Normalized differential distributions of the $\Delta R (\gamma,\mathrm{tt})$. The nominal MC prediction used to compare the experimental results to is obtained with Madgraph5 at NLO in QCD for photons from the production part of the process and Madgraph5 at LO in QCD for photons from the decay part of the process. The alternative prediction is obtained with Madgraph5 at NLO in QCD for photons from the production part of the process and a POWHEG+Pythia $\mathrm{tt}$ simulation at NLO in QCD for photons from the decay part of the process.

Absolute differential distributions of the min. $\Delta R (\gamma,\mathrm{t})$. The nominal MC prediction used to compare the experimental results to is obtained with Madgraph5 at NLO in QCD for photons from the production part of the process and Madgraph5 at LO in QCD for photons from the decay part of the process. The alternative prediction is obtained with Madgraph5 at NLO in QCD for photons from the production part of the process and a POWHEG+Pythia $\mathrm{tt}$ simulation at NLO in QCD for photons from the decay part of the process.

Normalized differential distributions of the min. $\Delta R (\gamma,\mathrm{t})$. The nominal MC prediction used to compare the experimental results to is obtained with Madgraph5 at NLO in QCD for photons from the production part of the process and Madgraph5 at LO in QCD for photons from the decay part of the process. The alternative prediction is obtained with Madgraph5 at NLO in QCD for photons from the production part of the process and a POWHEG+Pythia $\mathrm{tt}$ simulation at NLO in QCD for photons from the decay part of the process.

Absolute differential distributions of the $m(\mathrm{tt})$. The nominal MC prediction used to compare the experimental results to is obtained with Madgraph5 at NLO in QCD for photons from the production part of the process and Madgraph5 at LO in QCD for photons from the decay part of the process. The alternative prediction is obtained with Madgraph5 at NLO in QCD for photons from the production part of the process and a POWHEG+Pythia $\mathrm{tt}$ simulation at NLO in QCD for photons from the decay part of the process.

Normalized differential distributions of the $m(\mathrm{tt})$. The nominal MC prediction used to compare the experimental results to is obtained with Madgraph5 at NLO in QCD for photons from the production part of the process and Madgraph5 at LO in QCD for photons from the decay part of the process. The alternative prediction is obtained with Madgraph5 at NLO in QCD for photons from the production part of the process and a POWHEG+Pythia $\mathrm{tt}$ simulation at NLO in QCD for photons from the decay part of the process.

Absolute differential distributions of the leading lepton $p_{\mathrm{T}}$. The nominal MC prediction used to compare the experimental results to is obtained with Madgraph5 at NLO in QCD for photons from the production part of the process and Madgraph5 at LO in QCD for photons from the decay part of the process. The alternative prediction is obtained with Madgraph5 at NLO in QCD for photons from the production part of the process and a POWHEG+Pythia $\mathrm{tt}$ simulation at NLO in QCD for photons from the decay part of the process. The theory predictions are computed at fixed order, at NLO in QCD, as described in Section 9.2 of the paper.

Normalized differential distributions of the leading lepton $p_{\mathrm{T}}$. The nominal MC prediction used to compare the experimental results to is obtained with Madgraph5 at NLO in QCD for photons from the production part of the process and Madgraph5 at LO in QCD for photons from the decay part of the process. The alternative prediction is obtained with Madgraph5 at NLO in QCD for photons from the production part of the process and a POWHEG+Pythia $\mathrm{tt}$ simulation at NLO in QCD for photons from the decay part of the process. The theory predictions are computed at fixed order, at NLO in QCD, as described in Section 9.2 of the paper.

Absolute differential distributions of the photon $p_{\mathrm{T}}$. The nominal MC prediction used to compare the experimental results to is obtained with Madgraph5 at NLO in QCD for photons from the production part of the process and Madgraph5 at LO in QCD for photons from the decay part of the process. The alternative prediction is obtained with Madgraph5 at NLO in QCD for photons from the production part of the process and a POWHEG+Pythia $\mathrm{tt}$ simulation at NLO in QCD for photons from the decay part of the process. The theory predictions are computed at fixed order, at NLO in QCD, as described in Section 9.2 of the paper.

Normalized differential distributions of the photon $p_{\mathrm{T}}$. The nominal MC prediction used to compare the experimental results to is obtained with Madgraph5 at NLO in QCD for photons from the production part of the process and Madgraph5 at LO in QCD for photons from the decay part of the process. The alternative prediction is obtained with Madgraph5 at NLO in QCD for photons from the production part of the process and a POWHEG+Pythia $\mathrm{tt}$ simulation at NLO in QCD for photons from the decay part of the process. The theory predictions are computed at fixed order, at NLO in QCD, as described in Section 9.2 of the paper.

Absolute differential distributions of the $\Delta \phi (\ell,\ell)$. The nominal MC prediction used to compare the experimental results to is obtained with Madgraph5 at NLO in QCD for photons from the production part of the process and Madgraph5 at LO in QCD for photons from the decay part of the process. The alternative prediction is obtained with Madgraph5 at NLO in QCD for photons from the production part of the process and a POWHEG+Pythia $\mathrm{tt}$ simulation at NLO in QCD for photons from the decay part of the process. The theory predictions are computed at fixed order, at NLO in QCD, as described in Section 9.2 of the paper.

Normalized differential distributions of the $\Delta \phi (\ell,\ell)$. The nominal MC prediction used to compare the experimental results to is obtained with Madgraph5 at NLO in QCD for photons from the production part of the process and Madgraph5 at LO in QCD for photons from the decay part of the process. The alternative prediction is obtained with Madgraph5 at NLO in QCD for photons from the production part of the process and a POWHEG+Pythia $\mathrm{tt}$ simulation at NLO in QCD for photons from the decay part of the process. The theory predictions are computed at fixed order, at NLO in QCD, as described in Section 9.2 of the paper.

Absolute differential distributions of the ratio between the cross sections of $\mathrm{tt\gamma}$ and $\mathrm{tt}$, as a function of the leading top quark $p_{\mathrm{T}}$. The nominal MC prediction used to compare the experimental results to is obtained with Madgraph5 at NLO in QCD for photons from the production part of the process and Madgraph5 at LO in QCD for photons from the decay part of the process. The alternative prediction is obtained with Madgraph5 at NLO in QCD for photons from the production part of the process and a POWHEG+Pythia $\mathrm{tt}$ simulation at NLO in QCD for photons from the decay part of the process.

Absolute differential distributions of the ratio between the cross sections of $\mathrm{tt\gamma}$ and $\mathrm{tt}$, as a function of the leading lepton $p_{\mathrm{T}}$. The nominal MC prediction used to compare the experimental results to is obtained with Madgraph5 at NLO in QCD for photons from the production part of the process and Madgraph5 at LO in QCD for photons from the decay part of the process. The alternative prediction is obtained with Madgraph5 at NLO in QCD for photons from the production part of the process and a POWHEG+Pythia $\mathrm{tt}$ simulation at NLO in QCD for photons from the decay part of the process. The theory predictions are computed at fixed order, at NLO in QCD, as described in Section 9.2 of the paper.

Correlation matrix of the total uncertainty in the absolute differential cross section as a function of the leading top quark $p_{\mathrm{T}}$.

Correlation matrix of the statistical uncertainty in the absolute differential cross section as a function of the leading top quark $p_{\mathrm{T}}$.

Correlation matrix of the total uncertainty in the absolute differential cross section as a function of the $\Delta R (\gamma,\mathrm{tt})$.

Correlation matrix of the statistical uncertainty in the absolute differential cross section as a function of the $\Delta R (\gamma,\mathrm{tt})$.

Correlation matrix of the total uncertainty in the absolute differential cross section as a function of the min. $\Delta R (\gamma,\mathrm{t})$.

Correlation matrix of the statistical uncertainty in the absolute differential cross section as a function of the min. $\Delta R (\gamma,\mathrm{t})$.

Correlation matrix of the total uncertainty in the absolute differential cross section as a function of the $m(\mathrm{tt})$.

Correlation matrix of the statistical uncertainty in the absolute differential cross section as a function of the $m(\mathrm{tt})$.

Correlation matrix of the total uncertainty in the absolute differential cross section as a function of the leading lepton $p_{\mathrm{T}}$.

Correlation matrix of the statistical uncertainty in the absolute differential cross section as a function of the leading lepton $p_{\mathrm{T}}$.

Correlation matrix of the total uncertainty in the absolute differential cross section as a function of the photon $p_{\mathrm{T}}$.

Correlation matrix of the statistical uncertainty in the absolute differential cross section as a function of the photon $p_{\mathrm{T}}$.

Correlation matrix of the total uncertainty in the absolute differential cross section as a function of the $\Delta \phi (\ell,\ell)$.

Correlation matrix of the statistical uncertainty in the absolute differential cross section as a function of the $\Delta \phi (\ell,\ell)$.

Correlation matrix of the total uncertainty in the absolute differential $\mathrm{tt\gamma}$ / $\mathrm{tt}$ cross section ratio as a function of the leading top $p_{\mathrm{T}}$.

Correlation matrix of the statistical uncertainty in the absolute differential $\mathrm{tt\gamma}$ / $\mathrm{tt}$ cross section ratio as a function of the leading top $p_{\mathrm{T}}$.

Correlation matrix of the total uncertainty in the absolute differential $\mathrm{tt\gamma}$ / $\mathrm{tt}$ cross section ratio as a function of the leading lepton $p_{\mathrm{T}}$.

Correlation matrix of the statistical uncertainty in the absolute differential $\mathrm{tt\gamma}$ / $\mathrm{tt}$ cross section ratio as a function of the leading lepton $p_{\mathrm{T}}$.

Observed differential dijet spectrum using full Run-2 data.

The observed 95% CL upper limits on the product of the cross section, branching fraction, and acceptance for quark-quark type dijet resonances.

The observed 95% CL upper limits on the product of the cross section, branching fraction, and acceptance for quark-gluon type dijet resonances.

The observed 95% CL upper limits on the product of the cross section, branching fraction, and acceptance for gluon-gluon type dijet resonances.

The observed and expected 95% CL upper limits on the universal quark coupling $g_{q}'$ as a function of resonance mass for a leptophobic Z' resonance that only couples to quarks.

Predictions of a leading order (LO) QCD simulation, normalized to an integrated luminosity of 138 fb$^{-1}$. The number of events are examined within bins of the four-jet mass and the ratio $\alpha$, which is the average dijet mass divided by the four-jet mass.

The 68% probability contour in the $m_{\mathrm{4j}}$ vs. $\overline{m}_{\mathrm{2j}}$ plane from a signal simulation of a diquark with a width of 1.5% and a mass of 8.4 TeV, decaying to a pair of vector-like quarks, each with a mass of 2.1 TeV.

The 68% probability contour in the $m_{\mathrm{4j}}$ vs. $\overline{m}_{\mathrm{2j}}$ plane from a signal simulation of a diquark with a width of 5% and a mass of 8.4 TeV, decaying to a pair of vector-like quarks, each with a mass of 2.1 TeV.

The 68% probability contour in the $m_{\mathrm{4j}}$ vs. $\overline{m}_{\mathrm{2j}}$ plane from a signal simulation of a diquark with a width of 10% and a mass of 8.4 TeV, decaying to a pair of vector-like quarks, each with a mass of 2.1 TeV.

The 68% probability contour in the $m_{\mathrm{4j}}$ vs. $\alpha$ plane from a signal simulation of a diquark with a width of 1.5% and a mass of 8.4 TeV, decaying to a pair of vector-like quarks, each with a mass of 2.1 TeV.

The 68% probability contour in the $m_{\mathrm{4j}}$ vs. $\alpha$ plane from a signal simulation of a diquark with a width of 5% and a mass of 8.4 TeV, decaying to a pair of vector-like quarks, each with a mass of 2.1 TeV.

The 68% probability contour in the $m_{\mathrm{4j}}$ vs. $\alpha$ plane from a signal simulation of a diquark with a width of 10% and a mass of 8.4 TeV, decaying to a pair of vector-like quarks, each with a mass of 2.1 TeV.

Signal differential distributions as a function of four-jet mass for $\alpha_{\mathrm{true}}$ = 0.25, diquark masses of 2, 5, 8.6 TeV and various widths, for all $\alpha$ bins inclusively. The integral of each distribution has been normalized to unity.

The product of acceptance, $A$, and efficiency, $\varepsilon$, of a resonant signal with $\alpha_{\mathrm{true}}$ = 0.25 vs. the diquark mass for various diquark widths, and for all $\alpha$ bins inclusively. The acceptance is defined as the fraction of generated events passing the kinematic selection criteria, while the efficiency is the fraction of signal events satisfying $m_{\mathrm{4j}} > 1.6$ TeV. We also show the signal acceptance alone in the curves where $\varepsilon = 1$.

The four-jet mass distribution in data for 0.22 < $\alpha$ < 0.24, fitted with three background-only functions (Dijet-3p, PowExp-3p and ModDijet-3p), each with three free parameters. Examples of predicted diquark resonances with $\alpha_{\mathrm{true}}$ = 0.25, $M_{\mathrm{S}}$ = 8.6 TeV, and $\Gamma/M_{\mathrm{S}}$ = 1.5%, 10% are also shown, with cross sections equal to the observed upper limits at 95% confidence level.

The four-jet mass distribution in data for 0.24 < $\alpha$ < 0.26, fitted with three background-only functions (Dijet-3p, PowExp-3p and ModDijet-3p), each with three free parameters. Examples of predicted diquark resonances with $\alpha_{\mathrm{true}}$ = 0.25, $M_{\mathrm{S}}$ = 8.6 TeV, and $\Gamma/M_{\mathrm{S}}$ = 1.5%, 10% are also shown, with cross sections equal to the observed upper limits at 95% confidence level.

The four-jet mass distribution in data for 0.26 < $\alpha$ < 0.28, fitted with three background-only functions (Dijet-3p, PowExp-3p and ModDijet-3p), each with three free parameters. Examples of predicted diquark resonances with $\alpha_{\mathrm{true}}$ = 0.25, $M_{\mathrm{S}}$ = 8.6 TeV and $\alpha_{\mathrm{true}}$ = 0.29, $M_{\mathrm{S}}$ = 3.6 TeV, each shown for widths of $\Gamma/M_{\mathrm{S}}$ = 1.5% and 10% are also included, with cross sections equal to the observed upper limits at 95% confidence level.

The four-jet mass distribution in data for 0.28 < $\alpha$ < 0.30, fitted with three background-only functions (Dijet-3p, PowExp-3p and ModDijet-3p), each with three free parameters. Examples of predicted diquark resonances with $\alpha_{\mathrm{true}}$ = 0.25, $M_{\mathrm{S}}$ = 8.6 TeV and $\alpha_{\mathrm{true}}$ = 0.29, $M_{\mathrm{S}}$ = 3.6 TeV, each shown for widths of $\Gamma/M_{\mathrm{S}}$ = 1.5% and 10% are also included, with cross sections equal to the observed upper limits at 95% confidence level.

The four-jet mass distribution in data for 0.30 < $\alpha$ < 0.32, fitted with three background-only functions (Dijet-3p, PowExp-3p and ModDijet-3p), each with three free parameters. Examples of predicted diquark resonances with $\alpha_{\mathrm{true}}$ = 0.25, $M_{\mathrm{S}}$ = 8.6 TeV and $\alpha_{\mathrm{true}}$ = 0.29, $M_{\mathrm{S}}$ = 3.6 TeV, each shown for widths of $\Gamma/M_{\mathrm{S}}$ = 1.5% and 10% are also included, with cross sections equal to the observed upper limits at 95% confidence level.

The four-jet mass distribution in data for 0.32 < $\alpha$ < 0.34, fitted with three background-only functions (Dijet-3p, PowExp-3p and ModDijet-3p), each with three free parameters. Examples of predicted diquark resonances with $\alpha_{\mathrm{true}}$ = 0.25, $M_{\mathrm{S}}$ = 8.6 TeV, and $\Gamma/M_{\mathrm{S}}$ = 1.5%, 10% are also shown, with cross sections equal to the observed upper limits at 95% confidence level.

The inclusive four-jet mass distribution in data for $\alpha$ > 0.10, fitted with three background-only functions (Dijet-5p, PowExp-5p and ModDijet-5p), each with five free parameters. Examples of predicted diquark resonances with $\alpha_{\mathrm{true}}$ = 0.25, $M_{\mathrm{S}}$ = 8.6 TeV and $\alpha_{\mathrm{true}}$ = 0.29, $M_{\mathrm{S}}$ = 3.6 TeV, each shown for widths of $\Gamma/M_{\mathrm{S}}$ = 1.5% and 10% are also included, with cross sections equal to the observed upper limits at 95% confidence level.

The observed 95% CL upper limits on the product of the cross section, branching fraction, and acceptance for resonant production of paired dijet resonances, X, with $\alpha_{\mathrm{true}} = M_{\mathrm{X}} / M_{\mathrm{Y}} = 0.25$ and width of the initial resonance Y equal to 1.5%. The corresponding expected limits and their variations at the 1 and 2 standard deviation (s.d.) levels are also included. Limits are compared to predictions for scalar $\mathrm{S}_{\mathrm{uu}}$ and $\mathrm{S}_{\mathrm{dd}}$ diquarks with couplings to pairs of up and down quarks, $y_{\mathrm{uu}}$ and $y_{\mathrm{dd}}$, and to pairs of vector-like quarks, $y_{\chi}$ and $y_{\omega}$, set appropriately in order to generate a mediator width equal to 1.5%.

The observed 95% CL upper limits on the product of the cross section, branching fraction, and acceptance for resonant production of paired dijet resonances, X, with $\alpha_{\mathrm{true}} = M_{\mathrm{X}} / M_{\mathrm{Y}} = 0.25$ and width of the initial resonance Y equal to 5%. The corresponding expected limits and their variations at the 1 and 2 standard deviation (s.d.) levels are also included. Limits are compared to predictions for scalar $\mathrm{S}_{\mathrm{uu}}$ and $\mathrm{S}_{\mathrm{dd}}$ diquarks with couplings to pairs of up and down quarks, $y_{\mathrm{uu}}$ and $y_{\mathrm{dd}}$, and to pairs of vector-like quarks, $y_{\chi}$ and $y_{\omega}$, set appropriately in order to generate a mediator width equal to 5%.

The observed 95% CL upper limits on the product of the cross section, branching fraction, and acceptance for resonant production of paired dijet resonances, X, with $\alpha_{\mathrm{true}} = M_{\mathrm{X}} / M_{\mathrm{Y}} = 0.25$ and width of the initial resonance Y equal to 10%. The corresponding expected limits and their variations at the 1 and 2 standard deviation (s.d.) levels are also included. Limits are compared to predictions for scalar $\mathrm{S}_{\mathrm{uu}}$ and $\mathrm{S}_{\mathrm{dd}}$ diquarks with couplings to pairs of up and down quarks, $y_{\mathrm{uu}}$ and $y_{\mathrm{dd}}$, and to pairs of vector-like quarks, $y_{\chi}$ and $y_{\omega}$, set appropriately in order to generate a mediator width equal to 10%.

The observed 95% CL upper limits on the product of the cross section, branching fraction, and acceptance for resonant production of paired dijet resonances, X, with $\alpha_{\mathrm{true}} = M_{\mathrm{X}} / M_{\mathrm{Y}} = 0.11$ and width of the initial resonance Y equal to 10%. The corresponding expected limits and their variations at the 1 and 2 standard deviation (s.d.) levels are also included. Limits are compared to predictions for scalar $\mathrm{S}_{\mathrm{uu}}$ and $\mathrm{S}_{\mathrm{dd}}$ diquarks with couplings to pairs of up and down quarks, $y_{\mathrm{uu}}$ and $y_{\mathrm{dd}}$, and to pairs of vector-like quarks, $y_{\chi}$ and $y_{\omega}$, set appropriately in order to generate a mediator width equal to 10%.

The observed 95% CL upper limits on the product of the cross section, branching fraction, and acceptance for resonant production of paired dijet resonances, X, with $\alpha_{\mathrm{true}} = M_{\mathrm{X}} / M_{\mathrm{Y}} = 0.13$ and width of the initial resonance Y equal to 10%. The corresponding expected limits and their variations at the 1 and 2 standard deviation (s.d.) levels are also included. Limits are compared to predictions for scalar $\mathrm{S}_{\mathrm{uu}}$ and $\mathrm{S}_{\mathrm{dd}}$ diquarks with couplings to pairs of up and down quarks, $y_{\mathrm{uu}}$ and $y_{\mathrm{dd}}$, and to pairs of vector-like quarks, $y_{\chi}$ and $y_{\omega}$, set appropriately in order to generate a mediator width equal to 10%.

The observed 95% CL upper limits on the product of the cross section, branching fraction, and acceptance for resonant production of paired dijet resonances, X, with $\alpha_{\mathrm{true}} = M_{\mathrm{X}} / M_{\mathrm{Y}} = 0.15$ and width of the initial resonance Y equal to 10%. The corresponding expected limits and their variations at the 1 and 2 standard deviation (s.d.) levels are also included. Limits are compared to predictions for scalar $\mathrm{S}_{\mathrm{uu}}$ and $\mathrm{S}_{\mathrm{dd}}$ diquarks with couplings to pairs of up and down quarks, $y_{\mathrm{uu}}$ and $y_{\mathrm{dd}}$, and to pairs of vector-like quarks, $y_{\chi}$ and $y_{\omega}$, set appropriately in order to generate a mediator width equal to 10%.

The observed 95% CL upper limits on the product of the cross section, branching fraction, and acceptance for resonant production of paired dijet resonances, X, with $\alpha_{\mathrm{true}} = M_{\mathrm{X}} / M_{\mathrm{Y}} = 0.17$ and width of the initial resonance Y equal to 10%. The corresponding expected limits and their variations at the 1 and 2 standard deviation (s.d.) levels are also included. Limits are compared to predictions for scalar $\mathrm{S}_{\mathrm{uu}}$ and $\mathrm{S}_{\mathrm{dd}}$ diquarks with couplings to pairs of up and down quarks, $y_{\mathrm{uu}}$ and $y_{\mathrm{dd}}$, and to pairs of vector-like quarks, $y_{\chi}$ and $y_{\omega}$, set appropriately in order to generate a mediator width equal to 10%.

The observed 95% CL upper limits on the product of the cross section, branching fraction, and acceptance for resonant production of paired dijet resonances, X, with $\alpha_{\mathrm{true}} = M_{\mathrm{X}} / M_{\mathrm{Y}} = 0.19$ and width of the initial resonance Y equal to 10%. The corresponding expected limits and their variations at the 1 and 2 standard deviation (s.d.) levels are also included. Limits are compared to predictions for scalar $\mathrm{S}_{\mathrm{uu}}$ and $\mathrm{S}_{\mathrm{dd}}$ diquarks with couplings to pairs of up and down quarks, $y_{\mathrm{uu}}$ and $y_{\mathrm{dd}}$, and to pairs of vector-like quarks, $y_{\chi}$ and $y_{\omega}$, set appropriately in order to generate a mediator width equal to 10%.

The observed 95% CL upper limits on the product of the cross section, branching fraction, and acceptance for resonant production of paired dijet resonances, X, with $\alpha_{\mathrm{true}} = M_{\mathrm{X}} / M_{\mathrm{Y}} = 0.21$ and width of the initial resonance Y equal to 10%. The corresponding expected limits and their variations at the 1 and 2 standard deviation (s.d.) levels are also included. Limits are compared to predictions for scalar $\mathrm{S}_{\mathrm{uu}}$ and $\mathrm{S}_{\mathrm{dd}}$ diquarks with couplings to pairs of up and down quarks, $y_{\mathrm{uu}}$ and $y_{\mathrm{dd}}$, and to pairs of vector-like quarks, $y_{\chi}$ and $y_{\omega}$, set appropriately in order to generate a mediator width equal to 10%.

The observed 95% CL upper limits on the product of the cross section, branching fraction, and acceptance for resonant production of paired dijet resonances, X, with $\alpha_{\mathrm{true}} = M_{\mathrm{X}} / M_{\mathrm{Y}} = 0.23$ and width of the initial resonance Y equal to 10%. The corresponding expected limits and their variations at the 1 and 2 standard deviation (s.d.) levels are also included. Limits are compared to predictions for scalar $\mathrm{S}_{\mathrm{uu}}$ and $\mathrm{S}_{\mathrm{dd}}$ diquarks with couplings to pairs of up and down quarks, $y_{\mathrm{uu}}$ and $y_{\mathrm{dd}}$, and to pairs of vector-like quarks, $y_{\chi}$ and $y_{\omega}$, set appropriately in order to generate a mediator width equal to 10%.

The observed 95% CL upper limits on the product of the cross section, branching fraction, and acceptance for resonant production of paired dijet resonances, X, with $\alpha_{\mathrm{true}} = M_{\mathrm{X}} / M_{\mathrm{Y}} = 0.27$ and width of the initial resonance Y equal to 10%. The corresponding expected limits and their variations at the 1 and 2 standard deviation (s.d.) levels are also included. Limits are compared to predictions for scalar $\mathrm{S}_{\mathrm{uu}}$ and $\mathrm{S}_{\mathrm{dd}}$ diquarks with couplings to pairs of up and down quarks, $y_{\mathrm{uu}}$ and $y_{\mathrm{dd}}$, and to pairs of vector-like quarks, $y_{\chi}$ and $y_{\omega}$, set appropriately in order to generate a mediator width equal to 10%.

The observed 95% CL upper limits on the product of the cross section, branching fraction, and acceptance for resonant production of paired dijet resonances, X, with $\alpha_{\mathrm{true}} = M_{\mathrm{X}} / M_{\mathrm{Y}} = 0.29$ and width of the initial resonance Y equal to 10%. The corresponding expected limits and their variations at the 1 and 2 standard deviation (s.d.) levels are also included. Limits are compared to predictions for scalar $\mathrm{S}_{\mathrm{uu}}$ and $\mathrm{S}_{\mathrm{dd}}$ diquarks with couplings to pairs of up and down quarks, $y_{\mathrm{uu}}$ and $y_{\mathrm{dd}}$, and to pairs of vector-like quarks, $y_{\chi}$ and $y_{\omega}$, set appropriately in order to generate a mediator width equal to 10%.

The observed 95% CL upper limits on the product of the cross section, branching fraction, and acceptance for resonant production of paired dijet resonances, X, with $\alpha_{\mathrm{true}} = M_{\mathrm{X}} / M_{\mathrm{Y}} = 0.31$ and width of the initial resonance Y equal to 10%. The corresponding expected limits and their variations at the 1 and 2 standard deviation (s.d.) levels are also included. Limits are compared to predictions for scalar $\mathrm{S}_{\mathrm{uu}}$ and $\mathrm{S}_{\mathrm{dd}}$ diquarks with couplings to pairs of up and down quarks, $y_{\mathrm{uu}}$ and $y_{\mathrm{dd}}$, and to pairs of vector-like quarks, $y_{\chi}$ and $y_{\omega}$, set appropriately in order to generate a mediator width equal to 10%.

The observed 95% CL upper limits on the product of the cross section, branching fraction, and acceptance for resonant production of paired dijet resonances, X, with $\alpha_{\mathrm{true}} = M_{\mathrm{X}} / M_{\mathrm{Y}} = 0.33$ and width of the initial resonance Y equal to 10%. The corresponding expected limits and their variations at the 1 and 2 standard deviation (s.d.) levels are also included. Limits are compared to predictions for scalar $\mathrm{S}_{\mathrm{uu}}$ and $\mathrm{S}_{\mathrm{dd}}$ diquarks with couplings to pairs of up and down quarks, $y_{\mathrm{uu}}$ and $y_{\mathrm{dd}}$, and to pairs of vector-like quarks, $y_{\chi}$ and $y_{\omega}$, set appropriately in order to generate a mediator width equal to 10%.

The observed 95% CL upper limits on the product of the cross section, branching fraction, and acceptance for resonant production of paired dijet resonances, X, with $\alpha_{\mathrm{true}} = M_{\mathrm{X}} / M_{\mathrm{Y}} = 0.42$ and width of the initial resonance Y equal to 10%. The corresponding expected limits and their variations at the 1 and 2 standard deviation (s.d.) levels are also included. Limits are compared to predictions for scalar $\mathrm{S}_{\mathrm{uu}}$ and $\mathrm{S}_{\mathrm{dd}}$ diquarks with couplings to pairs of up and down quarks, $y_{\mathrm{uu}}$ and $y_{\mathrm{dd}}$, and to pairs of vector-like quarks, $y_{\chi}$ and $y_{\omega}$, set appropriately in order to generate a mediator width equal to 10%.

The observed 95% CL upper limits on the product of the cross section, branching fraction, and acceptance for resonant production of paired dijet resonances, X, with $\alpha_{\mathrm{true}} = M_{\mathrm{X}} / M_{\mathrm{Y}} = 0.11$ and widths of the initial resonance Y equal to 1.5, 5, and 10%. Limits are compared to predictions for scalar $\mathrm{S}_{\mathrm{uu}}$ and $\mathrm{S}_{\mathrm{dd}}$ diquarks with couplings to pairs of up and down quarks, $y_{\mathrm{uu}}$ and $y_{\mathrm{dd}}$, and to pairs of vector-like quarks, $y_{\chi}$ and $y_{\omega}$, set appropriately in order to generate the corresponding widths.

The observed 95% CL upper limits on the product of the cross section, branching fraction, and acceptance for resonant production of paired dijet resonances, X, with $\alpha_{\mathrm{true}} = M_{\mathrm{X}} / M_{\mathrm{Y}} = 0.13$ and widths of the initial resonance Y equal to 1.5, 5, and 10%. Limits are compared to predictions for scalar $\mathrm{S}_{\mathrm{uu}}$ and $\mathrm{S}_{\mathrm{dd}}$ diquarks with couplings to pairs of up and down quarks, $y_{\mathrm{uu}}$ and $y_{\mathrm{dd}}$, and to pairs of vector-like quarks, $y_{\chi}$ and $y_{\omega}$, set appropriately in order to generate the corresponding widths.

The observed 95% CL upper limits on the product of the cross section, branching fraction, and acceptance for resonant production of paired dijet resonances, X, with $\alpha_{\mathrm{true}} = M_{\mathrm{X}} / M_{\mathrm{Y}} = 0.15$ and widths of the initial resonance Y equal to 1.5, 5, and 10%. Limits are compared to predictions for scalar $\mathrm{S}_{\mathrm{uu}}$ and $\mathrm{S}_{\mathrm{dd}}$ diquarks with couplings to pairs of up and down quarks, $y_{\mathrm{uu}}$ and $y_{\mathrm{dd}}$, and to pairs of vector-like quarks, $y_{\chi}$ and $y_{\omega}$, set appropriately in order to generate the corresponding widths.

The observed 95% CL upper limits on the product of the cross section, branching fraction, and acceptance for resonant production of paired dijet resonances, X, with $\alpha_{\mathrm{true}} = M_{\mathrm{X}} / M_{\mathrm{Y}} = 0.17$ and widths of the initial resonance Y equal to 1.5, 5, and 10%. Limits are compared to predictions for scalar $\mathrm{S}_{\mathrm{uu}}$ and $\mathrm{S}_{\mathrm{dd}}$ diquarks with couplings to pairs of up and down quarks, $y_{\mathrm{uu}}$ and $y_{\mathrm{dd}}$, and to pairs of vector-like quarks, $y_{\chi}$ and $y_{\omega}$, set appropriately in order to generate the corresponding widths.

The observed 95% CL upper limits on the product of the cross section, branching fraction, and acceptance for resonant production of paired dijet resonances, X, with $\alpha_{\mathrm{true}} = M_{\mathrm{X}} / M_{\mathrm{Y}} = 0.19$ and widths of the initial resonance Y equal to 1.5, 5, and 10%. Limits are compared to predictions for scalar $\mathrm{S}_{\mathrm{uu}}$ and $\mathrm{S}_{\mathrm{dd}}$ diquarks with couplings to pairs of up and down quarks, $y_{\mathrm{uu}}$ and $y_{\mathrm{dd}}$, and to pairs of vector-like quarks, $y_{\chi}$ and $y_{\omega}$, set appropriately in order to generate the corresponding widths.

The observed 95% CL upper limits on the product of the cross section, branching fraction, and acceptance for resonant production of paired dijet resonances, X, with $\alpha_{\mathrm{true}} = M_{\mathrm{X}} / M_{\mathrm{Y}} = 0.21$ and widths of the initial resonance Y equal to 1.5, 5, and 10%. Limits are compared to predictions for scalar $\mathrm{S}_{\mathrm{uu}}$ and $\mathrm{S}_{\mathrm{dd}}$ diquarks with couplings to pairs of up and down quarks, $y_{\mathrm{uu}}$ and $y_{\mathrm{dd}}$, and to pairs of vector-like quarks, $y_{\chi}$ and $y_{\omega}$, set appropriately in order to generate the corresponding widths.

The observed 95% CL upper limits on the product of the cross section, branching fraction, and acceptance for resonant production of paired dijet resonances, X, with $\alpha_{\mathrm{true}} = M_{\mathrm{X}} / M_{\mathrm{Y}} = 0.23$ and widths of the initial resonance Y equal to 1.5, 5, and 10%. Limits are compared to predictions for scalar $\mathrm{S}_{\mathrm{uu}}$ and $\mathrm{S}_{\mathrm{dd}}$ diquarks with couplings to pairs of up and down quarks, $y_{\mathrm{uu}}$ and $y_{\mathrm{dd}}$, and to pairs of vector-like quarks, $y_{\chi}$ and $y_{\omega}$, set appropriately in order to generate the corresponding widths.

The observed 95% CL upper limits on the product of the cross section, branching fraction, and acceptance for resonant production of paired dijet resonances, X, with $\alpha_{\mathrm{true}} = M_{\mathrm{X}} / M_{\mathrm{Y}} = 0.27$ and widths of the initial resonance Y equal to 1.5, 5, and 10%. Limits are compared to predictions for scalar $\mathrm{S}_{\mathrm{uu}}$ and $\mathrm{S}_{\mathrm{dd}}$ diquarks with couplings to pairs of up and down quarks, $y_{\mathrm{uu}}$ and $y_{\mathrm{dd}}$, and to pairs of vector-like quarks, $y_{\chi}$ and $y_{\omega}$, set appropriately in order to generate the corresponding widths.

The observed 95% CL upper limits on the product of the cross section, branching fraction, and acceptance for resonant production of paired dijet resonances, X, with $\alpha_{\mathrm{true}} = M_{\mathrm{X}} / M_{\mathrm{Y}} = 0.29$ and widths of the initial resonance Y equal to 1.5, 5, and 10%. Limits are compared to predictions for scalar $\mathrm{S}_{\mathrm{uu}}$ and $\mathrm{S}_{\mathrm{dd}}$ diquarks with couplings to pairs of up and down quarks, $y_{\mathrm{uu}}$ and $y_{\mathrm{dd}}$, and to pairs of vector-like quarks, $y_{\chi}$ and $y_{\omega}$, set appropriately in order to generate the corresponding widths.

The observed 95% CL upper limits on the product of the cross section, branching fraction, and acceptance for resonant production of paired dijet resonances, X, with $\alpha_{\mathrm{true}} = M_{\mathrm{X}} / M_{\mathrm{Y}} = 0.31$ and widths of the initial resonance Y equal to 1.5, 5, and 10%. Limits are compared to predictions for scalar $\mathrm{S}_{\mathrm{uu}}$ and $\mathrm{S}_{\mathrm{dd}}$ diquarks with couplings to pairs of up and down quarks, $y_{\mathrm{uu}}$ and $y_{\mathrm{dd}}$, and to pairs of vector-like quarks, $y_{\chi}$ and $y_{\omega}$, set appropriately in order to generate the corresponding widths.

The observed 95% CL upper limits on the product of the cross section, branching fraction, and acceptance for resonant production of paired dijet resonances, X, with $\alpha_{\mathrm{true}} = M_{\mathrm{X}} / M_{\mathrm{Y}} = 0.33$ and widths of the initial resonance Y equal to 1.5, 5, and 10%. Limits are compared to predictions for scalar $\mathrm{S}_{\mathrm{uu}}$ and $\mathrm{S}_{\mathrm{dd}}$ diquarks with couplings to pairs of up and down quarks, $y_{\mathrm{uu}}$ and $y_{\mathrm{dd}}$, and to pairs of vector-like quarks, $y_{\chi}$ and $y_{\omega}$, set appropriately in order to generate the corresponding widths.

The observed 95% CL upper limits on the product of the cross section, branching fraction, and acceptance for resonant production of paired dijet resonances, X, with $\alpha_{\mathrm{true}} = M_{\mathrm{X}} / M_{\mathrm{Y}} = 0.42$ and widths of the initial resonance Y equal to 1.5, 5, and 10%. Limits are compared to predictions for scalar $\mathrm{S}_{\mathrm{uu}}$ and $\mathrm{S}_{\mathrm{dd}}$ diquarks with couplings to pairs of up and down quarks, $y_{\mathrm{uu}}$ and $y_{\mathrm{dd}}$, and to pairs of vector-like quarks, $y_{\chi}$ and $y_{\omega}$, set appropriately in order to generate the corresponding widths.

Observed local $p$-value for a four-jet resonance, Y, decaying to a pair of dijet resonances, X, with $\alpha_{\mathrm{true}} = M_{\mathrm{X}}/M_{\mathrm{Y}}$ = 0.25, and various widths of Y superimposed.

Observed local $p$-value for a four-jet resonance, Y, decaying to a pair of dijet resonances, X, with $\alpha_{\mathrm{true}} = M_{\mathrm{X}}/M_{\mathrm{Y}}$ = 0.29, and various widths of Y superimposed.

The table presents the cumulative cutflow for a signal with $M_{\mathrm{S}} = 2.0$ TeV, $M_{\chi} = 0.5$ TeV and different width hypotheses ($\Gamma/M_{\mathrm{S}} =$ 1.5, 5, and 10%). Each row corresponds to the number of signal events that survive all cuts up to and including the one listed. The percentage in parentheses shows the efficiency of the current cut alone, defined as the ratio of the number of events that survive all cuts up to and including this one to the number of events that survived all previous cuts.

The table presents the cumulative cutflow for a signal with $M_{\mathrm{S}} = 5.0$ TeV, $M_{\chi} = 1.25$ TeV and different width hypotheses ($\Gamma/M_{\mathrm{S}} =$ 1.5, 5, and 10%). Each row corresponds to the number of signal events that survive all cuts up to and including the one listed. The percentage in parentheses shows the efficiency of the current cut alone, defined as the ratio of the number of events that survive all cuts up to and including this one to the number of events that survived all previous cuts.

The table presents the cumulative cutflow for a signal with $M_{\mathrm{S}} = 8.6$ TeV, $M_{\chi} = 2.15$ TeV and different width hypotheses ($\Gamma/M_{\mathrm{S}} =$ 1.5, 5, and 10%). Each row corresponds to the number of signal events that survive all cuts up to and including the one listed. The percentage in parentheses shows the efficiency of the current cut alone, defined as the ratio of the number of events that survive all cuts up to and including this one to the number of events that survived all previous cuts.

The observed and expected 95% CL upper limits on the universal quark coupling $g_{q}$ as a function of resonance mass for a vector mediator of interactions between quarks and dark matter.

The observed and expected 95% CL upper limits on the universal quark coupling $g_{q}'$ as a function of resonance mass for a leptophobic Z' resonance that only couples to quarks.