Figure 3 top left. Expected and observed 95% CL upper limits on the product of the production cross section and branching fraction as a function of the RS graviton mass $m_{G}$ for the full Run 2 data set are shown. Expected $1\sigma$ and $2\sigma$ limit bands are shown in green and yellow, respectively

Figure 3 top right. Expected and observed 95% CL upper limits on the product of the production cross section and branching fraction as a function of the heavy higgs mass $m_{S}$ for the full Run 2 data set are shown. Expected $1\sigma$ and $2\sigma$ limit bands are shown in green and yellow, respectively

Figure 3 mid left. Expected and observed 95% CL upper limits on the product of the production cross section and branching fraction as a function of the RS graviton mass $m_{G}$ for the full Run 2 data set are shown. Expected $1\sigma$ and $2\sigma$ limit bands are shown in green and yellow, respectively

Figure 3 mid right. Expected and observed 95% CL upper limits on the product of the production cross section and branching fraction as a function of the heavy higgs mass $m_{S}$ for the full Run 2 data set are shown. Expected $1\sigma$ and $2\sigma$ limit bands are shown in green and yellow, respectively

Figure 3 bottom left. Expected and observed 95% CL upper limits on the product of the production cross section and branching fraction as a function of the RS graviton mass $m_{G}$ for the full Run 2 data set are shown. Expected $1\sigma$ and $2\sigma$ limit bands are shown in green and yellow, respectively

Figure 3 bottom right. Expected and observed 95% CL upper limits on the product of the production cross section and branching fraction as a function of the heavy higgs mass $m_{S}$ for the full Run 2 data set are shown. Expected $1\sigma$ and $2\sigma$ limit bands are shown in green and yellow, respectively

Figure 4 top left. Expected 95% CL upper limits on the product of the cross section and branching fraction as a function of the $m_{G}$ versus the resonance width for the full Run 2 data set.

Figure 4 top right. Observed 95% CL upper limits on the product of the cross section and branching fraction as a function of the $m_{G}$ versus the resonance width for the full Run 2 data set.

Figure 4 bottom left. Expected 95% CL upper limits on the product of the cross section and branching fraction as a function of the $m_{S}$ versus the resonance width for the full Run 2 data set.

Figure 4 bottom right. Observed 95% CL upper limits on the product of the cross section and branching fraction as a function of the $m_{S}$ versus the resonance width for the full Run 2 data set.

Figure 6. The $m_{\gamma\gamma}$ spectra and background prediction after nuisance paramter marginalization (post-fit) due to SM diphoton production ($\gamma\gamma$) and fake photon production (j$\gamma$, jj) for the EBEB, combining the 2016, 2017, and 2018 data sets. The prediction with a large extra dimensions signal (GRW convention with $M_{S}$ = 9 TeV) is also shown. The pull distributions, normalized to the statistical uncertainty only, are shown underneath the spectra. The last bin contains the overflow of events beyond $m_{\gamma\gamma}$ > 3.5 TeV.

Figure 6. The $m_{\gamma\gamma}$ spectra and background prediction after nuisance paramter marginalization (post-fit) due to SM diphoton production ($\gamma\gamma$) and fake photon production (j$\gamma$, jj) for the EBEE, combining the 2016, 2017, and 2018 data sets. The prediction with a large extra dimensions signal (GRW convention with $M_{S}$ = 9 TeV) is also shown. The pull distributions, normalized to the statistical uncertainty only, are shown underneath the spectra. The last bin contains the overflow of events beyond $m_{\gamma\gamma}$ > 3.5 TeV.

Figure 7. The exclusion limit for the clockwork framework over the k--M5 parameter space. The shaded region denotes where the theory becomes nonperturbative. The region below and to the left of the solid line constitutes the excluded region. Expected 1std and 2std limit bands are shown in green and yellow, respectively.

Correlation matrix for the differential branching fraction extraction between different $q^2$ bins in the simultaneous fit.

The product of acceptance and efficiency ($A\epsilon$) of the $\mathcal{B}(\mathrm{B}^+\to\mathrm{K}^+\mu^+\mu^-)$ channel, as a function of the muon pair $q^2$, as measured in simulated signal events, after all the corrections applied. In the figure, regions corresponding to resonances are displayed with red markers.

Same as Table 5, but for the bins containing the J$\psi$ and $\psi$(2S) resonances.

Integrated branching fraction $\mathcal{B}(\mathrm{B}^\pm \to \mathrm{K}^\pm\mu^+\mu^-)$ in the low-$q^2$ region.

Ratio of branching fractions $\mathcal{B}(\text{B}^\pm \to \text{K}^\pm\mu^+\mu^-)$ to $\mathcal{B}(\text{B}^\pm \to \text{K}^\pm\text{e}^+\text{e}^-)$, determined from the measured double ratio $R$(K) of these decays to the respective branching fractions of the decay chains $\text{B}^\pm\to\text{J/}\psi\text{K}^\pm$ with $\text{J/}\psi\to\mu^+\mu^-$ and $\text{e}^+\text{e}^-$.

Negative log likelihood function from the fit profiled as a function of the inverse ratio $R(\mathrm{K})^{-1}$.

Observed profiled likelihood on $f_{\Lambda1}$ using Approach 1. The signal strength modifiers are treated as free parameters. Axis scales are varied to improve the visibility of important features.

Expected profiled likelihood on $f_{a3}$ using Approach 1. The signal strength modifiers are treated as free parameters.

Observed profiled likelihood on $f_{a3}$ using Approach 1. The signal strength modifiers are treated as free parameters.

Expected profiled likelihood on $f_{\Lambda1}^{Z\gamma}$ using Approach 1. The signal strength modifiers are treated as free parameters.

Observed profiled likelihood on $f_{\Lambda1}^{Z\gamma}$ using Approach 1. The signal strength modifiers are treated as free parameters.

Expected profiled likelihood on $f_{a2}$ using Approach 2. The other two anomalous coupling cross section fractions are fixed to zero. The signal strength modifiers are treated as free parameters. Axis scales are varied to improve the visibility of important features.

Observed profiled likelihood on $f_{a2}$ using Approach 2. The other two anomalous coupling cross section fractions are fixed to zero. The signal strength modifiers are treated as free parameters. Axis scales are varied to improve the visibility of important features.

Expected profiled likelihood on $f_{\Lambda1}$ using Approach 2. The other two anomalous coupling cross section fractions are fixed to zero. The signal strength modifiers are treated as free parameters. Axis scales are varied to improve the visibility of important features.

Observed profiled likelihood on $f_{\Lambda1}$ using Approach 2. The other two anomalous coupling cross section fractions are fixed to zero. The signal strength modifiers are treated as free parameters. Axis scales are varied to improve the visibility of important features.

Expected profiled likelihood on $f_{a3}$ using Approach 2. The other two anomalous coupling cross section fractions are fixed to zero. The signal strength modifiers are treated as free parameters.

Observed profiled likelihood on $f_{a3}$ using Approach 2. The other two anomalous coupling cross section fractions are fixed to zero. The signal strength modifiers are treated as free parameters.

Expected profiled likelihood on $f_{a2}$ using Approach 2. The other two anomalous coupling cross section fractions are left floating in the fit. The signal strength modifiers are treated as free parameters. Axis scales are varied to improve the visibility of important features.

Observed profiled likelihood on $f_{a2}$ using Approach 2. The other two anomalous coupling cross section fractions are left floating in the fit. The signal strength modifiers are treated as free parameters. Axis scales are varied to improve the visibility of important features.

Expected profiled likelihood on $f_{\Lambda1}$ using Approach 2. The other two anomalous coupling cross section fractions are left floating in the fit. The signal strength modifiers are treated as free parameters. Axis scales are varied to improve the visibility of important features.

Observed profiled likelihood on $f_{\Lambda1}$ using Approach 2. The other two anomalous coupling cross section fractions are left floating in the fit. The signal strength modifiers are treated as free parameters. Axis scales are varied to improve the visibility of important features.

Expected profiled likelihood on $f_{a3}$ using Approach 2. The other two anomalous coupling cross section fractions are left floating in the fit. The signal strength modifiers are treated as free parameters.

Observed profiled likelihood on $f_{a3}$ using Approach 2. The other two anomalous coupling cross section fractions are left floating in the fit. The signal strength modifiers are treated as free parameters.

Expected profiled likelihood on the $\delta c_{Z}$ coupling of the SMEFT Higgs basis.

Observed profiled likelihood on the $\delta c_{Z}$ coupling of the SMEFT Higgs basis.

Expected profiled likelihood on the $c_{Z\Box}$ coupling of the SMEFT Higgs basis.

Observed profiled likelihood on the $c_{Z\Box}$ coupling of the SMEFT Higgs basis.

Expected profiled likelihood on the $c_{ZZ}$ coupling of the SMEFT Higgs basis.

Observed profiled likelihood on the $c_{ZZ}$ coupling of the SMEFT Higgs basis.

Expected profiled likelihood on the $\tilde{c}_{ZZ}$ coupling of the SMEFT Higgs basis.

Observed profiled likelihood on the $\tilde{c}_{ZZ}$ coupling of the SMEFT Higgs basis.

Expected profiled likelihood on $f_{a3}^{ggH}$. The signal strength modifiers and the CP-odd HVV anomalous coupling cross section fraction are treated as free parameters.

Observed profiled likelihood on $f_{a3}^{ggH}$. The signal strength modifiers and the CP-odd HVV anomalous coupling cross section fraction are treated as free parameters.

Observed differential $m_{\Gamma\Gamma}$ mass spectrum for 0.4$ < \alpha < $0.44%, where $\alpha = m_\phi/m_X$. The cross-section is calculated by dividing the event yield by the bin width and luminosity.

Observed differential $m_{\Gamma\Gamma}$ mass spectrum for 0.49$ < \alpha < $0.55%, where $\alpha = m_\phi/m_X$. The cross-section is calculated by dividing the event yield by the bin width and luminosity.

Observed differential $m_{\Gamma\Gamma}$ mass spectrum for 0.55$ < \alpha < $0.6%, where $\alpha = m_\phi/m_X$. The cross-section is calculated by dividing the event yield by the bin width and luminosity.

Observed differential $m_{\Gamma\Gamma}$ mass spectrum for 0.6$ < \alpha < $0.7%, where $\alpha = m_\phi/m_X$. The cross-section is calculated by dividing the event yield by the bin width and luminosity.

Observed differential $m_{\Gamma\Gamma}$ mass spectrum for 0.7$ < \alpha < $0.81%, where $\alpha = m_\phi/m_X$. The cross-section is calculated by dividing the event yield by the bin width and luminosity.

Observed differential $m_{\Gamma\Gamma}$ mass spectrum for 0.81$ < \alpha < $3.0%, where $\alpha = m_\phi/m_X$. The cross-section is calculated by dividing the event yield by the bin width and luminosity.

Two dimensional plot where the Z-axis is the observed (paper Fig. 3) or expected (Supp. Fig. 20) 95% CL upper limits on the product of the cross section for $X \to \phi\phi \to (\gamma\gamma)(\gamma\gamma)$. The corresponding expected limits and their variations at the 1 and 2 standard deviation levels are also shown. Limits are compared to various extended higgs sector model cross sections as a function of the parameter $m_X N / f$.

Expected exclusion limits for $m_X N / f = 1/9$ for signal cross sections for for the production of $X \to \phi\phi \to (\gamma\gamma)(\gamma\gamma)$.

Expected exclusion limits for $m_X N / f = 1$ for signal cross sections for for the production of $X \to \phi\phi \to (\gamma\gamma)(\gamma\gamma)$

The observed 95% CL upper limits on the product of the cross section, and branching fraction for the production of $X \to \phi\phi \to (\gamma\gamma)(\gamma\gamma)$, with $\alpha = m_\phi/m_X = 0.005$. The corresponding expected limits and their variations at the 1 and 2 standard deviation levels are also shown. Limits are compared to various extended higgs sector model cross sections as a function of the parameter $m_X N / f$.

The observed 95% CL upper limits on the product of the cross section, and branching fraction for the production of $X \to \phi\phi \to (\gamma\gamma)(\gamma\gamma)$, with $\alpha = m_\phi/m_X = 0.006$. The corresponding expected limits and their variations at the 1 and 2 standard deviation levels are also shown. Limits are compared to various extended higgs sector model cross sections as a function of the parameter $m_X N / f$.

The observed 95% CL upper limits on the product of the cross section, and branching fraction for the production of $X \to \phi\phi \to (\gamma\gamma)(\gamma\gamma)$, with $\alpha = m_\phi/m_X = 0.007$. The corresponding expected limits and their variations at the 1 and 2 standard deviation levels are also shown. Limits are compared to various extended higgs sector model cross sections as a function of the parameter $m_X N / f$.

The observed 95% CL upper limits on the product of the cross section, and branching fraction for the production of $X \to \phi\phi \to (\gamma\gamma)(\gamma\gamma)$, with $\alpha = m_\phi/m_X = 0.008$. The corresponding expected limits and their variations at the 1 and 2 standard deviation levels are also shown. Limits are compared to various extended higgs sector model cross sections as a function of the parameter $m_X N / f$.

The observed 95% CL upper limits on the product of the cross section, and branching fraction for the production of $X \to \phi\phi \to (\gamma\gamma)(\gamma\gamma)$, with $\alpha = m_\phi/m_X = 0.009$. The corresponding expected limits and their variations at the 1 and 2 standard deviation levels are also shown. Limits are compared to various extended higgs sector model cross sections as a function of the parameter $m_X N / f$.

The observed 95% CL upper limits on the product of the cross section, and branching fraction for the production of $X \to \phi\phi \to (\gamma\gamma)(\gamma\gamma)$, with $\alpha = m_\phi/m_X = 0.01$. The corresponding expected limits and their variations at the 1 and 2 standard deviation levels are also shown. Limits are compared to various extended higgs sector model cross sections as a function of the parameter $m_X N / f$.

The observed 95% CL upper limits on the product of the cross section, and branching fraction for the production of $X \to \phi\phi \to (\gamma\gamma)(\gamma\gamma)$, with $\alpha = m_\phi/m_X = 0.011$. The corresponding expected limits and their variations at the 1 and 2 standard deviation levels are also shown. Limits are compared to various extended higgs sector model cross sections as a function of the parameter $m_X N / f$.

The observed 95% CL upper limits on the product of the cross section, and branching fraction for the production of $X \to \phi\phi \to (\gamma\gamma)(\gamma\gamma)$, with $\alpha = m_\phi/m_X = 0.012$. The corresponding expected limits and their variations at the 1 and 2 standard deviation levels are also shown. Limits are compared to various extended higgs sector model cross sections as a function of the parameter $m_X N / f$.

The observed 95% CL upper limits on the product of the cross section, and branching fraction for the production of $X \to \phi\phi \to (\gamma\gamma)(\gamma\gamma)$, with $\alpha = m_\phi/m_X = 0.013$. The corresponding expected limits and their variations at the 1 and 2 standard deviation levels are also shown. Limits are compared to various extended higgs sector model cross sections as a function of the parameter $m_X N / f$.

The observed 95% CL upper limits on the product of the cross section, and branching fraction for the production of $X \to \phi\phi \to (\gamma\gamma)(\gamma\gamma)$, with $\alpha = m_\phi/m_X = 0.014$. The corresponding expected limits and their variations at the 1 and 2 standard deviation levels are also shown. Limits are compared to various extended higgs sector model cross sections as a function of the parameter $m_X N / f$.

The observed 95% CL upper limits on the product of the cross section, and branching fraction for the production of $X \to \phi\phi \to (\gamma\gamma)(\gamma\gamma)$, with $\alpha = m_\phi/m_X = 0.015$. The corresponding expected limits and their variations at the 1 and 2 standard deviation levels are also shown. Limits are compared to various extended higgs sector model cross sections as a function of the parameter $m_X N / f$.

The observed 95% CL upper limits on the product of the cross section, and branching fraction for the production of $X \to \phi\phi \to (\gamma\gamma)(\gamma\gamma)$, with $\alpha = m_\phi/m_X = 0.016$. The corresponding expected limits and their variations at the 1 and 2 standard deviation levels are also shown. Limits are compared to various extended higgs sector model cross sections as a function of the parameter $m_X N / f$.

The observed 95% CL upper limits on the product of the cross section, and branching fraction for the production of $X \to \phi\phi \to (\gamma\gamma)(\gamma\gamma)$, with $\alpha = m_\phi/m_X = 0.017$. The corresponding expected limits and their variations at the 1 and 2 standard deviation levels are also shown. Limits are compared to various extended higgs sector model cross sections as a function of the parameter $m_X N / f$.

The observed 95% CL upper limits on the product of the cross section, and branching fraction for the production of $X \to \phi\phi \to (\gamma\gamma)(\gamma\gamma)$, with $\alpha = m_\phi/m_X = 0.018$. The corresponding expected limits and their variations at the 1 and 2 standard deviation levels are also shown. Limits are compared to various extended higgs sector model cross sections as a function of the parameter $m_X N / f$.

The observed 95% CL upper limits on the product of the cross section, and branching fraction for the production of $X \to \phi\phi \to (\gamma\gamma)(\gamma\gamma)$, with $\alpha = m_\phi/m_X = 0.019$. The corresponding expected limits and their variations at the 1 and 2 standard deviation levels are also shown. Limits are compared to various extended higgs sector model cross sections as a function of the parameter $m_X N / f$.

The observed 95% CL upper limits on the product of the cross section, and branching fraction for the production of $X \to \phi\phi \to (\gamma\gamma)(\gamma\gamma)$, with $\alpha = m_\phi/m_X = 0.02$. The corresponding expected limits and their variations at the 1 and 2 standard deviation levels are also shown. Limits are compared to various extended higgs sector model cross sections as a function of the parameter $m_X N / f$.

The observed 95% CL upper limits on the product of the cross section, and branching fraction for the production of $X \to \phi\phi \to (\gamma\gamma)(\gamma\gamma)$, with $\alpha = m_\phi/m_X = 0.021$. The corresponding expected limits and their variations at the 1 and 2 standard deviation levels are also shown. Limits are compared to various extended higgs sector model cross sections as a function of the parameter $m_X N / f$.

The observed 95% CL upper limits on the product of the cross section, and branching fraction for the production of $X \to \phi\phi \to (\gamma\gamma)(\gamma\gamma)$, with $\alpha = m_\phi/m_X = 0.022$. The corresponding expected limits and their variations at the 1 and 2 standard deviation levels are also shown. Limits are compared to various extended higgs sector model cross sections as a function of the parameter $m_X N / f$.

The observed 95% CL upper limits on the product of the cross section, and branching fraction for the production of $X \to \phi\phi \to (\gamma\gamma)(\gamma\gamma)$, with $\alpha = m_\phi/m_X = 0.023$. The corresponding expected limits and their variations at the 1 and 2 standard deviation levels are also shown. Limits are compared to various extended higgs sector model cross sections as a function of the parameter $m_X N / f$.

The observed 95% CL upper limits on the product of the cross section, and branching fraction for the production of $X \to \phi\phi \to (\gamma\gamma)(\gamma\gamma)$, with $\alpha = m_\phi/m_X = 0.024$. The corresponding expected limits and their variations at the 1 and 2 standard deviation levels are also shown. Limits are compared to various extended higgs sector model cross sections as a function of the parameter $m_X N / f$.

The observed 95% CL upper limits on the product of the cross section, and branching fraction for the production of $X \to \phi\phi \to (\gamma\gamma)(\gamma\gamma)$, with $\alpha = m_\phi/m_X = 0.025$. The corresponding expected limits and their variations at the 1 and 2 standard deviation levels are also shown. Limits are compared to various extended higgs sector model cross sections as a function of the parameter $m_X N / f$.

Signal fractional efficiencies

Local significance in units of standard deviations in the $(m_\phi/m_X) − m_X$ plane.

Electroweak corrections for the $R_{\Delta\phi}(p_\mathrm{T})$ distribution. The multiplicative combination is considered as the main electroweak correction factor and the additive combination as an uncertainty estimate.