Data vs. the ABCD method background prediction for 2017 in $\mathrm{SR_{b}^{mm}}$. Events are divided by the bin width, hence fractional data counts. Error bars show statistical uncertainties of data. The blue band shows the propagated uncertainty of all individual fit variations in a given bin, which we consider to be uncorrelated. The lower panels show the ratio of the observed data to the background estimation.

Data vs. the ABCD method background prediction for 2018 in $\mathrm{SR_{b}^{mm}}$. Events are divided by the bin width, hence fractional data counts. Error bars show statistical uncertainties of data. The blue band shows the propagated uncertainty of all individual fit variations in a given bin, which we consider to be uncorrelated. The lower panels show the ratio of the observed data to the background estimation.

Data vs. the ABCD method background prediction for 2016 in $\mathrm{SR_{b+\textrm{j}/b}^{mm}}$. Events are divided by the bin width, hence fractional data counts. Error bars show statistical uncertainties of data. The blue band shows the propagated uncertainty of all individual fit variations in a given bin, which we consider to be uncorrelated. The lower panels show the ratio of the observed data to the background estimation.

Data vs. the ABCD method background prediction for 2017 in $\mathrm{SR_{b+\textrm{j}/b}^{mm}}$. Events are divided by the bin width, hence fractional data counts. Error bars show statistical uncertainties of data. The blue band shows the propagated uncertainty of all individual fit variations in a given bin, which we consider to be uncorrelated. The lower panels show the ratio of the observed data to the background estimation.

Data vs. the ABCD method background prediction for 2018 in $\mathrm{SR_{b+\textrm{j}/b}^{mm}}$. Events are divided by the bin width, hence fractional data counts. Error bars show statistical uncertainties of data. The blue band shows the propagated uncertainty of all individual fit variations in a given bin, which we consider to be uncorrelated. The lower panels show the ratio of the observed data to the background estimation.

The asymptotic 95% CL limits on the product of cross section ($\sigma$), branching fraction into a pair of muons ($\mathcal{B}$) to dimuons, acceptance (A), and efficiency ($\epsilon$) in $\mathrm{SR_{b}^{mm}}$. A combination of both limits depends on the relative acceptance contributions in each region and is omitted here.

The asymptotic 95% CL limits on the product of cross section ($\sigma$), branching fraction into a pair of muons ($\mathcal{B}$) to dimuons, acceptance (A), and efficiency ($\epsilon$) in $\mathrm{SR_{b+\textrm{j}/b}^{mm}}$. A combination of both limits depends on the relative acceptance contributions in each region and is omitted here.

Cutflow for signal samples in 2016. Samples are divided by generated mass, signal region, and the b to s quark flavor changing coupling of the $Z^\prime$, dbs. For some mass values, multiple values of this coupling strength have been generated. It is described in this minimal lagrangian: $\mathcal{L} \supset Z^{\prime}_{\eta} \Big[ g_{\mu}\, \bar{\mu}\, \gamma^{\eta}\, \mu + \big( g_b\, \delta_{bs}\, \bar{s}\, \gamma^{\eta}\, P_{L}\, b + \text{h.c.} \big) \Big]$. The cutflow shows the selection into signal regions, and then the effects of specialized HTLT and RelMET selections, which grow with greater mass.

Cutflow for signal samples in 2017. Samples are divided by generated mass, signal region, and the b to s quark flavor changing coupling of the $Z^\prime$, dbs. For some mass values, multiple values of this coupling strength have been generated. It is described in this minimal lagrangian: $\mathcal{L} \supset Z^{\prime}_{\eta} \Big[ g_{\mu}\, \bar{\mu}\, \gamma^{\eta}\, \mu + \big( g_b\, \delta_{bs}\, \bar{s}\, \gamma^{\eta}\, P_{L}\, b + \text{h.c.} \big) \Big]$. The cutflow shows the selection into signal regions, and then the effects of specialized HTLT and RelMET selections, which grow with greater mass.

Cutflow for signal samples in 2018. Samples are divided by generated mass, signal region, and the b to s quark flavor changing coupling of the $Z^\prime$, dbs. For some mass values, multiple values of this coupling strength have been generated. It is described in this minimal lagrangian: $\mathcal{L} \supset Z^{\prime}_{\eta} \Big[ g_{\mu}\, \bar{\mu}\, \gamma^{\eta}\, \mu + \big( g_b\, \delta_{bs}\, \bar{s}\, \gamma^{\eta}\, P_{L}\, b + \text{h.c.} \big) \Big]$. The cutflow shows the selection into signal regions, and then the effects of specialized HTLT and RelMET selections, which grow with greater mass.

The groomed momentum balance distribution of b jets.

The jet fragmentation function distribution of b jets.

The b jet to inclusive jet ratio of the groomed jet radius distributions.

The b jet to inclusive jet ratio of the groomed momentum balance distributions.

Observed (black markers) and expected distributions of number of jets after event selection. The hatched (grey) areas denote the systematic (total) uncertainties in the expected yields. Events from all data-taking periods and all channels are combined. The lower panel of each plot shows the ratio between observed and expected distributions. The last bin includes all events above the plotted range. The entry Background corresponds to the sum of all the SM predictions.

Observed (black markers) and expected distributions of number of b tagged jets after event selection. The hatched (grey) areas denote the systematic (total) uncertainties in the expected yields. Events from all data-taking periods and all channels are combined. The lower panel of each plot shows the ratio between observed and expected distributions. The last bin includes all events above the plotted range. The entry Background corresponds to the sum of all the SM predictions.

Difference between $p_{\mathrm{T,gen.}}^\text{miss}$ and $p_{\mathrm{T,rec.}}^\text{miss}$ as a function of the $p_{\mathrm{T,gen.}}^\text{miss}$ for signal events. The mean difference between the generated and the $p_{\mathrm{T,rec.}}^\text{miss}$ per bin is shown as solid line. The results for $p_{\mathrm{T}}^\text{miss}$ corrected by the DNN regression (light blue), derived with the PUPPI algorithm (red), and the PF algorithm (orange) are shown. A simulated sample for the 2018 data-taking period is used.

Difference between $p_{\mathrm{T,gen.}}^\text{miss}$ and $p_{\mathrm{T,rec.}}^\text{miss}$ as a function of the $p_{\mathrm{T,gen.}}^\text{miss}$ for signal events. The dashed line shows the standard deviation $\sigma$, which corresponds to the resolution of the $p_{\mathrm{T,gen.}}^\text{miss}$ and $p_{\mathrm{T,rec.}}^\text{miss}$ difference. The results for $p_{\mathrm{T}}^\text{miss}$ corrected by the DNN regression (light blue), derived with the PUPPI algorithm (red), and the PF algorithm (orange) are shown. A simulated sample for the 2018 data-taking period is used.

Difference between $p_{\mathrm{T,gen.}}^\text{miss}$ and $p_{\mathrm{T,rec.}}^\text{miss}$ as a function of the number of primary vertices for signal events. The mean difference between the generated and the $p_{\mathrm{T,rec.}}^\text{miss}$ per bin is shown as solid line. The results for $p_{\mathrm{T}}^\text{miss}$ corrected by the DNN regression (light blue), derived with the PUPPI algorithm (red), and the PF algorithm (orange) are shown. A simulated sample for the 2018 data-taking period is used.

Difference between $p_{\mathrm{T,gen.}}^\text{miss}$ and $p_{\mathrm{T,rec.}}^\text{miss}$ as a function of the $p_{\mathrm{T,gen.}}^\text{miss}$ for signal events. The dashed line shows the standard deviation $\sigma$, which corresponds to the resolution of the $p_{\mathrm{T,gen.}}^\text{miss}$ and $p_{\mathrm{T,rec.}}^\text{miss}$ difference. The results for $p_{\mathrm{T}}^\text{miss}$ corrected by the DNN regression (light blue), derived with the PUPPI algorithm (red), and the PF algorithm (orange) are shown. A simulated sample for the 2018 data-taking period is used.

Results of the $\chi^{2}$ tests for the absolute and normalized differential cross section measurements for each of the predictions. The $\chi^{2}$ values including uncertainties on the predictions are given in parentheses in the table in the paper and in a separate column here.

The p-value of the $\chi^{2}$ tests for the absolute and normalized cross section measurements for each of the predictions. The resulting p-values including uncertainties on the predictions are given in parentheses in the table in the paper and in a separate column here.

Breakdown of the relative contribution from experimental uncertainties in the differential cross section measurement as a function of $p_{\text{T}}^{\nu\nu}$. The statistical uncertainty (dark grey) takes the size of the available simulated samples and the recorded data into account. The last bin includes all events above the plotted range.

Breakdown of the relative contribution from theory uncertainties in the differential cross section measurement as a function of $p_{\text{T}}^{\nu\nu}$. The statistical uncertainty (dark grey) takes the size of the available simulated samples and the recorded data into account. The last bin includes all events above the plotted range.

Breakdown of the relative contribution from experimental uncertainties in the differential cross section measurement as a function of $\text{min}[\Delta\phi(\vec{p}_{\text{T}}^{\nu\nu},\vec{p}_{\text{T}}^{\ell})]$. The statistical uncertainty (dark grey) takes the size of the available simulated samples and the recorded data into account. The last bin includes all events above the plotted range.

Breakdown of the relative contribution from theory uncertainties in the differential cross section measurement as a function of $\text{min}[\Delta\phi(\vec{p}_{\text{T}}^{\nu\nu},\vec{p}_{\text{T}}^{\ell})]$. The statistical uncertainty (dark grey) takes the size of the available simulated samples and the recorded data into account. The last bin includes all events above the plotted range.

Breakdown of the relative contribution from experimental uncertainties in the differential cross section measurement as a function of $p_{\text{T}}^{\nu\nu}$ and $\text{min}[\Delta\phi(\vec{p}_{\text{T}}^{\nu\nu},\vec{p}_{\text{T}}^{\ell})]$ for the azimuthal angle range 0<$\phi$<0.56. Each group of four bins corresponds to $p_{\text{T}}^{\nu\nu}$ bins, and $\text{min}[\Delta\phi(\vec{p}_{\text{T}}^{\nu\nu},\vec{p}_{\text{T}}^{\ell})]$ bin edges are indicated by vertical solid lines. The statistical uncertainty (dark grey) takes the size of the available simulated samples and the recorded data into account. The last bin includes all events above the plotted range.

Breakdown of the relative contribution from experimental uncertainties in the differential cross section measurement as a function of $p_{\text{T}}^{\nu\nu}$ and $\text{min}[\Delta\phi(\vec{p}_{\text{T}}^{\nu\nu},\vec{p}_{\text{T}}^{\ell})]$ for the azimuthal angle range 0.56<$\phi$<1.08. Each group of four bins corresponds to $p_{\text{T}}^{\nu\nu}$ bins, and $\text{min}[\Delta\phi(\vec{p}_{\text{T}}^{\nu\nu},\vec{p}_{\text{T}}^{\ell})]$ bin edges are indicated by vertical solid lines. The statistical uncertainty (dark grey) takes the size of the available simulated samples and the recorded data into account. The last bin includes all events above the plotted range.

Breakdown of the relative contribution from experimental uncertainties in the differential cross section measurement as a function of $p_{\text{T}}^{\nu\nu}$ and $\text{min}[\Delta\phi(\vec{p}_{\text{T}}^{\nu\nu},\vec{p}_{\text{T}}^{\ell})]$ for the azimuthal angle range 1.08<$\phi$<3.14. Each group of four bins corresponds to $p_{\text{T}}^{\nu\nu}$ bins, and $\text{min}[\Delta\phi(\vec{p}_{\text{T}}^{\nu\nu},\vec{p}_{\text{T}}^{\ell})]$ bin edges are indicated by vertical solid lines. The statistical uncertainty (dark grey) takes the size of the available simulated samples and the recorded data into account. The last bin includes all events above the plotted range.

Breakdown of the relative contribution from theory uncertainties in the differential cross section measurement as a function of $p_{\text{T}}^{\nu\nu}$ and $\text{min}[\Delta\phi(\vec{p}_{\text{T}}^{\nu\nu},\vec{p}_{\text{T}}^{\ell})]$ for the azimuthal angle range 0<$\phi$<0.56. Each group of four bins corresponds to $p_{\text{T}}^{\nu\nu}$ bins, and $\text{min}[\Delta\phi(\vec{p}_{\text{T}}^{\nu\nu},\vec{p}_{\text{T}}^{\ell})]$ bin edges are indicated by vertical solid lines. The statistical uncertainty (dark grey) takes the size of the available simulated samples and the recorded data into account. The last bin includes all events above the plotted range.

Breakdown of the relative contribution from theory uncertainties in the differential cross section measurement as a function of $p_{\text{T}}^{\nu\nu}$ and $\text{min}[\Delta\phi(\vec{p}_{\text{T}}^{\nu\nu},\vec{p}_{\text{T}}^{\ell})]$ for the azimuthal angle range 0.56<$\phi$<1.08. Each group of four bins corresponds to $p_{\text{T}}^{\nu\nu}$ bins, and $\text{min}[\Delta\phi(\vec{p}_{\text{T}}^{\nu\nu},\vec{p}_{\text{T}}^{\ell})]$ bin edges are indicated by vertical solid lines. The statistical uncertainty (dark grey) takes the size of the available simulated samples and the recorded data into account. The last bin includes all events above the plotted range.

Breakdown of the relative contribution from theory uncertainties in the differential cross section measurement as a function of $p_{\text{T}}^{\nu\nu}$ and $\text{min}[\Delta\phi(\vec{p}_{\text{T}}^{\nu\nu},\vec{p}_{\text{T}}^{\ell})]$ for the azimuthal angle range 1.08<$\phi$<3.14. Each group of four bins corresponds to $p_{\text{T}}^{\nu\nu}$ bins, and $\text{min}[\Delta\phi(\vec{p}_{\text{T}}^{\nu\nu},\vec{p}_{\text{T}}^{\ell})]$ bin edges are indicated by vertical solid lines. The statistical uncertainty (dark grey) takes the size of the available simulated samples and the recorded data into account. The last bin includes all events above the plotted range.

The observed (black markers) and simulated distributions of $p_{\mathrm{T,DNN}}^\text{miss}$ is shown. Events from all data-taking periods and all channels are combined. The hatched (grey) areas indicate the systematic (total) uncertainty in the simulation. The lower panel of each plot shows the ratio of observed data to the expectation from MC simulation in each bin. The last bin includes all events above the plotted range.

The observed (black markers) and simulated distributions of $\text{min}[\Delta\phi(\vec{p}_{\text{T, DNN}}^{\text{miss}},\vec{p}_{\text{T}}^{\ell})]$ is shown. Events from all data-taking periods and all channels are combined. The hatched (grey) areas indicate the systematic (total) uncertainty in the simulation. The lower panel of each plot shows the ratio of observed data to the expectation from MC simulation in each bin. The last bin includes all events above the plotted range.

The observed (black markers) and simulated two-dimensional distribution of $p_{\mathrm{T,DNN}}^\text{miss}$ and $\text{min}[\Delta\phi(\vec{p}_{\text{T, DNN}}^{\text{miss}},\vec{p}_{\text{T}}^{\ell})]$ for the azimuthal angle range 0<$\phi$<0.28 is shown. Events from all data-taking periods and all channels are combined. The hatched (grey) areas indicate the systematic (total) uncertainty in the simulation. The lower panel of each plot shows the ratio of observed data to the expectation from MC simulation in each bin. The last bin includes all events above the plotted range.

The observed (black markers) and simulated two-dimensional distribution of $p_{\mathrm{T,DNN}}^\text{miss}$ and $\text{min}[\Delta\phi(\vec{p}_{\text{T, DNN}}^{\text{miss}},\vec{p}_{\text{T}}^{\ell})]$ for the azimuthal angle range 0.28<$\phi$<0.56 is shown. Events from all data-taking periods and all channels are combined. The hatched (grey) areas indicate the systematic (total) uncertainty in the simulation. The lower panel of each plot shows the ratio of observed data to the expectation from MC simulation in each bin. The last bin includes all events above the plotted range.

The observed (black markers) and simulated two-dimensional distribution of $p_{\mathrm{T,DNN}}^\text{miss}$ and $\text{min}[\Delta\phi(\vec{p}_{\text{T, DNN}}^{\text{miss}},\vec{p}_{\text{T}}^{\ell})]$ for the azimuthal angle range 0.56<$\phi$<0.82 is shown. Events from all data-taking periods and all channels are combined. The hatched (grey) areas indicate the systematic (total) uncertainty in the simulation. The lower panel of each plot shows the ratio of observed data to the expectation from MC simulation in each bin. The last bin includes all events above the plotted range.

The observed (black markers) and simulated two-dimensional distribution of $p_{\mathrm{T,DNN}}^\text{miss}$ and $\text{min}[\Delta\phi(\vec{p}_{\text{T, DNN}}^{\text{miss}},\vec{p}_{\text{T}}^{\ell})]$ for the azimuthal angle range 0.82<$\phi$<1.08 is shown. Events from all data-taking periods and all channels are combined. The hatched (grey) areas indicate the systematic (total) uncertainty in the simulation. The lower panel of each plot shows the ratio of observed data to the expectation from MC simulation in each bin. The last bin includes all events above the plotted range.

The observed (black markers) and simulated two-dimensional distribution of $p_{\mathrm{T,DNN}}^\text{miss}$ and $\text{min}[\Delta\phi(\vec{p}_{\text{T, DNN}}^{\text{miss}},\vec{p}_{\text{T}}^{\ell})]$ for the azimuthal angle range 1.08<$\phi$<2.14 is shown. Events from all data-taking periods and all channels are combined. The hatched (grey) areas indicate the systematic (total) uncertainty in the simulation. The lower panel of each plot shows the ratio of observed data to the expectation from MC simulation in each bin. The last bin includes all events above the plotted range.

The observed (black markers) and simulated two-dimensional distribution of $p_{\mathrm{T,DNN}}^\text{miss}$ and $\text{min}[\Delta\phi(\vec{p}_{\text{T, DNN}}^{\text{miss}},\vec{p}_{\text{T}}^{\ell})]$ for the azimuthal angle range 2.14<$\phi$<3.2 is shown. Events from all data-taking periods and all channels are combined. The hatched (grey) areas indicate the systematic (total) uncertainty in the simulation. The lower panel of each plot shows the ratio of observed data to the expectation from MC simulation in each bin. The last bin includes all events above the plotted range.

Result of the closure test based on simulation accounting for potential BSM contributions based on a top squark pair production scenario with a stop mass of 525 GeV and a neutralino mass of 350 GeV. The potential BSM contribution is scaled by a factor of ten. The test is performed for the $p_{\text{T}}^{\nu\nu}$ using the nominal (black), the regularized (orange), and the bin-by-bin unfolding (purple), based on all data-taking periods combined. The unfolded distributions are compared to the expected distribution (red) based on the sum of the nominal dileptonic $t\bar{t}$ signal sample and BSM signal with the corresponding $\chi^2/\text{ndf}$ values given in the legend in square brackets. The distribution used for the response matrix, is shown in blue. The error bars correspond to the statistical uncertainty. The lower part shows the ratios between the unfolded and the expected distributions.

Result of the closure test based on simulation. The potential BSM contribution is scaled by a factor of ten. The test is performed for the 2D measurement of $p_{\text{T}}^{\nu\nu}$ and $\text{min}[\Delta\phi(\vec{p}_{\text{T}}^{\nu\nu},\vec{p}_{\text{T}}^{\ell})]$ in the azimuthal angle range 0<$\phi$<0.56 using the nominal (black), the regularized (orange), and the bin-by-bin unfolding (purple), based on all data-taking periods combined. The unfolded distributions are compared to the expected distribution (red) based on the sum of the nominal dileptonic $t\bar{t}$ signal sample and BSM signal with the corresponding $\chi^2/\text{ndf}$ values given in the legend. The nominal distribution, used for the response matrix, is shown in blue. The error bars correspond to the statistical uncertainty. The lower part shows the ratios between the unfolded and the expected distributions.

Result of the closure test based on simulation. The potential BSM contribution is scaled by a factor of ten. The test is performed for the 2D measurement of $p_{\text{T}}^{\nu\nu}$ and $\text{min}[\Delta\phi(\vec{p}_{\text{T}}^{\nu\nu},\vec{p}_{\text{T}}^{\ell})]$ in the azimuthal angle range 0.56<$\phi$<1.08 using the nominal (black), the regularized (orange), and the bin-by-bin unfolding (purple), based on all data-taking periods combined. The unfolded distributions are compared to the expected distribution (red) based on the sum of the nominal dileptonic $t\bar{t}$ signal sample and BSM signal with the corresponding $\chi^2/\text{ndf}$ values given in the legend. The nominal distribution, used for the response matrix, is shown in blue. The error bars correspond to the statistical uncertainty. The lower part shows the ratios between the unfolded and the expected distributions.

Result of the closure test based on simulation. The potential BSM contribution is scaled by a factor of ten. The test is performed for the 2D measurement of $p_{\text{T}}^{\nu\nu}$ and $\text{min}[\Delta\phi(\vec{p}_{\text{T}}^{\nu\nu},\vec{p}_{\text{T}}^{\ell})]$ in the azimuthal angle range 1.08<$\phi$<3.14 using the nominal (black), the regularized (orange), and the bin-by-bin unfolding (purple), based on all data-taking periods combined. The unfolded distributions are compared to the expected distribution (red) based on the sum of the nominal dileptonic $t\bar{t}$ signal sample and BSM signal with the corresponding $\chi^2/\text{ndf}$ values given in the legend. The nominal distribution, used for the response matrix, is shown in blue. The error bars correspond to the statistical uncertainty. The lower part shows the ratios between the unfolded and the expected distributions.

The measured differential signal cross section (black markers) as a function of $p_{\text{T}}^{\nu\nu}$ is shown. The theoretical predictions from POWHEG+PYTHIA (dark red), POWHEG+HERWIG (orange), MC@NLO+PYTHIA (purple), and the fixed-order NLO (light blue) and NNLO (brown) calculations are compared to the measurement. The total (statistical) uncertainty in the measurement is shown as an orange (dark grey) band. The lower panel of each plot shows the ratio between theoretical predictions and the measurement.

The measured differential signal cross section (black markers) as a function of $\text{min}[\Delta\phi(\vec{p}_{\text{T}}^{\nu\nu},\vec{p}_{\text{T}}^{\ell})]$ is shown. The theoretical predictions from POWHEG+PYTHIA (dark red), POWHEG+HERWIG (orange), MC@NLO+PYTHIA (purple), and the fixed-order NLO (light blue) and NNLO (brown) calculations are compared to the measurement. The total (statistical) uncertainty in the measurement is shown as an orange (dark grey) band. The lower panel of each plot shows the ratio between theoretical predictions and the measurement.

The measured two-dimensional differential signal cross section (black markers) as a function of $p_{\text{T}}^{\nu\nu}$ and $\text{min}[\Delta\phi(\vec{p}_{\text{T}}^{\nu\nu},\vec{p}_{\text{T}}^{\ell})]$ for the azimuthal angle range 0<$\phi$<0.56 is shown. The theoretical predictions from POWHEG+PYTHIA (dark red), POWHEG+HERWIG (orange), MC@NLO+PYTHIA (purple), and the fixed-order NLO (light blue) and NNLO (brown) calculations are compared to the measurement. The total (statistical) uncertainty in the measurement is shown as an orange (dark grey) band. The lower panel of each plot shows the ratio between theoretical predictions and the measurement.

The measured two-dimensional differential signal cross section (black markers) as a function of $p_{\text{T}}^{\nu\nu}$ and $\text{min}[\Delta\phi(\vec{p}_{\text{T}}^{\nu\nu},\vec{p}_{\text{T}}^{\ell})]$ for the azimuthal angle range 0.56<$\phi$<1.08 is shown. The theoretical predictions from POWHEG+PYTHIA (dark red), POWHEG+HERWIG (orange), MC@NLO+PYTHIA (purple), and the fixed-order NLO (light blue) and NNLO (brown) calculations are compared to the measurement. The total (statistical) uncertainty in the measurement is shown as an orange (dark grey) band. The lower panel of each plot shows the ratio between theoretical predictions and the measurement.

The measured two-dimensional differential signal cross section (black markers) as a function of $p_{\text{T}}^{\nu\nu}$ and $\text{min}[\Delta\phi(\vec{p}_{\text{T}}^{\nu\nu},\vec{p}_{\text{T}}^{\ell})]$ for the azimuthal angle range 1.08<$\phi$<3.14 is shown. The theoretical predictions from POWHEG+PYTHIA (dark red), POWHEG+HERWIG (orange), MC@NLO+PYTHIA (purple), and the fixed-order NLO (light blue) and NNLO (brown) calculations are compared to the measurement. The total (statistical) uncertainty in the measurement is shown as an orange (dark grey) band. The lower panel of each plot shows the ratio between theoretical predictions and the measurement.

The normalized measured differential signal cross section (black markers) as a function of $p_{\text{T}}^{\nu\nu}$ is shown. The theoretical predictions from POWHEG+PYTHIA (dark red), POWHEG+HERWIG (orange), MC@NLO+PYTHIA (purple), and the fixed-order NLO (light blue) and NNLO (brown) calculations are compared to the measurement. The total (statistical) uncertainty in the measurement is shown as an orange (dark grey) band. The lower panel of each plot shows the ratio between theoretical predictions and the measurement.

The normalized measured differential signal cross section (black markers) as a function of $\text{min}[\Delta\phi(\vec{p}_{\text{T}}^{\nu\nu},\vec{p}_{\text{T}}^{\ell})]$ is shown. The theoretical predictions from POWHEG+PYTHIA (dark red), POWHEG+HERWIG (orange), MC@NLO+PYTHIA (purple), and the fixed-order NLO (light blue) and NNLO (brown) calculations are compared to the measurement. The total (statistical) uncertainty in the measurement is shown as an orange (dark grey) band. The lower panel of each plot shows the ratio between theoretical predictions and the measurement.

The normalized measured two-dimensional differential signal cross section (black markers) as a function of $p_{\text{T}}^{\nu\nu}$ and $\text{min}[\Delta\phi(\vec{p}_{\text{T}}^{\nu\nu},\vec{p}_{\text{T}}^{\ell})]$ for the azimuthal angle range 0<$\phi$<0.56 is shown. The theoretical predictions from POWHEG+PYTHIA (dark red), POWHEG+HERWIG (orange), MC@NLO+PYTHIA (purple), and the fixed-order NLO (light blue) and NNLO (brown) calculations are compared to the measurement. The total (statistical) uncertainty in the measurement is shown as an orange (dark grey) band. The lower panel of each plot shows the ratio between theoretical predictions and the measurement.

The normalized measured two-dimensional differential signal cross section (black markers) as a function of $p_{\text{T}}^{\nu\nu}$ and $\text{min}[\Delta\phi(\vec{p}_{\text{T}}^{\nu\nu},\vec{p}_{\text{T}}^{\ell})]$ for the azimuthal angle range 0.56<$\phi$<1.08 is shown. The theoretical predictions from POWHEG+PYTHIA (dark red), POWHEG+HERWIG (orange), MC@NLO+PYTHIA (purple), and the fixed-order NLO (light blue) and NNLO (brown) calculations are compared to the measurement. The total (statistical) uncertainty in the measurement is shown as an orange (dark grey) band. The lower panel of each plot shows the ratio between theoretical predictions and the measurement.

The normalized measured two-dimensional differential signal cross section (black markers) as a function of $p_{\text{T}}^{\nu\nu}$ and $\text{min}[\Delta\phi(\vec{p}_{\text{T}}^{\nu\nu},\vec{p}_{\text{T}}^{\ell})]$ for the azimuthal angle range 1.08<$\phi$<3.14 is shown. The theoretical predictions from POWHEG+PYTHIA (dark red), POWHEG+HERWIG (orange), MC@NLO+PYTHIA (purple), and the fixed-order NLO (light blue) and NNLO (brown) calculations are compared to the measurement. The total (statistical) uncertainty in the measurement is shown as an orange (dark grey) band. The lower panel of each plot shows the ratio between theoretical predictions and the measurement.

The correlation matrix corresponding to the statistical uncertainties on the differential cross-section ($d\sigma/dp_T$) fit results for $W^-$. To combine with $W^+$ results (Fig8a), use the rows and columns ordered as $W^+$ and then $W^-$. Assume no correlation in the statistical uncertainties between $W^+$ and $W^-$ (zero entries in the off-diagonal blocks).

The correlation matrix corresponding to all of the systematic uncertainties on the differential cross-section ($d\sigma/dp_T$) fit results for $W^+$ and $W^-$ combined together, with rows and columns ordered as $W^+$ and then $W^-$.

Observed 95% $\text{CL}_\text{S}$ upper limits on the production cross-section times acceptance times branching ratio to jets, $\sigma \cdot A \cdot \text{BR}$, of Gaussian-shaped signals of 5%, 10%, and 15% width relative to their peak mass, $m_G$. Also included are the corresponding expected upper limits predicted for the case the $m_{jj}$ distribution is observed to be identical to the background prediction in each bin and the $1\sigma$ and $2\sigma$ envelopes of outcomes expected for Poisson fluctuations around the background expectation. Limits are derived from the J100 signal region.

Observed 95% $\text{CL}_\text{S}$ upper limits on the the value of the coupling to quarks, $g_q$, of the $Z^\prime$ model as a function of the resonance mass $m_{Z^\prime}$. Also included are the corresponding expected upper limits predicted for the case the $m_{jj}$ distribution is observed to be identical to the background prediction in each bin and the $1\sigma$ and $2\sigma$ envelopes of outcomes expected for Poisson fluctuations around the background expectation. Limits are derived from the J50 signal region.

Observed 95% $\text{CL}_\text{S}$ upper limits on the the value of the coupling to quarks, $g_q$, of the $Z^\prime$ model as a function of the resonance mass $m_{Z^\prime}$. Also included are the corresponding expected upper limits predicted for the case the $m_{jj}$ distribution is observed to be identical to the background prediction in each bin and the $1\sigma$ and $2\sigma$ envelopes of outcomes expected for Poisson fluctuations around the background expectation. Limits are derived from the J100 signal region.

Acceptance of simulated $Z^\prime$ signal events given the analysis event selection as a function of $m_{Z^\prime}$. The solid black line corresponds to the acceptance without a lower $m_{jj}$ requirement applied, the solid blue line includes the $m_{jj} > 344$ GeV requirement of the J50 signal region, and the solid red line includes the $m_{jj} > 481$ GeV requirement of the J100 signal region.

Numbers of events in each of the two considered datasets after consecutively applying the analysis selections.

Observed upper limits at 95% CL on the product of the cross section and branching fraction squared, $\sigma (\tilde{\mathrm{t}} \, \bar{\tilde{\mathrm{t}}}) \, \mathcal{B}^{2} ( \tilde{\mathrm{t}} \rightarrow \mathrm{c} \tilde{\chi}_1^0 )$ (left panel), are shown using the color scale where the $\tilde{\mathrm{t}}$ mass is on the $x$-axis and the mass difference between the $\tilde{\mathrm{t}}$ and the LSP is on the $y$-axis. The expected lower mass limits (magenta line) together with their $\pm 1\sigma$ uncertainties (magenta dashed lines) and the observed lower mass limits (black line) are indicated for 100% branching fractions.

Chargino-neutralino production. Observed upper limits at 95% CL on the product of the cross section and the two branching fractions, $\sigma (\tilde{\chi}_1^\pm \tilde{\chi}_2^0) \, \mathcal{B} ( \tilde{\chi}_1^\pm \rightarrow \mathrm{W}^{\pm} \tilde{\chi}_1^0 ) \, \mathcal{B} ( \tilde{\chi}_2^0 \rightarrow \mathrm{Z} \tilde{\chi}_1^0 )$, are shown using the color scale where the $\tilde{\chi}_1^\pm/\tilde{\chi}_2^0$ mass is on the $x$-axis and the mass difference between the $\tilde{\chi}_1^\pm/\tilde{\chi}_2^0$ and the LSP is on the $y$-axis. For these results, based on the TChiWZ simplified model, the $\tilde{\chi}_1^\pm$ and $\tilde{\chi}_2^0$ masses are set equal. The expected lower mass limits (magenta line) together with their $\pm 1\sigma$ uncertainties (magenta dashed lines) and the observed lower mass limits (black line) are indicated for 100% branching fractions for Wino-like cross-sections (left panel) and for Higgsino-like cross-sections (right panel).

Chargino-neutralino production. Observed upper limits at 95% CL on the product of the cross section and the two branching fractions, $\sigma (\tilde{\chi}_1^\pm \tilde{\chi}_2^0) \, \mathcal{B} ( \tilde{\chi}_1^\pm \rightarrow \mathrm{W}^{\pm} \tilde{\chi}_1^0 ) \, \mathcal{B} ( \tilde{\chi}_2^0 \rightarrow \mathrm{Z} \tilde{\chi}_1^0 )$, are shown using the color scale where the $\tilde{\chi}_1^\pm/\tilde{\chi}_2^0$ mass is on the $x$-axis and the mass difference between the $\tilde{\chi}_1^\pm/\tilde{\chi}_2^0$ and the LSP is on the $y$-axis. For these results, based on the TChiWZ simplified model, the $\tilde{\chi}_1^\pm$ and $\tilde{\chi}_2^0$ masses are set equal. The expected lower mass limits (magenta line) together with their $\pm 1\sigma$ uncertainties (magenta dashed lines) and the observed lower mass limits (black line) are indicated for 100% branching fractions for Wino-like cross-sections (left panel) and for Higgsino-like cross-sections (right panel).

Chargino pair production. The left panel shows the observed upper limits at 95% CL on the product of the cross section and the branching fraction squared, $\sigma (\tilde{\chi}_1^+ \tilde{\chi}_1^- ) \, \mathcal{B}^{2} ( \tilde{\chi}_1^\pm \rightarrow \mathrm{W}^{\pm} \tilde{\chi}_1^0 ) $ are shown using the color scale where the $\tilde{\chi}_1^\pm$ mass is on the $x$-axis and the mass difference between the $\tilde{\chi}_1^\pm $ and the LSP is on the $y$-axis. The expected lower mass limits (magenta line) together with their $\pm 1\sigma$ uncertainties (magenta dashed lines) and the observed lower mass limits (black line) are indicated for 100% branching fractions for Wino-like cross-sections. The right panel shows the results for chargino pair production with decays as in the TChiSlepSnu model with democratic decay via an intermediate sneutrino or charged slepton ($\widetilde{\ell}^{\pm}_{\mathrm{L}}$) with mass halfway between the chargino and the lightest neutralino. These model predictions also assume Wino-like cross sections.

Chargino pair production. The left panel shows the observed upper limits at 95% CL on the product of the cross section and the branching fraction squared, $\sigma (\tilde{\chi}_1^+ \tilde{\chi}_1^- ) \, \mathcal{B}^{2} ( \tilde{\chi}_1^\pm \rightarrow \mathrm{W}^{\pm} \tilde{\chi}_1^0 ) $ are shown using the color scale where the $\tilde{\chi}_1^\pm$ mass is on the $x$-axis and the mass difference between the $\tilde{\chi}_1^\pm $ and the LSP is on the $y$-axis. The expected lower mass limits (magenta line) together with their $\pm 1\sigma$ uncertainties (magenta dashed lines) and the observed lower mass limits (black line) are indicated for 100% branching fractions for Wino-like cross-sections. The right panel shows the results for chargino pair production with decays as in the TChiSlepSnu model with democratic decay via an intermediate sneutrino or charged slepton ($\widetilde{\ell}^{\pm}_{\mathrm{L}}$) with mass halfway between the chargino and the lightest neutralino. These model predictions also assume Wino-like cross sections.

Slepton pair production. Observed 95% CL upper limits on the product of the cross section and branching fraction squared for direct slepton pair production followed by decay of both sleptons to the corresponding lepton and neutralino (color scale). Slepton $\tilde{l}_{\mathrm{L}/\mathrm{R}}$ indicates the scalar supersymmetric partner of left- and right-handed electrons and muons. The limit is shown as a function of the slepton mass and the mass difference between the slepton and the lightest neutralino. The regions to the left of the lines denote the regions excluded for a branching fraction of 100%. The median expected exclusion regions for 100% branching fraction are delimited by the dashed lines.

Slepton pair production. Observed 95% CL upper limits on the product of the cross section and branching fraction squared for direct slepton pair production followed by decay of both sleptons to the corresponding lepton and neutralino (color scale). Slepton $\tilde{l}_{\mathrm{L}/\mathrm{R}}$ indicates the scalar supersymmetric partner of left- and right-handed electrons and muons. The limit is shown as a function of the slepton mass and the mass difference between the slepton and the lightest neutralino. The regions to the left of the lines denote the regions excluded for a branching fraction of 100%. The median expected exclusion regions for 100% branching fraction are delimited by the dashed lines.

Slepton pair production. Observed 95% CL upper limits on the product of the cross section and branching fraction squared for direct slepton pair production followed by decay of both sleptons to the corresponding lepton and neutralino (color scale). Slepton $\tilde{l}_{\mathrm{L}/\mathrm{R}}$ indicates the scalar supersymmetric partner of left- and right-handed electrons and muons. The limit is shown as a function of the slepton mass and the mass difference between the slepton and the lightest neutralino. The regions to the left of the lines denote the regions excluded for a branching fraction of 100%. The median expected exclusion regions for 100% branching fraction are delimited by the dashed lines.

Slepton pair production. Observed 95% CL upper limits on the cross section times branching fraction squared for direct selectron pair production (left) and smuon pair production (right) followed by decay of both sleptons to the corresponding lepton and neutralino (color scale). The limits are shown as a function of the slepton mass and the mass difference between the slepton and the lightest neutralino for the three different simplified possibilities of only RR, only LL, and both RR and LL where it is assumed that the R and L masses are identical. The regions to the left of the lines denote the regions excluded for a branching fraction of 100%. Median expected limits for 100% branching fraction are delimited by the dashed lines.

Slepton pair production. Observed 95% CL upper limits on the cross section times branching fraction squared for direct selectron pair production (left) and smuon pair production (right) followed by decay of both sleptons to the corresponding lepton and neutralino (color scale). The limits are shown as a function of the slepton mass and the mass difference between the slepton and the lightest neutralino for the three different simplified possibilities of only RR, only LL, and both RR and LL where it is assumed that the R and L masses are identical. The regions to the left of the lines denote the regions excluded for a branching fraction of 100%. Median expected limits for 100% branching fraction are delimited by the dashed lines.

Slepton pair production. Observed 95% CL upper limits on the cross section times branching fraction squared for direct selectron pair production (left) and smuon pair production (right) followed by decay of both sleptons to the corresponding lepton and neutralino (color scale). The limits are shown as a function of the slepton mass and the mass difference between the slepton and the lightest neutralino for the three different simplified possibilities of only RR, only LL, and both RR and LL where it is assumed that the R and L masses are identical. The regions to the left of the lines denote the regions excluded for a branching fraction of 100%. Median expected limits for 100% branching fraction are delimited by the dashed lines.

Slepton pair production. Observed 95% CL upper limits on the cross section times branching fraction squared for direct selectron pair production (left) and smuon pair production (right) followed by decay of both sleptons to the corresponding lepton and neutralino (color scale). The limits are shown as a function of the slepton mass and the mass difference between the slepton and the lightest neutralino for the three different simplified possibilities of only RR, only LL, and both RR and LL where it is assumed that the R and L masses are identical. The regions to the left of the lines denote the regions excluded for a branching fraction of 100%. Median expected limits for 100% branching fraction are delimited by the dashed lines.

Slepton pair production. Observed 95% CL upper limits on the cross section times branching fraction squared for direct selectron pair production (left) and smuon pair production (right) followed by decay of both sleptons to the corresponding lepton and neutralino (color scale). The limits are shown as a function of the slepton mass and the mass difference between the slepton and the lightest neutralino for the three different simplified possibilities of only RR, only LL, and both RR and LL where it is assumed that the R and L masses are identical. The regions to the left of the lines denote the regions excluded for a branching fraction of 100%. Median expected limits for 100% branching fraction are delimited by the dashed lines.

Slepton pair production. Observed 95% CL upper limits on the cross section times branching fraction squared for direct selectron pair production (left) and smuon pair production (right) followed by decay of both sleptons to the corresponding lepton and neutralino (color scale). The limits are shown as a function of the slepton mass and the mass difference between the slepton and the lightest neutralino for the three different simplified possibilities of only RR, only LL, and both RR and LL where it is assumed that the R and L masses are identical. The regions to the left of the lines denote the regions excluded for a branching fraction of 100%. Median expected limits for 100% branching fraction are delimited by the dashed lines.

Ratio between the prompt $\Xi_c^+$ baryons in a multiplicity class to the multiplicity-integrated (INEL $>$ 0) class.

The prompt production yield ratios between $\Xi_c^0$ and $\rm {D}^0$ measured in the same multiplicity classes.

The prompt production yield ratios between $\Xi_c^+$ and $\rm {D}^0$ measured in the same multiplicity classes.

The prompt production yield ratios between $\Xi_c^0$ and $\Lambda_c^+$ measured in the same multiplicity classes.

The prompt production yield ratios between $\Xi_c^+$ and $\Lambda_c^+$ measured in the same multiplicity classes.

The branching-fraction ratio of BR($\Xi_c^0 \rightarrow \Xi^-e^+\nu_e$)/BR($\Xi_c^0 \rightarrow \Xi^-\pi^+$)

The observed and expected upper limits at 95% CLs on $\sigma (\mathrm{pp} \to \mathrm{H}+\text{X}) {\mathcal{B}} (\mathrm{H} \to \mathrm{a}_1\,\mathrm{a}_1)$, relative to $\sigma_\text{SM}$, as a function of $m_{\mathrm{a}_1}$ for Type III 2HD+S model, $\tan\beta = 2$.

The observed and expected upper limits at 95% CLs on $\sigma (\mathrm{pp} \to \mathrm{H}+\text{X}) {\mathcal{B}} (\mathrm{H} \to \mathrm{a}_1\,\mathrm{a}_1)$, relative to $\sigma_\text{SM}$, as a function of $m_{\mathrm{a}_1}$ for Type IV 2HD+S model, $\tan\beta = 0.5$.

The observed and expected 95% CL upper limits on $\sigma (\mathrm{pp} \to \mathrm{H}+\text{X}) {\mathcal{B}} (\mathrm{H} \to \mathrm{a}_1\,\mathrm{a}_1)$, relative to $\sigma_\text{SM}$, as a function of $\tan\beta$ for the Type II 2HD+S model for $m_{\mathrm{a}_1} = 5$ GeV.

The observed and expected 95% CL upper limits on $\sigma (\mathrm{pp} \to \mathrm{H}+\text{X}) {\mathcal{B}} (\mathrm{H} \to \mathrm{a}_1\,\mathrm{a}_1)$, relative to $\sigma_\text{SM}$, as a function of $\tan\beta$ for the Type II 2HD+S model for $m_{\mathrm{a}_1} = 8$ GeV.

The observed and expected 95% CL upper limits on $\sigma (\mathrm{pp} \to \mathrm{H}+\text{X}) {\mathcal{B}} (\mathrm{H} \to \mathrm{a}_1\,\mathrm{a}_1)$, relative to $\sigma_\text{SM}$, as a function of $\tan\beta$ for the Type II 2HD+S model for $m_{\mathrm{a}_1} = 12$ GeV.

The observed and expected 95% CL upper limits on $\sigma (\mathrm{pp} \to \mathrm{H}+\text{X}) {\mathcal{B}} (\mathrm{H} \to \mathrm{a}_1\,\mathrm{a}_1)$, relative to $\sigma_\text{SM}$, as a function of $\tan\beta$ for the Type II 2HD+S model for $m_{\mathrm{a}_1} = 15$ GeV.

The observed and expected 95% CL upper limits on $\sigma (\mathrm{pp} \to \mathrm{H}+\text{X}) {\mathcal{B}} (\mathrm{H} \to \mathrm{a}_1\,\mathrm{a}_1)$, relative to $\sigma_\text{SM}$, as a function of $\tan\beta$ for the Type III 2HD+S model for $m_{\mathrm{a}_1} = 5$ GeV.

The observed and expected 95% CL upper limits on $\sigma (\mathrm{pp} \to \mathrm{H}+\text{X}) {\mathcal{B}} (\mathrm{H} \to \mathrm{a}_1\,\mathrm{a}_1)$, relative to $\sigma_\text{SM}$, as a function of $\tan\beta$ for the Type III 2HD+S model for $m_{\mathrm{a}_1} = 8$ GeV.

The observed and expected 95% CL upper limits on $\sigma (\mathrm{pp} \to \mathrm{H}+\text{X}) {\mathcal{B}} (\mathrm{H} \to \mathrm{a}_1\,\mathrm{a}_1)$, relative to $\sigma_\text{SM}$, as a function of $\tan\beta$ for the Type III 2HD+S model for $m_{\mathrm{a}_1} = 12$ GeV.

The observed and expected 95% CL upper limits on $\sigma (\mathrm{pp} \to \mathrm{H}+\text{X}) {\mathcal{B}} (\mathrm{H} \to \mathrm{a}_1\,\mathrm{a}_1)$, relative to $\sigma_\text{SM}$, as a function of $\tan\beta$ for the Type III 2HD+S model for $m_{\mathrm{a}_1} = 15$ GeV.

Single Event Sensitivity (SES) for the $K^{+}\rightarrow\pi^{+}X$ search as a function of X mass.

Model-independent constraints on the branching ratio of the $K^{+}\rightarrow\pi^{+}X$ decay

Model-independent constraints on the branching ratio of the $K^{+}\rightarrow\pi^{+}X$ decay

Observed model-independent upper limits at 90 % CL of $\mathcal{B}(K^{+}\rightarrow\pi^{+}X)$ as function of $X$ mass, for several $X$ lifetime hypotheses, assuming $X$ decays to visible SM particles.

Observed model-independent upper limits at 90 % CL of $\mathcal{B}(K^{+}\rightarrow\pi^{+}X)$ as function of $X$ mass, for several $X$ lifetime hypotheses, assuming $X$ decays to visible SM particles.

Di-muon mass spectrum of selected $K^{+}\rightarrow\pi^{+}\mu^{+}\mu^{-}$ events from 2017–2018 data.

Di-muon mass spectrum of selected $K^{+}\rightarrow\pi^{+}\mu^{+}\mu^{-}$ events from 2017–2018 data.

Expected and observed model-independent upper limits at 90 % CL for $\mathcal{B}(K^{+}\rightarrow\pi^{+}X)\times\mathcal{B}(X\rightarrow\mu^{+}\mu^{-})$ as a function of $m_{X}$ for $\tau_{X}=0$.

Expected and observed model-independent upper limits at 90 % CL for $\mathcal{B}(K^{+}\rightarrow\pi^{+}X)\times\mathcal{B}(X\rightarrow\mu^{+}\mu^{-})$ as a function of $m_{X}$ for $\tau_{X}=0$.

Observed model-independent upper limits at 90 % CL for $\mathcal{B}(K^{+}\rightarrow\pi^{+}X)\times\mathcal{B}(X\rightarrow\mu^{+}\mu^{-})$ for several $\tau_{X}$ values.

Observed model-independent upper limits at 90 % CL for $\mathcal{B}(K^{+}\rightarrow\pi^{+}X)\times\mathcal{B}(X\rightarrow\mu^{+}\mu^{-})$ for several $\tau_{X}$ values.

Branching ratio of the $K^{+}\rightarrow\pi^{+}A^{\prime}$ decay divided by the kinetic mixing coupling squared, $\varepsilon^{2}$, as a function of $m_{A^{\prime}}$ for the BC2 model with dark photon $A^{\prime}$.

Branching ratio of the $K^{+}\rightarrow\pi^{+}A^{\prime}$ decay divided by the kinetic mixing coupling squared, $\varepsilon^{2}$, as a function of $m_{A^{\prime}}$ for the BC2 model with dark photon $A^{\prime}$.

Excluded region, at 90 % CL, of the parameter space $(m_{A^{\prime}},\varepsilon)$ for a dark photon $A^{\prime}$, decaying invisibly, in the BC2 model for the NA62 $K^{+}\rightarrow\pi^{+}X_{\rm inv}$ search.

Excluded region, at 90 % CL, of the parameter space $(m_{A^{\prime}},\varepsilon)$ for a dark photon $A^{\prime}$, decaying invisibly, in the BC2 model for the NA62 $K^{+}\rightarrow\pi^{+}X_{\rm inv}$ search.

Excluded region, at 90 % CL, of the parameter space $(m_{A^{\prime}},\varepsilon)$ for a dark photon $A^{\prime}$, decaying invisibly, in the BC2 model for the NA62 $\pi^{0}\rightarrow{\rm inv}$ search.

Excluded region, at 90 % CL, of the parameter space $(m_{A^{\prime}},\varepsilon)$ for a dark photon $A^{\prime}$, decaying invisibly, in the BC2 model for the NA62 $\pi^{0}\rightarrow{\rm inv}$ search.

Branching ratio of the $K^{+}\rightarrow\pi^{+}S$ decay divided by $\text{sin}^{2}\theta$, as a function of $m_{S}$.

Branching ratio of the $K^{+}\rightarrow\pi^{+}S$ decay divided by $\text{sin}^{2}\theta$, as a function of $m_{S}$.

Excluded regions, at 90 % CL, of the parameter space $(m_{S},\rm{sin}^{2}\theta)$ for a dark scalar $S$, in the BC4-inv model for the NA62 $K^{+}\rightarrow\pi^{+}X_{\rm inv}$ search.

Excluded regions, at 90 % CL, of the parameter space $(m_{S},\rm{sin}^{2}\theta)$ for a dark scalar $S$, in the BC4-inv model for the NA62 $K^{+}\rightarrow\pi^{+}X_{\rm inv}$ search.

Excluded regions, at 90 % CL, of the parameter space $(m_{S},\rm{sin}^{2}\theta)$ for a dark scalar $S$, in the BC4-inv model for the NA62 $\pi^{0}\rightarrow{\rm inv}$ search.

Excluded regions, at 90 % CL, of the parameter space $(m_{S},\rm{sin}^{2}\theta)$ for a dark scalar $S$, in the BC4-inv model for the NA62 $\pi^{0}\rightarrow{\rm inv}$ search.

Excluded regions, at 90 % CL, of the parameter space $(m_{S},\rm{sin}^{2}\theta$) for a dar scalar S, in the BC4 model, from the NA62 $K^{+}\rightarrow\pi^{+}X_{\rm inv}$ search.

Excluded regions, at 90 % CL, of the parameter space $(m_{S},\rm{sin}^{2}\theta$) for a dar scalar S, in the BC4 model, from the NA62 $K^{+}\rightarrow\pi^{+}X_{\rm inv}$ search.

Excluded regions, at 90 % CL, of the parameter space $(m_{S},\rm{sin}^{2}\theta$) for a dar scalar S, in the BC4 model, from the NA62 $K^{+}\rightarrow\pi^{+}\mu^{+}\mu^{-}$ study.

Excluded regions, at 90 % CL, of the parameter space $(m_{S},\rm{sin}^{2}\theta$) for a dar scalar S, in the BC4 model, from the NA62 $K^{+}\rightarrow\pi^{+}\mu^{+}\mu^{-}$ study.

Branching ratio of the $K^{+}\rightarrow\pi^{+}a$ decay divided by $(C_{ff}/\Lambda)^{2}$, as a function of $m_{a}$, assuming Λ = 1 TeV.

Branching ratio of the $K^{+}\rightarrow\pi^{+}a$ decay divided by $(C_{ff}/\Lambda)^{2}$, as a function of $m_{a}$, assuming Λ = 1 TeV.

Excluded regions, at 90 % CL, of the parameter space $(m_{a}, C_{ff}/\Lambda)$ for an ALP $a$, in the BC10-inv model, evaluated assuming $\Lambda = 1$ TeV, for the NA62 $K^{+}\rightarrow\pi^{+}X_{\rm inv}$ search.

Excluded regions, at 90 % CL, of the parameter space $(m_{a}, C_{ff}/\Lambda)$ for an ALP $a$, in the BC10-inv model, evaluated assuming $\Lambda = 1$ TeV, for the NA62 $K^{+}\rightarrow\pi^{+}X_{\rm inv}$ search.

Excluded regions, at 90 % CL, of the parameter space $(m_{a}, C_{ff}/\Lambda)$ for an ALP $a$, in the BC10-inv model, evaluated assuming $\Lambda = 1$ TeV, for the NA62 $\pi^{0}\rightarrow\rm{inv}$ search.

Excluded regions, at 90 % CL, of the parameter space $(m_{a}, C_{ff}/\Lambda)$ for an ALP $a$, in the BC10-inv model, evaluated assuming $\Lambda = 1$ TeV, for the NA62 $\pi^{0}\rightarrow\rm{inv}$ search.

Excluded regions, at 90 % CL, of the parameter space $(m_{a}, C_{ff}/\lambda)$ for an ALP $a$, in the BC10 model, evaluated assuming $\Lambda = 1$ TeV for the NA62 $K^{+}\rightarrow\pi^{+}X_{\rm inv}$ search.

Excluded regions, at 90 % CL, of the parameter space $(m_{a}, C_{ff}/\lambda)$ for an ALP $a$, in the BC10 model, evaluated assuming $\Lambda = 1$ TeV for the NA62 $K^{+}\rightarrow\pi^{+}X_{\rm inv}$ search.

Excluded regions, at 90 % CL, of the parameter space $(m_{a}, C_{ff}/\lambda)$ for an ALP $a$, in the BC10 model, evaluated assuming $\Lambda = 1$ TeV for the NA62 $\pi^{0}\rightarrow\rm{inv}$ search.

Excluded regions, at 90 % CL, of the parameter space $(m_{a}, C_{ff}/\lambda)$ for an ALP $a$, in the BC10 model, evaluated assuming $\Lambda = 1$ TeV for the NA62 $\pi^{0}\rightarrow\rm{inv}$ search.

Excluded regions, at 90 % CL, of the parameter space $(m_{a}, C_{ff}/\lambda)$ for an ALP $a$, in the BC10 model, evaluated assuming $\Lambda = 1$ TeV for the NA62 $K^{+}\rightarrow\pi^{+}\mu^{+}\mu^{-}$ study.

Excluded regions, at 90 % CL, of the parameter space $(m_{a}, C_{ff}/\lambda)$ for an ALP $a$, in the BC10 model, evaluated assuming $\Lambda = 1$ TeV for the NA62 $K^{+}\rightarrow\pi^{+}\mu^{+}\mu^{-}$ study.

Branching ratio of the $K^{+}\rightarrow\pi^{+}a$ decay divided by $(C_{GG}/\Lambda)^{2}$, as a function of $m_{a}$, assuming $\Lambda = 1$ TeV.

Branching ratio of the $K^{+}\rightarrow\pi^{+}a$ decay divided by $(C_{GG}/\Lambda)^{2}$, as a function of $m_{a}$, assuming $\Lambda = 1$ TeV.

Excluded regions, at 90 % CL, of the parameter space $(m_{a}, C_{GG}/\Lambda)$ for an ALP $a$, of the BC11 model, evaluated assuming $\Lambda = 1$ TeV, from the NA62 search for $K^{+}\rightarrow\pi^{+}X_{\rm inv}$.

Excluded regions, at 90 % CL, of the parameter space $(m_{a}, C_{GG}/\Lambda)$ for an ALP $a$, of the BC11 model, evaluated assuming $\Lambda = 1$ TeV, from the NA62 search for $K^{+}\rightarrow\pi^{+}X_{\rm inv}$.

Excluded regions, at 90 % CL, of the parameter space $(m_{a}, C_{GG}/\Lambda)$ for an ALP $a$, of the BC11 model, evaluated assuming $\Lambda = 1$ TeV, from the NA62 search for $\pi^{0}\rightarrow\rm{inv}$.

Excluded regions, at 90 % CL, of the parameter space $(m_{a}, C_{GG}/\Lambda)$ for an ALP $a$, of the BC11 model, evaluated assuming $\Lambda = 1$ TeV, from the NA62 search for $\pi^{0}\rightarrow\rm{inv}$.

Excluded regions, at 90 % CL, of the parameter space $(m_{a}, C_{GG}/\Lambda)$ for an ALP $a$, of the BC11 model, evaluated assuming $\Lambda = 1$ TeV, from the NA62 $K^{+}\rightarrow\pi^{+}\gamma\gamma$ study.

Excluded regions, at 90 % CL, of the parameter space $(m_{a}, C_{GG}/\Lambda)$ for an ALP $a$, of the BC11 model, evaluated assuming $\Lambda = 1$ TeV, from the NA62 $K^{+}\rightarrow\pi^{+}\gamma\gamma$ study.