The expected 95% CL exclusion contour (-1$\sigma$) for a simplified model of dark-matter production involving an axial-vector operator, Dirac DM and couplings $g_{q}$ = 0.25, $g_{\chi}$ = 1 and $g_{l}$ = 0 as a function of the dark-matter mass $m_{\chi}$ and the mediator mass $m_{\mathrm{med}}$. The plane under the limit curve is excluded.

The expected 95% CL exclusion contour for a simplified model of dark-matter production involving an axial-vector operator, Dirac DM and couplings $g_{q}$ = 0.25, $g_{\chi}$ = 1 and $g_{l}$ = 0 as a function of the dark-matter mass $m_{\chi}$ and the mediator mass $m_{\mathrm{med}}$. The plane under the limit curve is excluded.

The observed 95% CL exclusion contour for a simplified model of dark-matter production involving an axial-vector operator, Dirac DM and couplings $g_{q}$ = 0.1, $g_{\chi}$ = 1 and $g_{l}$ = 0.1 as a function of the dark-matter mass $m_{\chi}$ and the mediator mass $m_{\mathrm{med}}$. The plane under the limit curve is excluded.

The expected 95% CL exclusion contour (+1$\sigma$) for a simplified model of dark-matter production involving an axial-vector operator, Dirac DM and couplings $g_{q}$ = 0.1, $g_{\chi}$ = 1 and $g_{l}$ = 0.1 as a function of the dark-matter mass $m_{\chi}$ and the mediator mass $m_{\mathrm{med}}$. The plane under the limit curve is excluded.

The expected 95% CL exclusion contour (-1$\sigma$) for a simplified model of dark-matter production involving an axial-vector operator, Dirac DM and couplings $g_{q}$ = 0.1, $g_{\chi}$ = 1 and $g_{l}$ = 0.1 as a function of the dark-matter mass $m_{\chi}$ and the mediator mass $m_{\mathrm{med}}$. The plane under the limit curve is excluded.

The expected 95% CL exclusion contour for a simplified model of dark-matter production involving an axial-vector operator, Dirac DM and couplings $g_{q}$ = 0.1, $g_{\chi}$ = 1 and $g_{l}$ = 0.1 as a function of the dark-matter mass $m_{\chi}$ and the mediator mass $m_{\mathrm{med}}$. The plane under the limit curve is excluded.

The observed 95% CL exclusion contour for a simplified model of dark-matter production involving a vector operator with couplings $g_{q}$ = 0.25, $g_{\chi}$ =1 and $g_{l}$ = 0 as a function of the dark-matter mass $m_{\chi}$ and the mediator mass $m_{\mathrm{med}}$. The plane under the limit curve is excluded.

The expected 95% CL exclusion contour ($+1\sigma$) for a simplified model of dark-matter production involving a vector operator with couplings $g_{q}$ = 0.25, $g_{\chi}$ =1 and $g_{l}$ = 0 as a function of the dark-matter mass $m_{\chi}$ and the mediator mass $m_{\mathrm{med}}$. The plane under the limit curve is excluded.

The expected 95% CL exclusion contour ($-1\sigma$) for a simplified model of dark-matter production involving a vector operator with couplings $g_{q}$ = 0.25, $g_{\chi}$ =1 and $g_{l}$ = 0 as a function of the dark-matter mass $m_{\chi}$ and the mediator mass $m_{\mathrm{med}}$. The plane under the limit curve is excluded.

The expected 95% CL exclusion contour for a simplified model of dark-matter production involving a vector operator with couplings $g_{q}$ = 0.25, $g_{\chi}$ =1 and $g_{l}$ = 0 as a function of the dark-matter mass $m_{\chi}$ and the mediator mass $m_{\mathrm{med}}$. The plane under the limit curve is excluded.

The observed 95% CL exclusion contour for a simplified model of dark-matter production involving for a vector operator with couplings $g_{q}$ = 0.1, $g_{\chi}$ = 1 and $g_{l}$ = 0.01 as a function of the dark-matter mass $m_{\chi}$ and the mediator mass $m_{\mathrm{med}}$. The plane under the limit curve is excluded.

The expected 95% CL exclusion contour ($+1\sigma$) for a simplified model of dark-matter production involving for a vector operator with couplings $g_{q}$ = 0.1, $g_{\chi}$ = 1 and $g_{l}$ = 0.01 as a function of the dark-matter mass $m_{\chi}$ and the mediator mass $m_{\mathrm{med}}$. The plane under the limit curve is excluded.

The expected 95% CL exclusion contour ($-1\sigma$) for a simplified model of dark-matter production involving for a vector operator with couplings $g_{q}$ = 0.1, $g_{\chi}$ = 1 and $g_{l}$ = 0.01 as a function of the dark-matter mass $m_{\chi}$ and the mediator mass $m_{\mathrm{med}}$. The plane under the limit curve is excluded.

The expected 95% CL exclusion contour for a simplified model of dark-matter production involving for a vector operator with couplings $g_{q}$ = 0.1, $g_{\chi}$ = 1 and $g_{l}$ = 0.01 as a function of the dark-matter mass $m_{\chi}$ and the mediator mass $m_{\mathrm{med}}$. The plane under the limit curve is excluded.

The 90% CL exclusion limit on the $\chi$-proton scattering cross section in a simplifed model of dark-matter production involving an axial-vector operator, Dirac DM and couplings $g_{q}$ = 0.25, $g_{\chi}$ = 1 and $g_{l}$ = 0 as a function of the dark-matter mass $m_{\chi}$.

The 90% CL exclusion limit on the $\chi$-nucleon scattering cross section in a simplifed model of dark-matter production involving a vector operator, Dirac DM and couplings $g_{q}$ = 0.25, $g_{\chi}$ = 1 and $g_{l}$ = 0 as a function of the dark-matter mass $m_{\chi}$.

The observed and expected 95% CL limits on M* for a dimension-7 operator EFT model with a contact interaction of type $\gamma\gamma\chi\chi$ as a function of dark-matter mass $m_{\chi}$.

The observed and expected limit at 95% CL on the production cross section of a $Z\gamma$ resonance as a function of its mass.

The observed 95% CL upper limits on signal strength $\mu$, the ratio of the experimental limit to the predicted signal cross section, for a simplified model of dark matter production involving an axial-vector operator, Dirac DM and couplings $g_{q}$ = 0.25 and $g_{\chi}$ = 1 as a function of the DM and the mediator particle masses. The bound on $\mu$ only applies for choices of couplings that yield the same kinematic distributions as the benchmark model.

Acceptance, in %, for a simplified model of dark matter production involving an axial-vector operator, Dirac DM and couplings $g_{q}$= 0.25 and $g_{\chi}$ = 1 for various $m_{\chi}$ and $m_{\textrm{med}}$ values. It is constant as a function of $m_{\chi}$ for a fixed $m_{\textrm{med}}$ in the region $m_{\textrm{med}}>2m_{\chi}$.

Fiducial reconstruction efficiencies in the three inclusive signal regions for a simplified model of dark matter production involving an axial-vector operator, Dirac DM and couplings $g_{q}$= 0.25 and $g_{\chi}$ = 1 for various $m_{\chi}$ and $m_{\textrm{med}}$ values. It is constant as a function of $m_{\chi}$ for a fixed $m_{\textrm{med}}$ in the region $m_{\textrm{med}}>2m_{\chi}$.

The ratios (μ) of the 95% C.L. upper limits on the combined s→ W^±W^∓ and s→ ZZ cross section to simplified model expectations for the m_Z'=1 TeV scenario, for various m_s hypotheses. The observed limits (solid line) are consistent with the expectation under the SM-only hypothesis (dashed line) within uncertainties (filled band), except for a small excess for m_s=160 GeV, discussed in the text.

The ratios (μ) of the 95% C.L. upper limits on the combined s→ W^±W^∓ and s→ ZZ cross section to simplified model expectations for the m_Z'=1.7 TeV scenario, for various m_s hypotheses. The observed limits (solid line) are consistent with the expectation under the SM-only hypothesis (dashed line) within uncertainties (filled band), except for a small excess for m_s=160 GeV, discussed in the text.

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

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

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

SM background post-fit yields stacked in each SR and CR category and E_T^miss bin and data overlaid with the maximum likelihood estimators set to the conditional values of the combined signal and control region fit. The hatched uncertainty band shown includes simulation statistics uncertainties, experimental systematic uncertainties, and V+jets theory modelling systematic uncertainties. Pre-fit uncertainties cover differences between the data and pre-fit background prediction.

Cumulative efficiencies for the merged category for signal samples with m_s=160 GeV (a), m_s=235 GeV (b) and m_s=310 GeV (c), each with m_Z'=1 TeV. The dark Higgs candidate selection includes stringent jet substructure requirements and typically at most one candidate is present in signal events. Here, Δ φ_{jets_1,2,3 E_T^miss} is the smallest azimuthal angle between the E_T^miss and any of the three highest-p_T (leading) small-R jets.

Cumulative efficiencies for the intermediate category for signal samples with m_s=160 GeV (a), m_s=235 GeV (b) and m_s=310 GeV (c), each with m_Z'=1 TeV. The TAR+Comb algorithm reconstructs the dark Higgs candidate from a TAR jet with m^TAR>60 GeV that is supplemented by up to two additional small-R jets within ΔR_cone=2.5 of the TAR jet. Here, Δ φ_{jets_1,2,3 E_T^miss} is the smallest azimuthal angle between the E_T^miss and any of the three highest-p_T (leading) small-R jets. For details see text.

The product of acceptance and efficiency (A × ϵ), defined as the number of signal events satisfying the full set of selection criteria in the merged or intermediate signal regions, divided by the total number of generated signal events, for the s(W^±W^∓) dark Higgs signal points with dark Higgs boson mass m_s and Z' boson mass m_Z'.

The product of acceptance and efficiency (A × ϵ), defined as the number of signal events satisfying the full set of selection criteria in the merged or intermediate signal regions, divided by the total number of generated signal events, for the s(ZZ) dark Higgs signal points with dark Higgs boson mass m_s and Z' boson mass m_Z'.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Observed exclusion contour at 95&#37; C.L. for the dark Higgs model in the (m_Z', m_s) plane for g_q=0.25, g_&chi;=1, m_&chi;=200 GeV, and sin&theta;=0.01.

Expected exclusion contour at 95&#37; C.L. for the dark Higgs model in the (m_Z', m_s) plane for g_q=0.25, g_&chi;=1, m_&chi;=200 GeV, and sin&theta;=0.01.

Expected+1&sigma; exclusion contour at 95&#37; C.L. for the dark Higgs model in the (m_Z', m_s) plane for g_q=0.25, g_&chi;=1, m_&chi;=200 GeV, and sin&theta;=0.01.

Expected-1&sigma; exclusion contour at 95&#37; C.L. for the dark Higgs model in the (m_Z', m_s) plane for g_q=0.25, g_&chi;=1, m_&chi;=200 GeV, and sin&theta;=0.01.

Expected+2&sigma; exclusion contour at 95&#37; C.L. for the dark Higgs model in the (m_Z', m_s) plane for g_q=0.25, g_&chi;=1, m_&chi;=200 GeV, and sin&theta;=0.01.

Expected-2&sigma; exclusion contour at 95&#37; C.L. for the dark Higgs model in the (m_Z', m_s) plane for g_q=0.25, g_&chi;=1, m_&chi;=200 GeV, and sin&theta;=0.01.

Observed upper limits at 95&#37; C.L. on &sigma;(pp &rarr; s &chi;&chi;) &times; B(s &rarr; W^&pm; W^&mp;) for m_Z'=0.5 TeV as a function of m_s. The expected limits, varied up and down by one and two standard deviations, are shown as green and yellow bands, respectively. The observed and expected limits are compared to the theoretical LO cross section for the &sigma;(pp &rarr; s &chi;&chi;) &times; B(s &rarr; W^&pm; W^&mp;) process for m_Z'=0.5 TeV, shown in dashed blue.

Observed upper limits at 95&#37; C.L. on &sigma;(pp &rarr; s &chi;&chi;) &times; B(s &rarr; W^&pm; W^&mp;) for m_Z'=1 TeV as a function of m_s. The expected limits, varied up and down by one and two standard deviations, are shown as green and yellow bands, respectively. The observed and expected limits are compared to the theoretical LO cross section for the &sigma;(pp &rarr; s &chi;&chi;) &times; B(s &rarr; W^&pm; W^&mp;) process for m_Z'=1 TeV, shown in dashed blue.

Observed upper limits at 95&#37; C.L. on &sigma;(pp &rarr; s &chi;&chi;) &times; B(s &rarr; W^&pm; W^&mp;) for m_Z'=1.7 TeV as a function of m_s. The expected limits, varied up and down by one and two standard deviations, are shown as green and yellow bands, respectively. The observed and expected limits are compared to the theoretical LO cross section for the &sigma;(pp &rarr; s &chi;&chi;) &times; B(s &rarr; W^&pm; W^&mp;) process for m_Z'=1.7 TeV, shown in dashed blue.

Observed upper limits at 95&#37; C.L. on &sigma;(pp &rarr; s &chi;&chi;) &times; B(s &rarr; W^&pm; W^&mp;) for m_Z'=2.1 TeV as a function of m_s. The expected limits, varied up and down by one and two standard deviations, are shown as green and yellow bands, respectively. The observed and expected limits are compared to the theoretical LO cross section for the &sigma;(pp &rarr; s &chi;&chi;) &times; B(s &rarr; W^&pm; W^&mp;) process for m_Z'=2.1 TeV, shown in dashed blue.

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

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

Cumulative efficiencies in the merged category for three representative dark Higgs signal scenarios with g_q=0.25, g_&chi;=1.0, sin&theta;=0.01, m_Z' = 1 TeV, and m_&chi;=200 GeV considering s&rarr;W(&ell;&nu;)W(qq) decays only.

Cumulative efficiencies in the resolved category for three representative dark Higgs signal scenarios with g_q=0.25, g_&chi;=1.0, sin&theta;=0.01, m_Z' = 1 TeV, and m_&chi;=200 GeV considering s&rarr;W(&ell;&nu;)W(qq) decays only.

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

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

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