph5_aMC@NLO. The last bin includes overflow events.

The measured single-differential cross sections in leading lepton transverse momenta for the pure electroweak Z$\gamma$jj production. The total uncertainty includes the stastical uncertianty and the systematic uncertainty, while the uncertainty of the predicted results is the theoretical uncertainty from the MadGraph5_aMC@NLO. The last bin includes overflow events.

The measured double-differential cross sections as functions of $m_{\mathrm{jj}}$ and $|\Delta\eta_{\mathrm{jj}}|$ for the pure electroweak Z$\gamma$jj production. The total uncertainty includes the stastical uncertianty and the systematic uncertainty, while the uncertainty of the predicted results is the theoretical uncertainty from the MadGraph5_aMC@NLO. The last bin includes overflow events.

The measured single-differential cross sections in photon transverse momenta for the combined QCD-induced and electroweak Z$\gamma$jj production. The total uncertainty includes the stastical uncertianty and the systematic uncertainty, while the uncertainty of the predicted results is the theoretical uncertainty from the MadGraph5_aMC@NLO. The last bin includes overflow events.

The measured single-differential cross sections in leading jet transverse momenta for the combined QCD-induced and electroweak Z$\gamma$jj production. The total uncertainty includes the stastical uncertianty and the systematic uncertainty, while the uncertainty of the predicted results is the theoretical uncertainty from the MadGraph5_aMC@NLO. The last bin includes overflow events.

The measured single-differential cross sections in leading lepton transverse momenta for the combined QCD-induced and electroweak Z$\gamma$jj production. The total uncertainty includes the stastical uncertianty and the systematic uncertainty, while the uncertainty of the predicted results is the theoretical uncertainty from the MadGraph5_aMC@NLO. The last bin includes overflow events.

The measured double-differential cross sections as functions of $m_{\mathrm{jj}}$ and $|\Delta\eta_{\mathrm{jj}}|$ for the combined QCD-induced and electroweak Z$\gamma$jj production. The total uncertainty includes the stastical uncertianty and the systematic uncertainty, while the uncertainty of the predicted results is the theoretical uncertainty from the MadGraph5_aMC@NLO. The last bin includes overflow events.

The expected and observed limits on the aQGC parameters at 95% confidence level. The last column presents the scattering energy values for which the amplitude would violate unitarity for the observed value of the aQGC parameter. All coupling parameter limits are set in TeV$^{-4}$, whereas the unitarity bounds are in TeV.

Fitted 4th order polynomials to the product of the signal efficiency and acceptance for narrow and broad, scalar and vector Wgamma resonances. This quantity is defined as the ratio between the number of signal events passing full analysis cuts to the number of signal events generated. The fitting function is $ A \epsilon = p0 + p1*m + p2*m^2 + p3*m^3 + p4*m^4$, where $ A \epsilon$ is the product of the signal efficiency and acceptance, m is the signal mass.

W tagging efficiency, averaged for different spin and width hypotheses. The Standard deviation shown below is the standard deviation between the W tagging efficiencies for different spin and width hypotheses.

W tagging efficiency, averaged for different spin and width hypotheses. The Standard deviation shown below is the standard deviation between the W tagging efficiencies for different spin and width hypotheses.

Observed and expected (background-only fitted) invariant mass spectra of Wgamma events. The fitted function is ${ d N}/{ d m} = p_{0} * (m/\sqrt{s})^{p_{1} + p_{2} * \log(m/\sqrt{s}) + p_{3} * \log^{2}(m/\sqrt{s})}$

Observed and expected (background-only fitted) invariant mass spectra of Wgamma events. The fitted function is ${ d N}/{ d m} = p_{0} * (m/\sqrt{s})^{p_{1} + p_{2} * \log(m/\sqrt{s}) + p_{3} * \log^{2}(m/\sqrt{s})}$

Expected and observed 95% CL upper limits on the product of the cross section and branching fraction for narrow scalar Wgamma resonances. Limits are compared to predicted cross sections for the heavy scalar triplet model described in arXiv:1912.08234

Expected and observed 95% CL upper limits on the product of the cross section and branching fraction for narrow scalar Wgamma resonances. Limits are compared to predicted cross sections for the heavy scalar triplet model described in arXiv:1912.08234

Expected and observed 95% CL upper limits on the product of the cross section and branching fraction for broad scalar Wgamma resonances.

Expected and observed 95% CL upper limits on the product of the cross section and branching fraction for broad scalar Wgamma resonances.

Expected and observed 95% CL upper limits on the product of the cross section and branching fraction for narrow vector Wgamma resonances. Limits are compared to predicted cross sections for the heavy vector triplet model described in arXiv:1912.08234

Expected and observed 95% CL upper limits on the product of the cross section and branching fraction for narrow vector Wgamma resonances. Limits are compared to predicted cross sections for the heavy vector triplet model described in arXiv:1912.08234

Expected and observed 95% CL upper limits on the product of the cross section and branching fraction for broad vector Wgamma resonances.

Expected and observed 95% CL upper limits on the product of the cross section and branching fraction for broad vector Wgamma resonances.

Expected and observed model-independent 95% CL upper limits on the product of the cross section, branching fraction and signal acceptance for general Wgamma resonances.

Expected and observed model-independent 95% CL upper limits on the product of the cross section, branching fraction and signal acceptance for general Wgamma resonances.

Expected and observed model-independent 95% CL upper limits on the product of the cross section, branching fraction, signal acceptance and W tagging efficiency for general Jgamma resonances.

Expected and observed model-independent 95% CL upper limits on the product of the cross section, branching fraction, signal acceptance and W tagging efficiency for general Jgamma resonances.

Differential cross sections as function of transverse momentum imbalance between Z boson and dijet for Z+ ≥ 2 jets events.

Differential cross sections as function of transverse momentum imbalance between leading and subleading jet for Z+ ≥ 2 jets events.

Area normalized distribution as function of Delta Phi between Z boson and the leading jet for Z+ ≥ 1 jet events.

Area normalized distribution as function of transverse momentum imbalance between Z boson and the leading jet for Z+ ≥ 1 jet events.

Area normalized distribution as function of Delta Phi between Z boson and dijet for Z+ ≥ 2 jets events.

Area normalized distribution as function of transverse momentum imbalance between Z boson and dijet for Z+ ≥ 2 jets events.

Area normalized distribution as function of transverse momentum imbalance between leading and subleading jet for Z+ ≥ 2 jets events

Response matrix for Delta Phi between Z boson and the leading jet for Z+ ≥ 1 jet events.

Response matrix for transverse momentum imbalance between Z boson and the leading jet for Z+ ≥ 1 jet events.

Response matrix for Delta Phi between Z boson and dijet for Z+ ≥ 2 jets events.

Response matrix for transverse momentum imbalance between Z boson and dijet for Z+ ≥ 2 jets events.

Response matrix for transverse momentum imbalance between the leading jet and subleading jet for Z+ ≥ 2 jets events.

Correlation matrix for Delta Phi between Z boson and the leading jet for Z+ ≥ 1 jet events (for absolute differential cross section measurements).

Correlation matrix for transverse momentum imbalance between Z boson and the leading jet for Z+ ≥ 1 jet events (for absolute differential cross section measurements).

Correlation matrix for Delta Phi between Z boson and dijet for Z+ ≥ 2 jets events (for absolute differential cross section measurements).

Correlation matrix for transverse momentum imbalance between Z boson and dijet for Z+ ≥ 2 jets events (for absolute differential cross section measurements).

Correlation matrix for transverse momentum imbalance between the leading jet and subleading jet for Z+ ≥ 2 jets events (for absolute differential cross section measurements).

Correlation matrix for Delta Phi between Z boson and the leading jet for Z+ ≥ 1 jet events (for normalized differential cross section measurements).

Correlation matrix for transverse momentum imbalance between Z boson and the leading jet for Z+ ≥ 1 jet events (for normalized differential cross section measurements).

Correlation matrix for Delta Phi between Z boson and dijet for Z+ ≥ 2 jets events (for normalized differential cross section measurements).

Correlation matrix for transverse momentum imbalance between Z boson and dijet for Z+ ≥ 2 jets events (for normalized differential cross section measurements).

Correlation matrix for transverse momentum imbalance between the leading jet and subleading jet for Z+ ≥ 2 jets events (for normalized differential cross section measurements).

Distribution of the transverse momentum of the diphoton system for the $\mathrm{Z}\gamma\gamma$ muon channel. The predicted yields are shown with their pre-fit normalisations. The observed data, the expected signal contribution and the background estimates are presented with error bars showing the corresponding statistical uncertainties.

Distribution of the transverse momentum of the diphoton system, obtained in the control region enriched in misidentified photons for the $\mathrm{W}\gamma\gamma$ electron channel. The predicted yields are shown with their pre-fit normalisations. The observed data, the expected signal contribution and the background estimates are presented with error bars showing the corresponding statistical uncertainties.

Distribution of the transverse momentum of the diphoton system, obtained in the control region enriched in misidentified photons for the $\mathrm{Z}\gamma\gamma$ electron channel. The predicted yields are shown with their pre-fit normalisations. The observed data, the expected signal contribution and the background estimates are presented with error bars showing the corresponding statistical uncertainties.

The measured $\mathrm{W}\gamma\gamma$ and $\mathrm{Z}\gamma\gamma$ fiducial cross sections and corresponding theoretical predictions from MadGraph5_aMC@NLO. The measured yields in the electron and muon channels are extrapolated to a common fiducial phase space determined from simulated signal events at the generated particle level. Generated particles are considered stable if their mean decay length is larger than $1\,\mathrm{cm}$. Generated leptons are required to have a $\mathrm{p}_\mathrm{t}>15\,\mathrm{GeV}$ and $|\eta|<2.5$. The momenta of photons in a cone of $\Delta R=0.1$, the same cone size as the one applied to reconstructed data, are added to the charged lepton momentum to correct for final-state radiation. Generated photons are required to have $\mathrm{p}_\mathrm{t}>15\,\mathrm{GeV}$ and $|\eta|<2.5$. Additionally, the candidate photons are required to have no selected leptons or photons in a cone of radius $\Delta R=0.4$ and no other stable particles, apart from photons and neutrinos, in a cone of radius $\Delta R=0.1$. Events are then selected in the $\mathrm{W}\gamma\gamma$ channel by requiring exactly one electron (muon) with $\mathrm{p}_\mathrm{t}>30\,\mathrm{GeV}$ and at least two photons with $\mathrm{p}_\mathrm{t}>20\,\mathrm{GeV}$. Events are selected in the $\mathrm{Z}\gamma\gamma$ channel by requiring two electrons (muons), at least one of them with $\mathrm{p}_\mathrm{t}>30\,\mathrm{GeV}$, and not less than two photons, each of them with $\mathrm{p}_\mathrm{t}>20\,\mathrm{GeV}$. Additionally, the invariant mass of the dilepton system is required to be $m_{\ell\ell}>55\,\mathrm{GeV}$.

Expected and observed 95% confidence level intervals for the different anomalous couplings parameters in both the $\ell\nu\gamma\gamma$ and $\ell\ell\gamma\gamma$ channels. All parameters are fixed to their SM values except the one that is fitted. No unitarity regularisation scheme is applied. Intervals with a NAN value are not measured in the corresponding channels.

The number of background events obtained from the 1- and 2-leg predictions derived from data, together with the direct observation in data, in bins in ChF, where either the leading or subleading jet has a ChF within the bin edges, and both have a ChF below the upper bin threshold. The bottom panel shows the ratios of the observation in data to the 1-leg and the 2-leg background predictions.

The expected and observed 95% CL upper limits on the production cross section for SIMPs with masses between 1 and 1000 GeV, with the assumption that the SIMP interaction in the detector can be approximated as neutron-like. The theoretical prediction of a simplified model incorporating this approximation and including a scalar mediator with couplings g_chi = -1 and g_q = 1 is also shown (red line). For masses above 100 GeV, where the modelling of the SIMP-nucleon interaction becomes more speculative, the obtained cross section upper limits are increasingly uncertain (shaded area).