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.

Number of data events for the 2-tag category with the loose selection in bins of diphoton mass.

Number of data events for the 1-tag category with the tight selection in bins of diphoton mass.

Number of data events for the 2-tag category with the tight selection in bins of diphoton mass.

Number of data events for the 1-tag category with the loose selection in bins of four-body mass.

Number of data events for the 2-tag category with the loose selection in bins of four-body mass.

Number of data events for the 1-tag category with the tight selection in bins of four-body mass.

Number of data events for the 2-tag category with the tight selection in bins of four-body mass.

Expected and observed upper limits at the 95% CL on the cross-section of gluon-fusion initiated Higgs boson pair production as a function of $\kappa_{\lambda}$.

Expected and observed upper limits at the 95% CL on the cross-section of gluon-fusion initiated resonant production of a Higgs boson pair as a function of the mass of the resonance, $m_X$.