Comparison of the $m_{miss}$ shapes for the simulated signal events within the fiducial region and those outside it, after including the effect of PU protons as describe in the text, for a generated $m_{X}$ mass of 1000 GeV. The distributions are shown for single(+z)-single(−z) proton reconstruction categories.

Product of the acceptance times the combined reconstruction and identification efficiency, as a function of $m_{X}$ , for events generated inside the fiducial volume defined in Table 1. The curves shown panel display the different final states. The definition of the fiducial region and signal model used to estimate the acceptance is provided in the text.

Product of the acceptance times the combined reconstruction and identification efficiency, as a function of $m_{X}$ , for different proton reconstruction categories in the $Z \rightarrow \mu\mu $ analysis, and for events generated inside the fiducial volume defined in Table 1. The curves shown panel display the different final states. The definition of the fiducial region and signal model used to estimate the acceptance is provided in the text.

Distributions of the reconstructed proton $\xi$ in the negative arm from the proton mixing procedure with simulated MC events, are compared to data. The ee final states are shown.The ee events are displayed without the Z boson $p_T$ requirement.For illustration, the simulated signal distributions are superimposed for various choices of $m_{X}$ , normalised to a generated fiducial cross section of 100 pb.

Distributions of the reconstructed proton $\xi$ in the positive arm from the proton mixing procedure with simulated MC events, are compared to data. The ee final states are shown.The ee events are displayed without the Z boson $p_T$ requirement.For illustration, the simulated signal distributions are superimposed for various choices of $m_{X}$ , normalised to a generated fiducial cross section of 100 pb.

Distributions of the reconstructed di-proton rapidity from the proton mixing procedure with simulated MC events, are compared to data. The ee final states are shown.The ee events are displayed without the Z boson $p_T$ requirement.For illustration, the simulated signal distributions are superimposed for various choices of $m_{X}$ , normalised to a generated fiducial cross section of 100 pb.

Distributions of the reconstructed proton $\xi$ in the negative arm from the proton mixing procedure with simulated MC events, are compared to data. The $\mu\mu$ final states are shown.The $\mu\mu$ events are displayed without the Z boson $p_T$ requirement.For illustration, the simulated signal distributions are superimposed for various choices of $m_{X}$ , normalised to a generated fiducial cross section of 100 pb.

Distributions of the reconstructed proton $\xi$ in the positive arm from the proton mixing procedure with simulated MC events, are compared to data. The $\mu\mu$ final states are shown.The $\mu\mu$ events are displayed without the Z boson $p_T$ requirement.For illustration, the simulated signal distributions are superimposed for various choices of $m_{X}$ , normalised to a generated fiducial cross section of 100 pb.

Distributions of the reconstructed di-proton rapidity from the proton mixing procedure with simulated MC events, are compared to data. The $\mu\mu$ final states are shown.The $\mu\mu$ events are displayed without the Z boson $p_T$ requirement.For illustration, the simulated signal distributions are superimposed for various choices of $m_{X}$ , normalised to a generated fiducial cross section of 100 pb.

Distributions of the reconstructed proton $\xi$ in the negative arm from the proton mixing procedure with simulated MC events, are compared to data. The $\gamma$ final states are shown.For illustration, the simulated signal distributions are superimposed for various choices of $m_{X}$ , normalised to a generated fiducial cross section of 100 pb.

Distributions of the reconstructed proton $\xi$ in the positive arm from the proton mixing procedure with simulated MC events, are compared to data. The $\gamma$ final states are shown.For illustration, the simulated signal distributions are superimposed for various choices of $m_{X}$ , normalised to a generated fiducial cross section of 100 pb.

Distributions of the reconstructed di-proton rapidity from the proton mixing procedure with simulated MC events, are compared to data. The $\gamma$ final states are shown.For illustration, the simulated signal distributions are superimposed for various choices of $m_{X}$ , normalised to a generated fiducial cross section of 100 pb.

Validation of the background modelling method, using the $e\mu$ control sample. Selected $e\mu$ events are mixed with protons from $Z\rightarrow \mu \mu$ events with $p_{T}(Z)<10$ GeV to simulate the combinatorial background shape, while the data points are unaltered $e\mu$ events. The proton $\xi$ distribution for the positive CT-PPS arm is shown.

Validation of the background modelling method, using the $e\mu$ control sample. Selected $e\mu$ events are mixed with protons from $Z\rightarrow \mu \mu$ events with $p_{T}(Z)<10$ GeV to simulate the combinatorial background shape, while the data points are unaltered $e\mu$ events. The proton $\xi$ distribution for the negative CT-PPS arm is shown.

Validation of the background modelling method, using the $e\mu$ control sample. Selected $e\mu$ events are mixed with protons from $Z\rightarrow \mu \mu$ events with $p_{T}(Z)<10$ GeV to simulate the combinatorial background shape, while the data points are unaltered $e\mu$ events. The di-proton invariant mass is shown.

Validation of the background modelling method, using the $e\mu$ control sample. Selected $e\mu$ events are mixed with protons from $Z\rightarrow \mu \mu$ events with $p_{T}(Z)<10$ GeV to simulate the combinatorial background shape, while the data points are unaltered $e\mu$ events. The $m_{miss}$ is shown.

$m_{miss}$ distributions in the $pp\rightarrow ppZeeX$, with the protons reconstructed with the multi(+z)-multi(-z)method. The background distributions are shown after the fit. The expectations for a signal with $m_{X} = 1000$ GeV are superimposed, where the fiducial production cross section is normalised to 1 pb.

$m_{miss}$ distributions in the $pp\rightarrow ppZeeX$, with the protons reconstructed with the multi(+z)-single(-z)method. The background distributions are shown after the fit. The expectations for a signal with $m_{X} = 1000$ GeV are superimposed, where the fiducial production cross section is normalised to 1 pb.

$m_{miss}$ distributions in the $pp\rightarrow ppZeeX$, with the protons reconstructed with the single(+z)-multi(-z)method. The background distributions are shown after the fit. The expectations for a signal with $m_{X} = 1000$ GeV are superimposed, where the fiducial production cross section is normalised to 1 pb.

$m_{miss}$ distributions in the $pp\rightarrow ppZeeX$, with the protons reconstructed with the single(+z)-single(-z)method. The background distributions are shown after the fit. The expectations for a signal with $m_{X} = 1000$ GeV are superimposed, where the fiducial production cross section is normalised to 1 pb.

$m_{miss}$ distributions in the $pp\rightarrow ppZ\mu\mu X$, with the protons reconstructed with the multi(+z)-multi(-z)method. The background distributions are shown after the fit. The expectations for a signal with $m_{X} = 1000$ GeV are superimposed, where the fiducial production cross section is normalised to 1 pb.

$m_{miss}$ distributions in the $pp\rightarrow ppZ\mu\mu X$, with the protons reconstructed with the multi(+z)-single(-z)method. The background distributions are shown after the fit. The expectations for a signal with $m_{X} = 1000$ GeV are superimposed, where the fiducial production cross section is normalised to 1 pb.

$m_{miss}$ distributions in the $pp\rightarrow ppZ\mu\mu X$, with the protons reconstructed with the single(+z)-multi(-z)method. The background distributions are shown after the fit. The expectations for a signal with $m_{X} = 1000$ GeV are superimposed, where the fiducial production cross section is normalised to 1 pb.

$m_{miss}$ distributions in the $pp\rightarrow ppZ\mu\mu X$, with the protons reconstructed with the single(+z)-single(-z)method. The background distributions are shown after the fit. The expectations for a signal with $m_{X} = 1000$ GeV are superimposed, where the fiducial production cross section is normalised to 1 pb.

$m_{miss}$ distributions in the $pp\rightarrow pp\gamma X$, with the protons reconstructed with the multi(+z)-multi(-z)method. The background distributions are shown after the fit. The expectations for a signal with $m_{X} = 1000$ GeV are superimposed, where the fiducial production cross section is normalised to 10 pb.

$m_{miss}$ distributions in the $pp\rightarrow pp\gamma X$, with the protons reconstructed with the multi(+z)-single(-z)method. The background distributions are shown after the fit. The expectations for a signal with $m_{X} = 1000$ GeV are superimposed, where the fiducial production cross section is normalised to 10 pb.

$m_{miss}$ distributions in the $pp\rightarrow pp\gamma X$, with the protons reconstructed with the single(+z)-multi(-z)method. The background distributions are shown after the fit. The expectations for a signal with $m_{X} = 1000$ GeV are superimposed, where the fiducial production cross section is normalised to 10 pb.

$m_{miss}$ distributions in the $pp\rightarrow pp\gamma X$, with the protons reconstructed with the single(+z)-single(-z)method. The background distributions are shown after the fit. The expectations for a signal with $m_{X} = 1000$ GeV are superimposed, where the fiducial production cross section is normalised to 10 pb.

Upper limits on the $pp\rightarrow ppZ/\gamma X$ cross section at 95% CL, as a function of $m_X$. The 68 and 95% central intervals of the expected limits are represented by the green and yellow bands, respectively, while the observed limit is superimposed as a curve. The plot corresponds to the $Z\rightarrow ee$ analysis.

Upper limits on the $pp\rightarrow ppZ/\gamma X$ cross section at 95% CL, as a function of $m_X$. The 68 and 95% central intervals of the expected limits are represented by the green and yellow bands, respectively, while the observed limit is superimposed as a curve. The plot corresponds to the $Z\rightarrow \mu\mu$ analysis.

Upper limits on the $pp\rightarrow ppZ/\gamma X$ cross section at 95% CL, as a function of $m_X$. The 68 and 95% central intervals of the expected limits are represented by the green and yellow bands, respectively, while the observed limit is superimposed as a curve. The plot corresponds to the $Z$ analysis.

Upper limits on the $pp\rightarrow ppZ/\gamma X$ cross section at 95% CL, as a function of $m_X$. The 68 and 95% central intervals of the expected limits are represented by the green and yellow bands, respectively, while the observed limit is superimposed as a curve. The plot corresponds to the $\gamma$ analysis.

The distribution of the BDT discriminants for the full 2016--2018 data set in the all-hadronic channel. The sample VR category shown is defined by $N_\textrm{RT} \geq 2$, $H_T > 1100$ GeV. The background from QCD multijet and $\textrm{t}\bar{\textrm{t}}$ production is derived from control regions in the data. Estimates for the $\textrm{t}\bar{\textrm{t}}\textrm{t}\bar{\textrm{t}}$ signal and other backgrounds are shown using simulated samples. The hatched bands correspond to the estimated total uncertainty.

The distribution of the BDT discriminants for the full 2016--2018 data set in the all-hadronic channel. The SR category shown in this figure is defined by $N_\textrm{RT}=1$, $N_\textrm{BT} \geq 1$, $H_T > 1400$ GeV. The background from QCD multijet and $\textrm{t}\bar{\textrm{t}}$ production is derived from control regions in the data. Estimates for the $\textrm{t}\bar{\textrm{t}}\textrm{t}\bar{\textrm{t}}$ signal and other backgrounds are shown using simulated samples. The hatched bands correspond to the estimated total uncertainty after the fit.

The distribution of the BDT discriminants for the full 2016--2018 data set in the all-hadronic channel. The SR category shown in this figure is defined by $N_\textrm{RT} = 2$, $H_T > 1100$ GeV. The background from QCD multijet and $\textrm{t}\bar{\textrm{t}}$ production is derived from control regions in the data. Estimates for the $\textrm{t}\bar{\textrm{t}}\textrm{t}\bar{\textrm{t}}$ signal and other backgrounds are shown using simulated samples. The hatched bands correspond to the estimated total uncertainty after the fit.

Expected and observed significance (in standard deviations) for $\textrm{t}\bar{\textrm{t}}\textrm{t}\bar{\textrm{t}}$ production from each final state and the combination with previous CMS results (EPJC 80 (2020) 75 and JHEP 11 (2019) 082). The same-sign dilepton and multilepton (SSDL\&ML) final state results are from EPJC 80 (2020) 75.

Measured signal strength ($\mu = \sigma_{\textrm{t}\bar{\textrm{t}}\textrm{t}\bar{\textrm{t}}}/ \sigma_{\textrm{t}\bar{\textrm{t}}\textrm{t}\bar{\textrm{t}}} ^{\textrm{SM}}$), corresponding cross section (in fb), and the expected and observed significance (in standard deviations) for $\textrm{t}\bar{\textrm{t}}\textrm{t}\bar{\textrm{t}}$ production from all analysis channels. This table shows production from each analysis channel in this Letter, the combination of those channels, the results from previously published results, and the full combination of all CMS 2016-2018 results.

The observed and expected 95% CL upper limits on the minimal coupling vector LQ pair production cross-sections assuming B = 1 as a function of m$_\text{LQ}$.

The observed and expected 95% CL upper limits on the Yang-Mills coupling vector LQ pair production cross-sections assuming B = 1 as a function of m$_\text{LQ}$.

The observed and expected 95% CL upper limits on the branching ratio into charged leptons as a function of m$_\text{LQ}$ for the scalar LQ.

The observed and expected 95% CL upper limits on the branching ratio into charged leptons as a function of m$_\text{LQ}$ for the vector LQ minimal coupling scenario.

The observed and expected 95% CL upper limits on the branching ratio into charged leptons as a function of m$_\text{LQ}$ for the vector LQ Yang-Mills coupling scenario.

Observed and expected 95% CL upper limits on ${{(\sigma_{\text{H}}/\sigma_{\text{H}}^{\mathrm{SM}}) \times {{\mathcal{B}(\text{H} \to \text{inv})}}}}$ for the combined VBF, ttH, VH and ggH channels using all available CMS data for 2016--2018, Run1, 2015, and their combination, assuming a SM Higgs boson with a mass of 125 GeV.

Observed and expected 95% CL upper limits on ${{(\sigma_{\text{H}}/\sigma_{\text{H}}^{\mathrm{SM}}) \times {{\mathcal{B}(\text{H} \to \text{inv})}}}}$ for the VBF, ttH(lep), ttH(had), V(qq)H, Z(ll)H, Z(bb)H and ggH channels using all available CMS data, and their combination, assuming a SM Higgs boson with a mass of 125 GeV.

The 90% CL upper limits on the spin-independent DM-nucleon scattering cross section in Higgs-portal models, assuming a scalar, fermionic or vectorial DM candidate (with a UV-complete vector model), compared to direct detection experimets CRESST-III, DarkSide-50, LUX_ZEPLIN and PandaX-4T (2022 results).

Postfit event yields in each category and hadronic recoil bin of the ttH category SR for the different background and signal processes summed across 2016, 2017 and 2018 samples. The background and signal yields and the corresponding uncertainties are obtained after performing a combined fit across all of the CRs and SR or CR-only. The Postfit signal contributions for a Higgs boson, produced in ttH, VH (split into WH and ZH), ggH and VBF, decaying to invisible particles with a branching fraction of $\mathcal{B}(\text{H} \to \text{inv}) = 1$, and the observed event yields are reported.

Postfit event yields in each category and hadronic recoil bin of the VH category SR for the different background and signal processes summed across 2016, 2017 and 2018 samples. The background and signal yields and the corresponding uncertainties are obtained after performing a combined fit across all of the CRs and SR or CR-only. The Postfit signal contributions for a Higgs boson, produced in ttH, VH (split into WH and ZH), ggH and VBF, decaying to invisible particles with a branching fraction of $\mathcal{B}(\text{H} \to \text{inv}) = 1$, and the observed event yields are reported.

Postfit event yields in each category and $p\mathrm{_{T}^{miss}}$ bin of the ttH category e$+$jets CR for the different background processes summed across 2016, 2017 and 2018 samples. The background yields and the corresponding uncertainties are obtained after performing a combined fit across all of the CRs and SR or CR-only.

Postfit event yields in each category and $p\mathrm{_{T}^{miss}}$ bin of the VH category e$+$jets CR for the different background processes summed across 2016, 2017 and 2018 samples. The background yields and the corresponding uncertainties are obtained after performing a combined fit across all of the CRs and SR or CR-only.

Postfit event yields in each category and $p\mathrm{_{T}^{miss}}$ bin of the ttH category $\mu+$jets CR for the different background processes summed across 2016, 2017 and 2018 samples. The background yields and the corresponding uncertainties are obtained after performing a combined fit across all of the CRs and SR or CR-only.

Postfit event yields in each category and $p\mathrm{_{T}^{miss}}$ bin of the VH category $\mu+$jets CR for the different background processes summed across 2016, 2017 and 2018 samples. The background yields and the corresponding uncertainties are obtained after performing a combined fit across all of the CRs and SR or CR-only.

Postfit event yields in each category and $p\mathrm{_{T}^{miss}}$ bin of the ttH category ee$+$jets, $\mu\mu+$jets, and $\ell\ell+$jets CRs for the different background processes summed across 2016, 2017 and 2018 samples. The background yields and the corresponding uncertainties are obtained after performing a combined fit across all of the CRs and SR or CR-only.

Postfit event yields in each category and $p\mathrm{_{T}^{miss}}$ bin of the VH category ee$+$jets, $\mu\mu+$jets, and $\gamma+$jets CRs for the different background processes summed across 2016, 2017 and 2018 samples. The background yields and the corresponding uncertainties are obtained after performing a combined fit across all of the CRs and SR or CR-only.

Pseudorapidity distribution of inclusive photons measured within $2.3<\eta_{\rm lab}<3.9$ in pp collisions at $\sqrt{s} = 5020~\mathrm{GeV}$.

Pseudorapidity distribution of inclusive photons measured within $2.3<\eta_{\rm lab}<3.9$ in p-Pb collisions at $\sqrt{s_\mathrm{NN}} = 5020~\mathrm{GeV}$.

Pseudorapidity distribution of inclusive photons measured within $2.3<\eta_{\rm lab}<3.9$ in Pb-p collisions at $\sqrt{s_\mathrm{NN}} = 5020~\mathrm{GeV}$.

Pseudorapidity distribution of inclusive photons measured within $2.3<\eta_{\rm lab}<3.9$ in pp collisions at various LHC energies.

$\langle N_{\rm \gamma} \rangle$ measured within $2.3<\eta_{\rm lab}<3.9$ as a function of collision energy in pp collisions.

Centrality-dependent pseudorapidity distribution of inclusive photons measured within $2.3<\eta_{\rm lab}<3.9$ in p-Pb collisions at $\sqrt{s_\mathrm{NN}} = 5020~\mathrm{GeV}$ (Centrality estimator - CL1).

Centrality-dependent pseudorapidity distribution of inclusive photons measured within $2.3<\eta_{\rm lab}<3.9$ in p-Pb collisions at $\sqrt{s_\mathrm{NN}} = 5020~\mathrm{GeV}$ (Centrality estimator - ZNA).

$\langle N_{\rm \gamma} \rangle$ measured within $2.3<\eta_{\rm lab}<3.9$ as a function of $\langle N_{\rm part} \rangle$ for CL1 centrality estimator in p-Pb collisions at $\sqrt{s_\mathrm{NN}} = 5020~\mathrm{GeV}$.

$\langle N_{\rm \gamma} \rangle$ measured within $2.3<\eta_{\rm lab}<3.9$ as a function of $\langle N_{\rm part} \rangle$ for ZNA (high-$p_{\rm T}$) centrality estimator in p-Pb collisions at $\sqrt{s_\mathrm{NN}} = 5020~\mathrm{GeV}$.

$\langle N_{\rm \gamma} \rangle$ measured within $2.3<\eta_{\rm lab}<3.9$ as a function of $\langle N_{\rm part} \rangle$ for ZNA (Pb-side) centrality estimator in p-Pb collisions at $\sqrt{s_\mathrm{NN}} = 5020~\mathrm{GeV}$.

Values of $\langle N_{\rm \gamma} \rangle$/$\langle N_{\rm part} \rangle$ as a function of $\langle N_{\rm part} \rangle$ for CL1 centrality estimator in p-Pb collisions at $\sqrt{s_\mathrm{NN}} = 5020~\mathrm{GeV}$.

Values of $\langle N_{\rm \gamma} \rangle$/$\langle N_{\rm part} \rangle$ as a function of $\langle N_{\rm part} \rangle$ for ZNA (high-$p_{\rm T}$) centrality estimator in p-Pb collisions at $\sqrt{s_\mathrm{NN}} = 5020~\mathrm{GeV}$.

Values of $\langle N_{\rm \gamma} \rangle$/$\langle N_{\rm part} \rangle$ as a function of $\langle N_{\rm part} \rangle$ for ZNA (Pb-side) centrality estimator in p-Pb collisions at $\sqrt{s_\mathrm{NN}} = 5020~\mathrm{GeV}$.

Values of $\langle N_{\rm \gamma} \rangle$/$\langle N_{\rm part} \rangle$ as a function of $\langle N_{\rm \gamma} \rangle$ for CL1 centrality estimator in p-Pb collisions at $\sqrt{s_\mathrm{NN}} = 5020~\mathrm{GeV}$.

Values of $\langle N_{\rm \gamma} \rangle$/$\langle N_{\rm part} \rangle$ as a function of $\langle N_{\rm \gamma} \rangle$ for ZNA (high-$p_{\rm T}$) centrality estimator in p-Pb collisions at $\sqrt{s_\mathrm{NN}} = 5020~\mathrm{GeV}$.

Values of $\langle N_{\rm \gamma} \rangle$/$\langle N_{\rm part} \rangle$ as a function of $\langle N_{\rm \gamma} \rangle$ for ZNA (Pb-side) centrality estimator in p-Pb collisions at $\sqrt{s_\mathrm{NN}} = 5020~\mathrm{GeV}$.

The expected (dotted black) and observed (solid black) upper limits at 95% CL on $\sigma_{T^\prime bq(T^\prime \rightarrow tH)}$ in the hadronic channel displayed as a function of $\rm{M}_{T^\prime}$. The green (yellow) band represents the 68% (95%) of the limit values expected under the background-only hypothesis. The theoretical cross sections for the singlet $T^\prime$ production with representative $\kappa_T$-values fixed at 0.1, 0.15, 0.2 and 0.25 (for $\Gamma/\rm{M}_{T^\prime} < 5\%$) are shown as solid red lines.

Selection of the hadronic signal region for the three BDTs and $\rm{M}_{T^\prime}$ windows.

Selection of the leptonic signal region for the three BDTs and $\rm{M}_{T^\prime}$ windows.

The expected yields of different processes in each signal window for events with a $T^{\prime}$ with mass in the range $\rm{M}_{T^\prime} \in [600, 1200]$ GeV, and the observed number of events in the signal region $m_{\gamma\gamma} \in [115, 135]$. Here, the yields for the $T^\prime$ are for $\kappa_{T}$ fixed at 0.2.

Signal efficiency for the hadronic channel (left) and the leptonic channel (right) in the signal regions as optimized for each of the three different $\rm{M}_{T^\prime}$ ranges, [600, 700], [700, 1000] and [1000, 1200] GeV, represented as red, green and blue curves respectively. The efficiency is defined as the ratio of the events after the final selection to the total expected events.

Signal selection efficiency ($\epsilon$) times acceptance ($A$) as a function of $H^{\pm}$. The estimated $\epsilon\times A$ arises from the lepton selection and triggering (∼30%) as well as jet selection and flavour tagging (∼10% or lower). The decrease of $\epsilon\times A$ for $m_{H^{\pm}}$ = 120 GeV and higher is expected from the kinematic constraint on the $H^{\pm}$ decay products due to the top-quark mass.

Fit results of the simultaneous measurements of the $H\to e\tau$ and $H\to \mu\tau$ signals (2POI) showing best-fit values of the LFV branching ratios of the Higgs boson $\hat{B}$($H\to \mu\tau$). The results from standalone channel/categories fits are compared with the results of the combined fit.

Fit results of the independent searches (1 POI) showing upper limits at 95% C.L. on the LFV branching ratios of the Higgs boson $H\to e\tau$. The results from standalone channel/categories fits are compared with the results of the combined fit.

Fit results of the independent searches (1 POI) showing best-fit values of the LFV branching ratios of the Higgs boson $\hat{B}$($H\to e\tau$). The results from standalone channel/categories fits are compared with the results of the combined fit.

Fit results of the independent searches (1 POI) showing upper limits at 95% C.L. on the LFV branching ratios of the Higgs boson $H\to \mu\tau$. The results from standalone channel/categories fits are compared with the results of the combined fit.

Fit results of the independent searches (1 POI) showing best-fit values of the LFV branching ratios of the Higgs boson $\hat{B}$($H\to \mu\tau$). The results from standalone channel/categories fits are compared with the results of the combined fit.

BDT score distribution, after the simultaneous fit of the $H\to e\tau$ and $H\to \mu\tau$ signals, obtained by fitting the data of the MC-template $\ell\tau_{\ell'}$ channel for $e\tau_{\mu}$ final state in the non-VBF category.

BDT score distribution, after the simultaneous fit of the $H\to e\tau$ and $H\to \mu\tau$ signals, obtained by fitting the data of the MC-template $\ell\tau_{\ell'}$ channel for $\mu\tau_{e}$ final state in the non-VBF category.

BDT score distribution, after the simultaneous fit of the $H\to e\tau$ and $H\to \mu\tau$ signals, obtained by fitting the data of the MC-template $\ell\tau_{\ell'}$ channel for $e\tau_{\mu}$ final state in the VBF category.

BDT score distribution, after the simultaneous fit of the $H\to e\tau$ and $H\to \mu\tau$ signals, obtained by fitting the data of the MC-template $\ell\tau_{\ell'}$ channel for $\mu\tau_{e}$ final state in the VBF category.

BDT score distribution, after the simultaneous fit of the $H\to e\tau$ and $H\to \mu\tau$ signals, obtained by fitting the data of the MC-template $\ell\tau_{had}$ channel for $e\tau_{had}$ final state in the non-VBF category.

BDT score distribution, after the simultaneous fit of the $H\to e\tau$ and $H\to \mu\tau$ signals, obtained by fitting the data of the MC-template $\ell\tau_{had}$ channel for $\mu\tau_{had}$ final state in the non-VBF category.

BDT score distribution, after the simultaneous fit of the $H\to e\tau$ and $H\to \mu\tau$ signals, obtained by fitting the data of the MC-template $\ell\tau_{had}$ channel for $e\tau_{had}$ final state in the VBF category.

BDT score distribution, after the simultaneous fit of the $H\to e\tau$ and $H\to \mu\tau$ signals, obtained by fitting the data of the MC-template $\ell\tau_{had}$ channel for $\mu\tau_{had}$ final state in the VBF category.

NN score distribution, after an independent fit of the $H\to \mu\tau$ signal, obtained by fitting the data of the Symmetry $\ell\tau_{\ell'}$ channel, for the $\mu\tau_{e}$ final state in the non-VBF category.

NN score distribution, after an independent fit of the $H\to \mu\tau$ signal, obtained by fitting the data of the Symmetry $\ell\tau_{\ell'}$ channel, for the $\mu\tau_{e}$ final state in the VBF category.

Best-fit $\mathcal{B}(H\to \mu\tau)- \mathcal{B}(H\to e\tau)$ values, given in %, obtained from the standalone fits of the $\ell\tau_\ell'$ final state with either background estimation method. For the MC-template method, the correlated uncertainties are fixed to their best-fit values and the uncertainties are re-derived considering only the uncorrelated sources. For the Symmetry method, the full uncertainty is considered.

Best-fit value of the branching ratios $\mathcal{B}(H\to e\tau)$ and $\mathcal{B}(H\to \mu\tau)$, given in %, and likelihood contours at 68% and 95% C.L. Obtained from the simultaneous fit of $H\to e\tau$ and $H\to \mu\tau$ signals based on the MC-template method, compared to the SM expectation.