Measured $p_{\mathrm{T}}(D^{-})$ differential fiducial cross-section times the single-lepton-flavor W boson branching ratio in the $W^{+}+D^{-}$ channel. The last $p_{\mathrm{T}}$ bin has no upper bound. The displayed cross sections are integrated over each differential bin.

Measured $|\eta(\ell)|$ differential fiducial cross-section times the single-lepton-flavor W boson branching ratio in the $W^{-}+D^{+}$ channel. The displayed cross sections are integrated over each differential bin.

Measured $|\eta(\ell)|$ differential fiducial cross-section times the single-lepton-flavor W boson branching ratio in the $W^{+}+D^{-}$ channel. The displayed cross sections are integrated over each differential bin.

Measured $p_{\mathrm{T}}(D^{*+})$ differential fiducial cross-section times the single-lepton-flavor W boson branching ratio in the $W^{-}+D^{*+}$ channel. The last $p_{\mathrm{T}}$ bin has no upper bound. The displayed cross sections are integrated over each differential bin.

Measured $p_{\mathrm{T}}(D^{*-})$ differential fiducial cross-section times the single-lepton-flavor W boson branching ratio in the $W^{+}+D^{*-}$ channel. The last $p_{\mathrm{T}}$ bin has no upper bound. The displayed cross sections are integrated over each differential bin.

Measured $|\eta(\ell)|$ differential fiducial cross-section times the single-lepton-flavor W boson branching ratio in the $W^{-}+D^{*+}$ channel. The displayed cross sections are integrated over each differential bin.

Measured $|\eta(\ell)|$ differential fiducial cross-section times the single-lepton-flavor W boson branching ratio in the $W^{+}+D^{*-}$ channel. The displayed cross sections are integrated over each differential bin.

The data statistical uncertainty covariance matrix for the differential $p_{\mathrm{T}}(D^{\pm})$ fit in the $D^{\pm}$ channel (Tables 3 and 4).

The data statistical uncertainty covariance matrix for the differential $|\eta(\ell)|$ fit in the $D^{\pm}$ channel (Tables 5 and 6).

The data statistical uncertainty covariance matrix for the differential $p_{\mathrm{T}}(D^{*\pm})$ fit in the $D^{*\pm}$ channel (Tables 7 and 8).

The data statistical uncertainty covariance matrix for the differential $|\eta(\ell)|$ fit in the $D^{*\pm}$ channel (Tables 9 and 10).

The combined statistical and systematic uncertainty covariance matrix for the differential $p_{\mathrm{T}}(D^{\pm})$ fit in the $D^{\pm}$ channel (Tables 3 and 4).

The combined statistical and systematic uncertainty covariance matrix for the differential $|\eta(\ell)|$ fit in the $D^{\pm}$ channel (Tables 5 and 6).

The combined statistical and systematic uncertainty covariance matrix for the differential $p_{\mathrm{T}}(D^{*\pm})$ fit in the $D^{*\pm}$ channel (Tables 7 and 8).

The combined statistical and systematic uncertainty covariance matrix for the differential $|\eta(\ell)|$ fit in the $D^{*\pm}$ channel (Tables 9 and 10).

Measured $|\eta(\ell)|$ differential fiducial cross-section times the single-lepton-flavor W boson branching ratio in the $W^{-}+D^{+}$ channel with the full breakdown of uncertainties.

Measured $|\eta(\ell)|$ differential fiducial cross-section times the single-lepton-flavor W boson branching ratio in the $W^{+}+D^{-}$ channel with the full breakdown of uncertainties.

Measured $|\eta(\ell)|$ differential fiducial cross-section times the single-lepton-flavor W boson branching ratio in the $W^{-}+D^{*+}$ channel with the full breakdown of uncertainties.

Measured $|\eta(\ell)|$ differential fiducial cross-section times the single-lepton-flavor W boson branching ratio in the $W^{+}+D^{*-}$ channel with the full breakdown of uncertainties.

Descriptions of nuisance parameters.

The average tetrajet invariant mass distributions in data, along with the fitted background estimates for 0.16 < $\alpha$ < 0.18.

The average tetrajet invariant mass distributions in data, along with the fitted background estimates for 0.18 < $\alpha$ < 0.20.

The average tetrajet invariant mass distributions in data, along with the fitted background estimates for 0.20 < $\alpha$ < 0.22.

The average tetrajet invariant mass distributions in data, along with the fitted background estimates for 0.22 < $\alpha$ < 0.24.

The average tetrajet invariant mass distributions in data, along with the fitted background estimates for 0.24 < $\alpha$ < 0.26.

The average tetrajet invariant mass distributions in data, along with the fitted background estimates for 0.26 < $\alpha$ < 0.28.

The average tetrajet invariant mass distributions in data, along with the fitted background estimates for 0.28 < $\alpha$ < 0.30.

The average tetrajet invariant mass distributions in data, along with the fitted background estimates for 0.30 < $\alpha$ < 0.32.

The average tetrajet invariant mass distributions in data, along with the fitted background estimates for 0.32 < $\alpha$ < 0.34.

The average dijet invariant mass distributions in data, along with the fitted background estimates for 0.10 < $\alpha$ < 0.12.

The average dijet invariant mass distributions in data, along with the fitted background estimates for 0.12 < $\alpha$ < 0.14.

The average dijet invariant mass distributions in data, along with the fitted background estimates for 0.14 < $\alpha$ < 0.16.

The average dijet invariant mass distributions in data, along with the fitted background estimates for 0.16 < $\alpha$ < 0.18.

The average dijet invariant mass distributions in data, along with the fitted background estimates for 0.18 < $\alpha$ < 0.20.

The average dijet invariant mass distributions in data, along with the fitted background estimates for 0.20 < $\alpha$ < 0.22.

The average dijet invariant mass distributions in data, along with the fitted background estimates for 0.22 < $\alpha$ < 0.24.

The average dijet invariant mass distributions in data, along with the fitted background estimates for 0.24 < $\alpha$ < 0.26.

The average dijet invariant mass distributions in data, along with the fitted background estimates for 0.26 < $\alpha$ < 0.28.

The average dijet invariant mass distributions in data, along with the fitted background estimates for 0.28 < $\alpha$ < 0.30.

The average dijet invariant mass distributions in data, along with the fitted background estimates for 0.30 < $\alpha$ < 0.32.

The average dijet invariant mass distributions in data, along with the fitted background estimates for 0.32 < $\alpha$ < 0.34.

The expected and observed limits on $m_{4j}$ for signal templates using a 4-parameter fit function for 0.10 < $\alpha$ < 0.12.

The expected and observed limits on $m_{4j}$ for signal templates using a 4-parameter fit function for 0.12 < $\alpha$ < 0.14.

The expected and observed limits on $m_{4j}$ for signal templates using a 4-parameter fit function for 0.14 < $\alpha$ < 0.16.

The expected and observed limits on $m_{4j}$ for signal templates using a 4-parameter fit function for 0.16 < $\alpha$ < 0.18.

The expected and observed limits on $m_{4j}$ for signal templates using a 4-parameter fit function for 0.18 < $\alpha$ < 0.20.

The expected and observed limits on $m_{4j}$ for signal templates using a 4-parameter fit function for 0.20 < $\alpha$ < 0.22.

The expected and observed limits on $m_{4j}$ for signal templates using a 4-parameter fit function for 0.22 < $\alpha$ < 0.24.

The expected and observed limits on $m_{4j}$ for signal templates using a 4-parameter fit function for 0.24 < $\alpha$ < 0.26.

The expected and observed limits on $m_{4j}$ for signal templates using a 4-parameter fit function for 0.26 < $\alpha$ < 0.28.

The expected and observed limits on $m_{4j}$ for signal templates using a 4-parameter fit function for 0.28 < $\alpha$ < 0.30.

The expected and observed limits on $m_{4j}$ for signal templates using a 4-parameter fit function for 0.30 < $\alpha$ < 0.32.

The expected and observed limits on $m_{4j}$ for signal templates using a 4-parameter fit function for 0.32 < $\alpha$ < 0.34.

The expected and observed limits on $m_{\langle 2j \rangle}$ for signal templates using a 4-parameter fit function for 0.10 < $\alpha$ < 0.12.

The expected and observed limits on $m_{\langle 2j \rangle}$ for signal templates using a 4-parameter fit function for 0.12 < $\alpha$ < 0.14.

The expected and observed limits on $m_{\langle 2j \rangle}$ for signal templates using a 4-parameter fit function for 0.14 < $\alpha$ < 0.16.

The expected and observed limits on $m_{\langle 2j \rangle}$ for signal templates using a 4-parameter fit function for 0.16 < $\alpha$ < 0.18.

The expected and observed limits on $m_{\langle 2j \rangle}$ for signal templates using a 4-parameter fit function for 0.18 < $\alpha$ < 0.20.

The expected and observed limits on $m_{\langle 2j \rangle}$ for signal templates using a 4-parameter fit function for 0.20 < $\alpha$ < 0.22.

The expected and observed limits on $m_{\langle 2j \rangle}$ for signal templates using a 4-parameter fit function for 0.22 < $\alpha$ < 0.24.

The expected and observed limits on $m_{\langle 2j \rangle}$ for signal templates using a 4-parameter fit function for 0.24 < $\alpha$ < 0.26.

The expected and observed limits on $m_{\langle 2j \rangle}$ for signal templates using a 4-parameter fit function for 0.26 < $\alpha$ < 0.28.

The expected and observed limits on $m_{\langle 2j \rangle}$ for signal templates using a 4-parameter fit function for 0.28 < $\alpha$ < 0.30.

The expected and observed limits on $m_{\langle 2j \rangle}$ for signal templates using a 4-parameter fit function for 0.30 < $\alpha$ < 0.32.

The expected and observed limits on $m_{\langle 2j \rangle}$ for signal templates using a 4-parameter fit function for 0.32 < $\alpha$ < 0.34.

The expected and observed limits on $m_{4j}$ for Gaussian signal templates using a 4-parameter fit function for 0.10 < $\alpha$ < 0.12.

The expected and observed limits on $m_{4j}$ for Gaussian signal templates using a 4-parameter fit function for 0.12 < $\alpha$ < 0.14.

The expected and observed limits on $m_{4j}$ for Gaussian signal templates using a 4-parameter fit function for 0.14 < $\alpha$ < 0.16.

The expected and observed limits on $m_{4j}$ for Gaussian signal templates using a 4-parameter fit function for 0.16 < $\alpha$ < 0.18.

The expected and observed limits on $m_{4j}$ for Gaussian signal templates using a 4-parameter fit function for 0.18 < $\alpha$ < 0.20.

The expected and observed limits on $m_{4j}$ for Gaussian signal templates using a 4-parameter fit function for 0.20 < $\alpha$ < 0.22.

The expected and observed limits on $m_{4j}$ for Gaussian signal templates using a 4-parameter fit function for 0.22 < $\alpha$ < 0.24.

The expected and observed limits on $m_{4j}$ for Gaussian signal templates using a 4-parameter fit function for 0.24 < $\alpha$ < 0.26.

The expected and observed limits on $m_{4j}$ for Gaussian signal templates using a 4-parameter fit function for 0.26 < $\alpha$ < 0.28.

The expected and observed limits on $m_{4j}$ for Gaussian signal templates using a 4-parameter fit function for 0.28 < $\alpha$ < 0.30.

The expected and observed limits on $m_{4j}$ for Gaussian signal templates using a 4-parameter fit function for 0.30 < $\alpha$ < 0.32.

The expected and observed limits on $m_{4j}$ for Gaussian signal templates using a 4-parameter fit function for 0.32 < $\alpha$ < 0.34.

The expected and observed limits on $m_{\langle 2j \rangle}$ for Gaussian signal templates using a 4-parameter fit function for 0.10 < $\alpha$ < 0.12.

The expected and observed limits on $m_{\langle 2j \rangle}$ for Gaussian signal templates using a 4-parameter fit function for 0.12 < $\alpha$ < 0.14.

The expected and observed limits on $m_{\langle 2j \rangle}$ for Gaussian signal templates using a 4-parameter fit function for 0.14 < $\alpha$ < 0.16.

The expected and observed limits on $m_{\langle 2j \rangle}$ for Gaussian signal templates using a 4-parameter fit function for 0.16 < $\alpha$ < 0.18.

The expected and observed limits on $m_{\langle 2j \rangle}$ for Gaussian signal templates using a 4-parameter fit function for 0.18 < $\alpha$ < 0.20.

The expected and observed limits on $m_{\langle 2j \rangle}$ for Gaussian signal templates using a 4-parameter fit function for 0.20 < $\alpha$ < 0.22.

The expected and observed limits on $m_{\langle 2j \rangle}$ for Gaussian signal templates using a 4-parameter fit function for 0.22 < $\alpha$ < 0.24.

The expected and observed limits on $m_{\langle 2j \rangle}$ for Gaussian signal templates using a 4-parameter fit function for 0.24 < $\alpha$ < 0.26.

The expected and observed limits on $m_{\langle 2j \rangle}$ for Gaussian signal templates using a 4-parameter fit function for 0.26 < $\alpha$ < 0.28.

The expected and observed limits on $m_{\langle 2j \rangle}$ for Gaussian signal templates using a 4-parameter fit function for 0.28 < $\alpha$ < 0.30.

The expected and observed limits on $m_{\langle 2j \rangle}$ for Gaussian signal templates using a 4-parameter fit function for 0.30 < $\alpha$ < 0.32.

The expected and observed limits on $m_{\langle 2j \rangle}$ for Gaussian signal templates using a 4-parameter fit function for 0.32 < $\alpha$ < 0.34.

The product of the analysis acceptance and selection efficiency for all analysis selection criteria is shown as a function of $m_Y$ and $m_{X}/m_{Y}$.

The cross-section of the signal samples is shown as a function of $m_Y$ and $m_{X}/m_{Y}$.

The expected minus one standard deviation exclusion limit at 95% CL for the clockwork gravity model projected in the $k–M_{5}$ parameter space for the $ee$ channel for the case with mass thresholds.

The expected plus two standard deviation exclusion limit at 95% CL for the clockwork gravity model projected in the $k–M_{5}$ parameter space for the $ee$ channel for the case with mass thresholds.

The expected minus two standard deviation exclusion limit at 95% CL for the clockwork gravity model projected in the $k–M_{5}$ parameter space for the $ee$ channel for the case with mass thresholds.

The observed exclusion limit at 95% CL for the clockwork gravity model projected in the $k–M_{5}$ parameter space for the $\gamma\gamma$ channel for the case with mass thresholds.

The median expected exclusion limit at 95% CL for the clockwork gravity model projected in the $k–M_{5}$ parameter space for the $\gamma\gamma$ channel for the case with mass thresholds.

The expected plus one standard deviation exclusion limit at 95% CL for the clockwork gravity model projected in the $k–M_{5}$ parameter space for the $\gamma\gamma$ channel for the case with mass thresholds.

The expected minus one standard deviation exclusion limit at 95% CL for the clockwork gravity model projected in the $k–M_{5}$ parameter space for the $\gamma\gamma$ channel for the case with mass thresholds.

The expected plus two standard deviation exclusion limit at 95% CL for the clockwork gravity model projected in the $k–M_{5}$ parameter space for the $\gamma\gamma$ channel for the case with mass thresholds.

The expected minus two standard deviation exclusion limit at 95% CL for the clockwork gravity model projected in the $k–M_{5}$ parameter space for the $\gamma\gamma$ channel for the case with mass thresholds.

The observed exclusion limit at 95% CL for the clockwork gravity model projected in the $k–M_{5}$ parameter space for the $ee$ channel for the case without mass thresholds.

The median expected exclusion limit at 95% CL for the clockwork gravity model projected in the $k–M_{5}$ parameter space for the $ee$ channel for the case without mass thresholds.

The expected plus one standard deviation exclusion limit at 95% CL for the clockwork gravity model projected in the $k–M_{5}$ parameter space for the $ee$ channel for the case without mass thresholds.

The expected minus one standard deviation exclusion limit at 95% CL for the clockwork gravity model projected in the $k–M_{5}$ parameter space for the $ee$ channel for the case without mass thresholds.

The expected plus two standard deviation exclusion limit at 95% CL for the clockwork gravity model projected in the $k–M_{5}$ parameter space for the $ee$ channel for the case without mass thresholds.

The expected minus two standard deviation exclusion limit at 95% CL for the clockwork gravity model projected in the $k–M_{5}$ parameter space for the $ee$ channel for the case without mass thresholds.

The observed exclusion limit at 95% CL for the clockwork gravity model projected in the $k–M_{5}$ parameter space for the $\gamma\gamma$ channel for the case without mass thresholds.

The median expected exclusion limit at 95% CL for the clockwork gravity model projected in the $k–M_{5}$ parameter space for the $\gamma\gamma$ channel for the case without mass thresholds.

The expected plus one standard deviation exclusion limit at 95% CL for the clockwork gravity model projected in the $k–M_{5}$ parameter space for the $\gamma\gamma$ channel for the case without mass thresholds.

The expected minus one standard deviation exclusion limit at 95% CL for the clockwork gravity model projected in the $k–M_{5}$ parameter space for the $\gamma\gamma$ channel for the case without mass thresholds.

The expected plus two standard deviation exclusion limit at 95% CL for the clockwork gravity model projected in the $k–M_{5}$ parameter space for the $\gamma\gamma$ channel for the case without mass thresholds.

The expected minus two standard deviation exclusion limit at 95% CL for the clockwork gravity model projected in the $k–M_{5}$ parameter space for the $\gamma\gamma$ channel for the case without mass thresholds.

Event yields after a background-only fit and data in the three signal regions. All the backgrounds except the fake $\tau_{\mathrm{had}}$ are estimated using the real $\tau_{\mathrm{had}}$ contributions from MC. The fake $\tau_{\mathrm{had}}$ background contribution is data-driven. The top-quark, $V$+jets, and small backgrounds are included in "Others". The total uncertainties include both systematic and statistical. In the $WW1\ell2\tau_{\mathrm{had}}$ channel, the smaller uncertainty in the total background than the fake $\tau_{\mathrm{had}}$ is due to the anticorrelations between the nuisance parameters of the fake $\tau_{\mathrm{had}}$ and diboson backgrounds obtained in the fit.

Uncertainties on $\sigma(pp\to X\to SH)$ obtained from the combined fit to the data for the least and most sensitive mass points. The uncertainties are symmetrised and grouped into the categories described in the systematic section.

Summary of observed and expected 95\% CL upper limits on the production cross-section of $\sigma(pp\to X\to SH)$ in fb in the combination of $WW$+$ZZ$, and in the $WW$ and $ZZ$ individual channels. The best expected limit is set to 85 fb for $m_{X}$ = 1250 GeV and $_{S}$ = 300 GeV. The combination limits gain about 26--53% over the best individual limit from the $WW1\ell2\tau_{\mathrm{had}}$ channel.

Observed 95% CL upper limits on B(H&rarr;&nbsp;2&gamma;_d+X) for different &gamma;_d masses and a 125&nbsp;GeV Higgs boson, as a function of the dark-photon mean proper decay length c&tau;. The limits are shown for all search channels combined, assuming an FRVZ signal model. The hatched band denotes the region in which the branching ratio is larger than unity.

Observed 95% CL upper limits on B(H&rarr;&nbsp;2&gamma;_d+X) for a &gamma;_d mass of 100&nbsp;MeV, as a function of the dark-photon mean proper decay length c&tau;. The solid black curve shows the observed exclusion limit from their statistical combination. The hatched band denotes the region in which the branching ratio is larger than unity.

Observed 95% CL upper limits on B(H&rarr;&nbsp;2&gamma;_d+X) for a &gamma;_d mass of 10&nbsp;GeV, as a function of the dark-photon mean proper decay length c&tau;. The solid black curve shows the observed exclusion limit from their statistical combination. The hatched band denotes the region in which the branching ratio is larger than unity.

Acceptance times efficiency extrapolated as a function of c&tau;_&gamma;d for the &mu;DPJ channel (SR_&mu;), obtained for the different FRVZ MC signal mass points.

Acceptance times efficiency extrapolated as a function of c&tau;_&gamma;d for the low E_T^miss caloDPJ channel (SR_c^L), obtained for the different FRVZ MC signal mass points.

Acceptance times efficiency extrapolated as a function of c&tau;_&gamma;d for the high E_T^miss caloDPJ channel (SR_c^H), obtained for the different FRVZ MC signal mass points.

Observed (solid line) and expected (dashed line) 95% CL upper limits on B(H&rarr;&nbsp;2&gamma;_d+X) for FRVZ processes with a 125&nbsp;GeV Higgs boson as a function of dark photon mean proper decay length for the ggF, WH and VBF analyses. The full combination is shown as solid or dashed black lines for a dark photon mass of 17&nbsp;MeV.

Observed (solid line) and expected (dashed line) 95% CL upper limits on B(H&rarr;&nbsp;2&gamma;_d+X) for FRVZ processes with a 125&nbsp;GeV Higgs boson as a function of dark photon mean proper decay length for the ggF, WH and VBF analyses. The full combination is shown as solid or dashed black lines for a dark photon mass of 50&nbsp;MeV.

Observed (solid line) and expected (dashed line) 95% CL upper limits on B(H&rarr;&nbsp;2&gamma;_d+X) for FRVZ processes with a 125&nbsp;GeV Higgs boson as a function of dark photon mean proper decay length for the ggF, WH and VBF analyses. The full combination is shown as solid or dashed black lines for a dark photon mass of 400&nbsp;MeV.

Observed (solid line) and expected (dashed line) 95% CL upper limits on B(H&rarr;&nbsp;2&gamma;_d+X) for FRVZ processes with a 125&nbsp;GeV Higgs boson as a function of dark photon mean proper decay length for the ggF, WH and VBF analyses. The full combination is shown as solid or dashed black lines for a dark photon mass of 900&nbsp;MeV.

Observed (solid line) and expected (dashed line) 95% CL upper limits on B(H&rarr;&nbsp;2&gamma;_d+X) for FRVZ processes with a 125&nbsp;GeV Higgs boson as a function of dark photon mean proper decay length for the ggF, WH and VBF analyses. The full combination is shown as solid or dashed black lines for a dark photon mass of 2&nbsp;GeV.

Observed (solid line) and expected (dashed line) 95% CL upper limits on B(H&rarr;&nbsp;2&gamma;_d+X) for FRVZ processes with a 125&nbsp;GeV Higgs boson as a function of dark photon mean proper decay length for the ggF, WH and VBF analyses. The full combination is shown as solid or dashed black lines for a dark photon mass of 6&nbsp;GeV.

Observed (solid line) and expected (dashed line) 95% CL upper limits on B(H&rarr;&nbsp;2&gamma;_d+X) for FRVZ processes with a 125&nbsp;GeV Higgs boson as a function of dark photon mean proper decay length for the ggF, WH and VBF analyses. The full combination is shown as solid or dashed black lines for a dark photon mass of 15&nbsp;GeV.

Observed 95% CL upper limits on B(H&rarr;&nbsp;2&gamma;_d+X) for different &gamma;_d masses and a 125&nbsp;GeV Higgs boson, as a function of the dark-photon mean proper decay length c&tau;. The limits are shown for the SR_&mu; search channel, assuming an FRVZ signal model. The hatched band denotes the region in which the branching ratio is larger than unity.

Observed 95% CL upper limits on B(H&rarr;&nbsp;2&gamma;_d+X) for different &gamma;_d masses and a 125&nbsp;GeV Higgs boson, as a function of the dark-photon mean proper decay length c&tau;. The limits are shown for the SR_c^L search channel, assuming an FRVZ signal model. The hatched band denotes the region in which the branching ratio is larger than unity.

Observed 95% CL upper limits on B(H&rarr;&nbsp;2&gamma;_d+X) for different &gamma;_d masses and a 125&nbsp;GeV Higgs boson, as a function of the dark-photon mean proper decay length c&tau;. The limits are shown for the SR_c^H search channel, assuming an FRVZ signal model. The hatched band denotes the region in which the branching ratio is larger than unity.

Observed 95% CL upper limits on B(H&rarr;&nbsp;2&gamma;_d+X) for different &gamma;_d masses and a 125&nbsp;GeV Higgs boson, as a function of the dark-photon mean proper decay length c&tau;. The limits are shown for all search channels combined, assuming an FRVZ signal model. The hatched band denotes the region in which the branching ratio is larger than unity.

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

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

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

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

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

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

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

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

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

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

Expected (dashed line) value of $-2\ln\Lambda$ as a function of $\kappa_{2V}$, when all other coupling modifiers are fixed to their SM predictions.

Likelihood observed contours at 68% CL (solid line) and 95% CL (dashed line) in the $\kappa_{\lambda}$, $\kappa_{2V}$ parameter space, when all other coupling modifiers are fixed to their SM predictions. The best-fit value, denoted by a cross in the plot, corresponds to the very first entry in the table.

Likelihood expected contours at 68% CL (teal shaded region) and 95% CL (yellow shaded region) in the $\kappa_{\lambda}$, $\kappa_{2V}$ parameter space, when all other coupling modifiers are fixed to their SM predictions.In the plot, the SM prediction is indicated by the star.

Likelihood observed contours at 68% CL (solid line) and 95% CL (dashed line) in the $c_{gghh}$ versus $c_{hhh}$ HEFT parameter space, with the remaining coefficient fixed to its SM value. The best-fit value, denoted by a cross in the plot, corresponds to the very first entry in the table.

Likelihood expected contours at 68% CL (teal shaded region) 95% CL (yellow shaded region) in the $c_{gghh}$ versus $c_{hhh}$ HEFT parameter space, with the remaining coefficient fixed to its SM value. In the plot, the SM prediction is indicated by the star.

Likelihood observed contours at 68% CL (solid line) and 95% CL (dashed line) in the $c_{tthh}$ versus $c_{hhh}$ HEFT parameter space, with the remaining coefficient fixed to its SM value. The best-fit value, denoted by a cross in the plot, corresponds to the very first entry in the table.

Likelihood exptected contours at 68% CL (teal shaded region) and 95% CL (yellow shaded region) in the $c_{tthh}$ versus $c_{hhh}$ HEFT parameter space, with the remaining coefficient fixed to its SM value. In the plot, the SM prediction is indicated by the star.

The observed (filled circles) and expected (hollow circles) 95% CL upper limits on the $HH$ ggF production cross-section in the Standard Model and for seven HEFT benchmark points. The teal and yellow colored bands indicate the $\pm 1\sigma$ and $\pm 2\sigma$ variations on the expected limit due to statistical and systematic uncertainties. The predicted cross-sections of each of the models under consideration are shown by the red crosses. The contribution from VBF production to the total $HH$ production cross-section is neglected.

Likelihood observed contours at 68% CL (solid line) and 95% CL (dashed line) in the $c_{{H}\boxed{}}$ versus $c_{H}$ SMEFT parameter space, with the remaining coefficient fixed to its SM value. The best-fit value, denoted by a cross in the plot, corresponds to the very first entry in the table.

Likelihood expected contours at 68% CL (teal shaded region) 95% CL (yellow shaded region) in the $c_{{H}\boxed{}}$ versus $c_{H}$ SMEFT parameter space, with the remaining coefficient fixed to its SM value. In the plot, the SM prediction is indicated by the star.

The acceptance times efficiency for the signal ggF $HH$ process as a function of the coupling modifier $\kappa_{\lambda}$ in each analysis category. The other coupling modifiers affecting ggF $HH$ production are fixed to their SM predictions. The bands indicate the simulation statistical uncertainty.

The acceptance times efficiency for the signal VBF $HH$ process as a function of the coupling modifier $\kappa_{\lambda}$ in each analysis category. When varying $\kappa_{\lambda}$, the other coupling modifiers affecting the VBF $HH$ production mode are set to their SM predictions. The bands indicate the simulation statistical uncertainty.

The acceptance times efficiency for the signal VBF $HH$ process as a function of the coupling modifier $\kappa_{2V}$ in each analysis category. When varying $\kappa_{2V}$, the other coupling modifiers affecting the VBF $HH$ production mode are set to their SM predictions. The bands indicate the simulation statistical uncertainty.

Expected yields of the signal $HH$ process as a function of the coupling modifier $\kappa_{\lambda}$ after applying the analysis preselection and in each analysis category after the final selection. The $HH$ yield is obtained considering both the $ggF$ and $VBF$ contributions. The other coupling modifiers affecting $HH$ production are fixed to their SM predictions. The bands indicate the simulation statistical uncertainty.

The acceptance times efficiency for the signal ggF $HH$ process in each analysis category as a function of the $c_{hhh}$ HEFT coefficients. The dashed lines denote values that are excluded at 95% CL. The bottom panels show the efficiency of the sum of all analysis categories.

The acceptance times efficiency for the signal ggF $HH$ process in each analysis category as a function of the $c_{tthh}$ HEFT coefficients. The dashed lines denote values that are excluded at 95% CL. The bottom panels show the efficiency of the sum of all analysis categories.

The acceptance times efficiency for the signal ggF $HH$ process in each analysis category as a function of the $c_{gghh}$ HEFT coefficients. The dashed lines denote values that are excluded at 95% CL. The bottom panels show the efficiency of the sum of all analysis categories.

The acceptance times efficiency for the signal ggF $HH$ process in each analysis category as a function of the $c_{H}$ SMEFT coefficients. The dashed lines denote values that are excluded at 95% CL. The bottom panels show the efficiency of the sum of all analysis categories.

The acceptance times efficiency for the signal ggF $HH$ process in each analysis category as a function of the $c_{{H}\boxed{}}$ SMEFT coefficients. The dashed lines denote values that are excluded at 95% CL. The bottom panels show the efficiency of the sum of all analysis categories.

The yield of the signal ggF $HH$ process in each analysis category as a function of the $c_{hhh}$ HEFT coefficients. The dashed lines denote values that are excluded at 95% CL. The bottom panels show the efficiency of the sum of all analysis categories.

The yield of the signal ggF $HH$ process in each analysis category as a function of the $c_{tthh}$ HEFT coefficients. The dashed lines denote values that are excluded at 95% CL. The bottom panels show the efficiency of the sum of all analysis categories.

The yield of the signal ggF $HH$ process in each analysis category as a function of the $c_{gghh}$ HEFT coefficients. The dashed lines denote values that are excluded at 95% CL. The bottom panels show the efficiency of the sum of all analysis categories.

The yield of the signal ggF $HH$ process in each analysis category as a function of the $c_{H}$ SMEFT coefficients. The dashed lines denote values that are excluded at 95% CL. The bottom panels show the efficiency of the sum of all analysis categories.

The yield of the signal ggF $HH$ process in each analysis category as a function of the $c_{{H}\boxed{}}$ SMEFT coefficients. The dashed lines denote values that are excluded at 95% CL. The bottom panels show the efficiency of the sum of all analysis categories.

Distributions of the diphoton invariant mass for events in data (black dots with error bars) compared to the sum of the expected signal and backgrounds (histograms) in the low mass 1 region.

Distributions of the diphoton invariant mass for events in data (black dots with error bars) compared to the sum of the expected signal and backgrounds (histograms) in the low mass 2 region.

Distributions of the diphoton invariant mass for events in data (black dots with error bars) compared to the sum of the expected signal and backgrounds (histograms) in the low mass 3 region.

Distributions of the diphoton invariant mass for events in data (black dots with error bars) compared to the sum of the expected signal and backgrounds (histograms) in the low mass 4 region.

Distributions of the diphoton invariant mass for events in data (black dots with error bars) compared to the sum of the expected signal and backgrounds (histograms) in the high mass 1 region.

Distributions of the diphoton invariant mass for events in data (black dots with error bars) compared to the sum of the expected signal and backgrounds (histograms) in the high mass 2 region.

Distributions of the diphoton invariant mass for events in data (black dots with error bars) compared to the sum of the expected signal and backgrounds (histograms) in the high mass 3 region.

Observed (solid line) value of $-2\ln\Lambda$ as a function of the $c_{hhh}$ HEFT coefficients when all other coupling modifiers are fixed to the SM value

Expected (dashed line) value of $-2\ln\Lambda$ as a function of the $c_{hhh}$ HEFT coefficients when all other coupling modifiers are fixed to the SM value

Observed (solid line) value of $-2\ln\Lambda$ as a function of the $c_{gghh}$ HEFT coefficients when all other coupling modifiers are fixed to the SM value

Expected (dashed line) value of $-2\ln\Lambda$ as a function of the $c_{gghh}$ HEFT coefficients when all other coupling modifiers are fixed to the SM value

Observed (solid line) value of $-2\ln\Lambda$ as a function of the $c_{tthh}$ HEFT coefficients when all other coupling modifiers are fixed to the SM value

Expected (dashed line) value of $-2\ln\Lambda$ as a function of the $c_{tthh}$ HEFT coefficients when all other coupling modifiers are fixed to the SM value

Observed (solid line) value of $-2\ln\Lambda$ as a function of the $c_{H}$ SMEFT coefficients when all other coupling modifiers are fixed to the SM value.

Expected (dashed line) value of $-2\ln\Lambda$ as a function of the $c_{H}$ SMEFT coefficients when all other coupling modifiers are fixed to the SM value.

Observed (solid line) value of $-2\ln\Lambda$ as a function of the $c_{{H}\boxed{}}$ SMEFT coefficients when all other coupling modifiers are fixed to the SM value.

Expected (dashed line) value of $-2\ln\Lambda$ as a function of the $c_{{H}\boxed{}}$ SMEFT coefficients when all other coupling modifiers are fixed to the SM value.

Summary of the expected (blue) and observed (orange) one-dimensional constraints at 68% (solid error bars) and 95% (dashed error bars) CL on the coefficients of selected HEFT (top) and SMEFT (bottom) operators describing Higgs boson interactions affecting $HH$ production through gluon--gluon fusion. The results are obtained from one dimensional scans of the profile log-likelihood assuming that all other Wilson coefficients are fixed to their SM values. The contribution from VBF $HH$ production is neglected.

Expected and observed 95% CL upper limits on the branching ratio of the Higgs boson decay to $Za$ times the branching ratio $a $->$ \gamma \gamma$ as a function of the $a$ particle mass in the merged ($m_a \le 2$ GeV) and the resolved ($m_a > 2$ GeV) categories. The figure uses $pp$ collision data at $\sqrt{s}=13$ TeV corresponding to 139 fb$^{-1}$.

ATLAS observed 95% CL exclusion contours limits in terms of the ALP mass and its effective coupling to photons, $|C_{\gamma\gamma}|/\Lambda$, for different values of the Higgs coupling to $Za$, $|C_{Zh}|/\Lambda$. The figure uses $pp$ collision data at $\sqrt{s}=13$ TeV corresponding to 139 fb$^{-1}$. The value 100 in the tables is presentational, denoting the upper edge of the plot.