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

Observed (solid line) value of $-2\ln\Lambda$ as a function of $\kappa_{2V}$ for the combined fit, when all other coupling modifiers are fixed to their SM predictions.

Expected (dashed line) value of $-2\ln\Lambda$ as a function of $\kappa_{2V}$ for the combined fit, 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 contours at 68% (solid line) and 95% (dashed line) CL in the ($c_{hhh}$, $c_{gghh}$) parameter space, when all other Wilson coefficients are fixed to their SM values. The corresponding expected contours are shown by the inner and outer shaded regions. The SM prediction is indicated by the star, while the observed best-fit value is denoted by the black cross. The best-fit value corresponds to the very first entry in the table.

Likelihood contours at 68% (solid line) and 95% (dashed line) CL in the ($c_{hhh}$, $c_{gghh}$) parameter space, when all other Wilson coefficients are fixed to their SM values. The corresponding expected contours are shown by the inner and outer shaded regions. The SM prediction is indicated by the star, while the observed best-fit value is denoted by the black cross.

Likelihood contours at 68% (solid line) and 95% (dashed line) CL in the ($c_{hhh}$, $c_{tthh}$) parameter space, when all other Wilson coefficients are fixed to their SM values. The corresponding expected contours are shown by the inner and outer shaded regions. The SM prediction is indicated by the star, while the observed best-fit value is denoted by the black cross. The best-fit value corresponds to the very first entry in the table.

Likelihood contours at 68% (solid line) and 95% (dashed line) CL in the ($c_{hhh}$, $c_{tthh}$) parameter space, when all other Wilson coefficients are fixed to their SM values. The corresponding expected contours are shown by the inner and outer shaded regions. The SM prediction is indicated by the star, while the observed best-fit value is denoted by the black cross.

Likelihood contours at 68% (solid line) and 95% (dashed line) CL in the ($c_{H}$, $c_{H◻}$) parameter space, when all other Wilson coefficients are fixed to their SM values. The corresponding expected contours are shown by the inner and outer shaded regions. The SM prediction is indicated by the star, while the observed best-fit value is denoted by the black cross. The best-fit value corresponds to the very first entry in the table.

Likelihood contours at 68% (solid line) and 95% (dashed line) CL in the ($c_{H}$, $c_{H◻}$) parameter space, when all other Wilson coefficients are fixed to their SM values. The corresponding expected contours are shown by the inner and outer shaded regions. The SM prediction is indicated by the star, while the observed best-fit value is denoted by the black cross.

The acceptance times efficiency [in %] for the signal ggF $HH$ process as a function of the coupling modifier $\kappa_{\lambda}$ in each analysis category for the $\tau_{\mathrm{had}}\tau_{\mathrm{had}}$ channel. The other coupling modifiers affecting ggF $HH$ production are fixed to their SM predictions.

The acceptance times efficiency [in %] for the signal ggF $HH$ process as a function of the coupling modifier $\kappa_{\lambda}$ in each analysis category for the $\tau_{\mathrm{lep}}\tau_{\mathrm{had}}$ SLT channel. The other coupling modifiers affecting ggF $HH$ production are fixed to their SM predictions.

The acceptance times efficiency [in %] for the signal ggF $HH$ process as a function of the coupling modifier $\kappa_{\lambda}$ in each analysis category for the $\tau_{\mathrm{lep}}\tau_{\mathrm{had}}$ LTT channel. The other coupling modifiers affecting ggF $HH$ production are fixed to their SM predictions.

The acceptance times efficiency [in %] for the signal VBF $HH$ process as a function of the coupling modifier $\kappa_{\lambda}$ in each analysis category for the $\tau_{\mathrm{had}}\tau_{\mathrm{had}}$ channel. The other coupling modifiers affecting VBF $HH$ production are fixed to their SM predictions.

The acceptance times efficiency [in %] for the signal VBF $HH$ process as a function of the coupling modifier $\kappa_{\lambda}$ in each analysis category for the $\tau_{\mathrm{lep}}\tau_{\mathrm{had}}$ SLT channel. The other coupling modifiers affecting VBF $HH$ production are fixed to their SM predictions.

The acceptance times efficiency [in %] for the signal VBF $HH$ process as a function of the coupling modifier $\kappa_{\lambda}$ in each analysis category for the $\tau_{\mathrm{lep}}\tau_{\mathrm{had}}$ LTT channel. The other coupling modifiers affecting VBF $HH$ production are fixed to their SM predictions.

The acceptance times efficiency [in %] for the signal VBF $HH$ process as a function of the coupling modifier $\kappa_{2V}$ in each analysis category for the $\tau_{\mathrm{had}}\tau_{\mathrm{had}}$ channel. The other coupling modifiers affecting VBF $HH$ production are fixed to their SM predictions.

The acceptance times efficiency [in %] for the signal VBF $HH$ process as a function of the coupling modifier $\kappa_{2V}$ in each analysis category for the $\tau_{\mathrm{lep}}\tau_{\mathrm{had}}$ SLT channel. The other coupling modifiers affecting VBF $HH$ production are fixed to their SM predictions.

The acceptance times efficiency [in %] for the signal VBF $HH$ process as a function of the coupling modifier $\kappa_{2V}$ in each analysis category for the $\tau_{\mathrm{lep}}\tau_{\mathrm{had}}$ LTT channel. The other coupling modifiers affecting VBF $HH$ production are fixed to their SM predictions.

Expected (dashed line) value of $-2\ln\Lambda$ as a function of $\kappa_{\lambda}$ for the fit to the $\tau_{\mathrm{had}}\tau_{\mathrm{had}}$ channel, when all other coupling modifiers are fixed to their SM predictions.

Expected (dashed line) value of $-2\ln\Lambda$ as a function of $\kappa_{\lambda}$ for the fit to the $\tau_{\mathrm{lep}}\tau_{\mathrm{had}}$ channel, when all other coupling modifiers are fixed to their SM predictions.

Observed (solid line) value of $-2\ln\Lambda$ as a function of $\kappa_{\lambda}$ for the fit to the $\tau_{\mathrm{had}}\tau_{\mathrm{had}}$ channel, when all other coupling modifiers are fixed to their SM predictions.

Observed (solid line) value of $-2\ln\Lambda$ as a function of $\kappa_{\lambda}$ for the fit to the $\tau_{\mathrm{lep}}\tau_{\mathrm{had}}$ channel, when all other coupling modifiers are fixed to their SM predictions.

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

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

Observed (solid line) value of $-2\ln\Lambda$ as a function of $\kappa_{2V}$ for the fit to the $\tau_{\mathrm{had}}\tau_{\mathrm{had}}$ channel, when all other coupling modifiers are fixed to their SM predictions.

Observed (solid line) value of $-2\ln\Lambda$ as a function of $\kappa_{2V}$ for the fit to the $\tau_{\mathrm{lep}}\tau_{\mathrm{had}}$ channel, when all other coupling modifiers are fixed to their SM predictions.

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 CLs values in the High mA SR, mA vs ma signal grid.

Observed CLs values in the High mA SR, mA vs ma signal grid.

Expected CLs values in the Low mA SR, mA vs ma signal grid.

Observed CLs values in the High mA SR, mA vs ma signal grid.

CLs+b values in the Low mA SR, mA vs tanB signal grid.

CLs+b values in the High mA SR, mA vs ma signal grid.

CLs+b values in the Low mA SR, mA vs ma signal grid.

Cut flow of the 2HDM+a signal points, gluon–gluon fusion production, Low mA SR. tanB = 1, $sin\theta$ = 0.35. The first two entries in the tables are number of raw MC events, third entry is theoretical prediction, and all other lines include the correct weights. Note that during the generation Higgs boson’s branching ratio to taus has been set to 1. An additional factor of 0.0627 is used to account for that, starting from the ‘Initial’ entry.

Cut flow of the 2HDM+a signal points, gluon–gluon fusion production, High mA SR. tanB = 1, $sin\theta$ = 0.35. The first two entries in the tables are number of raw MC events, third entry is theoretical prediction, and all other lines include the correct weights. Note that during the generation Higgs boson’s branching ratio to taus has been set to 1. An additional factor of 0.0627 is used to account for that, starting from the ‘Initial’ entry.

Cut flow of the 2HDM+a signal points, bb annihilation production, Low mA SR. tanB = 1, $sin\theta$ = 0.35. The first two entries in the tables are number of raw MC events, third entry is theoretical prediction, and all other lines include the correct weights. Note that during the generation Higgs boson’s branching ratio to taus has been set to 1. An additional factor of 0.0627 is used to account for that, starting from the ‘Initial’ entry.

Cut flow of the 2HDM+a signal points, bb annihilation production, High mA SR. tanB = 1, $sin\theta$ = 0.35. The first two entries in the tables are number of raw MC events, third entry is theoretical prediction, and all other lines include the correct weights. Note that during the generation Higgs boson’s branching ratio to taus has been set to 1. An additional factor of 0.0627 is used to account for that, starting from the ‘Initial’ entry.

A comparison of the observed and expected yields in the four bins of the Low mA SR.

A comparison of the observed and expected yields in the two bins of the High mA SR.

Expected exclusion contours at 95% CL as a function of mA and ma.

Observed exclusion contours at 95% CL as a function of mA and ma.

Expected +- 1sigma exclusion contours at 95% CL as a function of mA and ma.

Expected exclusion contours at 95% CL as a function of mA and ma.

Observed exclusion contours at 95% CL as a function of mA and ma.

Expected +- 1sigma exclusion contours at 95% CL as a function of mA and ma.

Acceptance, High mA SR, mA vs tanB grid, 400-750 GeV, bb prod

Acceptance, High mA SR, mA vs tanB grid, >750 GeV, bb prod

Acceptance, Low mA SR, mA vs tanB grid, 100-250 GeV, bb prod

Acceptance, Low mA SR, mA vs tanB grid, 250-400 GeV, bb prod

Acceptance, Low mA SR, mA vs tanB grid, 400-550 GeV, bb prod

Acceptance, Low mA SR, mA vs tanB grid, >550 GeV, bb prod

Acceptance, High mA SR, mA vs ma grid, 400-750 GeV, bb prod

Acceptance, High mA SR, mA vs ma grid, >750 GeV, bb prod

Acceptance, Low mA SR, mA vs ma grid, 100-250 GeV, bb prod

Acceptance, Low mA SR, mA vs ma grid, 250-400 GeV, bb prod

Acceptance, Low mA SR, mA vs ma grid, 400-550 GeV, bb prod

Acceptance, Low mA SR, mA vs ma grid, >550 GeV, bb prod

Acceptance, High mA SR, mA vs tanB grid, 400-750 GeV, ggF prod

Acceptance, High mA SR, mA vs tanB grid, >750 GeV, ggF prod

Acceptance, Low mA SR, mA vs tanB grid, 100-250 GeV, ggF prod

Acceptance, Low mA SR, mA vs tanB grid, 250-400 GeV, ggF prod

Acceptance, Low mA SR, mA vs tanB grid, 400-550 GeV, ggF prod

Acceptance, Low mA SR, mA vs tanB grid, >550 GeV, ggF prod

Acceptance, High mA SR, mA vs ma grid, 400-750 GeV, ggF prod

Acceptance, High mA SR, mA vs ma grid, >750 GeV, ggF prod

Acceptance, Low mA SR, mA vs ma grid, 100-250 GeV, ggF prod

Acceptance, Low mA SR, mA vs ma grid, 250-400 GeV, ggF prod

Acceptance, Low mA SR, mA vs ma grid, 400-550 GeV, ggF prod

Acceptance, Low mA SR, mA vs ma grid, >550 GeV, ggF prod

Efficiency, High mA SR, mA vs tanB grid, 400-750 GeV, bb prod

Efficiency, High mA SR, mA vs tanB grid, >750 GeV, bb prod

Efficiency, Low mA SR, mA vs tanB grid, 100-250 GeV, bb prod

Efficiency, Low mA SR, mA vs tanB grid, 250-400 GeV, bb prod

Efficiency, Low mA SR, mA vs tanB grid, 400-550 GeV, bb prod

Efficiency, Low mA SR, mA vs tanB grid, >550 GeV, bb prod

Efficiency, High mA SR, mA vs ma grid, 400-750 GeV, bb prod

Efficiency, High mA SR, mA vs ma grid, >750 GeV, bb prod

Efficiency, Low mA SR, mA vs ma grid, 100-250 GeV, bb prod

Efficiency, Low mA SR, mA vs ma grid, 250-400 GeV, bb prod

Efficiency, Low mA SR, mA vs ma grid, 400-550 GeV, bb prod

Efficiency, Low mA SR, mA vs ma grid, >550 GeV, bb prod

Efficiency, High mA SR, mA vs tanB grid, 400-750 GeV, ggF prod

Efficiency, High mA SR, mA vs tanB grid, >750 GeV, ggF prod

Efficiency, Low mA SR, mA vs tanB grid, 100-250 GeV, ggF prod

Efficiency, Low mA SR, mA vs tanB grid, 250-400 GeV, ggF prod

Efficiency, Low mA SR, mA vs tanB grid, 400-550 GeV, ggF prod

Efficiency, Low mA SR, mA vs tanB grid, >550 GeV, ggF prod

Efficiency, High mA SR, mA vs ma grid, 400-750 GeV, ggF prod

Efficiency, High mA SR, mA vs ma grid, >750 GeV, ggF prod

Efficiency, Low mA SR, mA vs ma grid, 100-250 GeV, ggF prod

Efficiency, Low mA SR, mA vs ma grid, 250-400 GeV, ggF prod

Efficiency, Low mA SR, mA vs ma grid, 400-550 GeV, ggF prod

Efficiency, Low mA SR, mA vs ma grid, >550 GeV, ggF prod

Total efficiencies for the selection of signal events after categorization and application of the tighter photon $E_{\mathrm{T}}^{\gamma}$ selection used to optimize the signal significance spin-1 $q\bar{q'}\to X^{\pm} \to W^{\pm}\gamma$. In addition to the total efficiency, contributions to the signal selection from each of the separate event categories are shown. The efficiencies calculated from MC samples with $W/Z$ hadronic decays are shown as the points on each curve. The line presents interpolated results.

Total efficiencies for the selection of signal events after categorization and application of the tighter photon $E_{\mathrm{T}}^{\gamma}$ selection used to optimize the signal significance spin-2 $q\bar{q}\to X^0 \to Z\gamma$. In addition to the total efficiency, contributions to the signal selection from each of the separate event categories are shown. The efficiencies calculated from MC samples with $W/Z$ hadronic decays are shown as the points on each curve. The line presents interpolated results.

Total efficiencies for the selection of signal events after categorization and application of the tighter photon $E_{\mathrm{T}}^{\gamma}$ selection used to optimize the signal significance spin-2 $gg\to X^0 \to Z\gamma$. In addition to the total efficiency, contributions to the signal selection from each of the separate event categories are shown. The efficiencies calculated from MC samples with $W/Z$ hadronic decays are shown as the points on each curve. The line presents interpolated results.

The $m_{J\gamma}$ distributions of data events selected for the spin-1 $q\bar{q'}\to X^{\pm} \to W^{\pm}\gamma$ search in the D2 category. The background-only fit function shape is shown as the solid curve overlaid with a shaded band corresponding to statistical uncertainties in background parameters. Various signal shapes with cross-sections corresponding to expected limits obtained in this analysis are shown as dashed lines.

The $m_{J\gamma}$ distributions of data events selected for the spin-1 $q\bar{q'}\to X^{\pm} \to W^{\pm}\gamma$ search in the WMASS category. The background-only fit function shape is shown as the solid curve overlaid with a shaded band corresponding to statistical uncertainties in background parameters. Various signal shapes with cross-sections corresponding to expected limits obtained in this analysis are shown as dashed lines.

The $m_{J\gamma}$ distributions of data events selected for the spin-0 $gg \to X^{0} \to Z\gamma$ search in the BTAG category. The background-only fit function shape is shown as the solid curve overlaid with a shaded band corresponding to statistical uncertainties in background parameters. Various signal shapes with cross-sections corresponding to expected limits obtained in this analysis are shown as dashed lines.

The $m_{J\gamma}$ distributions of data events selected for the spin-0 $gg \to X^{0} \to Z\gamma$ search in the D2 category. The background-only fit function shape is shown as the solid curve overlaid with a shaded band corresponding to statistical uncertainties in background parameters. Various signal shapes with cross-sections corresponding to expected limits obtained in this analysis are shown as dashed lines.

The $m_{J\gamma}$ distributions of data events selected for the spin-0 $gg \to X^{0} \to Z\gamma$ search in the ZMASS category. The background-only fit function shape is shown as the solid curve overlaid with a shaded band corresponding to statistical uncertainties in background parameters. Various signal shapes with cross-sections corresponding to expected limits obtained in this analysis are shown as dashed lines.

The $m_{J\gamma}$ distributions of data events selected for the spin-2 $gg \to X^{0} \to Z\gamma$ search in the BTAG category. The background-only fit function shape is shown as the solid curve overlaid with a shaded band corresponding to statistical uncertainties in background parameters. Various signal shapes with cross-sections corresponding to expected limits obtained in this analysis are shown as dashed lines.

The $m_{J\gamma}$ distributions of data events selected for the spin-2 $gg \to X^{0} \to Z\gamma$ search in the D2 category. The background-only fit function shape is shown as the solid curve overlaid with a shaded band corresponding to statistical uncertainties in background parameters. Various signal shapes with cross-sections corresponding to expected limits obtained in this analysis are shown as dashed lines.

The $m_{J\gamma}$ distributions of data events selected for the spin-2 $gg \to X^{0} \to Z\gamma$ search in the ZMASS category. The background-only fit function shape is shown as the solid curve overlaid with a shaded band corresponding to statistical uncertainties in background parameters. Various signal shapes with cross-sections corresponding to expected limits obtained in this analysis are shown as dashed lines.

The $m_{J\gamma}$ distributions of data events selected for the spin-2 $q\bar{q} \to X^{0} \to Z\gamma$ search in the BTAG category. The background-only fit function shape is shown as the solid curve overlaid with a shaded band corresponding to statistical uncertainties in background parameters. Various signal shapes with cross-sections corresponding to expected limits obtained in this analysis are shown as dashed lines.

The $m_{J\gamma}$ distributions of data events selected for the spin-2 $q\bar{q} \to X^{0} \to Z\gamma$ search in the D2 category. The background-only fit function shape is shown as the solid curve overlaid with a shaded band corresponding to statistical uncertainties in background parameters. Various signal shapes with cross-sections corresponding to expected limits obtained in this analysis are shown as dashed lines.

The $m_{J\gamma}$ distributions of data events selected for the spin-2 $q\bar{q} \to X^{0} \to Z\gamma$ search in the ZMASS category. The background-only fit function shape is shown as the solid curve overlaid with a shaded band corresponding to statistical uncertainties in background parameters. Various signal shapes with cross-sections corresponding to expected limits obtained in this analysis are shown as dashed lines.

The 95% CL upper limits on $\sigma(pp\to X)\times B(X\to W/Z\gamma)$ as a function of $m_{X}$ for spin-0 $gg \to X^{0} \to Z\gamma$. The observed limits are shown as a solid black line and the expected ones are shown as a dashed line with the 1$\sigma$ (2$\sigma$) uncertainty band presented as the green (yellow) band.

The 95% CL upper limits on $\sigma(pp\to X)\times B(X\to W/Z\gamma)$ as a function of $m_{X}$ for spin-2 $gg \to X^{0} \to Z\gamma$. The observed limits are shown as a solid black line and the expected ones are shown as a dashed line with the 1$\sigma$ (2$\sigma$) uncertainty band presented as the green (yellow) band.

The 95% CL upper limits on $\sigma(pp\to X)\times B(X\to W/Z\gamma)$ as a function of $m_{X}$ for spin-2 $q\bar{q} \to X^{0} \to Z\gamma$. The observed limits are shown as a solid black line and the expected ones are shown as a dashed line with the 1$\sigma$ (2$\sigma$) uncertainty band presented as the green (yellow) band.

The 95% CL upper limits on $\sigma(pp\to X)\times B(X\to W/Z\gamma)$ as a function of $m_{X}$ for spin-1 $q\bar{q'}\to X^{\pm} \to W^{\pm}\gamma$. The observed limits are shown as a solid black line and the expected ones are shown as a dashed line with the 1$\sigma$ (2$\sigma$) uncertainty band presented as the green (yellow) band.

The jet mass distribution of large-$R$ jets originating from the hadronic decay of $W$ and $Z$ bosons produced from the decay of BSM bosons with mass $m_X = 2000$ GeV. The decays simulated are for the production models $q\bar{q'}\to X^{\pm} \to W^{\pm}\gamma$ with a spin-1 resonance $X^{\pm}$ and $gg\to X^0 \to Z\gamma$ with a spin-0 resonance $X^{0}$.

The photon $E_{T}$ selection criteria as a function of resonance mass for D2 categories. Selections for four different signal channels are shown together.

The photon $E_{T}$ selection criteria as a function of resonance mass for ZMASS or WMASS categories. Selections for four different signal channels are shown together.