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CMS-HIG-19-010 ; CERN-EP-2022-027

Measurements of Higgs boson production in the decay channel with a pair of $\tau$ leptons in proton-proton collisions at $\sqrt{s}=$ 13 TeV

CMS Collaboration

27 April 2022

Eur. Phys. J. C 83 (2023) 562

Abstract: Measurements of Higgs boson production, where the Higgs boson decays into a pair of $\tau$ leptons, are presented, using a sample of proton-proton collisions collected with the CMS experiment at a center-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 138 fb$^{-1}$. Three analyses are presented. Two are targeting Higgs boson production via gluon fusion and vector boson fusion: a neural network based analysis and an analysis based on an event categorization optimized on the ratio of signal over background events. These are complemented by an analysis targeting vector boson associated Higgs boson production. Results are presented in the form of signal strengths relative to the standard model predictions and products of cross sections and branching fraction to $\tau$ leptons, in up to 16 different kinematic regions. For the simultaneous measurements of the neural network based analysis and the analysis targeting vector boson associated Higgs boson production signal strengths are found to be 0.82 $\pm$ 0.11 for inclusive Higgs boson production, 0.67 $\pm$ 0.19 (0.81 $\pm$ 0.17) for the production mainly via gluon fusion (vector boson fusion), and 1.79 $\pm$ 0.45 for vector boson associated Higgs boson production.

Links: e-print arXiv:2204.12957 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; HepData record ; CADI line (restricted) ;

Figures
png pdf	Figure 1: Binning for ggH production in the reduced STXS stage-1.2 scheme as exploited by the analyses presented in this paper. The dark gray boxes indicate the STXS bins measured by the analyses. Depending on the analysis, a split is applied to the 0-jet bin, as is indicated by the dashed line. The boxes colored in light gray indicate a finer subdivision of the NN signal classes for $N_{\text{jet}} \geq$ 2 used for the classification task, as explained in Section 7. Thresholds on $p_{\mathrm{T}} ^{ \mathrm{H} }$ are given in GeV.
png pdf	Figure 2: Binning for qqH production in the reduced STXS stage-1.2 scheme as exploited by the analyses presented in this paper. The gray boxes indicate the STXS bins measured by the analyses. Thresholds on $p_{\mathrm{T}} ^{ \mathrm{H} }$ and $m_{\mathrm{jj}}$ are given in GeV.
png pdf	Figure 3: Binning for VH production in the reduced STXS stage-1.2 scheme as exploited by the analysis presented in this paper. The gray boxes indicate the STXS bins measured by the analysis. Thresholds on $p_{\mathrm{T}} ^{ \mathrm{V} }$ are given in GeV.
png pdf	Figure 4: Confusion matrices for the NN classification tasks used for the (upper) STXS stage-0/inclusive and (lower) STXS stage-1.2 cross section measurements described in Section 7. These confusion matrices have been evaluated on the full test data set, comprising all data-taking years in the $\mu \tau _\mathrm{h}$ final state. They are normalized such that all entries in each column, corresponding to a given true event class, sum to unity.
png pdf	Figure 4-a: Confusion matrix for the NN classification tasks used for the STXS stage-0/inclusive cross section measurements described in Section 7. The matrix has been evaluated on the full test data set, comprising all data-taking years in the $\mu \tau _\mathrm{h}$ final state. It is normalized such that all entries in each column, corresponding to a given true event class, sum to unity.
png pdf	Figure 4-b: Confusion matrix for the NN classification tasks used for the STXS stage-1.2 cross section measurements described in Section 7. The matrix has been evaluated on the full test data set, comprising all data-taking years in the $\mu \tau _\mathrm{h}$ final state. It is normalized such that all entries in each column, corresponding to a given true event class, sum to unity.
png pdf	Figure 5: Observed and predicted distributions of $y_{l}$ for the signal classes for the ggH $N_{\text{jet}} =$ 1 subspace in three increasing STXS stage-1.2 bins in $p_{\mathrm{T}} ^{ \mathrm{H} }$ and the qqH $N_{\text{jet}} \geq$ 2 bin with $m_{\mathrm{jj}} \geq$ 700 GeV, $p_{\mathrm{T}} ^{ \mathrm{H} } [0, 200]$ GeV, in the $\mu \tau _\mathrm{h}$ final state of the NN-analysis. The distributions show all data-taking years combined. The signal contributions for (red) each STXS bin corresponding to the given event class, and the remaining inclusive (blue) ggH and (orange) qqH processes, excluding the STXS bin in consideration, are also shown as unstacked open histograms. All distributions are shown after the fit of the model, used for the extraction of the STXS stage-1.2 signals, to the data from all final states and data-taking years. Signal contributions in particular have been scaled according to the obtained fit results. In the lower panel of each plot the differences either of the corresponding additional signals or the data relative to the background expectation after fit are shown.
png pdf	Figure 5-a: Observed and predicted distributions of $y_{l}$ for the signal classes for the ggH $N_{\text{jet}} =$ 1 subspace in STXS stage-1.2 bin in $p_{\mathrm{T}} ^{ \mathrm{H} } [0,60]$ GeV, in the $\mu \tau _\mathrm{h}$ final state of the NN-analysis. The distribution shows all data-taking years combined. The signal contributions for (red) each STXS bin corresponding to the given event class, and the remaining inclusive (blue) ggH and (orange) qqH processes, excluding the STXS bin in consideration, are also shown as unstacked open histograms. All distributions are shown after the fit of the model, used for the extraction of the STXS stage-1.2 signals, to the data from all final states and data-taking years. Signal contributions in particular have been scaled according to the obtained fit results. In the lower panel \the differences either of the corresponding additional signals or the data relative to the background expectation after fit are shown.
png pdf	Figure 5-b: Observed and predicted distributions of $y_{l}$ for the signal classes for the ggH $N_{\text{jet}} =$ 1 subspace in STXS stage-1.2 bin in $p_{\mathrm{T}} ^{ \mathrm{H} } [60,120]$ GeV, in the $\mu \tau _\mathrm{h}$ final state of the NN-analysis. The distribution shows all data-taking years combined. The signal contributions for (red) each STXS bin corresponding to the given event class, and the remaining inclusive (blue) ggH and (orange) qqH processes, excluding the STXS bin in consideration, are also shown as unstacked open histograms. All distributions are shown after the fit of the model, used for the extraction of the STXS stage-1.2 signals, to the data from all final states and data-taking years. Signal contributions in particular have been scaled according to the obtained fit results. In the lower panel \the differences either of the corresponding additional signals or the data relative to the background expectation after fit are shown.
png pdf	Figure 5-c: Observed and predicted distributions of $y_{l}$ for the signal classes for the ggH $N_{\text{jet}} =$ 1 subspace in STXS stage-1.2 bin in $p_{\mathrm{T}} ^{ \mathrm{H} } [120,200]$ GeV, in the $\mu \tau _\mathrm{h}$ final state of the NN-analysis. The distribution shows all data-taking years combined. The signal contributions for (red) each STXS bin corresponding to the given event class, and the remaining inclusive (blue) ggH and (orange) qqH processes, excluding the STXS bin in consideration, are also shown as unstacked open histograms. All distributions are shown after the fit of the model, used for the extraction of the STXS stage-1.2 signals, to the data from all final states and data-taking years. Signal contributions in particular have been scaled according to the obtained fit results. In the lower panel \the differences either of the corresponding additional signals or the data relative to the background expectation after fit are shown.
png pdf	Figure 5-d: Observed and predicted distributions of $y_{l}$ for the signal classes for the qqH $N_{\text{jet}} \geq$ 2 bin with $m_{\mathrm{jj}} \geq$ 700 GeV, $p_{\mathrm{T}} ^{ \mathrm{H} } [0, 200]$ GeV, in the $\mu \tau _\mathrm{h}$ final state of the NN-analysis. The distribution shows all data-taking years combined. The signal contributions for (red) each STXS bin corresponding to the given event class, and the remaining inclusive (blue) ggH and (orange) qqH processes, excluding the STXS bin in consideration, are also shown as unstacked open histograms. All distributions are shown after the fit of the model, used for the extraction of the STXS stage-1.2 signals, to the data from all final states and data-taking years. Signal contributions in particular have been scaled according to the obtained fit results. In the lower panel \the differences either of the corresponding additional signals or the data relative to the background expectation after fit are shown.
png pdf	Figure 6: Observed and predicted distributions of the 2D discriminant as used for the extraction of the STXS stage-0 and inclusive signals, for all data-taking years in the $\mu \tau _\mathrm{h}$ final state of the NN-analysis. Also shown is the definition of each individual bin, on the right. The background distributions are shown after the fit of the model, used for the extraction of the inclusive signal to the data from all final states and data-taking years. For this fit some of the bins have been merged to ensure a sufficient population of each bin. The distributions are shown with the finest common binning across all data-taking years. The signal contributions for the (red) inclusive, (blue) ggH, and (orange) qqH signals are also shown as unstacked open histograms, scaled according to the correspondingly obtained fit results. The vertical gray dashed lines indicate six primary bins in $y_{ \mathrm{q} \mathrm{q} \mathrm{H} }$, the last four of which to the right have been enhanced by factors ranging from 3 to 15 for improved visibility. In the lower panel of the plot on the left the differences either of the corresponding additional signals or the data relative to the background expectation after fit are shown.
png pdf	Figure 6-a: Observed and predicted distributions of the 2D discriminant as used for the extraction of the STXS stage-0 and inclusive signals, for all data-taking years in the $\mu \tau _\mathrm{h}$ final state of the NN-analysis. The background distributions are shown after the fit of the model, used for the extraction of the inclusive signal to the data from all final states and data-taking years. For this fit some of the bins have been merged to ensure a sufficient population of each bin. The distributions are shown with the finest common binning across all data-taking years. The signal contributions for the (red) inclusive, (blue) ggH, and (orange) qqH signals are also shown as unstacked open histograms, scaled according to the correspondingly obtained fit results. The vertical gray dashed lines indicate six primary bins in $y_{ \mathrm{q} \mathrm{q} \mathrm{H} }$, the last four of which to the right have been enhanced by factors ranging from 3 to 15 for improved visibility. In the lower panel of the plot the differences either of the corresponding additional signals or the data relative to the background expectation after fit are shown.
png pdf	Figure 6-b: Shown is the definition of each individual bin.
png pdf	Figure 7: Signal composition of the subcategories of the CB-analysis, in terms of the STXS stage-1.2 bins (in %). The rows correspond to the signal categories described in the text including the signal categories of the VH -analysis as described in Section 9. The columns refer to the STXS bins specified in Figs. 3--5. The STXS stage-1.2 qqH bin with $N_{\text{jet}} <$ 2 or $m_{\mathrm{jj}} <$ 350 GeV is labeled by ``qqH/non-VBF-topo''. This figure is based on all $\tau \tau$ final states.
png pdf	Figure 8: Observed and predicted 2D distributions in the ${\geq}$ 2 jet category of the (upper) $\mathrm{e} \mu$, (middle) $\ell \tau _\mathrm{h}$, and (lower) $\tau _\mathrm{h} \tau _\mathrm{h}$ final states of the CB-analysis. The predicted signal and background distributions are shown after the fit used for the extraction of the inclusive signal. The ``Others'' background contribution includes events from diboson and single t quark production, as well as $\mathrm{H} \to \mathrm{W} \mathrm{W}$ decays. The uncertainty bands account for all systematic and statistical sources of uncertainty, after the fit to the data.
png pdf	Figure 8-a: Observed and predicted 2D distributions in the ${\geq}$ 2 jet category of the $\mathrm{e} \mu$ final state of the CB-analysis. The predicted signal and background distributions are shown after the fit used for the extraction of the inclusive signal. The ``Others'' background contribution includes events from diboson and single t quark production, as well as $\mathrm{H} \to \mathrm{W} \mathrm{W}$ decays. The uncertainty band accounts for all systematic and statistical sources of uncertainty, after the fit to the data.
png pdf	Figure 8-b: Observed and predicted 2D distributions in the ${\geq}$ 2 jet category of the $\ell \tau _\mathrm{h}$ final state of the CB-analysis. The predicted signal and background distributions are shown after the fit used for the extraction of the inclusive signal. The ``Others'' background contribution includes events from diboson and single t quark production, as well as $\mathrm{H} \to \mathrm{W} \mathrm{W}$ decays. The uncertainty band accounts for all systematic and statistical sources of uncertainty, after the fit to the data.
png pdf	Figure 8-c: Observed and predicted 2D distributions in the ${\geq}$ 2 jet category of the $\tau _\mathrm{h} \tau _\mathrm{h}$ final state of the CB-analysis. The predicted signal and background distributions are shown after the fit used for the extraction of the inclusive signal. The ``Others'' background contribution includes events from diboson and single t quark production, as well as $\mathrm{H} \to \mathrm{W} \mathrm{W}$ decays. The uncertainty band accounts for all systematic and statistical sources of uncertainty, after the fit to the data.
png pdf	Figure 9: Observed and predicted distribution of $m_{ \tau \tau }$ in three bins of $\hat{p}_{\mathrm{T}}^{ \mathrm{V} }$, combined for all final states and all data-taking years for the (upper) WH and (lower) ZH analyses.
png pdf	Figure 9-a: Observed and predicted distribution of $m_{ \tau \tau }$ in three bins of $\hat{p}_{\mathrm{T}}^{ \mathrm{V} }$, combined for all final states and all data-taking years for the WH analysis.
png pdf	Figure 9-b: Observed and predicted distribution of $m_{ \tau \tau }$ in three bins of $\hat{p}_{\mathrm{T}}^{ \mathrm{V} }$, combined for all final states and all data-taking years for the ZH analysis.
png pdf	Figure 10: Measurements of the signal strength parameters for inclusive H production ($\mu_{\text{incl}}$) and the ggH ($\mu_{ \mathrm{g} \mathrm{g} \mathrm{H} }$), qqH ($\mu_{ \mathrm{q} \mathrm{q} \mathrm{H} }$), and VH ($\mu_{ \mathrm{V} \mathrm{H} }$) STXS stage-0 processes. The combination of the CB- and VH -analyses is labeled by CB. The combination of the NN- and VH -analyses is labeled by NN. Central values maximizing the likelihood and a split of uncertainties as explained in the text are provided with each result.
png pdf	Figure 11: Observed and expected $m_{ \tau \tau }$ distributions of the analyzed data in all $\tau \tau$ final states. For the (upper left) CB-, (lower left) WH -, and (lower right) ZH -analyses, $m_{ \tau \tau }$ from all event categories and data-taking years in a predefined window around the assumed H mass [13] is histogrammed, weighted by the signal (S) over combined background (B) ratio in each event category. For the (upper right) NN-analysis, the events fulfilling $y_{ \mathrm{g} \mathrm{g} \mathrm{H} } + y_{ \mathrm{q} \mathrm{q} \mathrm{H} } >$ 0.8 are shown without further weight applied. The inclusive contribution of the H signal with $\mu_{\text{incl}}$ as obtained from the maximum likelihood estimates is also shown, in each subfigure. For the upper right figure $\mu_{\text{incl}}$ is obtained from the combination of the VH- and the NN-analyses, for the other figures $\mu_{\text{incl}}$ is obtained from the combination of the VH- and the CB-analyses.
png pdf	Figure 11-a: Observed and expected $m_{ \tau \tau }$ distributions of the analyzed data in all $\tau \tau$ final states. For the CB-analysis, $m_{ \tau \tau }$ from all event categories and data-taking years in a predefined window around the assumed H mass [13] is histogrammed, weighted by the signal (S) over combined background (B) ratio in each event category. The inclusive contribution of the H signal with $\mu_{\text{incl}}$ as obtained from the maximum likelihood estimates is also shown. $\mu_{\text{incl}}$ is obtained from the combination of the VH- and the CB-analyses.
png pdf	Figure 11-b: Observed and expected $m_{ \tau \tau }$ distributions of the analyzed data in all $\tau \tau$ final states. For the NN-analysis, the events fulfilling $y_{ \mathrm{g} \mathrm{g} \mathrm{H} } + y_{ \mathrm{q} \mathrm{q} \mathrm{H} } >$ 0.8 are shown without further weight applied. The inclusive contribution of the H signal with $\mu_{\text{incl}}$ as obtained from the maximum likelihood estimates is also shown. $\mu_{\text{incl}}$ is obtained from the combination of the VH- and the NN-analyses,
png pdf	Figure 11-c: Observed and expected $m_{ \tau \tau }$ distributions of the analyzed data in all $\tau \tau$ final states. For the WH-analysis, $m_{ \tau \tau }$ from all event categories and data-taking years in a predefined window around the assumed H mass [13] is histogrammed, weighted by the signal (S) over combined background (B) ratio in each event category. The inclusive contribution of the H signal with $\mu_{\text{incl}}$ as obtained from the maximum likelihood estimates is also shown. $\mu_{\text{incl}}$ is obtained from the combination of the VH- and the CB-analyses.
png pdf	Figure 11-d: Observed and expected $m_{ \tau \tau }$ distributions of the analyzed data in all $\tau \tau$ final states. For ZH-analysis, $m_{ \tau \tau }$ from all event categories and data-taking years in a predefined window around the assumed H mass [13] is histogrammed, weighted by the signal (S) over combined background (B) ratio in each event category. The inclusive contribution of the H signal with $\mu_{\text{incl}}$ as obtained from the maximum likelihood estimates is also shown. $\mu_{\text{incl}}$ is obtained from the combination of the VH- and the CB-analyses.
png pdf	Figure 12: Measurements of the signal strength parameters $\mu_{s}$ in the STXS stage-1.2 bins for the (upper row) ggH, (lower left) qqH, and (lower right) VH processes. The combination of the CB- and VH -analyses is labeled by CB. The combination of the NN- and VH -analyses is labeled by NN. Central values maximizing the likelihood and a split of uncertainties are also provided with each result.
png pdf	Figure 12-a: Measurements of the signal strength parameters $\mu_{s}$ in the STXS stage-1.2 bins for the ggH process. The combination of the CB- and VH -analyses is labeled by CB. The combination of the NN- and VH -analyses is labeled by NN. Central values maximizing the likelihood and a split of uncertainties are also provided with each result.
png pdf	Figure 12-b: Measurements of the signal strength parameters $\mu_{s}$ in the STXS stage-1.2 bins for the ggH process. The combination of the CB- and VH -analyses is labeled by CB. The combination of the NN- and VH -analyses is labeled by NN. Central values maximizing the likelihood and a split of uncertainties are also provided with each result.
png pdf	Figure 12-c: Measurements of the signal strength parameters $\mu_{s}$ in the STXS stage-1.2 bins for the qqH process. The combination of the CB- and VH -analyses is labeled by CB. The combination of the NN- and VH -analyses is labeled by NN. Central values maximizing the likelihood and a split of uncertainties are also provided with each result.
png pdf	Figure 12-d: Measurements of the signal strength parameters $\mu_{s}$ in the STXS stage-1.2 bins for the VH process. The combination of the CB- and VH -analyses is labeled by CB. The combination of the NN- and VH -analyses is labeled by NN. Central values maximizing the likelihood and a split of uncertainties are also provided with each result.
png pdf	Figure 13: Correlation matrices of the POIs of the measured STXS stage-1.2 signal strengths for the combination of the (upper) CB-, resp. (lower) NN-analysis with the VH -analysis.
png pdf	Figure 13-a: Correlation matrices of the POIs of the measured STXS stage-1.2 signal strengths for the combination of the CB-analysis with the VH-analysis.
png pdf	Figure 13-b: Correlation matrices of the POIs of the measured STXS stage-1.2 signal strengths for the combination of the NN-analysis with the VH-analysis.
png pdf	Figure 14: Cross section measurements in the (upper left) stage-0 bins, and in the stage-1.2 bins related to the (lower left) VH, (upper right) qqH, and (lower right) ggH processes. The combination of the CB- and VH -analyses is labeled by CB, the combination of the NN- and VH -analyses is labeled by NN. Central values and combined statistical and systematic uncertainties are given for each measurement.
png pdf	Figure 14-a: Cross section measurements in the (upper) stage-0 bins, and in the stage-1.2 bins related to the (lower) VH, (upper) qqH processes. The combination of the CB- and VH -analyses is labeled by CB, the combination of the NN- and VH -analyses is labeled by NN. Central values and combined statistical and systematic uncertainties are given for each measurement.
png pdf	Figure 14-b: Cross section measurements in the (upper) stage-0 bins, and in the stage-1.2 bins related to the ggH process. The combination of the CB- and VH -analyses is labeled by CB, the combination of the NN- and VH -analyses is labeled by NN. Central values and combined statistical and systematic uncertainties are given for each measurement.
png pdf	Figure 15: Most probable values, 68, and 95% confidence interval contours obtained from a negative log-likelihood scan, for a model treating the H couplings to vector bosons ($\kappa_{ \mathrm{V} }$) and fermions ($\kappa_{\mathrm{F}}$) as POIs. The combination of the CB- (NN-) with VH -analyses is shown in light red (dark blue). For the likelihood evaluation all nuisance parameters are profiled in each point in the plane. The $\mathrm{H} \to \mathrm{W} \mathrm{W}$ decay is treated as signal.

Tables
png pdf	Table 1: Selected working points for each of the analyses presented in this paper. For each analysis, the working point of $D_{\text{jet}}$ is the same for all final states. The working points for $D_{ \mathrm{e} }$ and $D_{ \mu }$ vary by final state. The labels WH and ZH stand for the individual production modes addressed by the VH -analysis. More details on the efficiency and misidentification rates of the individual working points are given in the text and in Ref. [54].
png pdf	Table 2: Offline selection requirements applied to the electron, muon, and $\tau _\mathrm{h}$ candidates used for the selection of the $\tau$ pair. The expressions first and second lepton refer to the label of the final state in the first column. The $p_{\mathrm{T}}$ requirements are given in GeV. For the $\mathrm{e} \mu$ final state two lepton pair trigger paths, with a stronger requirement on the $p_{\mathrm{T}}$ of electron (muon), are used for the online selection of the event. For the $\mathrm{e} \tau _\mathrm{h}$ and $\mu \tau _\mathrm{h}$ final states, the values (in parentheses) correspond to the lepton pair (single lepton) trigger paths that have been used in the online selection. A detailed discussion is given in the text.
png pdf	Table 3: Background processes and event classes for each $\tau \tau$ final state for the NN-analysis. All event classes enter the NN trainings for the event multiclassification with the same statistical weight (i.e., with uniform prevalence). The label ${ \mathrm{t} \overline{\mathrm{t}} } ( \mathrm{e} / \mu +X)$ refers to the fraction of $\mathrm{t \bar{t}}$ production that is not covered by any of the estimation methods from data, as listed in the first two rows. The classes tt, misc, zll, and db are defined in the introduction of Section 7.
png pdf	Table 4: Event categories of the CB-analysis. The STXS stage-0 and -1.2 measurements are extracted by performing a maximum likelihood fit of 1D and 2D distributions in these categories using the observables listed in the last column.
png pdf	Table 5: Selection requirements for $\mathrm{e}$, $\mu$ and $\tau _\mathrm{h}$ candidates used in the WH analysis. The three $p_{\mathrm{T}}$ thresholds specified for the $\mathrm{e}$ in the $\mathrm{e} \tau _\mathrm{h} \tau _\mathrm{h}$ final state refer to the years 2016, 2017, and 2018, respectively. The column labeled $I_{\text{rel}}^{ \mathrm{e} ( \mu )}$ refers to the lepton isolation variable, defined in Eq. (1).
png pdf	Table 6: Selection requirements for $\mathrm{e}$ and $\mu$ candidates that are associated with the $\mathrm{Z} \to \ell \ell$ decay in the ZH analysis. The three $p_{\mathrm{T}}$ thresholds and the three $\eta$ restrictions specified for the triggering leptons refer to the years 2016, 2017, and 2018, respectively. The column labeled $I_{\text{rel}}^{ \mathrm{e} ( \mu )}$ refers to the lepton isolation variable, defined in Eq. (1).
png pdf	Table 7: Selection requirements for $\mathrm{e}$, $\mu$, and $\tau _\mathrm{h}$ candidates associated with the $\tau \tau$ decay in the ZH analysis. First and second lepton refers to the label of the final state in the first column. The column labeled $I_{\text{rel}}^{ \mathrm{e} ( \mu )}$ refers to the lepton isolation variable, defined in Eq. (1).
png pdf	Table 8: Summary of the most important systematic uncertainties discussed in the text. The columns indicate the source of uncertainty, the process class that it applies to, the variation, and how it is correlated. A checkmark is given also for partial correlations. More details are given in the text.
png pdf	Table 9: Tabulated values of the STXS stage-0 and -1.2 signal strengths for the combination of the (CB) CB-, resp. (NN) NN-analysis with the VH -analysis. The upper four lines refer to the inclusive and STXS stage-0 measurements. The values in braces correspond to the expected 68% confidence intervals for an assumed SM signal. The products of cross sections and branching fraction to $\tau$ leptons as expected from the SM with the uncertainties as discussed in Section 4 are also given.

Summary

Measurements of Higgs boson production, where the Higgs boson decays into a pair of $\tau$ leptons, have been presented. The analyzed data are selected from proton-proton collisions at a center-of-mass energy of 13 TeV collected by the CMS experiment at the LHC from 2016--2018, corresponding to an integrated luminosity of 138 fb$^{-1}$. Results are presented in the form of signal strengths relative to the standard model predictions and products of cross sections and branching fraction to $\tau$ leptons, in up to 16 different kinematic regions, following the simplified template cross section scheme of the LHC Higgs Working Group. For the simultaneous measurements of a neural network based analysis and an analysis targeting vector boson associated Higgs boson production signal strengths are found to be 0.82 $\pm$ 0.11 for inclusive Higgs boson production, 0.67 $\pm$ 0.19 (0.81 $\pm$ 0.17) for the production mainly via gluon fusion (vector boson fusion), and 1.79 $\pm$ 0.45 for vector boson associated Higgs boson production. The latter result significantly improves an earlier measurement performed by the CMS Collaboration on a smaller data set.

Additional Figures
png pdf	Additional Figure 1: Observed and expected distributions of the NN output function $y_{l}$ in the signal class of the ggH STXS stage-1.2 bin with $\text{0 jet},\, p_{\mathrm{T}} ^{ \mathrm{H} } [0, 10]$ GeV in the $\mu \tau _\mathrm{h}$ final state. The signal contributions for (red) the corresponding STXS bin, and for the remaining inclusive (blue) ggH and (orange) qqH processes, excluding the STXS bin in consideration are also shown as unstacked open histograms. All distributions are shown after the fit of the model, used for the extraction of the STXS stage-1.2 signals, to the data from all final states and data-taking years. Signal contributions in particular have been scaled according to the obtained fit results.
png pdf	Additional Figure 2: Observed and expected distributions of the NN output function $y_{l}$ in the signal class of the ggH STXS stage-1.2 bin with $\text{0 jet},\, p_{\mathrm{T}} ^{ \mathrm{H} } [10, 200]$ GeV for all data-taking years, in the $\mu \tau _\mathrm{h}$ final state. The signal contributions for (red) the corresponding STXS bin, and for the remaining inclusive (blue) ggH and (orange) qqH processes, excluding the STXS bin in consideration are also shown as unstacked open histograms. All distributions are shown after the fit of the model, used for the extraction of the STXS stage-1.2 signals, to the data from all final states and data-taking years. Signal contributions in particular have been scaled according to the obtained fit results.
png pdf	Additional Figure 3: Observed and expected distributions of the NN output function $y_{l}$ in the signal class of the ggH STXS stage-1.2 bin with $\geq\text{2 jet},\, m_{\mathrm{jj}} \geq$ 350 GeV, $p_{\mathrm{T}} ^{ \mathrm{H} } [0, 200]$ GeV in the $\mu \tau _\mathrm{h}$ final state. The signal contributions for (red) the corresponding STXS bin, and for the remaining inclusive (blue) ggH and (orange) qqH processes, excluding the STXS bin in consideration are also shown as unstacked open histograms. All distributions are shown after the fit of the model, used for the extraction of the STXS stage-1.2 signals, to the data from all final states and data-taking years. Signal contributions in particular have been scaled according to the obtained fit results.
png pdf	Additional Figure 4: Observed and expected distributions of the NN output function $y_{l}$ in the signal class of the qqH STXS stage-1.2 bin with $\geq\text{2 jet},\, m_{\mathrm{jj}} \geq$ 700 GeV, $p_{\mathrm{T}} ^{ \mathrm{H} } [0, 200]$ GeV in the $\mu \tau _\mathrm{h}$ final state. The signal contributions for (red) the corresponding STXS bin, and for the remaining inclusive (blue) ggH and (orange) qqH processes, excluding the STXS bin in consideration are also shown as unstacked open histograms. All distributions are shown after the fit of the model, used for the extraction of the STXS stage-1.2 signals, to the data from all final states and data-taking years. Signal contributions in particular have been scaled according to the obtained fit results.
png pdf	Additional Figure 5: Observed and expected distributions of the NN output function $y_{l}$ in the signal class of the ggH STXS stage-1.2 bin with $\text{0 jet},\, p_{\mathrm{T}} ^{ \mathrm{H} } [0, 10]$ GeV in the $\tau _\mathrm{h} \tau _\mathrm{h}$ final state. The signal contributions for (red) the corresponding STXS bin, and for the remaining inclusive (blue) ggH and (orange) qqH processes, excluding the STXS bin in consideration are also shown as unstacked open histograms. All distributions are shown after the fit of the model, used for the extraction of the STXS stage-1.2 signals, to the data from all final states and data-taking years. Signal contributions in particular have been scaled according to the obtained fit results.
png pdf	Additional Figure 6: Observed and expected distributions of the NN output function $y_{l}$ in the signal class of the ggH STXS stage-1.2 bin with $\text{0 jet},\, p_{\mathrm{T}} ^{ \mathrm{H} } [10, 200]$ GeV in the $\tau _\mathrm{h} \tau _\mathrm{h}$ final state. The signal contributions for (red) the corresponding STXS bin, and for the remaining inclusive (blue) ggH and (orange) qqH processes, excluding the STXS bin in consideration are also shown as unstacked open histograms. All distributions are shown after the fit of the model, used for the extraction of the STXS stage-1.2 signals, to the data from all final states and data-taking years. Signal contributions in particular have been scaled according to the obtained fit results.
png pdf	Additional Figure 7: Observed and expected distributions of the NN output function $y_{l}$ in the signal class of the ggH STXS stage-1.2 bin with $\text{1 jet},\, p_{\mathrm{T}} ^{ \mathrm{H} } [0, 60]$ GeV in the $\tau _\mathrm{h} \tau _\mathrm{h}$ final state. The signal contributions for (red) the corresponding STXS bin, and for the remaining inclusive (blue) ggH and (orange) qqH processes, excluding the STXS bin in consideration are also shown as unstacked open histograms. All distributions are shown after the fit of the model, used for the extraction of the STXS stage-1.2 signals, to the data from all final states and data-taking years. Signal contributions in particular have been scaled according to the obtained fit results.
png pdf	Additional Figure 8: Observed and expected distributions of the NN output function $y_{l}$ in the signal class of the ggH STXS stage-1.2 bin with $\text{1 jet},\, p_{\mathrm{T}} ^{ \mathrm{H} } [60, 120]$ GeV in the $\tau _\mathrm{h} \tau _\mathrm{h}$ final state. The signal contributions for (red) the corresponding STXS bin, and for the remaining inclusive (blue) ggH and (orange) qqH processes, excluding the STXS bin in consideration are also shown as unstacked open histograms. All distributions are shown after the fit of the model, used for the extraction of the STXS stage-1.2 signals, to the data from all final states and data-taking years. Signal contributions in particular have been scaled according to the obtained fit results.
png pdf	Additional Figure 9: Observed and expected distributions of the NN output function $y_{l}$ in the signal class of the ggH STXS stage-1.2 bin with $\text{1 jet},\, p_{\mathrm{T}} ^{ \mathrm{H} } [120, 200]$ GeV in the $\tau _\mathrm{h} \tau _\mathrm{h}$ final state. The signal contributions for (red) the corresponding STXS bin, and for the remaining inclusive (blue) ggH and (orange) qqH processes, excluding the STXS bin in consideration are also shown as unstacked open histograms. All distributions are shown after the fit of the model, used for the extraction of the STXS stage-1.2 signals, to the data from all final states and data-taking years. Signal contributions in particular have been scaled according to the obtained fit results.
png pdf	Additional Figure 10: Observed and expected distributions of the NN output function $y_{l}$ in the signal class of the ggH STXS stage-1.2 bin with $\geq\text{2 jet},\, m_{\mathrm{jj}} \geq$ 350 GeV, $p_{\mathrm{T}} ^{ \mathrm{H} } [0, 200]$ GeV in the $\tau _\mathrm{h} \tau _\mathrm{h}$ final state. The signal contributions for (red) the corresponding STXS bin, and for the remaining inclusive (blue) ggH and (orange) qqH processes, excluding the STXS bin in consideration are also shown as unstacked open histograms. All distributions are shown after the fit of the model, used for the extraction of the STXS stage-1.2 signals, to the data from all final states and data-taking years. Signal contributions in particular have been scaled according to the obtained fit results.
png pdf	Additional Figure 11: Observed and expected distributions of the NN output function $y_{l}$ in the signal class of the qqH STXS stage-1.2 bin with $\geq\text{2 jet},\, m_{\mathrm{jj}} [350, 700]$ GeV, $p_{\mathrm{T}} ^{ \mathrm{H} } [0, 200]$ GeV in the $\tau _\mathrm{h} \tau _\mathrm{h}$ final state. The signal contributions for (red) the corresponding STXS bin, and for the remaining inclusive (blue) ggH and (orange) qqH processes, excluding the STXS bin in consideration are also shown as unstacked open histograms. All distributions are shown after the fit of the model, used for the extraction of the STXS stage-1.2 signals, to the data from all final states and data-taking years. Signal contributions in particular have been scaled according to the obtained fit results.
png pdf	Additional Figure 12: Observed and expected distributions of the NN output function $y_{l}$ in the signal class of the qqH STXS stage-1.2 bin with $\geq\text{2 jet},\, m_{\mathrm{jj}} \geq$ 700 GeV, $p_{\mathrm{T}} ^{ \mathrm{H} } [0, 200]$ GeV in the $\tau _\mathrm{h} \tau _\mathrm{h}$ final state. The signal contributions for (red) the corresponding STXS bin, and for the remaining inclusive (blue) ggH and (orange) qqH processes, excluding the STXS bin in consideration are also shown as unstacked open histograms. All distributions are shown after the fit of the model, used for the extraction of the STXS stage-1.2 signals, to the data from all final states and data-taking years. Signal contributions in particular have been scaled according to the obtained fit results.
png pdf	Additional Figure 13: Observed and expected distributions of the NN output function $y_{l}$ in the signal class of the ggH STXS stage-1.2 bin with $\text{0 jet},\, p_{\mathrm{T}} ^{ \mathrm{H} } [0, 10]$ GeV for all final states and the data taken in 2016. The signal contributions for (red) the corresponding STXS bin, and for the remaining inclusive (blue) ggH and (orange) qqH processes, excluding the STXS bin in consideration are also shown as unstacked open histograms. All distributions are shown after the fit of the model, used for the extraction of the STXS stage-1.2 signals, to the data from all final states and data-taking years. Signal contributions in particular have been scaled according to the obtained fit results.
png pdf	Additional Figure 14: Observed and expected distributions of the NN output function $y_{l}$ in the signal class of the ggH STXS stage-1.2 bin with $\text{0 jet},\, p_{\mathrm{T}} ^{ \mathrm{H} } [10, 200]$ GeV for all final states and the data taken in 2016. The signal contributions for (red) the corresponding STXS bin, and for the remaining inclusive (blue) ggH and (orange) qqH processes, excluding the STXS bin in consideration are also shown as unstacked open histograms. All distributions are shown after the fit of the model, used for the extraction of the STXS stage-1.2 signals, to the data from all final states and data-taking years. Signal contributions in particular have been scaled according to the obtained fit results.
png pdf	Additional Figure 15: Observed and expected distributions of the NN output function $y_{l}$ in the signal class of the ggH STXS stage-1.2 bin with $\text{1 jet},\, p_{\mathrm{T}} ^{ \mathrm{H} } [0, 60]$ GeV for all final states and the data taken in 2016. The signal contributions for (red) the corresponding STXS bin, and for the remaining inclusive (blue) ggH and (orange) qqH processes, excluding the STXS bin in consideration are also shown as unstacked open histograms. All distributions are shown after the fit of the model, used for the extraction of the STXS stage-1.2 signals, to the data from all final states and data-taking years. Signal contributions in particular have been scaled according to the obtained fit results.
png pdf	Additional Figure 16: Observed and expected distributions of the NN output function $y_{l}$ in the signal class of the ggH STXS stage-1.2 bin with $\text{1 jet},\, p_{\mathrm{T}} ^{ \mathrm{H} } [60, 120]$ GeV for all final states and the data taken in 2016. The signal contributions for (red) the corresponding STXS bin, and for the remaining inclusive (blue) ggH and (orange) qqH processes, excluding the STXS bin in consideration are also shown as unstacked open histograms. All distributions are shown after the fit of the model, used for the extraction of the STXS stage-1.2 signals, to the data from all final states and data-taking years. Signal contributions in particular have been scaled according to the obtained fit results.
png pdf	Additional Figure 17: Observed and expected distributions of the NN output function $y_{l}$ in the signal class of the ggH STXS stage-1.2 bin with $\text{1 jet},\, p_{\mathrm{T}} ^{ \mathrm{H} } [120, 200]$ GeV for all final states and the data taken in 2016. The signal contributions for (red) the corresponding STXS bin, and for the remaining inclusive (blue) ggH and (orange) qqH processes, excluding the STXS bin in consideration are also shown as unstacked open histograms. All distributions are shown after the fit of the model, used for the extraction of the STXS stage-1.2 signals, to the data from all final states and data-taking years. Signal contributions in particular have been scaled according to the obtained fit results.
png pdf	Additional Figure 18: Observed and expected distributions of the NN output function $y_{l}$ in the signal class of the ggH STXS stage-1.2 bin with $\geq\text{2 jet},\, m_{\mathrm{jj}} \geq$ 350 GeV, $p_{\mathrm{T}} ^{ \mathrm{H} } [0, 200]$ GeV for all final states and the data taken in 2016. The signal contributions for (red) the corresponding STXS bin, and for the remaining inclusive (blue) ggH and (orange) qqH processes, excluding the STXS bin in consideration are also shown as unstacked open histograms. All distributions are shown after the fit of the model, used for the extraction of the STXS stage-1.2 signals, to the data from all final states and data-taking years. Signal contributions in particular have been scaled according to the obtained fit results.
png pdf	Additional Figure 19: Observed and expected distributions of the NN output function $y_{l}$ in the signal class of the qqH STXS stage-1.2 bin with $\geq\text{2 jet},\, m_{\mathrm{jj}} [350, 700]$ GeV, $p_{\mathrm{T}} ^{ \mathrm{H} } [0, 200]$ GeV for all final states and the data taken in 2016. The signal contributions for (red) the corresponding STXS bin, and for the remaining inclusive (blue) ggH and (orange) qqH processes, excluding the STXS bin in consideration are also shown as unstacked open histograms. All distributions are shown after the fit of the model, used for the extraction of the STXS stage-1.2 signals, to the data from all final states and data-taking years. Signal contributions in particular have been scaled according to the obtained fit results.
png pdf	Additional Figure 20: Observed and expected distributions of the NN output function $y_{l}$ in the signal class of the qqH STXS stage-1.2 bin with $\geq\text{2 jet},\, m_{\mathrm{jj}} \geq$ 700 GeV, $p_{\mathrm{T}} ^{ \mathrm{H} } [0, 200]$ GeV for all final states and the data taken in 2016. The signal contributions for (red) the corresponding STXS bin, and for the remaining inclusive (blue) ggH and (orange) qqH processes, excluding the STXS bin in consideration are also shown as unstacked open histograms. All distributions are shown after the fit of the model, used for the extraction of the STXS stage-1.2 signals, to the data from all final states and data-taking years. Signal contributions in particular have been scaled according to the obtained fit results.
png pdf	Additional Figure 21: Observed and expected distributions of the NN output function $y_{l}$ in the signal class of the ggH STXS stage-1.2 bin with $\text{0 jet},\, p_{\mathrm{T}} ^{ \mathrm{H} } [0, 10]$ GeV for all final states and the data taken in 2017. The signal contributions for (red) the corresponding STXS bin, and for the remaining inclusive (blue) ggH and (orange) qqH processes, excluding the STXS bin in consideration are also shown as unstacked open histograms. All distributions are shown after the fit of the model, used for the extraction of the STXS stage-1.2 signals, to the data from all final states and data-taking years. Signal contributions in particular have been scaled according to the obtained fit results.
png pdf	Additional Figure 22: Observed and expected distributions of the NN output function $y_{l}$ in the signal class of the ggH STXS stage-1.2 bin with $\text{0 jet},\, p_{\mathrm{T}} ^{ \mathrm{H} } [10, 200]$ GeV for all final states and the data taken in 2017. The signal contributions for (red) the corresponding STXS bin, and for the remaining inclusive (blue) ggH and (orange) qqH processes, excluding the STXS bin in consideration are also shown as unstacked open histograms. All distributions are shown after the fit of the model, used for the extraction of the STXS stage-1.2 signals, to the data from all final states and data-taking years. Signal contributions in particular have been scaled according to the obtained fit results.
png pdf	Additional Figure 23: Observed and expected distributions of the NN output function $y_{l}$ in the signal class of the ggH STXS stage-1.2 bin with $\text{1 jet},\, p_{\mathrm{T}} ^{ \mathrm{H} } [0, 60]$ GeV for all final states and the data taken in 2017. The signal contributions for (red) the corresponding STXS bin, and for the remaining inclusive (blue) ggH and (orange) qqH processes, excluding the STXS bin in consideration are also shown as unstacked open histograms. All distributions are shown after the fit of the model, used for the extraction of the STXS stage-1.2 signals, to the data from all final states and data-taking years. Signal contributions in particular have been scaled according to the obtained fit results.
png pdf	Additional Figure 24: Observed and expected distributions of the NN output function $y_{l}$ in the signal class of the ggH STXS stage-1.2 bin with $\text{1 jet},\, p_{\mathrm{T}} ^{ \mathrm{H} } [60, 120]$ GeV for all final states and the data taken in 2017. The signal contributions for (red) the corresponding STXS bin, and for the remaining inclusive (blue) ggH and (orange) qqH processes, excluding the STXS bin in consideration are also shown as unstacked open histograms. All distributions are shown after the fit of the model, used for the extraction of the STXS stage-1.2 signals, to the data from all final states and data-taking years. Signal contributions in particular have been scaled according to the obtained fit results.
png pdf	Additional Figure 25: Observed and expected distributions of the NN output function $y_{l}$ in the signal class of the ggH STXS stage-1.2 bin with $\text{1 jet},\, p_{\mathrm{T}} ^{ \mathrm{H} } [120, 200]$ GeV for all final states and the data taken in 2017. The signal contributions for (red) the corresponding STXS bin, and for the remaining inclusive (blue) ggH and (orange) qqH processes, excluding the STXS bin in consideration are also shown as unstacked open histograms. All distributions are shown after the fit of the model, used for the extraction of the STXS stage-1.2 signals, to the data from all final states and data-taking years. Signal contributions in particular have been scaled according to the obtained fit results.
png pdf	Additional Figure 26: Observed and expected distributions of the NN output function $y_{l}$ in the signal class of the ggH STXS stage-1.2 bin with $\geq\text{2 jet},\, m_{\mathrm{jj}} \geq$ 350 GeV, $p_{\mathrm{T}} ^{ \mathrm{H} } [0, 200]$ GeV for all final states and the data taken in 2017. The signal contributions for (red) the corresponding STXS bin, and for the remaining inclusive (blue) ggH and (orange) qqH processes, excluding the STXS bin in consideration are also shown as unstacked open histograms. All distributions are shown after the fit of the model, used for the extraction of the STXS stage-1.2 signals, to the data from all final states and data-taking years. Signal contributions in particular have been scaled according to the obtained fit results.
png pdf	Additional Figure 27: Observed and expected distributions of the NN output function $y_{l}$ in the signal class of the qqH STXS stage-1.2 bin with $\geq\text{2 jet},\, m_{\mathrm{jj}} [350, 700]$ GeV, $p_{\mathrm{T}} ^{ \mathrm{H} } [0, 200]$ GeV for all final states and the data taken in 2017. The signal contributions for (red) the corresponding STXS bin, and for the remaining inclusive (blue) ggH and (orange) qqH processes, excluding the STXS bin in consideration are also shown as unstacked open histograms. All distributions are shown after the fit of the model, used for the extraction of the STXS stage-1.2 signals, to the data from all final states and data-taking years. Signal contributions in particular have been scaled according to the obtained fit results.
png pdf	Additional Figure 28: Observed and expected distributions of the NN output function $y_{l}$ in the signal class of the qqH STXS stage-1.2 bin with $\geq\text{2 jet},\, m_{\mathrm{jj}} \geq$ 700 GeV, $p_{\mathrm{T}} ^{ \mathrm{H} } [0, 200]$ GeV for all final states and the data taken in 2017. The signal contributions for (red) the corresponding STXS bin, and for the remaining inclusive (blue) ggH and (orange) qqH processes, excluding the STXS bin in consideration are also shown as unstacked open histograms. All distributions are shown after the fit of the model, used for the extraction of the STXS stage-1.2 signals, to the data from all final states and data-taking years. Signal contributions in particular have been scaled according to the obtained fit results.
png pdf	Additional Figure 29: Observed and expected distributions of the NN output function $y_{l}$ in the signal class of the ggH STXS stage-1.2 bin with $\text{0 jet},\, p_{\mathrm{T}} ^{ \mathrm{H} } [0, 10]$ GeV for all final states and the data taken in 2018. The signal contributions for (red) the corresponding STXS bin, and for the remaining inclusive (blue) ggH and (orange) qqH processes, excluding the STXS bin in consideration are also shown as unstacked open histograms. All distributions are shown after the fit of the model, used for the extraction of the STXS stage-1.2 signals, to the data from all final states and data-taking years. Signal contributions in particular have been scaled according to the obtained fit results.
png pdf	Additional Figure 30: Observed and expected distributions of the NN output function $y_{l}$ in the signal class of the ggH STXS stage-1.2 bin with $\text{0 jet},\, p_{\mathrm{T}} ^{ \mathrm{H} } [10, 200]$ GeV for all final states and the data taken in 2018. The signal contributions for (red) the corresponding STXS bin, and for the remaining inclusive (blue) ggH and (orange) qqH processes, excluding the STXS bin in consideration are also shown as unstacked open histograms. All distributions are shown after the fit of the model, used for the extraction of the STXS stage-1.2 signals, to the data from all final states and data-taking years. Signal contributions in particular have been scaled according to the obtained fit results.
png pdf	Additional Figure 31: Observed and expected distributions of the NN output function $y_{l}$ in the signal class of the ggH STXS stage-1.2 bin with $\text{1 jet},\, p_{\mathrm{T}} ^{ \mathrm{H} } [0, 60]$ GeV for all final states and the data taken in 2018. The signal contributions for (red) the corresponding STXS bin, and for the remaining inclusive (blue) ggH and (orange) qqH processes, excluding the STXS bin in consideration are also shown as unstacked open histograms. All distributions are shown after the fit of the model, used for the extraction of the STXS stage-1.2 signals, to the data from all final states and data-taking years. Signal contributions in particular have been scaled according to the obtained fit results.
png pdf	Additional Figure 32: Observed and expected distributions of the NN output function $y_{l}$ in the signal class of the ggH STXS stage-1.2 bin with $\text{1 jet},\, p_{\mathrm{T}} ^{ \mathrm{H} } [60, 120]$ GeV for all final states and the data taken in 2018. The signal contributions for (red) the corresponding STXS bin, and for the remaining inclusive (blue) ggH and (orange) qqH processes, excluding the STXS bin in consideration are also shown as unstacked open histograms. All distributions are shown after the fit of the model, used for the extraction of the STXS stage-1.2 signals, to the data from all final states and data-taking years. Signal contributions in particular have been scaled according to the obtained fit results.
png pdf	Additional Figure 33: Observed and expected distributions of the NN output function $y_{l}$ in the signal class of the ggH STXS stage-1.2 bin with $\text{1 jet},\, p_{\mathrm{T}} ^{ \mathrm{H} } [120, 200]$ GeV for all final states and the data taken in 2018. The signal contributions for (red) the corresponding STXS bin, and for the remaining inclusive (blue) ggH and (orange) qqH processes, excluding the STXS bin in consideration are also shown as unstacked open histograms. All distributions are shown after the fit of the model, used for the extraction of the STXS stage-1.2 signals, to the data from all final states and data-taking years. Signal contributions in particular have been scaled according to the obtained fit results.
png pdf	Additional Figure 34: Observed and expected distributions of the NN output function $y_{l}$ in the signal class of the ggH STXS stage-1.2 bin with $\geq\text{2 jet},\, m_{\mathrm{jj}} \geq$ 350 GeV, $p_{\mathrm{T}} ^{ \mathrm{H} } [0, 200]$ GeV for all final states and the data taken in 2018. The signal contributions for (red) the corresponding STXS bin, and for the remaining inclusive (blue) ggH and (orange) qqH processes, excluding the STXS bin in consideration are also shown as unstacked open histograms. All distributions are shown after the fit of the model, used for the extraction of the STXS stage-1.2 signals, to the data from all final states and data-taking years. Signal contributions in particular have been scaled according to the obtained fit results.
png pdf	Additional Figure 35: Observed and expected distributions of the NN output function $y_{l}$ in the signal class of the qqH STXS stage-1.2 bin with $\geq\text{2 jet},\, m_{\mathrm{jj}} [350, 700]$ GeV, $p_{\mathrm{T}} ^{ \mathrm{H} } [0, 200]$ GeV for all final states and the data taken in 2018. The signal contributions for (red) the corresponding STXS bin, and for the remaining inclusive (blue) ggH and (orange) qqH processes, excluding the STXS bin in consideration are also shown as unstacked open histograms. All distributions are shown after the fit of the model, used for the extraction of the STXS stage-1.2 signals, to the data from all final states and data-taking years. Signal contributions in particular have been scaled according to the obtained fit results.
png pdf	Additional Figure 36: Observed and expected distributions of the NN output function $y_{l}$ in the signal class of the qqH STXS stage-1.2 bin with $\geq\text{2 jet},\, m_{\mathrm{jj}} \geq$ 700 GeV, $p_{\mathrm{T}} ^{ \mathrm{H} } [0, 200]$ GeV for all final states and the data taken in 2018. The signal contributions for (red) the corresponding STXS bin, and for the remaining inclusive (blue) ggH and (orange) qqH processes, excluding the STXS bin in consideration are also shown as unstacked open histograms. All distributions are shown after the fit of the model, used for the extraction of the STXS stage-1.2 signals, to the data from all final states and data-taking years. Signal contributions in particular have been scaled according to the obtained fit results.
png pdf	Additional Figure 37: Observed and expected distributions of the NN output function $y_{l}$ in the genuine $\tau$ class for all data-taking years, in the $\mu \tau _\mathrm{h}$ final state. All distributions are shown after the fit of the model, used for the extraction of the inclusive signal, to the data from all final states and data-taking years.
png pdf	Additional Figure 38: Observed and expected distributions of the NN output function $y_{l}$ in the tt class for all data-taking years, in the $\mu \tau _\mathrm{h}$ final state. All distributions are shown after the fit of the model, used for the extraction of the inclusive signal, to the data from all final states and data-taking years.
png pdf	Additional Figure 39: Observed and expected distributions of the NN output function $y_{l}$ in the zll class for all data-taking years, in the $\mu \tau _\mathrm{h}$ final state. All distributions are shown after the fit of the model, used for the extraction of the inclusive signal, to the data from all final states and data-taking years.
png pdf	Additional Figure 40: Observed and expected distributions of the NN output function $y_{l}$ in the misc class for all data-taking years, in the $\mu \tau _\mathrm{h}$ final state. All distributions are shown after the fit of the model, used for the extraction of the inclusive signal, to the data from all final states and data-taking years.
png pdf	Additional Figure 41: Observed and expected distributions of the NN output function $y_{l}$ in the $\text{jet}\to \tau _\mathrm{h}$ class for all data-taking years, in the $\mu \tau _\mathrm{h}$ final state. All distributions are shown after the fit of the model, used for the extraction of the inclusive signal, to the data from all final states and data-taking years.
png pdf	Additional Figure 42: Observed and expected distributions of the 2D discriminant as used for the extraction of the STXS stage-0 and inclusive signals, for all data-taking years in the $\tau _\mathrm{h} \tau _\mathrm{h}$ final state. The background distributions are shown after the fit of the model, used for the extraction of the inclusive signal, to the data from all final states and data-taking years. The signal contributions for the (red) inclusive, (blue) ggH, and (orange) qqH signals are also shown as unstacked open histograms, scaled according to the correspondingly obtained fit results. The vertical gray dashed lines indicate six primary bins in $y_\text{qqH}$, the last four of which to the right have been enhanced by factors 5 --25 for improved visibility.
png pdf	Additional Figure 43: Definition of histogram bins for the 2D discriminant used for the extraction of the STXS stage-0 and inclusive signals. For the combined signal plot shown in Fig. 11 (upper right) of the paper, events with ${ y_\text{ggH} }+{ y_\text{qqH} } >$ 0.8 have been selected corresponding to the value space of $y_\text{ggH}$ and $y_\text{qqH}$ above and to the right of the red dashed line shown in this figure.
png pdf	Additional Figure 44: Observed and expected distributions of the NN output function $y_{l}$ in the genuine $\tau$ class for all data-taking years, in the $\tau _\mathrm{h} \tau _\mathrm{h}$ final state. All distributions are shown after the fit of the model, used for the extraction of the inclusive signal, to the data from all final states and data-taking years.
png pdf	Additional Figure 45: Observed and expected distributions of the NN output function $y_{l}$ in the $\text{jet}\to \tau _\mathrm{h}$ class for all data-taking years, in the $\tau _\mathrm{h} \tau _\mathrm{h}$ final state. All distributions are shown after the fit of the model, used for the extraction of the inclusive signal, to the data from all final states and data-taking years.
png pdf	Additional Figure 46: Observed and expected distributions of the NN output function $y_{l}$ in the misc class for all data-taking years, in the $\tau _\mathrm{h} \tau _\mathrm{h}$ final state. All distributions are shown after the fit of the model, used for the extraction of the inclusive signal, to the data from all final states and data-taking years.
png pdf	Additional Figure 47: Confusion matrix for the NN classification task used for the stage-0 STXS and inclusive cross section measurements. The confusion matrix has been evaluated on the full test data set, comprising all data-taking years in the $\tau _\mathrm{h} \tau _\mathrm{h}$ final state. It is normalized such that all entries in each column, corresponding to a given true event class, sum to unity.
png pdf	Additional Figure 48: Confusion matrix for the NN classification task used for the stage-1.2 STXS cross section measurements. The confusion matrix has been evaluated on the full test data set, comprising all data-taking years in the $\tau _\mathrm{h} \tau _\mathrm{h}$ final state. It is normalized such that all entries in each column, corresponding to a given true event class, sum to unity.
png pdf	Additional Figure 49: Inclusive signal strength, relative to the expectation from the SM, as obtained from the fit of model, used for the extraction of the inclusive signal, to the data from all final states and data-taking years. To obtain the results for the individual final states four parameters of interest have been introduced to the model, one for each final state. The results are compared to the inclusive result with only one parameter of interest.
png pdf	Additional Figure 50: Inclusive signal strength as obtained from the fit of model, used for the extraction of the inclusive signal, to the data from all final states and data-taking years. To obtain the results for the individual data-taking years four parameters of interest have been introduced to the model, one for each data-taking year. The results are compared to the inclusive result with only one parameter of interest.
png pdf	Additional Figure 51: Post-fit distribution from the CB-analysis, in the $\mathrm{e} \mu$ final state, 0-jet category.
png pdf	Additional Figure 52: Post-fit distribution from the CB-analysis, in the $\mathrm{e} \mu$ final state, boosted 1-jet category.
png pdf	Additional Figure 53: Post-fit distribution from the CB-analysis, in the $\mathrm{e} \mu$ final state, boosted ${\geq2}$-jets category.
png pdf	Additional Figure 54: Post-fit distribution from the CB-analysis, in the $\mathrm{e} \mu$ final state, VBF high $p_{\mathrm{T}} ^{ \mathrm{H} }$ category.
png pdf	Additional Figure 55: Post-fit distribution from the CB-analysis, in the $\mathrm{e} \mu$ final state, VBF low $p_{\mathrm{T}} ^{ \mathrm{H} }$ category.
png pdf	Additional Figure 56: Post-fit distribution from the CB-analysis, in the $\mathrm{e} \tau _\mathrm{h} + \mu \tau _\mathrm{h}$ final states, 0-Jet category.
png pdf	Additional Figure 57: Post-fit distribution from the CB-analysis, in the $\mathrm{e} \tau _\mathrm{h} + \mu \tau _\mathrm{h}$ final states, boosted 1-jet category.
png pdf	Additional Figure 58: Post-fit distribution from the CB-analysis, in the $\mathrm{e} \tau _\mathrm{h} + \mu \tau _\mathrm{h}$ final states, boosted ${\geq2}$-jets category.
png pdf	Additional Figure 59: Post-fit distribution from the CB-analysis, in the $\mathrm{e} \tau _\mathrm{h} + \mu \tau _\mathrm{h}$ final states, VBF high $p_{\mathrm{T}} ^{ \mathrm{H} }$ category.
png pdf	Additional Figure 60: Post-fit distribution from the CB-analysis, in the $\mathrm{e} \tau _\mathrm{h} + \mu \tau _\mathrm{h}$ final states, VBF low $p_{\mathrm{T}} ^{ \mathrm{H} }$ category.
png pdf	Additional Figure 61: Post-fit distribution from the CB-analysis, in the $\tau _\mathrm{h} \tau _\mathrm{h}$ final state, 0-Jet category.
png pdf	Additional Figure 62: Post-fit distribution from the CB-analysis, in the $\tau _\mathrm{h} \tau _\mathrm{h}$ final state, boosted 1-jet category.
png pdf	Additional Figure 63: Post-fit distribution from the CB-analysis, in the $\tau _\mathrm{h} \tau _\mathrm{h}$ final state, boosted ${\geq2}$-jets category.
png pdf	Additional Figure 64: Post-fit distribution from the CB-analysis, in the $\tau _\mathrm{h} \tau _\mathrm{h}$ final state, VBF high $p_{\mathrm{T}} ^{ \mathrm{H} }$ category.
png pdf	Additional Figure 65: Post-fit distribution from the CB-analysis, in the $\tau _\mathrm{h} \tau _\mathrm{h}$ final state, VBF low $p_{\mathrm{T}} ^{ \mathrm{H} }$ category.
png pdf	Additional Figure 66: Pre-fit visible mass distribution from the $\mu \tau _\mathrm{h}$ final state of the CB-analysis. Only statistical errors are shown.
png pdf	Additional Figure 67: Pre-fit visible mass distribution from the $\tau _\mathrm{h} \tau _\mathrm{h}$ final state of the CB-analysis. Only statistical errors are shown.

Additional Tables
png pdf	Additional Table 1: List of features used for training of the NNs in the $\tau _\mathrm{h} \tau _\mathrm{h}$, $\mathrm{e} \tau _\mathrm{h}$, $\mu \tau _\mathrm{h}$, and $\mathrm{e} \mu$ final states of the NN-analysis. First and second lepton refers to the label of the final state of each corresponding column, $p_{\mathrm T}^{\text{jj}}$ refers to the vector sum of the $p_{\mathrm{T}}$ of the two leading jets, and $Q^{2}_{\mathrm{V}_{1(2)}}$ to the estimate of the momentum transfer of the first (second) exchanged vector boson under the VBF hypothesis, as described in the text of the paper. All other variables are also described in the text of the paper.
png pdf	Additional Table 2: Observed and expected event yields after the fit of the background model to the data. The yields are shown split by the STXS stage-0 categories in the $\mathrm{e} \mu$ final state of the NN-analysis. The relative fractions of the most important background processes with respect to the total expected background yield are also shown. The process labels are given as defined in Section 5 and summarized in Table 3 of the paper. Signal comprises the ggH and qqH categories.
png pdf	Additional Table 3: Observed and expected event yields after the fit of the background model to the data. The yields are shown split by the STXS stage-0 categories in the $\mathrm{e} \tau _\mathrm{h}$ final state of the NN-analysis. The relative fractions of the most important background processes with respect to the total expected background yield are also shown. The process labels are given as defined in Section 5 and summarized in Table 3 of the paper. Signal comprises the ggH and qqH categories.
png pdf	Additional Table 4: Observed and expected event yields after the fit of the background model to the data. The yields are shown split by the STXS stage-0 categories in the $\mu \tau _\mathrm{h}$ final state of the NN-analysis. The relative fractions of the most important background processes with respect to the total expected background yield are also shown. The process labels are given as defined in Section 5 and summarized in Table 3 of the paper. Signal comprises the ggH and qqH categories.
png pdf	Additional Table 5: Observed and expected event yields after the fit of the background model to the data. The yields are shown split by the STXS stage-0 categories in the $\tau _\mathrm{h} \tau _\mathrm{h}$ final state of the NN-analysis. The relative fractions of the most important background processes with respect to the total expected background yield are also shown. The process labels are given as defined in Section 5 and summarized in Table 3 of the paper. Signal comprises the ggH and qqH categories.
png pdf	Additional Table 6: Observed and expected event yields after the fit of the background model to the data. The yields are shown split by the STXS stage-0 categories in the $\mathrm{e} \mu$ final state of the NN-analysis, in the highest purity bin of each corresponding data-taking year. The relative fractions of the most important background processes with respect to the total expected background yield are also shown. The process labels are given as defined in Section 5 and summarized in Table 3 of the paper. Signal comprises the ggH and qqH categories.
png pdf	Additional Table 7: Observed and expected event yields after the fit of the background model to the data. The yields are shown split by the STXS stage-0 categories in the $\mathrm{e} \tau _\mathrm{h}$ final state of the NN-analysis, in the highest purity bin of each corresponding data-taking year. The relative fractions of the most important background processes with respect to the total expected background yield are also shown. The process labels are given as defined in Section 5 and summarized in Table 3 of the paper. Signal comprises the ggH and qqH categories.
png pdf	Additional Table 8: Observed and expected event yields after the fit of the background model to the data. The yields are shown split by the STXS stage-0 categories in the $\mu \tau _\mathrm{h}$ final state of the NN-analysis, in the highest purity bin of each corresponding data-taking year. The relative fractions of the most important background processes with respect to the total expected background yield are also shown. The process labels are given as defined in Section 5 and summarized in Table 3 of the paper. Signal comprises the ggH and qqH categories.
png pdf	Additional Table 9: Observed and expected event yields after the fit of the background model to the data. The yields are shown split by the STXS stage-0 categories in the $\tau _\mathrm{h} \tau _\mathrm{h}$ final state of the NN-analysis, in the highest purity bin of each corresponding data-taking year. The relative fractions of the most important background processes with respect to the total expected background yield are also shown. The process labels are given as defined in Section 5 and summarized in Table 3 of the paper. Signal comprises the ggH and qqH categories.

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