CMS-HIG-21-001

CMS-HIG-21-001 ; CERN-EP-2022-137
Searches for additional Higgs bosons and for vector leptoquarks in $\tau\tau$ final states in proton-proton collisions at $\sqrt{s} = $ 13 TeV
CMS Collaboration
4 August 2022
JHEP 07 (2023) 073
Abstract: Three searches are presented for signatures of physics beyond the standard model (SM) in $\tau\tau$ final states in proton-proton collisions at the LHC, using a data sample collected with the CMS detector at $\sqrt{s} = $ 13 TeV, corresponding to an integrated luminosity of 138 fb$^{-1}$. Upper limits at 95% confidence level (CL) are set on the products of the branching fraction for the decay into $\tau$ leptons and the cross sections for the production of a new boson $\phi$, in addition to the H(125) boson, via gluon fusion (gg$\phi$) or in association with b quarks, ranging from ${\mathcal{O}}$(10 pb) for a mass of 60 GeV to 0.3 fb for a mass of 3.5 TeV each. The data reveal two excesses for gg$\phi$ production with local $p$-values equivalent to about three standard deviations at ${m_{\phi}} =$ 0.1 and 1.2 TeV. In a search for $t$-channel exchange of a vector leptoquark U$_{1}$, 95% CL upper limits are set on the dimensionless U$_{1}$ leptoquark coupling to quarks and $\tau$ leptons ranging from 1 for a mass of 1 TeV to 6 for a mass of 5 TeV, depending on the scenario. In the interpretations of the ${M_{\mathrm{h}}^{125}}$ and ${M_{\mathrm{h},\,\text{EFT}}^{125}}$ minimal supersymmetric SM benchmark scenarios, additional Higgs bosons with masses below 350 GeV are excluded at 95% CL.
Links: e-print arXiv:2208.02717 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; HepData record ; CADI line (restricted) ;

Figures & Tables	Summary	Additional Figures	References	CMS Publications

Figures
png pdf	Figure 1: Diagrams for the production of neutral Higgs bosons ${\phi}$ (left) via gluon fusion, labelled as gg$\phi$, and (middle and right) in association with b quarks, labelled as bb$\phi$ in the text. In the middle diagram, a pair of b quarks is produced from the fusion of two gluons, one from each proton. In the right diagram, a b quark from one proton scatters from a gluon from the other proton. In both cases ${\phi}$ is radiated off one of the b quarks.
png pdf	Figure 1-a: Diagrams for the production of neutral Higgs bosons ${\phi}$ (left) via gluon fusion, labelled as gg$\phi$, and (middle and right) in association with b quarks, labelled as bb$\phi$ in the text. In the middle diagram, a pair of b quarks is produced from the fusion of two gluons, one from each proton. In the right diagram, a b quark from one proton scatters from a gluon from the other proton. In both cases ${\phi}$ is radiated off one of the b quarks.
png pdf	Figure 1-b: Diagrams for the production of neutral Higgs bosons ${\phi}$ (left) via gluon fusion, labelled as gg$\phi$, and (middle and right) in association with b quarks, labelled as bb$\phi$ in the text. In the middle diagram, a pair of b quarks is produced from the fusion of two gluons, one from each proton. In the right diagram, a b quark from one proton scatters from a gluon from the other proton. In both cases ${\phi}$ is radiated off one of the b quarks.
png pdf	Figure 1-c: Diagrams for the production of neutral Higgs bosons ${\phi}$ (left) via gluon fusion, labelled as gg$\phi$, and (middle and right) in association with b quarks, labelled as bb$\phi$ in the text. In the middle diagram, a pair of b quarks is produced from the fusion of two gluons, one from each proton. In the right diagram, a b quark from one proton scatters from a gluon from the other proton. In both cases ${\phi}$ is radiated off one of the b quarks.
png pdf	Figure 2: Diagram for the production of a pair of $\tau$ leptons via the $t$-channel exchange of a vector leptoquark U$_{1}$.
png pdf	Figure 3: Inputs to the reconstruction of the event observable D$_{\zeta}$, as described in the text.
png pdf	Figure 4: Observed and expected distributions of (left) D$_{\zeta}$ in the e$\mu$ final state and (right) ${m_{\mathrm {T}}^{\mu}}$ in the $\mu {\tau _\mathrm {h}}$ final state. The distributions are shown in the global "no b tag'' category before any further event categorization and after an individual background-only fit to the data in each corresponding variable. The grey shaded band represents the complete set of uncertainties used for signal extraction, after the fit. A detailed discussion of the data modelling is given in Section 6. The vertical dashed lines indicate the category definitions in each of the final states, as described in the text. In the lower panels of each figure the ratio of the observed numbers of events per bin to the background expectation is shown.
png pdf	Figure 4-a: Observed and expected distributions of (left) D$_{\zeta}$ in the e$\mu$ final state and (right) ${m_{\mathrm {T}}^{\mu}}$ in the $\mu {\tau _\mathrm {h}}$ final state. The distributions are shown in the global "no b tag'' category before any further event categorization and after an individual background-only fit to the data in each corresponding variable. The grey shaded band represents the complete set of uncertainties used for signal extraction, after the fit. A detailed discussion of the data modelling is given in Section 6. The vertical dashed lines indicate the category definitions in each of the final states, as described in the text. In the lower panels of each figure the ratio of the observed numbers of events per bin to the background expectation is shown.
png pdf	Figure 4-b: Observed and expected distributions of (left) D$_{\zeta}$ in the e$\mu$ final state and (right) ${m_{\mathrm {T}}^{\mu}}$ in the $\mu {\tau _\mathrm {h}}$ final state. The distributions are shown in the global "no b tag'' category before any further event categorization and after an individual background-only fit to the data in each corresponding variable. The grey shaded band represents the complete set of uncertainties used for signal extraction, after the fit. A detailed discussion of the data modelling is given in Section 6. The vertical dashed lines indicate the category definitions in each of the final states, as described in the text. In the lower panels of each figure the ratio of the observed numbers of events per bin to the background expectation is shown.
png pdf	Figure 5: Overview of the categories used for the extraction of the signal for the model-independent ${\phi}$ search for hypothesized values of $ {m_{\phi}} \geq $ 250 GeV, the vector leptoquark search, and the interpretation of the data in MSSM benchmark scenarios.
png pdf	Figure 6: Overview of the categories used for the extraction of the signal for the model-independent ${\phi}$ search for 60 $\leq {m_{\phi}} < $ 250 GeV.
png pdf	Figure 7: Composition of the signal for the MSSM interpretation of the data and the vector leptoquark search. The left figure shows the generator level A boson ${p_{\mathrm {T}}}$ density for the MSSM ${M_{\mathrm {h}}^{125}}$ scenario for $ {m_{{\mathrm {A}}}} = $ 1.6 TeV and $ {\tan\beta} =$ 30, split by the contributions from the t quark only, the b quark only, and the tb-interference term. The right figure shows the distribution of ${m_{\mathrm {T}}^{\text {tot}}}$ at reconstruction level in the ${{\tau _\mathrm {h}} {\tau _\mathrm {h}}}$ final state for U$_{1}$ $t$-channel exchange with $ {m_{\text {U}}} = $ 1 TeV and $ {g_{\text {U}}} =$ 1.5, for the signal with and without the interference term for the VLQ BM 1 scenario. The ${{\tau _\mathrm {h}} {\tau _\mathrm {h}}}$ final state is shown, since it is the most sensitive one for this search. The bins of the distributions are divided by their width and the distribution is normalized to the expected signal yield for 138 fb$^{-1}$.
png pdf	Figure 7-a: Composition of the signal for the MSSM interpretation of the data and the vector leptoquark search. The left figure shows the generator level A boson ${p_{\mathrm {T}}}$ density for the MSSM ${M_{\mathrm {h}}^{125}}$ scenario for $ {m_{{\mathrm {A}}}} = $ 1.6 TeV and $ {\tan\beta} =$ 30, split by the contributions from the t quark only, the b quark only, and the tb-interference term. The right figure shows the distribution of ${m_{\mathrm {T}}^{\text {tot}}}$ at reconstruction level in the ${{\tau _\mathrm {h}} {\tau _\mathrm {h}}}$ final state for U$_{1}$ $t$-channel exchange with $ {m_{\text {U}}} = $ 1 TeV and $ {g_{\text {U}}} =$ 1.5, for the signal with and without the interference term for the VLQ BM 1 scenario. The ${{\tau _\mathrm {h}} {\tau _\mathrm {h}}}$ final state is shown, since it is the most sensitive one for this search. The bins of the distributions are divided by their width and the distribution is normalized to the expected signal yield for 138 fb$^{-1}$.
png pdf	Figure 7-b: Composition of the signal for the MSSM interpretation of the data and the vector leptoquark search. The left figure shows the generator level A boson ${p_{\mathrm {T}}}$ density for the MSSM ${M_{\mathrm {h}}^{125}}$ scenario for $ {m_{{\mathrm {A}}}} = $ 1.6 TeV and $ {\tan\beta} =$ 30, split by the contributions from the t quark only, the b quark only, and the tb-interference term. The right figure shows the distribution of ${m_{\mathrm {T}}^{\text {tot}}}$ at reconstruction level in the ${{\tau _\mathrm {h}} {\tau _\mathrm {h}}}$ final state for U$_{1}$ $t$-channel exchange with $ {m_{\text {U}}} = $ 1 TeV and $ {g_{\text {U}}} =$ 1.5, for the signal with and without the interference term for the VLQ BM 1 scenario. The ${{\tau _\mathrm {h}} {\tau _\mathrm {h}}}$ final state is shown, since it is the most sensitive one for this search. The bins of the distributions are divided by their width and the distribution is normalized to the expected signal yield for 138 fb$^{-1}$.
png pdf	Figure 8: Distributions of ${m_{\mathrm {T}}^{\text {tot}}}$ in the global (left) "no b tag'' and (right) "b tag'' categories in the (upper) e$\mu$, (middle) e$ {\tau _\mathrm {h}}$ and $\mu {\tau _\mathrm {h}}$, and (lower) ${{\tau _\mathrm {h}} {\tau _\mathrm {h}}}$ final states. For the e$\mu$ final state, the medium-D$_{\zeta}$ category is displayed; for the e$ {\tau _\mathrm {h}}$ and $\mu {\tau _\mathrm {h}}$ final states the tight-${m_{\mathrm {T}}}$ categories are shown. The solid histograms show the stacked background predictions after a signal-plus-background fit to the data for $ {m_{\phi}} = $ 1.2 TeV. The best fit gg$\phi$ signal is shown by the red line. The bb$\phi$ and U$_{1}$ signals are also shown for illustrative purposes. For all histograms, the bin contents show the event yields divided by the bin widths. The lower panel shows the ratio of the data to the background expectation after the signal-plus-background fit to the data.
png pdf	Figure 8-a: Distributions of ${m_{\mathrm {T}}^{\text {tot}}}$ in the global (left) "no b tag'' and (right) "b tag'' categories in the (upper) e$\mu$, (middle) e$ {\tau _\mathrm {h}}$ and $\mu {\tau _\mathrm {h}}$, and (lower) ${{\tau _\mathrm {h}} {\tau _\mathrm {h}}}$ final states. For the e$\mu$ final state, the medium-D$_{\zeta}$ category is displayed; for the e$ {\tau _\mathrm {h}}$ and $\mu {\tau _\mathrm {h}}$ final states the tight-${m_{\mathrm {T}}}$ categories are shown. The solid histograms show the stacked background predictions after a signal-plus-background fit to the data for $ {m_{\phi}} = $ 1.2 TeV. The best fit gg$\phi$ signal is shown by the red line. The bb$\phi$ and U$_{1}$ signals are also shown for illustrative purposes. For all histograms, the bin contents show the event yields divided by the bin widths. The lower panel shows the ratio of the data to the background expectation after the signal-plus-background fit to the data.
png pdf	Figure 8-b: Distributions of ${m_{\mathrm {T}}^{\text {tot}}}$ in the global (left) "no b tag'' and (right) "b tag'' categories in the (upper) e$\mu$, (middle) e$ {\tau _\mathrm {h}}$ and $\mu {\tau _\mathrm {h}}$, and (lower) ${{\tau _\mathrm {h}} {\tau _\mathrm {h}}}$ final states. For the e$\mu$ final state, the medium-D$_{\zeta}$ category is displayed; for the e$ {\tau _\mathrm {h}}$ and $\mu {\tau _\mathrm {h}}$ final states the tight-${m_{\mathrm {T}}}$ categories are shown. The solid histograms show the stacked background predictions after a signal-plus-background fit to the data for $ {m_{\phi}} = $ 1.2 TeV. The best fit gg$\phi$ signal is shown by the red line. The bb$\phi$ and U$_{1}$ signals are also shown for illustrative purposes. For all histograms, the bin contents show the event yields divided by the bin widths. The lower panel shows the ratio of the data to the background expectation after the signal-plus-background fit to the data.
png pdf	Figure 8-c: Distributions of ${m_{\mathrm {T}}^{\text {tot}}}$ in the global (left) "no b tag'' and (right) "b tag'' categories in the (upper) e$\mu$, (middle) e$ {\tau _\mathrm {h}}$ and $\mu {\tau _\mathrm {h}}$, and (lower) ${{\tau _\mathrm {h}} {\tau _\mathrm {h}}}$ final states. For the e$\mu$ final state, the medium-D$_{\zeta}$ category is displayed; for the e$ {\tau _\mathrm {h}}$ and $\mu {\tau _\mathrm {h}}$ final states the tight-${m_{\mathrm {T}}}$ categories are shown. The solid histograms show the stacked background predictions after a signal-plus-background fit to the data for $ {m_{\phi}} = $ 1.2 TeV. The best fit gg$\phi$ signal is shown by the red line. The bb$\phi$ and U$_{1}$ signals are also shown for illustrative purposes. For all histograms, the bin contents show the event yields divided by the bin widths. The lower panel shows the ratio of the data to the background expectation after the signal-plus-background fit to the data.
png pdf	Figure 8-d: Distributions of ${m_{\mathrm {T}}^{\text {tot}}}$ in the global (left) "no b tag'' and (right) "b tag'' categories in the (upper) e$\mu$, (middle) e$ {\tau _\mathrm {h}}$ and $\mu {\tau _\mathrm {h}}$, and (lower) ${{\tau _\mathrm {h}} {\tau _\mathrm {h}}}$ final states. For the e$\mu$ final state, the medium-D$_{\zeta}$ category is displayed; for the e$ {\tau _\mathrm {h}}$ and $\mu {\tau _\mathrm {h}}$ final states the tight-${m_{\mathrm {T}}}$ categories are shown. The solid histograms show the stacked background predictions after a signal-plus-background fit to the data for $ {m_{\phi}} = $ 1.2 TeV. The best fit gg$\phi$ signal is shown by the red line. The bb$\phi$ and U$_{1}$ signals are also shown for illustrative purposes. For all histograms, the bin contents show the event yields divided by the bin widths. The lower panel shows the ratio of the data to the background expectation after the signal-plus-background fit to the data.
png pdf	Figure 8-e: Distributions of ${m_{\mathrm {T}}^{\text {tot}}}$ in the global (left) "no b tag'' and (right) "b tag'' categories in the (upper) e$\mu$, (middle) e$ {\tau _\mathrm {h}}$ and $\mu {\tau _\mathrm {h}}$, and (lower) ${{\tau _\mathrm {h}} {\tau _\mathrm {h}}}$ final states. For the e$\mu$ final state, the medium-D$_{\zeta}$ category is displayed; for the e$ {\tau _\mathrm {h}}$ and $\mu {\tau _\mathrm {h}}$ final states the tight-${m_{\mathrm {T}}}$ categories are shown. The solid histograms show the stacked background predictions after a signal-plus-background fit to the data for $ {m_{\phi}} = $ 1.2 TeV. The best fit gg$\phi$ signal is shown by the red line. The bb$\phi$ and U$_{1}$ signals are also shown for illustrative purposes. For all histograms, the bin contents show the event yields divided by the bin widths. The lower panel shows the ratio of the data to the background expectation after the signal-plus-background fit to the data.
png pdf	Figure 8-f: Distributions of ${m_{\mathrm {T}}^{\text {tot}}}$ in the global (left) "no b tag'' and (right) "b tag'' categories in the (upper) e$\mu$, (middle) e$ {\tau _\mathrm {h}}$ and $\mu {\tau _\mathrm {h}}$, and (lower) ${{\tau _\mathrm {h}} {\tau _\mathrm {h}}}$ final states. For the e$\mu$ final state, the medium-D$_{\zeta}$ category is displayed; for the e$ {\tau _\mathrm {h}}$ and $\mu {\tau _\mathrm {h}}$ final states the tight-${m_{\mathrm {T}}}$ categories are shown. The solid histograms show the stacked background predictions after a signal-plus-background fit to the data for $ {m_{\phi}} = $ 1.2 TeV. The best fit gg$\phi$ signal is shown by the red line. The bb$\phi$ and U$_{1}$ signals are also shown for illustrative purposes. For all histograms, the bin contents show the event yields divided by the bin widths. The lower panel shows the ratio of the data to the background expectation after the signal-plus-background fit to the data.
png pdf	Figure 9: Distributions of ${m_{\tau \tau}}$ in the (left) 100 $ < {{p_{\mathrm {T}}} ^{{\tau \tau}}} < $ 200 GeV and (right) $ {{p_{\mathrm {T}}} ^{{\tau \tau}}} > $ 200 GeV "no b tag'' categories for the (upper) e$\mu$, (middle) e$ {\tau _\mathrm {h}}$ and $\mu {\tau _\mathrm {h}}$, and (lower) ${{\tau _\mathrm {h}} {\tau _\mathrm {h}}}$ final states. The solid histograms show the stacked background predictions after a signal-plus-background fit to the data for $ {m_{\phi}} = $ 100 GeV. The best fit gg$\phi$ signal is shown by the red line. The total background prediction as estimated from a background-only fit to the data is shown by the dashed blue line for comparison. For all histograms, the bin contents show the event yields divided by the bin widths. The lower panel shows the ratio of the data to the background expectation after the signal-plus-background fit to the data. The signal-plus-background and background-only fit predictions are shown by the solid red and dashed blue lines, respectively, which are also shown relative to the background expectation obtained from the signal-plus-background fit to the data.
png pdf	Figure 9-a: Distributions of ${m_{\tau \tau}}$ in the (left) 100 $ < {{p_{\mathrm {T}}} ^{{\tau \tau}}} < $ 200 GeV and (right) $ {{p_{\mathrm {T}}} ^{{\tau \tau}}} > $ 200 GeV "no b tag'' categories for the (upper) e$\mu$, (middle) e$ {\tau _\mathrm {h}}$ and $\mu {\tau _\mathrm {h}}$, and (lower) ${{\tau _\mathrm {h}} {\tau _\mathrm {h}}}$ final states. The solid histograms show the stacked background predictions after a signal-plus-background fit to the data for $ {m_{\phi}} = $ 100 GeV. The best fit gg$\phi$ signal is shown by the red line. The total background prediction as estimated from a background-only fit to the data is shown by the dashed blue line for comparison. For all histograms, the bin contents show the event yields divided by the bin widths. The lower panel shows the ratio of the data to the background expectation after the signal-plus-background fit to the data. The signal-plus-background and background-only fit predictions are shown by the solid red and dashed blue lines, respectively, which are also shown relative to the background expectation obtained from the signal-plus-background fit to the data.
png pdf	Figure 9-b: Distributions of ${m_{\tau \tau}}$ in the (left) 100 $ < {{p_{\mathrm {T}}} ^{{\tau \tau}}} < $ 200 GeV and (right) $ {{p_{\mathrm {T}}} ^{{\tau \tau}}} > $ 200 GeV "no b tag'' categories for the (upper) e$\mu$, (middle) e$ {\tau _\mathrm {h}}$ and $\mu {\tau _\mathrm {h}}$, and (lower) ${{\tau _\mathrm {h}} {\tau _\mathrm {h}}}$ final states. The solid histograms show the stacked background predictions after a signal-plus-background fit to the data for $ {m_{\phi}} = $ 100 GeV. The best fit gg$\phi$ signal is shown by the red line. The total background prediction as estimated from a background-only fit to the data is shown by the dashed blue line for comparison. For all histograms, the bin contents show the event yields divided by the bin widths. The lower panel shows the ratio of the data to the background expectation after the signal-plus-background fit to the data. The signal-plus-background and background-only fit predictions are shown by the solid red and dashed blue lines, respectively, which are also shown relative to the background expectation obtained from the signal-plus-background fit to the data.
png pdf	Figure 9-c: Distributions of ${m_{\tau \tau}}$ in the (left) 100 $ < {{p_{\mathrm {T}}} ^{{\tau \tau}}} < $ 200 GeV and (right) $ {{p_{\mathrm {T}}} ^{{\tau \tau}}} > $ 200 GeV "no b tag'' categories for the (upper) e$\mu$, (middle) e$ {\tau _\mathrm {h}}$ and $\mu {\tau _\mathrm {h}}$, and (lower) ${{\tau _\mathrm {h}} {\tau _\mathrm {h}}}$ final states. The solid histograms show the stacked background predictions after a signal-plus-background fit to the data for $ {m_{\phi}} = $ 100 GeV. The best fit gg$\phi$ signal is shown by the red line. The total background prediction as estimated from a background-only fit to the data is shown by the dashed blue line for comparison. For all histograms, the bin contents show the event yields divided by the bin widths. The lower panel shows the ratio of the data to the background expectation after the signal-plus-background fit to the data. The signal-plus-background and background-only fit predictions are shown by the solid red and dashed blue lines, respectively, which are also shown relative to the background expectation obtained from the signal-plus-background fit to the data.
png pdf	Figure 9-d: Distributions of ${m_{\tau \tau}}$ in the (left) 100 $ < {{p_{\mathrm {T}}} ^{{\tau \tau}}} < $ 200 GeV and (right) $ {{p_{\mathrm {T}}} ^{{\tau \tau}}} > $ 200 GeV "no b tag'' categories for the (upper) e$\mu$, (middle) e$ {\tau _\mathrm {h}}$ and $\mu {\tau _\mathrm {h}}$, and (lower) ${{\tau _\mathrm {h}} {\tau _\mathrm {h}}}$ final states. The solid histograms show the stacked background predictions after a signal-plus-background fit to the data for $ {m_{\phi}} = $ 100 GeV. The best fit gg$\phi$ signal is shown by the red line. The total background prediction as estimated from a background-only fit to the data is shown by the dashed blue line for comparison. For all histograms, the bin contents show the event yields divided by the bin widths. The lower panel shows the ratio of the data to the background expectation after the signal-plus-background fit to the data. The signal-plus-background and background-only fit predictions are shown by the solid red and dashed blue lines, respectively, which are also shown relative to the background expectation obtained from the signal-plus-background fit to the data.
png pdf	Figure 9-e: Distributions of ${m_{\tau \tau}}$ in the (left) 100 $ < {{p_{\mathrm {T}}} ^{{\tau \tau}}} < $ 200 GeV and (right) $ {{p_{\mathrm {T}}} ^{{\tau \tau}}} > $ 200 GeV "no b tag'' categories for the (upper) e$\mu$, (middle) e$ {\tau _\mathrm {h}}$ and $\mu {\tau _\mathrm {h}}$, and (lower) ${{\tau _\mathrm {h}} {\tau _\mathrm {h}}}$ final states. The solid histograms show the stacked background predictions after a signal-plus-background fit to the data for $ {m_{\phi}} = $ 100 GeV. The best fit gg$\phi$ signal is shown by the red line. The total background prediction as estimated from a background-only fit to the data is shown by the dashed blue line for comparison. For all histograms, the bin contents show the event yields divided by the bin widths. The lower panel shows the ratio of the data to the background expectation after the signal-plus-background fit to the data. The signal-plus-background and background-only fit predictions are shown by the solid red and dashed blue lines, respectively, which are also shown relative to the background expectation obtained from the signal-plus-background fit to the data.
png pdf	Figure 9-f: Distributions of ${m_{\tau \tau}}$ in the (left) 100 $ < {{p_{\mathrm {T}}} ^{{\tau \tau}}} < $ 200 GeV and (right) $ {{p_{\mathrm {T}}} ^{{\tau \tau}}} > $ 200 GeV "no b tag'' categories for the (upper) e$\mu$, (middle) e$ {\tau _\mathrm {h}}$ and $\mu {\tau _\mathrm {h}}$, and (lower) ${{\tau _\mathrm {h}} {\tau _\mathrm {h}}}$ final states. The solid histograms show the stacked background predictions after a signal-plus-background fit to the data for $ {m_{\phi}} = $ 100 GeV. The best fit gg$\phi$ signal is shown by the red line. The total background prediction as estimated from a background-only fit to the data is shown by the dashed blue line for comparison. For all histograms, the bin contents show the event yields divided by the bin widths. The lower panel shows the ratio of the data to the background expectation after the signal-plus-background fit to the data. The signal-plus-background and background-only fit predictions are shown by the solid red and dashed blue lines, respectively, which are also shown relative to the background expectation obtained from the signal-plus-background fit to the data.
png pdf	Figure 10: Expected and observed 95% CL upper limits on the product of the cross sections and branching fraction for the decay into $\tau$ leptons for (left) gg$\phi$ and (right) bb$\phi$ production in a mass range of 60 $\leq {m_{\phi}} \leq 3500 GeV $, in addition to H(125). The expected median of the exclusion limit in the absence of signal is shown by the dashed line. The dark green and bright yellow bands indicate the central 68% and 95% intervals for the expected exclusion limit. The black dots correspond to the observed limits. The peak in the expected gg$\phi$ limit emerges from the loss of sensitivity around 90 GeV due to the background from Z/$\gamma$* $\to \tau\tau$ events.
png pdf	Figure 10-a: Expected and observed 95% CL upper limits on the product of the cross sections and branching fraction for the decay into $\tau$ leptons for (left) gg$\phi$ and (right) bb$\phi$ production in a mass range of 60 $\leq {m_{\phi}} \leq 3500 GeV $, in addition to H(125). The expected median of the exclusion limit in the absence of signal is shown by the dashed line. The dark green and bright yellow bands indicate the central 68% and 95% intervals for the expected exclusion limit. The black dots correspond to the observed limits. The peak in the expected gg$\phi$ limit emerges from the loss of sensitivity around 90 GeV due to the background from Z/$\gamma$* $\to \tau\tau$ events.
png pdf	Figure 10-b: Expected and observed 95% CL upper limits on the product of the cross sections and branching fraction for the decay into $\tau$ leptons for (left) gg$\phi$ and (right) bb$\phi$ production in a mass range of 60 $\leq {m_{\phi}} \leq 3500 GeV $, in addition to H(125). The expected median of the exclusion limit in the absence of signal is shown by the dashed line. The dark green and bright yellow bands indicate the central 68% and 95% intervals for the expected exclusion limit. The black dots correspond to the observed limits. The peak in the expected gg$\phi$ limit emerges from the loss of sensitivity around 90 GeV due to the background from Z/$\gamma$* $\to \tau\tau$ events.
png pdf	Figure 11: Maximum likelihood estimates, and 68% and 95% CL contours obtained from scans of the signal likelihood for the model-independent ${\phi}$ search. The scans are shown for selected values of ${m_{\phi}}$ between 60 GeV and 3.5 TeV. In each figure the SM expectation is $(0, 0)$.
png pdf	Figure 11-a: Maximum likelihood estimates, and 68% and 95% CL contours obtained from scans of the signal likelihood for the model-independent ${\phi}$ search. The scans are shown for selected values of ${m_{\phi}}$ between 60 GeV and 3.5 TeV. In each figure the SM expectation is $(0, 0)$.
png pdf	Figure 11-b: Maximum likelihood estimates, and 68% and 95% CL contours obtained from scans of the signal likelihood for the model-independent ${\phi}$ search. The scans are shown for selected values of ${m_{\phi}}$ between 60 GeV and 3.5 TeV. In each figure the SM expectation is $(0, 0)$.
png pdf	Figure 11-c: Maximum likelihood estimates, and 68% and 95% CL contours obtained from scans of the signal likelihood for the model-independent ${\phi}$ search. The scans are shown for selected values of ${m_{\phi}}$ between 60 GeV and 3.5 TeV. In each figure the SM expectation is $(0, 0)$.
png pdf	Figure 11-d: Maximum likelihood estimates, and 68% and 95% CL contours obtained from scans of the signal likelihood for the model-independent ${\phi}$ search. The scans are shown for selected values of ${m_{\phi}}$ between 60 GeV and 3.5 TeV. In each figure the SM expectation is $(0, 0)$.
png pdf	Figure 11-e: Maximum likelihood estimates, and 68% and 95% CL contours obtained from scans of the signal likelihood for the model-independent ${\phi}$ search. The scans are shown for selected values of ${m_{\phi}}$ between 60 GeV and 3.5 TeV. In each figure the SM expectation is $(0, 0)$.
png pdf	Figure 11-f: Maximum likelihood estimates, and 68% and 95% CL contours obtained from scans of the signal likelihood for the model-independent ${\phi}$ search. The scans are shown for selected values of ${m_{\phi}}$ between 60 GeV and 3.5 TeV. In each figure the SM expectation is $(0, 0)$.
png pdf	Figure 11-g: Maximum likelihood estimates, and 68% and 95% CL contours obtained from scans of the signal likelihood for the model-independent ${\phi}$ search. The scans are shown for selected values of ${m_{\phi}}$ between 60 GeV and 3.5 TeV. In each figure the SM expectation is $(0, 0)$.
png pdf	Figure 11-h: Maximum likelihood estimates, and 68% and 95% CL contours obtained from scans of the signal likelihood for the model-independent ${\phi}$ search. The scans are shown for selected values of ${m_{\phi}}$ between 60 GeV and 3.5 TeV. In each figure the SM expectation is $(0, 0)$.
png pdf	Figure 11-i: Maximum likelihood estimates, and 68% and 95% CL contours obtained from scans of the signal likelihood for the model-independent ${\phi}$ search. The scans are shown for selected values of ${m_{\phi}}$ between 60 GeV and 3.5 TeV. In each figure the SM expectation is $(0, 0)$.
png pdf	Figure 12: Expected and observed 95% CL upper limits on ${g_{\text {U}}}$ in the VLQ BM (left) 1 and (right) 2 scenarios, in a mass range of 1 $ < {m_{\text {U}}} < $ 5 TeV. The expected median of the exclusion limit in the absence of signal is shown by the dashed line. The dark and bright grey bands indicate the central 68% and 95% intervals of the expected exclusion limit. The observed excluded parameter space is indicated by the coloured blue area. For both scenarios, the 95% confidence interval for the preferred region from the global fit presented in Ref. [72] is also shown by the green shaded area.
png pdf	Figure 12-a: Expected and observed 95% CL upper limits on ${g_{\text {U}}}$ in the VLQ BM (left) 1 and (right) 2 scenarios, in a mass range of 1 $ < {m_{\text {U}}} < $ 5 TeV. The expected median of the exclusion limit in the absence of signal is shown by the dashed line. The dark and bright grey bands indicate the central 68% and 95% intervals of the expected exclusion limit. The observed excluded parameter space is indicated by the coloured blue area. For both scenarios, the 95% confidence interval for the preferred region from the global fit presented in Ref. [72] is also shown by the green shaded area.
png pdf	Figure 12-b: Expected and observed 95% CL upper limits on ${g_{\text {U}}}$ in the VLQ BM (left) 1 and (right) 2 scenarios, in a mass range of 1 $ < {m_{\text {U}}} < $ 5 TeV. The expected median of the exclusion limit in the absence of signal is shown by the dashed line. The dark and bright grey bands indicate the central 68% and 95% intervals of the expected exclusion limit. The observed excluded parameter space is indicated by the coloured blue area. For both scenarios, the 95% confidence interval for the preferred region from the global fit presented in Ref. [72] is also shown by the green shaded area.
png pdf	Figure 13: Expected and observed 95% CL exclusion contours in the MSSM (left) ${M_{\mathrm {h}}^{125}}$ and (right) ${M_{\mathrm {h},\,\text {EFT}}^{125}}$ scenarios. The expected median in the absence of a signal is shown as a dashed black line. The dark and bright grey bands indicate the central 68% and 95% intervals of the expected exclusion. The observed exclusion contour is indicated by the coloured blue area. For both scenarios, those parts of the parameter space where ${m_{\mathrm{h}}}$ deviates by more then ${\pm}$ 3 GeV from the mass of H(125) are indicated by a red hatched area. For the ${M_{\mathrm {h},\,\text {EFT}}^{125}}$ scenario, the dashed blue line indicates the threshold at $ {m_{{\mathrm {A}}}} = $ 2$ {m_{\mathrm{t}}} $ whereby the A $ \to {\mathrm{t} \mathrm{\bar{t}}} $ decay starts to influence the A $ \to \tau \tau$ branching fraction. The H $ \to \tau \tau$ branching fraction is influenced more gradually close to this threshold since A and H are not completely degenerate in mass.
png pdf	Figure 13-a: Expected and observed 95% CL exclusion contours in the MSSM (left) ${M_{\mathrm {h}}^{125}}$ and (right) ${M_{\mathrm {h},\,\text {EFT}}^{125}}$ scenarios. The expected median in the absence of a signal is shown as a dashed black line. The dark and bright grey bands indicate the central 68% and 95% intervals of the expected exclusion. The observed exclusion contour is indicated by the coloured blue area. For both scenarios, those parts of the parameter space where ${m_{\mathrm{h}}}$ deviates by more then ${\pm}$ 3 GeV from the mass of H(125) are indicated by a red hatched area. For the ${M_{\mathrm {h},\,\text {EFT}}^{125}}$ scenario, the dashed blue line indicates the threshold at $ {m_{{\mathrm {A}}}} = $ 2$ {m_{\mathrm{t}}} $ whereby the A $ \to {\mathrm{t} \mathrm{\bar{t}}} $ decay starts to influence the A $ \to \tau \tau$ branching fraction. The H $ \to \tau \tau$ branching fraction is influenced more gradually close to this threshold since A and H are not completely degenerate in mass.
png pdf	Figure 13-b: Expected and observed 95% CL exclusion contours in the MSSM (left) ${M_{\mathrm {h}}^{125}}$ and (right) ${M_{\mathrm {h},\,\text {EFT}}^{125}}$ scenarios. The expected median in the absence of a signal is shown as a dashed black line. The dark and bright grey bands indicate the central 68% and 95% intervals of the expected exclusion. The observed exclusion contour is indicated by the coloured blue area. For both scenarios, those parts of the parameter space where ${m_{\mathrm{h}}}$ deviates by more then ${\pm}$ 3 GeV from the mass of H(125) are indicated by a red hatched area. For the ${M_{\mathrm {h},\,\text {EFT}}^{125}}$ scenario, the dashed blue line indicates the threshold at $ {m_{{\mathrm {A}}}} = $ 2$ {m_{\mathrm{t}}} $ whereby the A $ \to {\mathrm{t} \mathrm{\bar{t}}} $ decay starts to influence the A $ \to \tau \tau$ branching fraction. The H $ \to \tau \tau$ branching fraction is influenced more gradually close to this threshold since A and H are not completely degenerate in mass.

Tables
png pdf	Table 1: Summary of the preferred values and uncertainties of ${{\beta _{\mathrm {L}}} ^{\mathrm {s}\tau}}$ in the two considered U$_{1}$ benchmark scenarios from Ref. [72].
png pdf	Table 2: Efficiencies for the identification of ${\tau _\mathrm {h}}$ decays and corresponding misidentification rates (given in parentheses) for the working points of D$_{\mathrm{e}}$, D$_{\mu}$, and D$_{\text{jet}}$, chosen for the $\tau \tau$ selection, depending on the $\tau \tau$ final state. The numbers are given as a percentages.
png pdf	Table 3: 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 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 e$ {\tau _\mathrm {h}}$, $\mu {\tau _\mathrm {h}}$, and ${{\tau _\mathrm {h}} {\tau _\mathrm {h}}}$ 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 4: Event categories and discriminants used for the extraction of the signals, for the searches described in this paper. We note that ${m_{\phi}}$ refers to the hypothesized mass of the model-independent ${\phi}$ search, while ${m_{\tau \tau}}$ refers to the reconstructed mass of the $\tau \tau$ system before the decays of the $\tau$ leptons, and thus to an estimate of ${m_{\phi}}$ in data. The variable $y_{l}$ refers to the output functions of the NNs used for signal extraction in Ref. [109].
png pdf	Table 5: Background processes contributing to the event selection, as discussed in Section 5. The symbol $\ell$ corresponds to an electron or muon. The second column refers to the experimental signature in the analysis, the last four columns indicate the estimation methods used to model each corresponding signature, as described in Sections 6.1-6.4. Diboson and single t production are part of the process group iv) discussed in Section 6. QCD(e$\mu$) refers to QCD multijet production with an e$\mu$ pair in the final state.
png pdf	Table 6: Summary of 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 with other uncertainties. A checkmark is given also for partial correlations. More details are given in the text.
png pdf	Table 7: Contribution of MSSM signals to the ${m_{\mathrm {T}}^{\text {tot}}}$ and NN output function template distributions used for signal extraction for the interpretation of the data in MSSM benchmark scenarios.

Summary

Three searches have been presented for signatures of physics beyond the standard model (SM) in $\tau\tau$ final states in proton-proton collisions at the LHC, using a data sample collected with the CMS detector at $\sqrt{s} = $ 13 TeV, corresponding to an integrated luminosity of 138 fb$^{-1}$. Upper limits at 95% confidence level (CL) have been set on the products of the branching fraction for the decay into $\tau$ leptons and the cross sections for the production of a resonance $\phi$ in addition to the observed Higgs boson via gluon fusion (gg$\phi$) or in association with b quarks, ranging from ${\mathcal{O}}$(10 pb) for a mass of 60 GeV to 0.3 fb for a mass of 3.5 TeV each. The data reveal two excesses for gg$\phi$ production with local $p$-values equivalent to about three standard deviations at ${m_{\phi}} =$ 0.1 and 1.2 TeV. Within the resolution of the reconstructed invariant mass of the $\tau\tau$ system, the excess at 100 GeV coincides with a similar excess observed in a previous search for low-mass resonances by the CMS Collaboration in the $\gamma\gamma$ final state at a mass of ${\approx}$95 GeV. In a search for $t$-channel exchange of a vector leptoquark U$_{1}$, 95% CL upper limits are set on the U$_{1}$ coupling to quarks and $\tau$ leptons ranging from 1 for a mass of 1 TeV to 6 for a mass of 5 TeV, depending on the scenario. The search is sensitive to and excludes a portion of the parameter space that can explain the b physics anomalies. In the interpretation of the ${M_{\mathrm{h}}^{125}}$ and ${M_{\mathrm{h},\,\text{EFT}}^{125}}$ minimal supersymmetric SM benchmark scenarios, additional Higgs bosons with masses below 350 GeV are excluded at 95% CL.

Additional Figures
png pdf	Additional Figure 1: Distribution of $m_{ \tau \tau }$ in the ``b tag'' category used for the model-independent $\phi$ search for $m_{\phi}< $ 250 GeV, in the $ \mathrm{e} \mu $ final state. The solid histograms show the stacked background predictions after a fit of the signal-plus-background hypothesis with $m_{\phi}= $ 100 GeV to the data. The best fit $ \mathrm{g} \mathrm{g} \phi$ signal is shown by the solid red line. The total background prediction estimated from a fit of the background-only hypothesis to the data is shown by the dashed blue line for comparison. The lower panel shows the ratio of the data over the background expectation after the fit of the signal-plus-background hypothesis to the data. The full predictions of the fits of the signal-plus-background (with signal) and background-only hypotheses are also shown by the solid red and dashed blue line, respectively.
png pdf	Additional Figure 2: Distribution of $m_{ \tau \tau }$ in the ``No b tag, $ p_{\mathrm{T}} ^{ \tau \tau }< $ 50 GeV'' category used for the model-independent $\phi$ search for $m_{\phi}< $ 250 GeV, in the $ \mathrm{e} \mu $ final state. The solid histograms show the stacked background predictions after a fit of the signal-plus-background hypothesis with $m_{\phi}= $ 100 GeV to the data. The best fit $ \mathrm{g} \mathrm{g} \phi$ signal is shown by the solid red line. The total background prediction estimated from a fit of the background-only hypothesis to the data is shown by the dashed blue line for comparison. The lower panel shows the ratio of the data over the background expectation after the fit of the signal-plus-background hypothesis to the data. The full predictions of the fits of the signal-plus-background (with signal) and background-only hypotheses are also shown by the solid red and dashed blue line, respectively.
png pdf	Additional Figure 3: Distribution of $m_{ \tau \tau }$ in the ``No b tag, 50 $ < p_{\mathrm{T}} ^{ \tau \tau }< $ 100 GeV'' category used for the model-independent $\phi$ search for $m_{\phi}< $ 250 GeV, in the $ \mathrm{e} \mu $ final state. The solid histograms show the stacked background predictions after a fit of the signal-plus-background hypothesis with $m_{\phi}= $ 100 GeV to the data. The best fit $ \mathrm{g} \mathrm{g} \phi$ signal is shown by the solid red line. The total background prediction estimated from a fit of the background-only hypothesis to the data is shown by the dashed blue line for comparison. The lower panel shows the ratio of the data over the background expectation after the fit of the signal-plus-background hypothesis to the data. The full predictions of the fits of the signal-plus-background (with signal) and background-only hypotheses are also shown by the solid red and dashed blue line, respectively.
png pdf	Additional Figure 4: Distribution of $m_{ \tau \tau }$ in the ``b tag'' category used for the model-independent $\phi$ search for $m_{\phi}< $ 250 GeV, in the $ \mathrm{e} \tau _{\mathrm{h}}$ and $ \mu \tau _{\mathrm{h}}$ final states combined. The solid histograms show the stacked background predictions after a fit of the signal-plus-background hypothesis with $m_{\phi}= $ 100 GeV to the data. The best fit $ \mathrm{g} \mathrm{g} \phi$ signal is shown by the solid red line. The total background prediction estimated from a fit of the background-only hypothesis to the data is shown by the dashed blue line for comparison. The lower panel shows the ratio of the data over the background expectation after the fit of the signal-plus-background hypothesis to the data. The full predictions of the fits of the signal-plus-background (with signal) and background-only hypotheses are also shown by the solid red and dashed blue line, respectively.
png pdf	Additional Figure 5: Distribution of $m_{ \tau \tau }$ in the ``No b tag, $ p_{\mathrm{T}} ^{ \tau \tau }< $ 50 GeV'' category used for the model-independent $\phi$ search for $m_{\phi}< $ 250 GeV, in the $ \mathrm{e} \tau _{\mathrm{h}}$ and $ \mu \tau _{\mathrm{h}}$ final states combined. The solid histograms show the stacked background predictions after a fit of the signal-plus-background hypothesis with $m_{\phi}= $ 100 GeV to the data. The best fit $ \mathrm{g} \mathrm{g} \phi$ signal is shown by the solid red line. The total background prediction estimated from a fit of the background-only hypothesis to the data is shown by the dashed blue line for comparison. The lower panel shows the ratio of the data over the background expectation after the fit of the signal-plus-background hypothesis to the data. The full predictions of the fits of the signal-plus-background (with signal) and background-only hypotheses are also shown by the solid red and dashed blue line, respectively.
png pdf	Additional Figure 6: Distribution of $m_{ \tau \tau }$ in the ``No b tag, 50 $ < p_{\mathrm{T}} ^{ \tau \tau }< $ 100 GeV'' category used for the model-independent $\phi$ search for $m_{\phi}< $ 250 GeV, in the $ \mathrm{e} \tau _{\mathrm{h}}$ and $ \mu \tau _{\mathrm{h}}$ final states combined. The solid histograms show the stacked background predictions after a fit of the signal-plus-background hypothesis with $m_{\phi}= $ 100 GeV to the data. The best fit $ \mathrm{g} \mathrm{g} \phi$ signal is shown by the solid red line. The total background prediction estimated from a fit of the background-only hypothesis to the data is shown by the dashed blue line for comparison. The lower panel shows the ratio of the data over the background expectation after the fit of the signal-plus-background hypothesis to the data. The full predictions of the fits of the signal-plus-background (with signal) and background-only hypotheses are also shown by the solid red and dashed blue line, respectively.
png pdf	Additional Figure 7: Distribution of $m_{ \tau \tau }$ in the ``b tag'' category used for the model-independent $\phi$ search for $m_{\phi}< $ 250 GeV, in the $ \tau _{\mathrm{h}} \tau _{\mathrm{h}}$ final state. The solid histograms show the stacked background predictions after a fit of the signal-plus-background hypothesis with $m_{\phi}= $ 100 GeV to the data. The best fit $ \mathrm{g} \mathrm{g} \phi$ signal is shown by the solid red line. The total background prediction estimated from a fit of the background-only hypothesis to the data is shown by the dashed blue line for comparison. The lower panel shows the ratio of the data over the background expectation after the fit of the signal-plus-background hypothesis to the data. The full predictions of the fits of the signal-plus-background (with signal) and background-only hypotheses are also shown by the solid red and dashed blue line, respectively.
png pdf	Additional Figure 8: Distribution of $m_{ \tau \tau }$ in the ``No b tag, $ p_{\mathrm{T}} ^{ \tau \tau }< $ 50 GeV'' category used for the model-independent $\phi$ search for $m_{\phi}< $ 250 GeV, in the $ \tau _{\mathrm{h}} \tau _{\mathrm{h}}$ final state. The solid histograms show the stacked background predictions after a fit of the signal-plus-background hypothesis with $m_{\phi}= $ 100 GeV to the data. The best fit $ \mathrm{g} \mathrm{g} \phi$ signal is shown by the solid red line. The total background prediction estimated from a fit of the background-only hypothesis to the data is shown by the dashed blue line for comparison. The lower panel shows the ratio of the data over the background expectation after the fit of the signal-plus-background hypothesis to the data. The full predictions of the fits of the signal-plus-background (with signal) and background-only hypotheses are also shown by the solid red and dashed blue line, respectively.
png pdf	Additional Figure 9: Distribution of $m_{ \tau \tau }$ in the ``No b tag, 50 $ < p_{\mathrm{T}} ^{ \tau \tau }< $ 100 GeV'' category used for the model-independent $\phi$ search for $m_{\phi}< $ 250 GeV, in the $ \tau _{\mathrm{h}} \tau _{\mathrm{h}}$ final state. The solid histograms show the stacked background predictions after a fit of the signal-plus-background hypothesis with $m_{\phi}= $ 100 GeV to the data. The best fit $ \mathrm{g} \mathrm{g} \phi$ signal is shown by the solid red line. The total background prediction estimated from a fit of the background-only hypothesis to the data is shown by the dashed blue line for comparison. The lower panel shows the ratio of the data over the background expectation after the fit of the signal-plus-background hypothesis to the data. The full predictions of the fits of the signal-plus-background (with signal) and background-only hypotheses are also shown by the solid red and dashed blue line, respectively.
png pdf	Additional Figure 10: Distribution of $m_{ \tau \tau }$ in the ``b tag'' category used for the model-independent $\phi$ search for $m_{\phi}< $ 250 GeV, in the $ \mathrm{e} \mu $ final state, after a fit of the background-only hypothesis to the data. A $ \mathrm{g} \mathrm{g} \phi$ signal with $m_{\phi}= $ 100 GeV and a cross section of 5.8 pb is also shown, for illustrative purposes.
png pdf	Additional Figure 11: Distribution of $m_{ \tau \tau }$ in the ``No b tag, $ p_{\mathrm{T}} ^{ \tau \tau }< $ 50 GeV'' category used for the model-independent $\phi$ search for $m_{\phi}\geq $ 250 GeV, in the $ \mathrm{e} \mu $ final state, after a fit of the background-only hypothesis to the data. A $ \mathrm{g} \mathrm{g} \phi$ signal with $m_{\phi}= $ 100 GeV and a cross section of 5.8 pb is also shown, for illustrative purposes.
png pdf	Additional Figure 12: Distribution of $m_{ \tau \tau }$ in the ``No b tag, 50 $ < p_{\mathrm{T}} ^{ \tau \tau }< $ 100 GeV'' category used for the model-independent $\phi$ search for $m_{\phi}< $ 250 GeV, in the $ \mathrm{e} \mu $ final state, after a fit of the background-only hypothesis to the data. A $ \mathrm{g} \mathrm{g} \phi$ signal with $m_{\phi}= $ 100 GeV and a cross section of 5.8 pb is also shown, for illustrative purposes.
png pdf	Additional Figure 13: Distribution of $m_{ \tau \tau }$ in the ``No b tag, 100 $ < p_{\mathrm{T}} ^{ \tau \tau }< $ 200 GeV'' category used for the model-independent $\phi$ search for $m_{\phi}< $ 250 GeV, in the $ \mathrm{e} \mu $ final state, after a fit of the background-only hypothesis to the data. A $ \mathrm{g} \mathrm{g} \phi$ signal with $m_{\phi}= $ 100 GeV and a cross section of 5.8 pb is also shown, for illustrative purposes.
png pdf	Additional Figure 14: Distribution of $m_{ \tau \tau }$ in the ``No b tag, $ p_{\mathrm{T}} ^{ \tau \tau }> $ 200 GeV'' category used for the model-independent $\phi$ search for $m_{\phi}< $ 250 GeV, in the $ \mathrm{e} \mu $ final state, after a fit of the background-only hypothesis to the data. A $ \mathrm{g} \mathrm{g} \phi$ signal with $m_{\phi}= $ 100 GeV and a cross section of 5.8 pb is also shown, for illustrative purposes.
png pdf	Additional Figure 15: Distribution of $m_{ \tau \tau }$ in the ``b tag'' category used for the model-independent $\phi$ search for $m_{\phi}< $ 250 GeV, in the $ \mathrm{e} \tau _{\mathrm{h}}$ and $ \mu \tau _{\mathrm{h}}$ final states combined, after a fit of the background-only hypothesis to the data. A $ \mathrm{g} \mathrm{g} \phi$ signal with $m_{\phi}= $ 100 GeV and a cross section of 5.8 pb is also shown, for illustrative purposes.
png pdf	Additional Figure 16: Distribution of $m_{ \tau \tau }$ in the ``No b tag, $ p_{\mathrm{T}} ^{ \tau \tau }< $ 50 GeV'' category used for the model-independent $\phi$ search for $m_{\phi}< $ 250 GeV, in the $ \mathrm{e} \tau _{\mathrm{h}}$ and $ \mu \tau _{\mathrm{h}}$ final states combined, after a fit of the background-only hypothesis to the data. A $ \mathrm{g} \mathrm{g} \phi$ signal with $m_{\phi}= $ 100 GeV and a cross section of 5.8 pb is also shown, for illustrative purposes.
png pdf	Additional Figure 17: Distribution of $m_{ \tau \tau }$ in the ``No b tag, 50 $ < p_{\mathrm{T}} ^{ \tau \tau }< $ 100 GeV'' category used for the model-independent $\phi$ search for $m_{\phi}< $ 250 GeV, in the $ \mathrm{e} \tau _{\mathrm{h}}$ and $ \mu \tau _{\mathrm{h}}$ final states combined, after a fit of the background-only hypothesis to the data. A $ \mathrm{g} \mathrm{g} \phi$ signal with $m_{\phi}= $ 100 GeV and a cross section of 5.8 pb is also shown, for illustrative purposes.
png pdf	Additional Figure 18: Distribution of $m_{ \tau \tau }$ in the ``No b tag, 100 $ < p_{\mathrm{T}} ^{ \tau \tau }< $ 200 GeV'' category used for the model-independent $\phi$ search for $m_{\phi}< $ 250 GeV, in the $ \mathrm{e} \tau _{\mathrm{h}}$ and $ \mu \tau _{\mathrm{h}}$ final states combined, after a fit of the background-only hypothesis to the data. A $ \mathrm{g} \mathrm{g} \phi$ signal with $m_{\phi}= $ 100 GeV and a cross section of 5.8 pb is also shown, for illustrative purposes.
png pdf	Additional Figure 19: Distribution of $m_{ \tau \tau }$ in the ``No b tag, $ p_{\mathrm{T}} ^{ \tau \tau }> $ 200 GeV'' category used for the model-independent $\phi$ search for $m_{\phi}< $ 250 GeV, in the $ \mathrm{e} \tau _{\mathrm{h}}$ and $ \mu \tau _{\mathrm{h}}$ final states combined, after a fit of the background-only hypothesis to the data. A $ \mathrm{g} \mathrm{g} \phi$ signal with $m_{\phi}= $ 100 GeV and a cross section of 5.8 pb is also shown, for illustrative purposes.
png pdf	Additional Figure 20: Distribution of $m_{ \tau \tau }$ in the ``b tag'' category used for the model-independent $\phi$ search for $m_{\phi}< $ 250 GeV, in the $ \tau _{\mathrm{h}} \tau _{\mathrm{h}}$ final state, after a fit of the background-only hypothesis to the data. A $ \mathrm{g} \mathrm{g} \phi$ signal with $m_{\phi}= $ 100 GeV and a cross section of 5.8 pb is also shown, for illustrative purposes.
png pdf	Additional Figure 21: Distribution of $m_{ \tau \tau }$ in the ``No b tag, $ p_{\mathrm{T}} ^{ \tau \tau }< $ 50 GeV'' category used for the model-independent $\phi$ search for $m_{\phi}< $ 250 GeV, in the $ \tau _{\mathrm{h}} \tau _{\mathrm{h}}$ final state, after a fit of the background-only hypothesis to the data. A $ \mathrm{g} \mathrm{g} \phi$ signal with $m_{\phi}= $ 100 GeV and a cross section of 5.8 pb is also shown, for illustrative purposes.
png pdf	Additional Figure 22: Distribution of $m_{ \tau \tau }$ in the ``No b tag, 50 $ < p_{\mathrm{T}} ^{ \tau \tau }< $ 100 GeV'' category used for the model-independent $\phi$ search for $m_{\phi}< $ 250 GeV, in the $ \tau _{\mathrm{h}} \tau _{\mathrm{h}}$ final state, after a fit of the background-only hypothesis to the data. A $ \mathrm{g} \mathrm{g} \phi$ signal with $m_{\phi}= $ 100 GeV and a cross section of 5.8 pb is also shown, for illustrative purposes.
png pdf	Additional Figure 23: Distribution of $m_{ \tau \tau }$ in the ``No b tag, 100 $ < p_{\mathrm{T}} ^{ \tau \tau }< $ 200 GeV'' category used for the model-independent $\phi$ search for $m_{\phi}< $ 250 GeV, in the $ \tau _{\mathrm{h}} \tau _{\mathrm{h}}$ final state, after a fit of the background-only hypothesis to the data. A $ \mathrm{g} \mathrm{g} \phi$ signal with $m_{\phi}= $ 100 GeV and a cross section of 5.8 pb is also shown, for illustrative purposes.
png pdf	Additional Figure 24: Distribution of $m_{ \tau \tau }$ in the ``No b tag, $ p_{\mathrm{T}} ^{ \tau \tau }> $ 200 GeV'' category used for the model-independent $\phi$ search in the $ \tau _{\mathrm{h}} \tau _{\mathrm{h}}$ final state, after a fit of the background-only hypothesis to the data. A $ \mathrm{g} \mathrm{g} \phi$ signal with $m_{\phi}= $ 100 GeV and a cross section of 5.8 pb is also shown, for illustrative purposes.
png pdf	Additional Figure 25: Distribution of $m_{\text{T}}^{\text{tot}}$ in the ``No b tag, High-$D_{\zeta}$'' category used for the model-independent $\phi$ search for $m_{\phi}\geq $ 250 GeV, the search for vector leptoquarks, and the interpretation in MSSM benchmark scenarios, in the $ \mathrm{e} \mu $ final state. The background model is shown after the fit of the background-only hypothesis to the data. A $ \mathrm{g} \mathrm{g} \phi$ and $ \mathrm{b} \mathrm{b} \phi$ signal with $m_{\phi} = $ 1.2 TeV scaled to 3.1 and 1.0 fb, and a vector leptoquark signal with $m_{\text{U}}= $ 1 TeV and $g_{\text{U}}= $ 1.2 are also shown for illustrative purposes.
png pdf	Additional Figure 26: Distribution of $m_{\text{T}}^{\text{tot}}$ in the ``No b tag, Low-$D_{\zeta}$'' category used for the model-independent $\phi$ search for $m_{\phi}\geq $ 250 GeV, the search for vector leptoquarks, and the interpretation in MSSM benchmark scenarios, in the $ \mathrm{e} \mu $ final state. The background model is shown after the fit of the background-only hypothesis to the data. A $ \mathrm{g} \mathrm{g} \phi$ and $ \mathrm{b} \mathrm{b} \phi$ signal with $m_{\phi} = $ 1.2 TeV scaled to 3.1 and 1.0 fb, and a vector leptoquark signal with $m_{\text{U}}= $ 1 TeV and $g_{\text{U}}= $ 1.2 are also shown for illustrative purposes.
png pdf	Additional Figure 27: Distribution of $m_{\text{T}}^{\text{tot}}$ in the ``b tag, High-$D_{\zeta}$'' category used for the model-independent $\phi$ search for $m_{\phi}\geq $ 250 GeV, the search for vector leptoquarks, and the interpretation in MSSM benchmark scenarios, in the $ \mathrm{e} \mu $ final state. The background model is shown after the fit of the background-only hypothesis to the data. A $ \mathrm{g} \mathrm{g} \phi$ and $ \mathrm{b} \mathrm{b} \phi$ signal with $m_{\phi}= $ 1.2 TeV scaled to 3.1 and 1.0 fb, and a vector leptoquark signal with $m_{\text{U}}= $ 1 TeV and $g_{\text{U}}= $ 1.2 are also shown for illustrative purposes.
png pdf	Additional Figure 28: Distribution of $m_{\text{T}}^{\text{tot}}$ in the ``b tag, Low-$D_{\zeta}$'' category used for the model-independent $\phi$ search for $m_{\phi}\geq $ 250 GeV, the search for vector leptoquarks, and the interpretation in MSSM benchmark scenarios, in the $ \mathrm{e} \mu $ final state. The background model is shown after the fit of the background-only hypothesis to the data. A $ \mathrm{g} \mathrm{g} \phi$ and $ \mathrm{b} \mathrm{b} \phi$ signal with $m_{\phi}= $ 1.2 TeV scaled to 3.1 and 1.0 fb, and a vector leptoquark signal with $m_{\text{U}}= $ 1 TeV and $g_{\text{U}}= $ 1.2 are also shown for illustrative purposes.
png pdf	Additional Figure 29: Distribution of $m_{\text{T}}^{\text{tot}}$ in the global ``No b tag, Loose-$ m_{\mathrm{T}} $'' category used for the model-independent $\phi$ search for $m_{\phi}\geq $ 250 GeV, the search for vector leptoquarks, and the interpretation in MSSM benchmark scenarios, in the $ \mathrm{e} \tau _{\mathrm{h}}$ and $ \mu \tau _{\mathrm{h}}$ final states combined. The background model is shown after the fit of the background-only hypothesis to the data. A $ \mathrm{g} \mathrm{g} \phi$ and $ \mathrm{b} \mathrm{b} \phi$ signal with $m_{\phi}= $ 1.2 TeV scaled to 3.1 and 1.0 fb, and a vector leptoquark signal with $m_{\text{U}}= $ 1 TeV and $g_{\text{U}}= $ 1.2 are also shown for illustrative purposes.
png pdf	Additional Figure 30: Distribution of $m_{\text{T}}^{\text{tot}}$ in the ``b tag, Loose-$ m_{\mathrm{T}} $'' category used for the model-independent $\phi$ search for $m_{\phi}\geq $ 250 GeV, the search for vector leptoquarks, and the interpretation in MSSM benchmark scenarios, in the $ \mathrm{e} \tau _{\mathrm{h}}$ and $ \mu \tau _{\mathrm{h}}$ final states combined. The background model is shown after the fit of the background-only hypothesis to the data. A $ \mathrm{g} \mathrm{g} \phi$ and $ \mathrm{b} \mathrm{b} \phi$ signal with $m_{\phi}= $ 1.2 TeV scaled to 3.1 and 1.0 fb, and a vector leptoquark signal with $m_{\text{U}}= $ 1 TeV and $g_{\text{U}}= $ 1.2 are also shown for illustrative purposes.
png pdf	Additional Figure 31: Local $p$-value and significance of a $ \mathrm{g} \mathrm{g} \phi$ signal as a function of the hypothesized value of $m_{\phi}$. For this figure the $ \mathrm{b} \mathrm{b} \phi$ production rate has been profiled.
png pdf	Additional Figure 32: Local $p$-value and significance of a $ \mathrm{b} \mathrm{b} \phi$ signal as a function of the hypothesized value of $m_{\phi}$. For this figure the $ \mathrm{g} \mathrm{g} \phi$ production rate has been profiled.
png pdf	Additional Figure 33: Local $p$-value and significance of a $ \mathrm{g} \mathrm{g} \phi$ signal as a function of the hypothesized value of $m_{\phi}$. For this figure the $ \mathrm{b} \mathrm{b} \phi$ production rate has been fixed to zero.
png pdf	Additional Figure 34: Local $p$-value and significance of a $ \mathrm{b} \mathrm{b} \phi$ signal as a function of the hypothesized value of $m_{\phi}$. For this figure the $ \mathrm{g} \mathrm{g} \phi$ production rate has been fixed to zero.
png pdf	Additional Figure 35: Local $p$-value and significance of a $ \mathrm{g} \mathrm{g} \phi$ signal as a function of the hypothesized value of $m_{\phi}$. For this figure the $ \mathrm{b} \mathrm{b} \phi$ production rate has been profiled and only t quarks are considered in the $ \mathrm{g} \mathrm{g} \phi$ loop.
png pdf	Additional Figure 36: Local $p$-value and significance of a $ \mathrm{g} \mathrm{g} \phi$ signal as a function of the hypothesized value of $m_{\phi}$. For this figure the $ \mathrm{b} \mathrm{b} \phi$ production rate has been profiled and only b quarks are considered in the $ \mathrm{g} \mathrm{g} \phi$ loop.
png pdf	Additional Figure 37: Expected and observed 95% CL upper limits on the product of the cross sections and branching fraction for the decay into $ \tau $ leptons for $ \mathrm{g} \mathrm{g} \phi$ production in a mass range of 60 $ < m_{\phi}< $ 3500 GeV. The expected median of the exclusion limit in the absence of signal is shown by the dashed line. The dark green and bright yellow bands indicate the central 68% and 95% intervals for the expected exclusion limits. The black dots correspond to the observed limits. For this figure the $ \mathrm{b} \mathrm{b} \phi$ production rate has been fixed to zero.
png pdf	Additional Figure 38: Expected and observed 95% CL upper limits on the product of the cross sections and branching fraction for the decay into $ \tau $ leptons for $ \mathrm{b} \mathrm{b} \phi$ production in a mass range of 60 $ < m_{\phi} < $ 3500 GeV. The expected median of the exclusion limit in the absence of signal is shown by the dashed line. The dark green and bright yellow bands indicate the central 68% and 95% intervals for the expected exclusion limits. The black dots correspond to the observed limits. For this figure the $ \mathrm{g} \mathrm{g} \phi$ production rate has been fixed to zero.
png pdf	Additional Figure 39: Expected and observed 95% CL upper limits on the product of the cross sections and branching fraction for the decay into $ \tau $ leptons for $ \mathrm{g} \mathrm{g} \phi$ production in a mass range of 60 $ < m_{\phi} < $ 3500 GeV. The expected median of the exclusion limit in the absence of signal is shown by the dashed line. The dark green and bright yellow bands indicate the central 68% and 95% intervals for the expected exclusion limits. The black dots correspond to the observed limits. For this figure the $ \mathrm{b} \mathrm{b} \phi$ production rate has been profiled and only t quarks are considered in the $ \mathrm{g} \mathrm{g} \phi$ loop.
png pdf	Additional Figure 40: Expected and observed 95% CL upper limits on the product of the cross sections and branching fraction for the decay into $ \tau $ leptons for $ \mathrm{g} \mathrm{g} \phi$ production in a mass range of 60 $ < m_{\phi} < $ 3500 GeV. The expected median of the exclusion limit in the absence of signal is shown by the dashed line. The dark green and bright yellow bands indicate the central 68% and 95% intervals for the expected exclusion limits. The black dots correspond to the observed limits. For this figure the $ \mathrm{b} \mathrm{b} \phi$ production rate has been profiled and only b quarks are considered in the $ \mathrm{g} \mathrm{g} \phi$ loop.
png pdf	Additional Figure 41: Maximum likelihood estimate, and 68% and 95% CL contours obtained from scans of the signal likelihood for the model-independent $\phi$ search. The scans are shown for $m_{\phi}= $ 80 GeV. The SM expectation is $(0, 0)$.
png pdf	Additional Figure 42: Maximum likelihood estimate, and 68% and 95% CL contours obtained from scans of the signal likelihood for the model-independent $\phi$ search. The scans are shown for $m_{\phi}= $ 95 GeV. The SM expectation is $(0, 0)$.
png pdf	Additional Figure 43: Maximum likelihood estimate, and 68% and 95% CL contours obtained from scans of the signal likelihood for the model-independent $\phi$ search. The scans are shown for $m_{\phi}= $ 120 GeV. The SM expectation is $(0, 0)$.
png pdf	Additional Figure 44: Maximum likelihood estimate, and 68% and 95% CL contours obtained from scans of the signal likelihood for the model-independent $\phi$ search. The scans are shown for $m_{\phi}= $ 130 GeV. The SM expectation is $(0, 0)$.
png pdf	Additional Figure 45: Maximum likelihood estimate, and 68% and 95% CL contours obtained from scans of the signal likelihood for the model-independent $\phi$ search. The scans are shown for $m_{\phi}= $ 140 GeV. The SM expectation is $(0, 0)$.
png pdf	Additional Figure 46: Maximum likelihood estimate, and 68% and 95% CL contours obtained from scans of the signal likelihood for the model-independent $\phi$ search. The scans are shown for $m_{\phi}= $ 180 GeV. The SM expectation is $(0, 0)$.
png pdf	Additional Figure 47: Maximum likelihood estimate, and 68% and 95% CL contours obtained from scans of the signal likelihood for the model-independent $\phi$ search. The scans are shown for $m_{\phi}= $ 200 GeV. The SM expectation is $(0, 0)$.
png pdf	Additional Figure 48: Maximum likelihood estimate, and 68% and 95% CL contours obtained from scans of the signal likelihood for the model-independent $\phi$ search. The scans are shown for $m_{\phi}= $ 300 GeV. The SM expectation is $(0, 0)$.
png pdf	Additional Figure 49: Maximum likelihood estimate, and 68% and 95% CL contours obtained from scans of the signal likelihood for the model-independent $\phi$ search. The scans are shown for $m_{\phi}= $ 350 GeV. The SM expectation is $(0, 0)$.
png pdf	Additional Figure 50: Maximum likelihood estimate, and 68% and 95% CL contours obtained from scans of the signal likelihood for the model-independent $\phi$ search. The scans are shown for $m_{\phi}= $ 400 GeV. The SM expectation is $(0, 0)$.
png pdf	Additional Figure 51: Maximum likelihood estimate, and 68% and 95% CL contours obtained from scans of the signal likelihood for the model-independent $\phi$ search. The scans are shown for $m_{\phi}= $ 450 GeV. The SM expectation is $(0, 0)$.
png pdf	Additional Figure 52: Maximum likelihood estimate, and 68% and 95% CL contours obtained from scans of the signal likelihood for the model-independent $\phi$ search. The scans are shown for $m_{\phi}= $ 600 GeV. The SM expectation is $(0, 0)$.
png pdf	Additional Figure 53: Maximum likelihood estimate, and 68% and 95% CL contours obtained from scans of the signal likelihood for the model-independent $\phi$ search. The scans are shown for $m_{\phi}= $ 700 GeV. The SM expectation is $(0, 0)$.
png pdf	Additional Figure 54: Maximum likelihood estimate, and 68% and 95% CL contours obtained from scans of the signal likelihood for the model-independent $\phi$ search. The scans are shown for $m_{\phi}= $ 800 GeV. The SM expectation is $(0, 0)$.
png pdf	Additional Figure 55: Maximum likelihood estimate, and 68% and 95% CL contours obtained from scans of the signal likelihood for the model-independent $\phi$ search. The scans are shown for $m_{\phi}= $ 900 GeV. The SM expectation is $(0, 0)$.
png pdf	Additional Figure 56: Maximum likelihood estimate, and 68% and 95% CL contours obtained from scans of the signal likelihood for the model-independent $\phi$ search. The scans are shown for $m_{\phi}= $ 1400 GeV. The SM expectation is $(0, 0)$.
png pdf	Additional Figure 57: Maximum likelihood estimate, and 68% and 95% CL contours obtained from scans of the signal likelihood for the model-independent $\phi$ search. The scans are shown for $m_{\phi}= $ 1600 GeV. The SM expectation is $(0, 0)$.
png pdf	Additional Figure 58: Maximum likelihood estimate, and 68% and 95% CL contours obtained from scans of the signal likelihood for the model-independent $\phi$ search. The scans are shown for $m_{\phi}= $ 1800 GeV. The SM expectation is $(0, 0)$.
png pdf	Additional Figure 59: Maximum likelihood estimate, and 68% and 95% CL contours obtained from scans of the signal likelihood for the model-independent $\phi$ search. The scans are shown for $m_{\phi}= $ 2000 GeV. The SM expectation is $(0, 0)$.
png pdf	Additional Figure 60: Maximum likelihood estimate, and 68% and 95% CL contours obtained from scans of the signal likelihood for the model-independent $\phi$ search. The scans are shown for $m_{\phi}= $ 2300 GeV. The SM expectation is $(0, 0)$.
png pdf	Additional Figure 61: Maximum likelihood estimate, and 68% and 95% CL contours obtained from scans of the signal likelihood for the model-independent $\phi$ search. The scans are shown for $m_{\phi}= $ 2600 GeV. The SM expectation is $(0, 0)$.
png pdf	Additional Figure 62: Maximum likelihood estimate, and 68% and 95% CL contours obtained from scans of the signal likelihood for the model-independent $\phi$ search. The scans are shown for $m_{\phi}= $ 2900 GeV. The SM expectation is $(0, 0)$.
png pdf	Additional Figure 63: Maximum likelihood estimate, and 68% and 95% CL contours obtained from scans of the signal likelihood for the model-independent $\phi$ search. The scans are shown for $m_{\phi}= $ 3200 GeV. The SM expectation is $(0, 0)$.
png pdf	Additional Figure 64: Maximum likelihood estimate, and 68% and 95% CL contours obtained from scans of the signal likelihood for a $\phi$ resonance with $m_{\phi}= $ 95 GeV, produced via $ \mathrm{g} \mathrm{g} \phi$ or vector boson fusion ($ \mathrm{q} \mathrm{q} \phi$). For this figure the $ \mathrm{b} \mathrm{b} \phi$ production rate has been profiled.
png pdf	Additional Figure 65: Maximum likelihood estimate, and 68% and 95% CL contours obtained from scans of the signal-plus-background likelihood for a scalar resonance $ \mathrm{H} $ with $m_{\mathrm{H}}= $ 60 GeV, produced via $ \mathrm{g} \mathrm{g} \mathrm{H}$ or $ \mathrm{b} \mathrm{b} \mathrm{H}$. For this scan, we assume that both processes are only influenced by the Yukawa couplings to t and b quarks and scale the predicted cross sections depending on these couplings. The estimates are shown for the product of the reduced Yukawa couplings $\mathrm{g}_{ \mathrm{t} ,\, \mathrm{b} }^{\mathrm{H}}$ and $\sqrt{B(\mathrm{H}\to \tau \tau )}$, where the former is defined as the ratio of the Yukawa coupling of $ \mathrm{H} $ over the Yukawa coupling expected for a SM-like Higgs boson of the same mass. An ambiguity on the relative sign of the two couplings can be resolved by the contribution of $ \mathrm{t} \mathrm{b} $-interference terms to the cross section predictions. By convention $\mathrm{g}_{ \mathrm{t} }^{\mathrm{H}}$ has been chosen positive.
png pdf	Additional Figure 66: Maximum likelihood estimate, and 68% and 95% CL contours obtained from scans of the signal-plus-background likelihood for a pseudoscalar resonance $\mathrm{A}$ with $m_{\mathrm{A}}= $ 60 GeV, produced via $ \mathrm{g} \mathrm{g} \mathrm{A}$ or $ \mathrm{b} \mathrm{b} \mathrm{A}$. For this scan, we assume that both processes are only influenced by the Yukawa couplings to t and b quarks and scale the predicted cross sections depending on these couplings. The estimates are shown for the product of the reduced Yukawa couplings $\mathrm{g}_{ \mathrm{t} ,\, \mathrm{b} }^{\mathrm{A}}$ and $\sqrt{B(\mathrm{A}\to \tau \tau )}$, where the former is defined as the ratio of the Yukawa coupling of $\mathrm{A}$ over the Yukawa coupling expected for a SM-like Higgs boson of the same mass. An ambiguity on the relative sign of the two couplings can be resolved by the contribution of $ \mathrm{t} \mathrm{b} $-interference terms to the cross section predictions. By convention $\mathrm{g}_{ \mathrm{t} }^{\mathrm{A}}$ has been chosen positive.
png pdf	Additional Figure 67: Maximum likelihood estimate, and 68% and 95% CL contours obtained from scans of the signal-plus-background likelihood for a scalar resonance ($ \mathrm{H} $) with $m_{\mathrm{H}}= $ 80 GeV, produced via $ \mathrm{g} \mathrm{g} \mathrm{H}$ or $ \mathrm{b} \mathrm{b} \mathrm{H}$. For this scan, we assume that both processes are only influenced by the Yukawa couplings to t and b quarks and scale the predicted cross sections depending on these couplings. The estimates are shown for the product of the reduced Yukawa couplings $\mathrm{g}_{ \mathrm{t} ,\, \mathrm{b} }^{\mathrm{H}}$ and $\sqrt{B(\mathrm{H}\to \tau \tau )}$, where the former is defined as the ratio of the Yukawa coupling of $ \mathrm{H} $ over the Yukawa coupling expected for a SM-like Higgs boson of the same mass. An ambiguity on the relative sign of the two couplings can be resolved by the contribution of $ \mathrm{t} \mathrm{b} $-interference terms to the cross section predictions. By convention $\mathrm{g}_{ \mathrm{t} }^{\mathrm{H}}$ has been chosen positive.
png pdf	Additional Figure 68: Maximum likelihood estimate, and 68% and 95% CL contours obtained from scans of the signal-plus-background likelihood for a pseudoscalar resonance ($\mathrm{A}$) with $m_{\mathrm{A}}= $ 80 GeV, produced via $ \mathrm{g} \mathrm{g} \mathrm{A}$ or $ \mathrm{b} \mathrm{b} \mathrm{A}$. For this scan, we assume that both processes are only influenced by the Yukawa couplings to t and b quarks and scale the predicted cross sections depending on these couplings. The estimates are shown for the product of the reduced Yukawa couplings $\mathrm{g}_{ \mathrm{t} ,\, \mathrm{b} }^{\mathrm{A}}$ and $\sqrt{B(\mathrm{A}\to \tau \tau )}$, where the former is defined as the ratio of the Yukawa coupling of $\mathrm{A}$ over the Yukawa coupling expected for a SM-like Higgs boson of the same mass. An ambiguity on the relative sign of the two couplings can be resolved by the contribution of $ \mathrm{t} \mathrm{b} $-interference terms to the cross section predictions. By convention $\mathrm{g}_{ \mathrm{t} }^{\mathrm{A}}$ has been chosen positive.
png pdf	Additional Figure 69: Maximum likelihood estimate, and 68% and 95% CL contours obtained from scans of the signal-plus-background likelihood for a scalar resonance ($ \mathrm{H} $) with $m_{\mathrm{H}}= $ 95 GeV, produced via $ \mathrm{g} \mathrm{g} \mathrm{H}$ or $ \mathrm{b} \mathrm{b} \mathrm{H}$. For this scan, we assume that both processes are only influenced by the Yukawa couplings to t and b quarks and scale the predicted cross sections depending on these couplings. The estimates are shown for the product of the reduced Yukawa couplings $\mathrm{g}_{ \mathrm{t} ,\, \mathrm{b} }^{\mathrm{H}}$ and $\sqrt{B(\mathrm{H}\to \tau \tau )}$, where the former is defined as the ratio of the Yukawa coupling of $ \mathrm{H} $ over the Yukawa coupling expected for a SM-like Higgs boson of the same mass. An ambiguity on the relative sign of the two couplings can be resolved by the contribution of $ \mathrm{t} \mathrm{b} $-interference terms to the cross section predictions. By convention $\mathrm{g}_{ \mathrm{t} }^{\mathrm{H}}$ has been chosen positive.
png pdf	Additional Figure 70: Maximum likelihood estimate, and 68% and 95% CL contours obtained from scans of the signal-plus-background likelihood for a pseudoscalar resonance ($\mathrm{A}$) with $m_{\mathrm{A}}= $ 95 GeV, produced via $ \mathrm{g} \mathrm{g} \mathrm{A}$ or $ \mathrm{b} \mathrm{b} \mathrm{A}$. For this scan, we assume that both processes are only influenced by the Yukawa couplings to t and b quarks and scale the predicted cross sections depending on these couplings. The estimates are shown for the product of the reduced Yukawa couplings $\mathrm{g}_{ \mathrm{t} ,\, \mathrm{b} }^{\mathrm{A}}$ and $\sqrt{B(\mathrm{A}\to \tau \tau )}$, where the former is defined as the ratio of the Yukawa coupling of $\mathrm{A}$ over the Yukawa coupling expected for a SM-like Higgs boson of the same mass. An ambiguity on the relative sign of the two couplings can be resolved by the contribution of $ \mathrm{t} \mathrm{b} $-interference terms to the cross section predictions. By convention $\mathrm{g}_{ \mathrm{t} }^{\mathrm{A}}$ has been chosen positive.
png pdf	Additional Figure 71: Maximum likelihood estimate, and 68% and 95% CL contours obtained from scans of the signal-plus-background likelihood for a scalar resonance ($ \mathrm{H} $) with $m_{\mathrm{H}}= $ 100 GeV, produced via $ \mathrm{g} \mathrm{g} \mathrm{H}$ or $ \mathrm{b} \mathrm{b} \mathrm{H}$. For this scan, we assume that both processes are only influenced by the Yukawa couplings to t and b quarks and scale the predicted cross sections depending on these couplings. The estimates are shown for the product of the reduced Yukawa couplings $\mathrm{g}_{ \mathrm{t} ,\, \mathrm{b} }^{\mathrm{H}}$ and $\sqrt{B(\mathrm{H}\to \tau \tau )}$, where the former is defined as the ratio of the Yukawa coupling of $ \mathrm{H} $ over the Yukawa coupling expected for a SM-like Higgs boson of the same mass. An ambiguity on the relative sign of the two couplings can be resolved by the contribution of $ \mathrm{t} \mathrm{b} $-interference terms to the cross section predictions. By convention $\mathrm{g}_{ \mathrm{t} }^{\mathrm{H}}$ has been chosen positive.
png pdf	Additional Figure 72: Maximum likelihood estimate, and 68% and 95% CL contours obtained from scans of the signal-plus-background likelihood for a pseudoscalar resonance ($\mathrm{A}$) with $m_{\mathrm{A}}= $ 100 GeV, produced via $ \mathrm{g} \mathrm{g} \mathrm{A}$ or $ \mathrm{b} \mathrm{b} \mathrm{A}$. For this scan, we assume that both processes are only influenced by the Yukawa couplings to t and b quarks and scale the predicted cross sections depending on these couplings. The estimates are shown for the product of the reduced Yukawa couplings $\mathrm{g}_{ \mathrm{t} ,\, \mathrm{b} }^{\mathrm{A}}$ and $\sqrt{B(\mathrm{A}\to \tau \tau )}$, where the former is defined as the ratio of the Yukawa coupling of $\mathrm{A}$ over the Yukawa coupling expected for a SM-like Higgs boson of the same mass. An ambiguity on the relative sign of the two couplings can be resolved by the contribution of $ \mathrm{t} \mathrm{b} $-interference terms to the cross section predictions. By convention $\mathrm{g}_{ \mathrm{t} }^{\mathrm{A}}$ has been chosen positive.
png pdf	Additional Figure 73: Maximum likelihood estimate, and 68% and 95% CL contours obtained from scans of the signal-plus-background likelihood for a scalar resonance ($ \mathrm{H} $) with $m_{\mathrm{H}}= $ 120 GeV, produced via $ \mathrm{g} \mathrm{g} \mathrm{H}$ or $ \mathrm{b} \mathrm{b} \mathrm{H}$. For this scan, we assume that both processes are only influenced by the Yukawa couplings to t and b quarks and scale the predicted cross sections depending on these couplings. The estimates are shown for the product of the reduced Yukawa couplings $\mathrm{g}_{ \mathrm{t} ,\, \mathrm{b} }^{\mathrm{H}}$ and $\sqrt{B(\mathrm{H}\to \tau \tau )}$, where the former is defined as the ratio of the Yukawa coupling of $ \mathrm{H} $ over the Yukawa coupling expected for a SM-like Higgs boson of the same mass. An ambiguity on the relative sign of the two couplings can be resolved by the contribution of $ \mathrm{t} \mathrm{b} $-interference terms to the cross section predictions. By convention $\mathrm{g}_{ \mathrm{t} }^{\mathrm{H}}$ has been chosen positive.
png pdf	Additional Figure 74: Maximum likelihood estimate, and 68% and 95% CL contours obtained from scans of the signal-plus-background likelihood for a pseudoscalar resonance ($\mathrm{A}$) with $m_{\mathrm{A}}= $ 120 GeV, produced via $ \mathrm{g} \mathrm{g} \mathrm{A}$ or $ \mathrm{b} \mathrm{b} \mathrm{A}$. For this scan, we assume that both processes are only influenced by the Yukawa couplings to t and b quarks and scale the predicted cross sections depending on these couplings. The estimates are shown for the product of the reduced Yukawa couplings $\mathrm{g}_{ \mathrm{t} ,\, \mathrm{b} }^{\mathrm{A}}$ and $\sqrt{B(\mathrm{A}\to \tau \tau )}$, where the former is defined as the ratio of the Yukawa coupling of $\mathrm{A}$ over the Yukawa coupling expected for a SM-like Higgs boson of the same mass. An ambiguity on the relative sign of the two couplings can be resolved by the contribution of $ \mathrm{t} \mathrm{b} $-interference terms to the cross section predictions. By convention $\mathrm{g}_{ \mathrm{t} }^{\mathrm{A}}$ has been chosen positive.
png pdf	Additional Figure 75: Maximum likelihood estimate, and 68% and 95% CL contours obtained from scans of the signal-plus-background likelihood for a scalar resonance ($ \mathrm{H} $) with $m_{\mathrm{H}}= $ 125 GeV, produced via $ \mathrm{g} \mathrm{g} \mathrm{H}$ or $ \mathrm{b} \mathrm{b} \mathrm{H}$. For this scan, we assume that both processes are only influenced by the Yukawa couplings to t and b quarks and scale the predicted cross sections depending on these couplings. The estimates are shown for the product of the reduced Yukawa couplings $\mathrm{g}_{ \mathrm{t} ,\, \mathrm{b} }^{\mathrm{H}}$ and $\sqrt{B(\mathrm{H}\to \tau \tau )}$, where the former is defined as the ratio of the Yukawa coupling of $ \mathrm{H} $ over the Yukawa coupling expected for a SM-like Higgs boson of the same mass. An ambiguity on the relative sign of the two couplings can be resolved by the contribution of $ \mathrm{t} \mathrm{b} $-interference terms to the cross section predictions. By convention $\mathrm{g}_{ \mathrm{t} }^{\mathrm{H}}$ has been chosen positive.
png pdf	Additional Figure 76: Maximum likelihood estimate, and 68% and 95% CL contours obtained from scans of the signal-plus-background likelihood for a pseudoscalar resonance ($\mathrm{A}$) with $m_{\mathrm{A}}= $ 125 GeV, produced via $ \mathrm{g} \mathrm{g} \mathrm{A}$ or $ \mathrm{b} \mathrm{b} \mathrm{A}$. For this scan, we assume that both processes are only influenced by the Yukawa couplings to t and b quarks and scale the predicted cross sections depending on these couplings. The estimates are shown for the product of the reduced Yukawa couplings $\mathrm{g}_{ \mathrm{t} ,\, \mathrm{b} }^{\mathrm{A}}$ and $\sqrt{B(\mathrm{A}\to \tau \tau )}$, where the former is defined as the ratio of the Yukawa coupling of $\mathrm{A}$ over the Yukawa coupling expected for a SM-like Higgs boson of the same mass. An ambiguity on the relative sign of the two couplings can be resolved by the contribution of $ \mathrm{t} \mathrm{b} $-interference terms to the cross section predictions. By convention $\mathrm{g}_{ \mathrm{t} }^{\mathrm{A}}$ has been chosen positive.
png pdf	Additional Figure 77: Maximum likelihood estimate, and 68% and 95% CL contours obtained from scans of the signal-plus-background likelihood for a scalar resonance ($ \mathrm{H} $) with $m_{\mathrm{H}}= $ 130 GeV, produced via $ \mathrm{g} \mathrm{g} \mathrm{H}$ or $ \mathrm{b} \mathrm{b} \mathrm{H}$. For this scan, we assume that both processes are only influenced by the Yukawa couplings to t and b quarks and scale the predicted cross sections depending on these couplings. The estimates are shown for the product of the reduced Yukawa couplings $\mathrm{g}_{ \mathrm{t} ,\, \mathrm{b} }^{\mathrm{H}}$ and $\sqrt{B(\mathrm{H}\to \tau \tau )}$, where the former is defined as the ratio of the Yukawa coupling of $ \mathrm{H} $ over the Yukawa coupling expected for a SM-like Higgs boson of the same mass. An ambiguity on the relative sign of the two couplings can be resolved by the contribution of $ \mathrm{t} \mathrm{b} $-interference terms to the cross section predictions. By convention $\mathrm{g}_{ \mathrm{t} }^{\mathrm{H}}$ has been chosen positive.
png pdf	Additional Figure 78: Maximum likelihood estimate, and 68% and 95% CL contours obtained from scans of the signal-plus-background likelihood for a pseudoscalar resonance ($\mathrm{A}$) with $m_{\mathrm{A}}= $ 130 GeV, produced via $ \mathrm{g} \mathrm{g} \mathrm{A}$ or $ \mathrm{b} \mathrm{b} \mathrm{A}$. For this scan, we assume that both processes are only influenced by the Yukawa couplings to t and b quarks and scale the predicted cross sections depending on these couplings. The estimates are shown for the product of the reduced Yukawa couplings $\mathrm{g}_{ \mathrm{t} ,\, \mathrm{b} }^{\mathrm{A}}$ and $\sqrt{B(\mathrm{A}\to \tau \tau )}$, where the former is defined as the ratio of the Yukawa coupling of $\mathrm{A}$ over the Yukawa coupling expected for a SM-like Higgs boson of the same mass. An ambiguity on the relative sign of the two couplings can be resolved by the contribution of $ \mathrm{t} \mathrm{b} $-interference terms to the cross section predictions. By convention $\mathrm{g}_{ \mathrm{t} }^{\mathrm{A}}$ has been chosen positive.
png pdf	Additional Figure 79: Maximum likelihood estimate, and 68% and 95% CL contours obtained from scans of the signal-plus-background likelihood for a scalar resonance ($ \mathrm{H} $) with $m_{\mathrm{H}}= $ 140 GeV, produced via $ \mathrm{g} \mathrm{g} \mathrm{H}$ or $ \mathrm{b} \mathrm{b} \mathrm{H}$. For this scan, we assume that both processes are only influenced by the Yukawa couplings to t and b quarks and scale the predicted cross sections depending on these couplings. The estimates are shown for the product of the reduced Yukawa couplings $\mathrm{g}_{ \mathrm{t} ,\, \mathrm{b} }^{\mathrm{H}}$ and $\sqrt{B(\mathrm{H}\to \tau \tau )}$, where the former is defined as the ratio of the Yukawa coupling of $ \mathrm{H} $ over the Yukawa coupling expected for a SM-like Higgs boson of the same mass. An ambiguity on the relative sign of the two couplings can be resolved by the contribution of $ \mathrm{t} \mathrm{b} $-interference terms to the cross section predictions. By convention $\mathrm{g}_{ \mathrm{t} }^{\mathrm{H}}$ has been chosen positive.
png pdf	Additional Figure 80: Maximum likelihood estimate, and 68% and 95% CL contours obtained from scans of the signal-plus-background likelihood for a pseudoscalar resonance ($\mathrm{A}$) with $m_{\mathrm{A}}= $ 140 GeV, produced via $ \mathrm{g} \mathrm{g} \mathrm{A}$ or $ \mathrm{b} \mathrm{b} \mathrm{A}$. For this scan, we assume that both processes are only influenced by the Yukawa couplings to t and b quarks and scale the predicted cross sections depending on these couplings. The estimates are shown for the product of the reduced Yukawa couplings $\mathrm{g}_{ \mathrm{t} ,\, \mathrm{b} }^{\mathrm{A}}$ and $\sqrt{B(\mathrm{A}\to \tau \tau )}$, where the former is defined as the ratio of the Yukawa coupling of $\mathrm{A}$ over the Yukawa coupling expected for a SM-like Higgs boson of the same mass. An ambiguity on the relative sign of the two couplings can be resolved by the contribution of $ \mathrm{t} \mathrm{b} $-interference terms to the cross section predictions. By convention $\mathrm{g}_{ \mathrm{t} }^{\mathrm{A}}$ has been chosen positive.
png pdf	Additional Figure 81: Maximum likelihood estimate, and 68% and 95% CL contours obtained from scans of the signal-plus-background likelihood for a scalar resonance ($ \mathrm{H} $) with $m_{\mathrm{H}}= $ 160 GeV, produced via $ \mathrm{g} \mathrm{g} \mathrm{H}$ or $ \mathrm{b} \mathrm{b} \mathrm{H}$. For this scan, we assume that both processes are only influenced by the Yukawa couplings to t and b quarks and scale the predicted cross sections depending on these couplings. The estimates are shown for the product of the reduced Yukawa couplings $\mathrm{g}_{ \mathrm{t} ,\, \mathrm{b} }^{\mathrm{H}}$ and $\sqrt{B(\mathrm{H}\to \tau \tau )}$, where the former is defined as the ratio of the Yukawa coupling of $ \mathrm{H} $ over the Yukawa coupling expected for a SM-like Higgs boson of the same mass. An ambiguity on the relative sign of the two couplings can be resolved by the contribution of $ \mathrm{t} \mathrm{b} $-interference terms to the cross section predictions. By convention $\mathrm{g}_{ \mathrm{t} }^{\mathrm{H}}$ has been chosen positive.
png pdf	Additional Figure 82: Maximum likelihood estimate, and 68% and 95% CL contours obtained from scans of the signal-plus-background likelihood for a pseudoscalar resonance ($\mathrm{A}$) with $m_{\mathrm{A}}= $ 160 GeV, produced via $ \mathrm{g} \mathrm{g} \mathrm{A}$ or $ \mathrm{b} \mathrm{b} \mathrm{A}$. For this scan, we assume that both processes are only influenced by the Yukawa couplings to t and b quarks and scale the predicted cross sections depending on these couplings. The estimates are shown for the product of the reduced Yukawa couplings $\mathrm{g}_{ \mathrm{t} ,\, \mathrm{b} }^{\mathrm{A}}$ and $\sqrt{B(\mathrm{A}\to \tau \tau )}$, where the former is defined as the ratio of the Yukawa coupling of $\mathrm{A}$ over the Yukawa coupling expected for a SM-like Higgs boson of the same mass. An ambiguity on the relative sign of the two couplings can be resolved by the contribution of $ \mathrm{t} \mathrm{b} $-interference terms to the cross section predictions. By convention $\mathrm{g}_{ \mathrm{t} }^{\mathrm{A}}$ has been chosen positive.
png pdf	Additional Figure 83: Maximum likelihood estimate, and 68% and 95% CL contours obtained from scans of the signal-plus-background likelihood for a scalar resonance ($ \mathrm{H} $) with $m_{\mathrm{H}}= $ 180 GeV, produced via $ \mathrm{g} \mathrm{g} \mathrm{H}$ or $ \mathrm{b} \mathrm{b} \mathrm{H}$. For this scan, we assume that both processes are only influenced by the Yukawa couplings to t and b quarks and scale the predicted cross sections depending on these couplings. The estimates are shown for the product of the reduced Yukawa couplings $\mathrm{g}_{ \mathrm{t} ,\, \mathrm{b} }^{\mathrm{H}}$ and $\sqrt{B(\mathrm{H}\to \tau \tau )}$, where the former is defined as the ratio of the Yukawa coupling of $ \mathrm{H} $ over the Yukawa coupling expected for a SM-like Higgs boson of the same mass. An ambiguity on the relative sign of the two couplings can be resolved by the contribution of $ \mathrm{t} \mathrm{b} $-interference terms to the cross section predictions. By convention $\mathrm{g}_{ \mathrm{t} }^{\mathrm{H}}$ has been chosen positive.
png pdf	Additional Figure 84: Maximum likelihood estimate, and 68% and 95% CL contours obtained from scans of the signal-plus-background likelihood for a pseudoscalar resonance ($\mathrm{A}$) with $m_{\mathrm{A}}= $ 180 GeV, produced via $ \mathrm{g} \mathrm{g} \mathrm{A}$ or $ \mathrm{b} \mathrm{b} \mathrm{A}$. For this scan, we assume that both processes are only influenced by the Yukawa couplings to t and b quarks and scale the predicted cross sections depending on these couplings. The estimates are shown for the product of the reduced Yukawa couplings $\mathrm{g}_{ \mathrm{t} ,\, \mathrm{b} }^{\mathrm{A}}$ and $\sqrt{B(\mathrm{A}\to \tau \tau )}$, where the former is defined as the ratio of the Yukawa coupling of $\mathrm{A}$ over the Yukawa coupling expected for a SM-like Higgs boson of the same mass. An ambiguity on the relative sign of the two couplings can be resolved by the contribution of $ \mathrm{t} \mathrm{b} $-interference terms to the cross section predictions. By convention $\mathrm{g}_{ \mathrm{t} }^{\mathrm{A}}$ has been chosen positive.
png pdf	Additional Figure 85: Maximum likelihood estimate, and 68% and 95% CL contours obtained from scans of the signal-plus-background likelihood for a scalar resonance ($ \mathrm{H} $) with $m_{\mathrm{H}}= $ 200 GeV, produced via $ \mathrm{g} \mathrm{g} \mathrm{H}$ or $ \mathrm{b} \mathrm{b} \mathrm{H}$. For this scan, we assume that both processes are only influenced by the Yukawa couplings to t and b quarks and scale the predicted cross sections depending on these couplings. The estimates are shown for the product of the reduced Yukawa couplings $\mathrm{g}_{ \mathrm{t} ,\, \mathrm{b} }^{\mathrm{H}}$ and $\sqrt{B(\mathrm{H}\to \tau \tau )}$, where the former is defined as the ratio of the Yukawa coupling of $ \mathrm{H} $ over the Yukawa coupling expected for a SM-like Higgs boson of the same mass. An ambiguity on the relative sign of the two couplings can be resolved by the contribution of $ \mathrm{t} \mathrm{b} $-interference terms to the cross section predictions. By convention $\mathrm{g}_{ \mathrm{t} }^{\mathrm{H}}$ has been chosen positive.
png pdf	Additional Figure 86: Maximum likelihood estimate, and 68% and 95% CL contours obtained from scans of the signal-plus-background likelihood for a pseudoscalar resonance ($\mathrm{A}$) with $m_{\mathrm{A}}= $ 200 GeV, produced via $ \mathrm{g} \mathrm{g} \mathrm{A}$ or $ \mathrm{b} \mathrm{b} \mathrm{A}$. For this scan, we assume that both processes are only influenced by the Yukawa couplings to t and b quarks and scale the predicted cross sections depending on these couplings. The estimates are shown for the product of the reduced Yukawa couplings $\mathrm{g}_{ \mathrm{t} ,\, \mathrm{b} }^{\mathrm{A}}$ and $\sqrt{B(\mathrm{A}\to \tau \tau )}$, where the former is defined as the ratio of the Yukawa coupling of $\mathrm{A}$ over the Yukawa coupling expected for a SM-like Higgs boson of the same mass. An ambiguity on the relative sign of the two couplings can be resolved by the contribution of $ \mathrm{t} \mathrm{b} $-interference terms to the cross section predictions. By convention $\mathrm{g}_{ \mathrm{t} }^{\mathrm{A}}$ has been chosen positive.
png pdf	Additional Figure 87: Best fit values of $\sigma( \mathrm{g} \mathrm{g} \phi)B(\phi\to \tau \tau )$ split by data-taking year compared to the fit result obtained from all data-taking years combined, for $m_{\phi}= $ 1.2 TeV. A test of the compatibility of the fit results from each data-taking year individually across all data-taking years exhibits a $p$-value of 64%.
png pdf	Additional Figure 88: Best fit values of $\sigma( \mathrm{g} \mathrm{g} \phi)B(\phi\to \tau \tau )$ split by $ \tau \tau $ final state compared to the fit result obtained from all $ \tau \tau $ final states combined, for $m_{\phi}= $ 1.2 TeV. A test of the compatibility of the fit results in each $ \tau \tau $ final state individually across all $ \tau \tau $ final states exhibits a $p$-value of 11%.
png pdf	Additional Figure 89: Best fit values of $\sigma( \mathrm{g} \mathrm{g} \phi)B(\phi\to \tau \tau )$ split by data-taking year compared to the fit result obtained from all data-taking years combined, for $m_{\phi}= $ 100 GeV. A test of the compatibility of the fit results from each data-taking year individually across all data-taking years exhibits a $p$-value of 58%.
png pdf	Additional Figure 90: Best fit values of $\sigma( \mathrm{g} \mathrm{g} \phi)B(\phi\to \tau \tau )$ split by $ \tau \tau $ final state compared to the fit result obtained from all $ \tau \tau $ final states combined, for $m_{\phi}= $ 100 GeV. A test of the compatibility of the fit results in each $ \tau \tau $ final state individually across all $ \tau \tau $ final states exhibits a $p$-value of 50%.
png pdf	Additional Figure 91: Best fit values of $\sigma( \mathrm{g} \mathrm{g} \phi)B(\phi\to \tau \tau )$ split by category used for the extraction of the signal compared to the fit result obtained from all categories combined, for $m_{\phi}= $ 100 GeV. A test of the compatibility of the fit results in each category individually across all categories exhibits a $p$-value of 40%.
png pdf	Additional Figure 92: Expected and observed 95% CL upper limits on $g_{\text{U}}$ in a benchmark scenario in which $\beta_{\mathrm{L}}^{ \mathrm{b} \tau }$ is taken to be 1 and the other couplings are set to zero (labeled as ``VLQ BM 3''), in a mass range of 1 $ \leq m_{\text{U}}\leq $ 5 TeV. The expected median of the exclusion limit in the absence of signal is shown by the dashed line. The dark and bright grey bands indicate the central 68% and 95% intervals of the expected exclusion limit. The observed excluded parameter space is indicated by the coloured blue area.
png pdf	Additional Figure 93: Expected 95% CL upper limits on $\sigma( \mathrm{g} \mathrm{g} \phi)B(\phi\to \tau \tau )$, in the mass range of 60 $ \leq m_{\phi}\leq $ 3500 GeV, split by $ \tau \tau $ final state.
png pdf	Additional Figure 94: Expected 95% CL upper limits on $\sigma( \mathrm{b} \mathrm{b} \phi)B(\phi\to \tau \tau )$, in the mass range of 60 $ \leq m_{\phi}\leq $ 3500 GeV, split by $ \tau \tau $ final state.
png pdf	Additional Figure 95: Expected 95% CL upper limits on $g_{\text{U}}$, in the mass range of 1 $ \leq m_{\text{U}}\leq $ 5 TeV, split by $ \tau \tau $ final state, for the VLQ BM 1 scenario.
png pdf	Additional Figure 96: Expected 95% CL upper limits on $g_{\text{U}}$, in the mass range of 1 $ \leq m_{\text{U}}\leq $ 5 TeV, split by $ \tau \tau $ final state, for the VLQ BM 2 scenario.
png pdf	Additional Figure 97: Expected 95% CL upper limits on $g_{\text{U}}$, in the mass range of 1 $ \leq m_{\text{U}}\leq $ 5 TeV, split by category used for the extraction of the signal, for the VLQ BM 1 scenario.
png pdf	Additional Figure 98: Expected 95% CL upper limits on $g_{\text{U}}$, in the mass range of 1 $ \leq m_{\text{U}}\leq $ 5 TeV, split by category used for the extraction of the signal, for the VLQ BM 2 scenario.
png pdf	Additional Figure 99: Scan of the likelihood function for the search for a vector leptoquark with $m_{\text{U}}= $ 1 TeV, in the VLQ BM 1 scenario. This is shown for the cases where the (green) ``b tag'' and (magenta) ``No btag'' categories are fitted separately, and (black) for the fit of both categories combined.
png pdf	Additional Figure 100: Scan of the likelihood function for the search for a vector leptoquark with $m_{\text{U}}= $ 1 TeV, in the VLQ BM 1 scenario. This is shown for the cases where the (green) ``b tag'' and (magenta) ``No btag'' categories are fitted separately, and (black) for the fit of both categories combined.
png pdf	Additional Figure 101: Scan of the likelihood function for the search for a vector leptoquark with $m_{\text{U}}= $ 3 TeV, in the VLQ BM 1 scenario. This is shown for the cases where the (green) ``b tag'' and (magenta) ``No btag'' categories are fitted separately, and (black) for the fit of both categories combined.
png pdf	Additional Figure 102: Scan of the likelihood function for the search for a vector leptoquark with $m_{\text{U}}= $ 4 TeV, in the VLQ BM 1 scenario. This is shown for the cases where the (green) ``b tag'' and (magenta) ``No btag'' categories are fitted separately, and (black) for the fit of both categories combined.
png pdf	Additional Figure 103: Scan of the likelihood function for the search for a vector leptoquark with $m_{\text{U}}= $ 5 TeV, in the VLQ BM 1 scenario. This is shown for the cases where the (green) ``b tag'' and (magenta) ``No btag'' categories are fitted separately, and (black) for the fit of both categories combined.
png pdf	Additional Figure 104: Scan of the likelihood function for the search for a vector leptoquark with $m_{\text{U}}= $ 1 TeV, in the VLQ BM 2 scenario. This is shown for the cases where the (green) ``b tag'' and (magenta) ``No btag'' categories are fitted separately, and (black) for the fit of both categories combined.
png pdf	Additional Figure 105: Scan of the likelihood function for the search for a vector leptoquark with $m_{\text{U}}= $ 2 TeV, in the VLQ BM 2 scenario. This is shown for the cases where the (green) ``b tag'' and (magenta) ``No btag'' categories are fitted separately, and (black) for the fit of both categories combined.
png pdf	Additional Figure 106: Scan of the likelihood function for the search for a vector leptoquark with $m_{\text{U}}= $ 3 TeV, in the VLQ BM 2 scenario. This is shown for the cases where the (green) ``b tag'' and (magenta) ``No btag'' categories are fitted separately, and (black) for the fit of both categories combined.
png pdf	Additional Figure 107: Scan of the likelihood function for the search for a vector leptoquark with $m_{\text{U}}= $ 4 TeV, in the VLQ BM 2 scenario. This is shown for the cases where the (green) ``b tag'' and (magenta) ``No btag'' categories are fitted separately, and (black) for the fit of both categories combined.
png pdf	Additional Figure 108: Scan of the likelihood function for the search for a vector leptoquark with $m_{\text{U}}= $ 5 TeV, in the VLQ BM 2 scenario. This is shown for the cases where the (green) ``b tag'' and (magenta) ``No btag'' categories are fitted separately, and (black) for the fit of both categories combined.
png pdf	Additional Figure 109: Scan of the likelihood function for the search for a vector leptoquark with $m_{\text{U}}= $ 1 TeV, in a benchmark scenario in which $\beta_{\mathrm{L}}^{ \mathrm{b} \tau }$ is taken to be 1 and the other couplings are set to zero (labeled as ``VLQ BM 3''). This is shown for the cases where the (green) ``b tag'' and (magenta) ``No btag'' categories are fitted separately, and (black) for the fit of both categories combined.
png pdf	Additional Figure 110: Scan of the likelihood function for the search for a vector leptoquark with $m_{\text{U}}= $ 2 TeV, in a benchmark scenario in which $\beta_{\mathrm{L}}^{ \mathrm{b} \tau }$ is taken to be 1 and the other couplings are set to zero (labeled as ``VLQ BM 3''). This is shown for the cases where the (green) ``b tag'' and (magenta) ``No btag'' categories are fitted separately, and (black) for the fit of both categories combined.
png pdf	Additional Figure 111: Scan of the likelihood function for the search for a vector leptoquark with $m_{\text{U}}= $ 3 TeV, in a benchmark scenario in which $\beta_{\mathrm{L}}^{ \mathrm{b} \tau }$ is taken to be 1 and the other couplings are set to zero (labeled as ``VLQ BM 3''). This is shown for the cases where the (green) ``b tag'' and (magenta) ``No btag'' categories are fitted separately, and (black) for the fit of both categories combined.
png pdf	Additional Figure 112: Scan of the likelihood function for the search for a vector leptoquark with $m_{\text{U}}= $ 4 TeV, in a benchmark scenario in which $\beta_{\mathrm{L}}^{ \mathrm{b} \tau }$ is taken to be 1 and the other couplings are set to zero (labeled as ``VLQ BM 3''). This is shown for the cases where the (green) ``b tag'' and (magenta) ``No btag'' categories are fitted separately, and (black) for the fit of both categories combined.
png pdf	Additional Figure 113: Scan of the likelihood function for the search for a vector leptoquark with $m_{\text{U}}= $ 5 TeV, in a benchmark scenario in which $\beta_{\mathrm{L}}^{ \mathrm{b} \tau }$ is taken to be 1 and the other couplings are set to zero (labeled as ``VLQ BM 3''). This is shown for the cases where the (green) ``b tag'' and (magenta) ``No btag'' categories are fitted separately, and (black) for the fit of both categories combined.
png pdf	Additional Figure 114: Expected and observed 95% CL exclusion contours in the MSSM $\mathrm{M_{h} }^{125}(\tilde{ \tau })$ scenario. The expected median in the absence of a signal is shown as a dashed black line. The dark and bright grey bands indicate the central 68% and 95% intervals of the expected exclusion. The observed exclusion contour is indicated by the coloured blue area. Those parts of the parameter space where $m_{\mathrm{h}}$ deviates by more than ${\pm}$3 GeV from the mass of H(125) are indicated by a red hatched area.
png pdf	Additional Figure 115: Expected and observed 95% CL exclusion contours in the MSSM $\mathrm{M_{h} }^{125}(\tilde{\chi})$ scenario. The expected median in the absence of a signal is shown as a dashed black line. The dark and bright grey bands indicate the central 68% and 95% intervals of the expected exclusion. The observed exclusion contour is indicated by the coloured blue area. Those parts of the parameter space where $m_{\mathrm{h}}$ deviates by more than ${\pm}$3 GeV from the mass of H(125) are indicated by a red hatched area.
png pdf	Additional Figure 116: Expected and observed 95% CL exclusion contours in the MSSM $\mathrm{M}_{\mathrm{h} }^{125\,\mu_{1}-}$ scenario. The expected median in the absence of a signal is shown as a dashed black line. The dark and bright grey bands indicate the central 68% and 95% intervals of the expected exclusion. The observed exclusion contour is indicated by the coloured blue area. Those parts of the parameter space where $m_{\mathrm{h}}$ deviates by more than ${\pm}$3 GeV from the mass of H(125) are indicated by a red hatched area.
png pdf	Additional Figure 117: Expected and observed 95% CL exclusion contours in the MSSM $\mathrm{M}_{ \mathrm{h}}^{125\,\mu_{2}-}$ scenario. The expected median in the absence of a signal is shown as a dashed black line. The dark and bright grey bands indicate the central 68% and 95% intervals of the expected exclusion. The observed exclusion contour is indicated by the coloured blue area. Those parts of the parameter space where $m_{\mathrm{h}}$ deviates by more than ${\pm}$3 GeV from the mass of H(125) are indicated by a red hatched area.
png pdf	Additional Figure 118: Expected and observed 95% CL exclusion contours in the MSSM $\mathrm{M}_{ \mathrm{h}}^{125\,\mu_{3}-}$ scenario. The expected median in the absence of a signal is shown as a dashed black line. The dark and bright grey bands indicate the central 68% and 95% intervals of the expected exclusion. The observed exclusion contour is indicated by the coloured blue area. Those parts of the parameter space where $m_{\mathrm{h}}$ deviates by more than ${\pm}$3 GeV from the mass of H(125) are indicated by a red hatched area.
png pdf	Additional Figure 119: Expected and observed 95% CL exclusion contours in the MSSM $\mathrm{M_{h_{1} }^{125}(CPV)}$ scenario. The expected median in the absence of a signal is shown as a dashed black line. The dark and bright grey bands indicate the central 68% and 95% intervals of the expected exclusion. The observed exclusion contour is indicated by the coloured blue area. Those parts of the parameter space where $m_{\mathrm{h}_{1}}$ deviates by more than ${\pm}$3 GeV from the mass of H(125) are indicated by a red hatched area.
png pdf	Additional Figure 120: Expected and observed 95% CL exclusion contours in the $\mathrm{hMSSM}$ scenario. The expected median in the absence of a signal is shown as a dashed black line. The dark and bright grey bands indicate the central 68% and 95% intervals of the expected exclusion. The observed exclusion contour is indicated by the coloured blue area.
png pdf	Additional Figure 121: Expected and observed 95% CL exclusion contours in the MSSM $\mathrm{M}_{\mathrm{H}}^{125}$ scenario. The expected median in the absence of a signal is shown as a dashed black line. The dark and bright grey bands indicate the central 68% and 95% intervals of the expected exclusion. The observed exclusion contour is indicated by the coloured blue area. Those parts of the parameter space where $m_{\mathrm{H}}$ deviates by more than ${\pm}$3 GeV from the mass of H(125) are indicated by a red hatched area.
png pdf	Additional Figure 122: Expected and observed 95% CL exclusion contours in the MSSM $\mathrm{M_{h, \,EFT}^{125}}(\tilde{\chi})$ scenario. The expected median in the absence of a signal is shown as a dashed black line. The dark and bright grey bands indicate the central 68% and 95% intervals of the expected exclusion. The observed exclusion contour is indicated by the coloured blue area. Those parts of the parameter space where $m_{\mathrm{h}}$ deviates by more than ${\pm}$3 GeV from the mass of H(125) are indicated by a red hatched area.
png pdf	Additional Figure 123: Expected and observed 95% CL exclusion contours in the $\mathrm{M}_{\mathrm{h}}^{125}$ (alignment) scenario. The expected median in the absence of a signal is shown as a dashed black line. The dark and bright grey bands indicate the central 68% and 95% intervals of the expected exclusion. The observed exclusion contour is indicated by the coloured blue area. Those parts of the parameter space where $m_{\mathrm{h}}$ deviates by more than ${\pm}$3 GeV from the mass of H(125) are indicated by a red hatched area.

Further information about Additional Figures

Additional Figs. 1—9 display the equivalent plots to Fig. 9 for the categories that are not displayed in the paper. In this case a signal-plus-background fit has been performed where the signal mass is fixed to 100 GeV.

Additional Figs. 10—24 display the distributions for all categories used in the search for low-mass signals (m_φ < 250 GeV) after performing a background-only fit to the data. These plots differ from Fig. 9 and Additional Figs. 1—9 which display the distributions after a signal-plus-background fit instead of the background-only. These background-only distributions are intended to be used for re-intpretations in different signal models.

Additional Figs. 25—30 display the equivalent plots to Fig. 8 for the categories that are not displayed in the paper. In this case a background-only fit has been performed.

Additional Figs. 31—36 display the local p-values for each tested mass point for different assumption about the production modes.

Additional Figs. 37—40 display limits on the cross sections times branching ratios similar to Fig. 10 except different assumptions are made about the production modes.

Additional Figs. 41—63 display the equivalent plots to Fig. 11 for the other mass points that are tested in the analysis but not displayed in the paper.

Additional Fig. 64 displays a 2D maximum likelihood scan for a 95 GeV signal under the assumption that the signal is produced by vector boson fusion or gluon fusion.

Additional Figs. 65—86 present the results of the low-mass analysis in terms of the effective coupling strengths to top and bottom quarks as an alternative to the cross section times branching fraction scans (e.g Fig. 11). The motivation for these scans is allow the results to be interpreted in models that predict sizeable contributions to the gluon fusion loop from both top and bottom quarks. As the kinematics, and therefore signal acceptance, depends strongly on the loop content, the limits derived for the top-only (Additional Fig. 39) and bottom-only (Additional Fig. 40) extremes might not apply in such scenarios and therefore it would be more appropriate to use these coupling scans to test such models.
In order produce scans in terms of couplings it is necessary to have predictions for the cross sections for the b-associated and gluon fusion production processes.
The b-associated cross sections including the interference with the gluon fusion process are determined by scaling the cross sections provided by the LHCXSWG (bbH cross sections) for a SM-like Higgs boson by the top and bottom Yukawa couplings. The b-associated cross section without interference is scaled by the bottom Yukawa coupling squared, while the interference contribution is scaled by the product of the top and bottom Yukawa couplings.
The gluon fusion cross sections are estimated as follows. The cross sections for the top-only, bottom-only, and top-bottom-interference are estimated using POWHEG at NLO accuracy. The top-only cross section is scaled by the top Yukawa coupling squared, the bottom-only is scaled by the bottom Yukawa coupling squared, and the top-bottom-interference is scaled by the product of the top and bottom Yukawa couplings. The three components are then summed together and multiplied by k-factors that account for higher order corrections. For each mass point, the k-factor is defined as the ratio of the cross sections computed at N3LO by the LHCXSWG (N3LO cross sections) to the cross section computed at NLO by POWHEG assuming SM Yukawa couplings.

Additional Figs. 87—91 display the results of the by-channel, by-era, and by-category compatibility checks for the 100 GeV and 1.2 TeV signal mass hypotheses.

Additional Fig. 92 displays the limits set on an alternative vector leptoquark model. The model parameters are chosen to align with another CMS analysis (CMS-EXO-19-016) targeting the same signature to allow a direct comparison between the two analyses.

Additional Figs. 93—98 display the expected limits broken down by channel, era, and category. The purpose of these plots are to show how the individual channels/eras/categories contribute to the overall sensitivity of the analysis.

Additional Figs. 99—113 display scans of the likelihood function vs the effective coupling for the leptoquark interpretation of the data. There are several purposes for these plots, which includes: to provide the likelihood scans for the combined result to allow the results to be re-intpreted more easily, to show how the no b-tag and b-tag categories each contribute to the combined result, and to compare the results more easily with the CMS-EXO-19-016 analysis.

Additional Fig. 114—123 display the limits in the m_A-tanβ plane for alternative MSSM benchmark models that were considered in the analysis but not displayed in the paper. The plots are equivalent to Fig. 13 in the paper.

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