Upper limits at 95% CL on the cross section times branching fraction for the process $H \to 2\gamma_d + X$ with $m_H$ = 800 GeV in the hadron-hadron final state.

Upper limits at 95% CL on the cross section times branching fraction for the process $H \to 2\gamma_d + X$ with $m_H$ = 800 GeV in the muon-hadron final state.

Upper limits at 95% CL on the cross section times branching fraction for the process $H \to 4\gamma_d + X$ with $m_H$ = 800 GeV in the muon-muon final state.

Upper limits at 95% CL on the cross section times branching fraction for the process $H \to 4\gamma_d + X$ with $m_H$ = 800 GeV in the muon-hadron final state.

Upper limits at 95% CL on the cross section times branching fraction for the process $H \to 4\gamma_d + X$ with $m_H$ = 800 GeV in the hadron-hadron final state.

Extrapolated signal efficiencies as a function of proper decay length of the dark photon for the $H \to 4\gamma_d + X$ process with $m_H$ = 125 GeV in the muon-muon final state.

Extrapolated signal efficiencies as a function of proper decay length of the dark photon for the $H \to 2\gamma_d + X$ process with $m_H$ = 125 GeV in the muon-muon final state.

Extrapolated signal efficiencies as a function of proper decay length of the dark photon for the $H \to 2\gamma_d + X$ process with $m_H$ = 800 GeV in the muon-muon final state.

Extrapolated signal efficiencies as a function of proper decay length of the dark photon for the $H \to 4\gamma_d + X$ process with $m_H$ = 800 GeV in the muon-muon final state.

Extrapolated signal efficiencies as a function of proper decay length of the dark photon for the $H \to 4\gamma_d + X$ process with $m_H$ = 125 GeV in the muon-hadron final state.

Extrapolated signal efficiencies as a function of proper decay length of the dark photon for the $H \to 2\gamma_d + X$ process with $m_H$ = 125 GeV in the muon-hadron final state.

Extrapolated signal efficiencies as a function of proper decay length of the dark photon for the $H \to 2\gamma_d + X$ process with $m_H$ = 800 GeV in the muon-hadron final state.

Extrapolated signal efficiencies as a function of proper decay length of the dark photon for the $H \to 4\gamma_d + X$ process with $m_H$ = 800 GeV in the muon-hadron final state.

Extrapolated signal efficiencies as a function of proper decay length of the dark photon for the $H \to 2\gamma_d + X$ process with $m_H$ = 125 GeV in the hadron-hadron final state.

Extrapolated signal efficiencies as a function of proper decay length of the dark photon for the $H \to 2\gamma_d + X$ process with $m_H$ = 800 GeV in the hadron-hadron final state.

Extrapolated signal efficiencies as a function of proper decay length of the dark photon for the $H \to 4\gamma_d + X$ process with $m_H$ = 800 GeV in the hadron-hadron final state.

Observed and expected 95% CL lower limits on the $T$-quark mass as a function of the $T$-quark width-to-mass ratio and the branching fraction of the $T \rightarrow Ht$ decay ($\Gamma_{T}$ is the $T$-quark width).

Cutflow table listing the number of events passing each criterion for a $T$-quark hypothesis with a mass of 1.6 TeV and $\kappa_{T} = 0.5$. The initial signal event yield is the predicted number of $T$-quark events inclusive in the Higgs-boson and top-quark decays for 139 fb$^{-1}$.

Observed 95% CL upper limits on the single $T$-quark production cross-section as a function of the $T$-quark coupling $\kappa_{T}$ and $m_{T}$.

Expected 95% CL upper limits on the single $T$-quark production cross-section as a function of the $T$-quark coupling $\kappa_{T}$ and $m_{T}$.

Observed and expected 95% CL lower limits on the $T$-quark mass as a function of the $T$-quark width-to-mass ratio and the branching fraction of the $T \rightarrow Wb$ decay ($\Gamma_{T}$ is the $T$-quark width).

95% CL observed upper limits on the Yukawa couplings

Distributions of $s_{\text{T}}$ in the single-tau one-bin SR. The stacked histograms show the various SM background contributions. The hatched band indicates the total statistical and systematic uncertainty of the SM background. The $t\bar{t}$ (2 real $\tau$) and $t\bar{t}$ (1 real $\tau$) as well as the single-top background contributions are scaled with the normalization factors obtained from the background-only fit. Minor backgrounds are grouped together and denoted as 'Other'. This includes $t\bar{t}$-fake, single top, and other top (di-tau channel) or $t\bar{t}$-fake, $t\bar{t}+H$, multiboson, and other top (single-tau channel). The overlaid dotted lines show the additional contributions for signal scenarios close to the expected exclusion contour with the particle type and the mass and $\beta$ parameters for the simplified models indicated in the legend. For the leptoquark signal model the shapes of the distributions for $\text{LQ}_{3}^{\text{d}}$ and $\text{LQ}_{3}^{\text{v}}$ (not shown) are similar to that of $\text{LQ}_{3}^{\text{u}}$. The rightmost bin includes the overflow.

Distributions of $m_{\text{T}}(\tau)$ in the single-tau one-bin SR. The stacked histograms show the various SM background contributions. The hatched band indicates the total statistical and systematic uncertainty of the SM background. The $t\bar{t}$ (2 real $\tau$) and $t\bar{t}$ (1 real $\tau$) as well as the single-top background contributions are scaled with the normalization factors obtained from the background-only fit. Minor backgrounds are grouped together and denoted as 'Other'. This includes $t\bar{t}$-fake, single top, and other top (di-tau channel) or $t\bar{t}$-fake, $t\bar{t}+H$, multiboson, and other top (single-tau channel). The overlaid dotted lines show the additional contributions for signal scenarios close to the expected exclusion contour with the particle type and the mass and $\beta$ parameters for the simplified models indicated in the legend. For the leptoquark signal model the shapes of the distributions for $\text{LQ}_{3}^{\text{d}}$ and $\text{LQ}_{3}^{\text{v}}$ (not shown) are similar to that of $\text{LQ}_{3}^{\text{u}}$. The rightmost bin includes the overflow.

Distributions of $\Sigma m_{\text{T}}(b_{1,2})$ in the single-tau $p_{\text{T}}(\tau)$-binned SR. The stacked histograms show the various SM background contributions. The hatched band indicates the total statistical and systematic uncertainty of the SM background. The $t\bar{t}$ (2 real $\tau$) and $t\bar{t}$ (1 real $\tau$) as well as the single-top background contributions are scaled with the normalization factors obtained from the background-only fit. Minor backgrounds are grouped together and denoted as 'Other'. This includes $t\bar{t}$-fake, single top, and other top (di-tau channel) or $t\bar{t}$-fake, $t\bar{t}+H$, multiboson, and other top (single-tau channel). The overlaid dotted lines show the additional contributions for signal scenarios close to the expected exclusion contour with the particle type and the mass and $\beta$ parameters for the simplified models indicated in the legend. For the leptoquark signal model the shapes of the distributions for $\text{LQ}_{3}^{\text{d}}$ and $\text{LQ}_{3}^{\text{v}}$ (not shown) are similar to that of $\text{LQ}_{3}^{\text{u}}$. The rightmost bin includes the overflow.

Distributions of $p_{\text{T}}(\tau)$ in the single-tau $p_{\text{T}}(\tau)$-binned SR. The stacked histograms show the various SM background contributions. The hatched band indicates the total statistical and systematic uncertainty of the SM background. The $t\bar{t}$ (2 real $\tau$) and $t\bar{t}$ (1 real $\tau$) as well as the single-top background contributions are scaled with the normalization factors obtained from the background-only fit. Minor backgrounds are grouped together and denoted as 'Other'. This includes $t\bar{t}$-fake, single top, and other top (di-tau channel) or $t\bar{t}$-fake, $t\bar{t}+H$, multiboson, and other top (single-tau channel). The overlaid dotted lines show the additional contributions for signal scenarios close to the expected exclusion contour with the particle type and the mass and $\beta$ parameters for the simplified models indicated in the legend. For the leptoquark signal model the shapes of the distributions for $\text{LQ}_{3}^{\text{d}}$ and $\text{LQ}_{3}^{\text{v}}$ (not shown) are similar to that of $\text{LQ}_{3}^{\text{u}}$. The rightmost bin includes the overflow.

Observed event yields in data ('Observed') and expected event yields for SM background processes obtained from the background-only fit ('Total bkg.' and rows below) in the signal regions of the di-tau and single-tau channels. The quoted uncertainties include both the statistical and systematic uncertainties and are truncated at zero yield. By construction, no $t\bar{t}$ (2 real $\tau$) events can pass the selections in the single-tau channel. As the individual uncertainties are correlated, they do not add in quadrature to equal the total background uncertainty.

From left to right: upper limits at the 95% confidence level (CL) on the visible cross section ($\sigma_\text{vis}$) and on the number of signal events ($S_{\text{obs}}^{95}$). The third column ($S_{\text{exp}}^{95}$) shows the upper limit at the 95% CL on the number of signal events, given the expected number (and $\pm 1\,\sigma$ excursions on the expectation) of background events. The last two columns indicate the confidence level observed for the background-only hypothesis ($\text{CL}_{b}$), the discovery $p$-value ($p(s=0)$) and the significance ($Z$). In the di-tau SR, where fewer events are observed than predicted by the fitted background estimate, the $p$-value is capped at 0.5.

Expected and observed exclusion contours at the 95% confidence level for the vector third-generation leptoquark signal model, as a function of the mass $m(\text{LQ}_{3}^{\text{v}})$ and the branching fraction $B(\text{LQ}_{3}^{\text{v}} \rightarrow b\tau)$ into a quark and a charged lepton. The plot shows the exclusion contour for the minimal-coupling scenario. The limits are derived from the binned single-tau signal region.

Expected and observed exclusion contours at the 95% confidence level for the vector third-generation leptoquark signal model, as a function of the mass $m(\text{LQ}_{3}^{\text{v}})$ and the branching fraction $B(\text{LQ}_{3}^{\text{v}} \rightarrow b\tau)$ into a quark and a charged lepton. The plot shows the exclusion contour for the minimal-coupling scenario. The limits are derived from the binned single-tau signal region.

Expected and observed exclusion contours at the 95% confidence level for the vector third-generation leptoquark signal model, as a function of the mass $m(\text{LQ}_{3}^{\text{v}})$ and the branching fraction $B(\text{LQ}_{3}^{\text{v}} \rightarrow b\tau)$ into a quark and a charged lepton. The plot shows the exclusion contour for vector leptoquarks with additional gauge couplings. The limits are derived from the binned single-tau signal region.

Expected and observed exclusion contours at the 95% confidence level for the vector third-generation leptoquark signal model, as a function of the mass $m(\text{LQ}_{3}^{\text{v}})$ and the branching fraction $B(\text{LQ}_{3}^{\text{v}} \rightarrow b\tau)$ into a quark and a charged lepton. The plot shows the exclusion contour for vector leptoquarks with additional gauge couplings. The limits are derived from the binned single-tau signal region.

Exclusion contours at the 95% confidence level for the stop-stau signal model as a function of the masses of the top squark $m(\tilde{t}_{1})$ and of the tau slepton $m(\tilde{\tau}_{1})$. Expected and observed limits are shown for the present search in comparison to observed limits from previous ATLAS analyses based on data from Run-1 of the LHC at $\sqrt{s} = 8$ TeV [Eur. Phys. J. C 76 (2016)] and on a partial dataset from Run 2 at $\sqrt{s} = 13$ TeV [Phys. Rev. D 98 (2018) 032008]. The green band indicates the limit on the mass of the tau slepton (for a massless LSP) from the LEP experiments.

Exclusion contours at the 95% confidence level for the stop-stau signal model as a function of the masses of the top squark $m(\tilde{t}_{1})$ and of the tau slepton $m(\tilde{\tau}_{1})$. Expected and observed limits are shown for the present search in comparison to observed limits from previous ATLAS analyses based on data from Run-1 of the LHC at $\sqrt{s} = 8$ TeV [Eur. Phys. J. C 76 (2016)] and on a partial dataset from Run 2 at $\sqrt{s} = 13$ TeV [Phys. Rev. D 98 (2018) 032008]. The green band indicates the limit on the mass of the tau slepton (for a massless LSP) from the LEP experiments.

Expected and observed exclusion contours at the 95% confidence level for the scalar third-generation leptoquark signal model, as a function of the mass $m(\text{LQ}_{3}^{\text{u}})$ and the branching fraction $B(\text{LQ}_{3}^{\text{u}} \rightarrow q\ell)$ into a quark and a charged lepton. The plot shows the exclusion contour for up-type leptoquarks $\text{LQ}_{3}^{\text{u}})$ with charge $+2/3e$. The limits are derived from the binned single-tau signal region. Shown in gray for comparison are the observed exclusion-limit contours from the previous ATLAS publication that targets the same leptoquark models but is based on a subset of the Run-2 data [JHEP 06 (2019) 144]. In this previous publication five different analyses are considered that target not only the final state studied here but also the final states that correspond to a branching fraction $B(\text{LQ}_{3}^{\text{u}} \rightarrow q\ell)$ of 0 or 1, leading to the concave shapes of the gray exclusion contours.

Expected and observed exclusion contours at the 95% confidence level for the scalar third-generation leptoquark signal model, as a function of the mass $m(\text{LQ}_{3}^{\text{u}})$ and the branching fraction $B(\text{LQ}_{3}^{\text{u}} \rightarrow q\ell)$ into a quark and a charged lepton. The plot shows the exclusion contour for up-type leptoquarks $\text{LQ}_{3}^{\text{u}})$ with charge $+2/3e$. The limits are derived from the binned single-tau signal region. Shown in gray for comparison are the observed exclusion-limit contours from the previous ATLAS publication that targets the same leptoquark models but is based on a subset of the Run-2 data [JHEP 06 (2019) 144]. In this previous publication five different analyses are considered that target not only the final state studied here but also the final states that correspond to a branching fraction $B(\text{LQ}_{3}^{\text{u}} \rightarrow q\ell)$ of 0 or 1, leading to the concave shapes of the gray exclusion contours.

Expected and observed exclusion contours at the 95% confidence level for the scalar third-generation leptoquark signal model, as a function of the mass $m(\text{LQ}_{3}^{\text{d}})$ and the branching fraction $B(\text{LQ}_{3}^{\text{d}} \rightarrow q\ell)$ into a quark and a charged lepton. The plot shows the exclusion contour for down-type leptoquarks $\text{LQ}_{3}^{\text{d}})$ with charge $-1/3e$. The limits are derived from the binned single-tau signal region. Shown in gray for comparison are the observed exclusion-limit contours from the previous ATLAS publication that targets the same leptoquark models but is based on a subset of the Run-2 data [JHEP 06 (2019) 144]. In this previous publication five different analyses are considered that target not only the final state studied here but also the final states that correspond to a branching fraction $B(\text{LQ}_{3}^{\text{d}} \rightarrow q\ell)$ of 0 or 1, leading to the concave shapes of the gray exclusion contours.

Expected and observed exclusion contours at the 95% confidence level for the scalar third-generation leptoquark signal model, as a function of the mass $m(\text{LQ}_{3}^{\text{d}})$ and the branching fraction $B(\text{LQ}_{3}^{\text{d}} \rightarrow q\ell)$ into a quark and a charged lepton. The plot shows the exclusion contour for down-type leptoquarks $\text{LQ}_{3}^{\text{d}})$ with charge $-1/3e$. The limits are derived from the binned single-tau signal region. Shown in gray for comparison are the observed exclusion-limit contours from the previous ATLAS publication that targets the same leptoquark models but is based on a subset of the Run-2 data [JHEP 06 (2019) 144]. In this previous publication five different analyses are considered that target not only the final state studied here but also the final states that correspond to a branching fraction $B(\text{LQ}_{3}^{\text{d}} \rightarrow q\ell)$ of 0 or 1, leading to the concave shapes of the gray exclusion contours.

Upper limits on the signal cross section at the 95 % confidence level for the stop-stau signal model.

Upper limits on the signal cross section at the 95 % confidence level for the scalar third-generation leptoquark signal model with up-type leptoquarks.

Upper limits on the signal cross section at the 95 % confidence level for the scalar third-generation leptoquark signal model with down-type leptoquarks.

Upper limits on the signal cross section at the 95 % confidence level for the vector third-generation leptoquark signal model with minimal coupling (MC).

Upper limits on the signal cross section at the 95 % confidence level for the vector third-generation leptoquark signal model with additional gauge couplings (YM).

Acceptance of the one-bin signal region of the single-tau channel for pair production of up-type leptoquarks $\text{LQ}_{3}^{\text{u}}$.

Efficiency of the one-bin signal region of the single-tau channel for pair production of up-type leptoquarks $\text{LQ}_{3}^{\text{u}}$. The plot does not show efficiencies for a branching fraction $B(\text{LQ}_{3}^{\text{u}} \rightarrow b\tau)$ of 0 or 1 because here the acceptance at generator level becomes zero and the efficiency is thus undefined.

Acceptance of the first bin of the multi-bin signal region (50 GeV $< p_{\text{T}}(\tau) <$ 100 GeV) of the single-tau channel for pair production of up-type leptoquarks $\text{LQ}_{3}^{\text{u}}$.

Efficiency of the first bin of the multi-bin signal region (50 GeV $< p_{\text{T}}(\tau) <$ 100 GeV) of the single-tau channel for pair production of up-type leptoquarks $\text{LQ}_{3}^{\text{u}}$. The plot does not show efficiencies for a branching fraction $B(\text{LQ}_{3}^{\text{u}} \rightarrow b\tau)$ of 0 or 1 because here the acceptance at generator level becomes zero and the efficiency is thus undefined.

Acceptance of the middle bin of the multi-bin signal region (100 GeV $< p_{\text{T}}(\tau) <$ 200 GeV) of the single-tau channel for pair production of up-type leptoquarks $\text{LQ}_{3}^{\text{u}}$.

Efficiency of the middle bin of the multi-bin signal region (100 GeV $< p_{\text{T}}(\tau) <$ 200 GeV) of the single-tau channel for pair production of up-type leptoquarks $\text{LQ}_{3}^{\text{u}}$. The plot does not show efficiencies for a branching fraction $B(\text{LQ}_{3}^{\text{u}} \rightarrow b\tau)$ of 0 or 1 because here the acceptance at generator level becomes zero and the efficiency is thus undefined.

Acceptance of the last bin of the multi-bin signal region (200 GeV $< p_{\text{T}}(\tau)$) of the single-tau channel for pair production of up-type leptoquarks $\text{LQ}_{3}^{\text{u}}$.

Efficiency of the last bin of the multi-bin signal region (200 GeV $< p_{\text{T}}(\tau)$) of the single-tau channel for pair production of up-type leptoquarks $\text{LQ}_{3}^{\text{u}}$. The plot does not show efficiencies for a branching fraction $B(\text{LQ}_{3}^{\text{u}} \rightarrow b\tau)$ of 0 or 1 because here the acceptance at generator level becomes zero and the efficiency is thus undefined.

Acceptance of the signal region of the di-tau channel for pair production of up-type leptoquarks $\text{LQ}_{3}^{\text{u}}$.

Efficiency of the signal region of the di-tau channel for pair production of up-type leptoquarks $\text{LQ}_{3}^{\text{u}}$. The plot does not show efficiencies for a branching fraction $B(\text{LQ}_{3}^{\text{u}} \rightarrow b\tau)$ of 0 because here the acceptance at generator level becomes zero and the efficiency is thus undefined.

Acceptance of the one-bin signal region of the single-tau channel for pair production of down-type leptoquarks $\text{LQ}_{3}^{\text{d}}$.

Efficiency of the one-bin signal region of the single-tau channel for pair production of down-type leptoquarks $\text{LQ}_{3}^{\text{d}}$. The plot does not show efficiencies for a branching fraction $B(\text{LQ}_{3}^{\text{d}} \rightarrow t\tau)$ of 0 or 1 because here the acceptance at generator level becomes zero and the efficiency is thus undefined.

Acceptance of the first bin of the multi-bin signal region (50 GeV $< p_{\text{T}}(\tau) <$ 100 GeV) of the single-tau channel for pair production of down-type leptoquarks $\text{LQ}_{3}^{\text{d}}$.

Efficiency of the first bin of the multi-bin signal region (50 GeV $< p_{\text{T}}(\tau) <$ 100 GeV) of the single-tau channel for pair production of down-type leptoquarks $\text{LQ}_{3}^{\text{d}}$. The plot does not show efficiencies for a branching fraction $B(\text{LQ}_{3}^{\text{d}} \rightarrow t\tau)$ of 0 or 1 because here the acceptance at generator level becomes zero and the efficiency is thus undefined.

Acceptance of the middle bin of the multi-bin signal region (100 GeV $< p_{\text{T}}(\tau) <$ 200 GeV) of the single-tau channel for pair production of down-type leptoquarks $\text{LQ}_{3}^{\text{d}}$.

Efficiency of the middle bin of the multi-bin signal region (100 GeV $< p_{\text{T}}(\tau) <$ 200 GeV) of the single-tau channel for pair production of down-type leptoquarks $\text{LQ}_{3}^{\text{d}}$. The plot does not show efficiencies for a branching fraction $B(\text{LQ}_{3}^{\text{d}} \rightarrow t\tau)$ of 0 or 1 because here the acceptance at generator level becomes zero and the efficiency is thus undefined.

Acceptance of the last bin of the multi-bin signal region (200 GeV $< p_{\text{T}}(\tau)$) of the single-tau channel for pair production of down-type leptoquarks $\text{LQ}_{3}^{\text{d}}$.

Efficiency of the last bin of the multi-bin signal region (200 GeV $< p_{\text{T}}(\tau)$) of the single-tau channel for pair production of down-type leptoquarks $\text{LQ}_{3}^{\text{d}}$. The plot does not show efficiencies for a branching fraction $B(\text{LQ}_{3}^{\text{d}} \rightarrow t\tau)$ of 0 or 1 because here the acceptance at generator level becomes zero and the efficiency is thus undefined.

Acceptance of the signal region of the di-tau channel for pair production of down-type leptoquarks $\text{LQ}_{3}^{\text{d}}$.

Efficiency of the signal region of the di-tau channel for pair production of down-type leptoquarks $\text{LQ}_{3}^{\text{d}}$. The plot does not show efficiencies for a branching fraction $B(\text{LQ}_{3}^{\text{d}} \rightarrow t\tau)$ of 0 because here the acceptance at generator level becomes zero and the efficiency is thus undefined.

Acceptance of the one-bin signal region of the single-tau channel for pair production of vector leptoquarks $\text{LQ}_{3}^{\text{v}}$ in the minimal-coupling scenario.

Efficiency of the one-bin signal region of the single-tau channel for pair production of vector leptoquarks $\text{LQ}_{3}^{\text{v}}$ in the minimal-coupling scenario. The plot does not show efficiencies for a branching fraction $B(\text{LQ}_{3}^{\text{v}} \rightarrow b\tau)$ of 0 or 1 because here the acceptance at generator level becomes zero and the efficiency is thus undefined.

Acceptance of the first bin of the multi-bin signal region (50 GeV $< p_{\text{T}}(\tau) <$ 100 GeV) of the single-tau channel for pair production of vector leptoquarks $\text{LQ}_{3}^{\text{v}}$ in the minimal-coupling scenario.

Efficiency of the first bin of the multi-bin signal region (50 GeV $< p_{\text{T}}(\tau) <$ 100 GeV) of the single-tau channel for pair production of vector leptoquarks $\text{LQ}_{3}^{\text{v}}$ in the minimal-coupling scenario. The plot does not show efficiencies for a branching fraction $B(\text{LQ}_{3}^{\text{v}} \rightarrow b\tau)$ of 0 or 1 because here the acceptance at generator level becomes zero and the efficiency is thus undefined.

Acceptance of the middle bin of the multi-bin signal region (100 GeV $< p_{\text{T}}(\tau) <$ 200 GeV) of the single-tau channel for pair production of vector leptoquarks $\text{LQ}_{3}^{\text{v}}$ in the minimal-coupling scenario.

Efficiency of the middle bin of the multi-bin signal region (100 GeV $< p_{\text{T}}(\tau) <$ 200 GeV) of the single-tau channel for pair production of vector leptoquarks $\text{LQ}_{3}^{\text{v}}$ in the minimal-coupling scenario. The plot does not show efficiencies for a branching fraction $B(\text{LQ}_{3}^{\text{v}} \rightarrow b\tau)$ of 0 or 1 because here the acceptance at generator level becomes zero and the efficiency is thus undefined.

Acceptance of the last bin of the multi-bin signal region (200 GeV $< p_{\text{T}}(\tau)$) of the single-tau channel for pair production of vector leptoquarks $\text{LQ}_{3}^{\text{v}}$ in the minimal-coupling scenario.

Efficiency of the last bin of the multi-bin signal region (200 GeV $< p_{\text{T}}(\tau)$) of the single-tau channel for pair production of vector leptoquarks $\text{LQ}_{3}^{\text{v}}$ in the minimal-coupling scenario. The plot does not show efficiencies for a branching fraction $B(\text{LQ}_{3}^{\text{v}} \rightarrow b\tau)$ of 0 or 1 because here the acceptance at generator level becomes zero and the efficiency is thus undefined.

Acceptance of the signal region of the di-tau channel for pair production of vector leptoquarks $\text{LQ}_{3}^{\text{v}}$ in the minimal-coupling scenario.

Efficiency of the signal region of the di-tau channel for pair production of vector leptoquarks $\text{LQ}_{3}^{\text{v}}$ in the minimal-coupling scenario. The plot does not show efficiencies for a branching fraction $B(\text{LQ}_{3}^{\text{v}} \rightarrow b\tau)$ of 0 because here the acceptance at generator level becomes zero and the efficiency is thus undefined.

Acceptance of the one-bin signal region of the single-tau channel for pair production of vector leptoquarks $\text{LQ}_{3}^{\text{v}}$ with additional gauge couplings.

Efficiency of the one-bin signal region of the single-tau channel for pair production of vector leptoquarks $\text{LQ}_{3}^{\text{v}}$ with additional gauge couplings. The plot does not show efficiencies for a branching fraction $B(\text{LQ}_{3}^{\text{v}} \rightarrow b\tau)$ of 0 or 1 because here the acceptance at generator level becomes zero and the efficiency is thus undefined.

Acceptance of the first bin of the multi-bin signal region (50 GeV $< p_{\text{T}}(\tau) <$ 100 GeV) of the single-tau channel for pair production of vector leptoquarks $\text{LQ}_{3}^{\text{v}}$ with additional gauge couplings.

Efficiency of the first bin of the multi-bin signal region (50 GeV $< p_{\text{T}}(\tau) <$ 100 GeV) of the single-tau channel for pair production of vector leptoquarks $\text{LQ}_{3}^{\text{v}}$ with additional gauge couplings. The plot does not show efficiencies for a branching fraction $B(\text{LQ}_{3}^{\text{v}} \rightarrow b\tau)$ of 0 or 1 because here the acceptance at generator level becomes zero and the efficiency is thus undefined.

Acceptance of the middle bin of the multi-bin signal region (100 GeV $< p_{\text{T}}(\tau) <$ 200 GeV) of the single-tau channel for pair production of vector leptoquarks $\text{LQ}_{3}^{\text{v}}$ with additional gauge couplings.

Efficiency of the middle bin of the multi-bin signal region (100 GeV $< p_{\text{T}}(\tau) <$ 200 GeV) of the single-tau channel for pair production of vector leptoquarks $\text{LQ}_{3}^{\text{v}}$ with additional gauge couplings. The plot does not show efficiencies for a branching fraction $B(\text{LQ}_{3}^{\text{v}} \rightarrow b\tau)$ of 0 or 1 because here the acceptance at generator level becomes zero and the efficiency is thus undefined.

Acceptance of the last bin of the multi-bin signal region (200 GeV $< p_{\text{T}}(\tau)$) of the single-tau channel for pair production of vector leptoquarks $\text{LQ}_{3}^{\text{v}}$ with additional gauge couplings.

Efficiency of the last bin of the multi-bin signal region (200 GeV $< p_{\text{T}}(\tau)$) of the single-tau channel for pair production of vector leptoquarks $\text{LQ}_{3}^{\text{v}}$ with additional gauge couplings. The plot does not show efficiencies for a branching fraction $B(\text{LQ}_{3}^{\text{v}} \rightarrow b\tau)$ of 0 or 1 because here the acceptance at generator level becomes zero and the efficiency is thus undefined.

Acceptance of the signal region of the di-tau channel for pair production of vector leptoquarks $\text{LQ}_{3}^{\text{v}}$ with additional gauge couplings.

Efficiency of the signal region of the di-tau channel for pair production of vector leptoquarks $\text{LQ}_{3}^{\text{v}}$ with additional gauge couplings. The plot does not show efficiencies for a branching fraction $B(\text{LQ}_{3}^{\text{v}} \rightarrow b\tau)$ of 0 because here the acceptance at generator level becomes zero and the efficiency is thus undefined.

Acceptance of the one-bin signal region of the single-tau channel for pair production of top squarks with decays via tau sleptons.

Efficiency of the one-bin signal region of the single-tau channel for pair production of top squarks with decays via tau sleptons.

Acceptance of the first bin of the multi-bin signal region (50 GeV $< p_{\text{T}}(\tau) <$ 100 GeV) of the single-tau channel for pair production of top squarks with decays via tau sleptons.

Efficiency of the first bin of the multi-bin signal region (50 GeV $< p_{\text{T}}(\tau) <$ 100 GeV) of the single-tau channel for pair production of top squarks with decays via tau sleptons.

Acceptance of the middle bin of the multi-bin signal region (100 GeV $< p_{\text{T}}(\tau) <$ 200 GeV) of the single-tau channel for pair production of top squarks with decays via tau sleptons.

Efficiency of the middle bin of the multi-bin signal region (100 GeV $< p_{\text{T}}(\tau) <$ 200 GeV) of the single-tau channel for pair production of top squarks with decays via tau sleptons.

Acceptance of the last bin of the multi-bin signal region (200 GeV $< p_{\text{T}}(\tau)$) of the single-tau channel for pair production of top squarks with decays via tau sleptons.

Efficiency of the last bin of the multi-bin signal region (200 GeV $< p_{\text{T}}(\tau)$) of the single-tau channel for pair production of top squarks with decays via tau sleptons.

Acceptance of the signal region of the di-tau channel for pair production of top squarks with decays via tau sleptons.

Efficiency of the signal region of the di-tau channel for pair production of top squarks with decays via tau sleptons.

Cutflow for the benchmark signal model $m(\tilde{t}_{1}) = 1350$ GeV, $m(\tilde{\tau}_{1}) = 1090$ GeV for the di-tau SR. The simulated sample contains 30,000 raw MC events. Weighted event yields are reported, normalized to an integrated luminosity of 139 fb$^{-1}$. 'Preselection' refers to the preselection for the di-tau channel.

Cutflow for the benchmark signal model $m(\tilde{t}_{1}) = 1350$ GeV, $m(\tilde{\tau}_{1}) = 1090$ GeV for the single-tau one-bin SR. The simulated sample contains 30,000 raw MC events. Weighted event yields are reported, normalized to an integrated luminosity of 139 fb$^{-1}$. 'Preselection' refers to the preselection for the single-tau channel.

Cutflow for the benchmark signal model $m(\tilde{t}_{1}) = 1350$ GeV, $m(\tilde{\tau}_{1}) = 1090$ GeV for the single-tau multi-bin SR. The simulated sample contains 30,000 raw MC events. Weighted event yields are reported, normalized to an integrated luminosity of 139 fb$^{-1}$. 'Preselection' refers to the preselection for the single-tau channel.

Cutflow for the benchmark signal model $m(\text{LQ}_{3}^{\text{u}}) = 1.2$ TeV, $\beta = 0.5$ for the di-tau SR. The simulated sample contains 210,000 raw MC events. Weighted event yields are reported, normalized to an integrated luminosity of 139 fb$^{-1}$. 'Preselection' refers to the preselection for the di-tau channel.

Cutflow for the benchmark signal model $m(\text{LQ}_{3}^{\text{u}}) = 1.2$ TeV, $\beta = 0.5$ for the single-tau one-bin SR. The simulated sample contains 210,000 raw MC events. Weighted event yields are reported, normalized to an integrated luminosity of 139 fb$^{-1}$. 'Preselection' refers to the preselection for the single-tau channel.

Cutflow for the benchmark signal model $m(\text{LQ}_{3}^{\text{u}}) = 1.2$ TeV, $\beta = 0.5$ for the single-tau multi-bin SR. The simulated sample contains 210,000 raw MC events. Weighted event yields are reported, normalized to an integrated luminosity of 139 fb$^{-1}$. 'Preselection' refers to the preselection for the single-tau channel.

Cutflow for the benchmark signal model $m(\text{LQ}_{3}^{\text{d}}) = 1.2$ TeV, $\beta = 0.5$ for the di-tau SR. The simulated sample contains 210,000 raw MC events. Weighted event yields are reported, normalized to an integrated luminosity of 139 fb$^{-1}$. 'Preselection' refers to the preselection for the di-tau channel.

Cutflow for the benchmark signal model $m(\text{LQ}_{3}^{\text{d}}) = 1.2$ TeV, $\beta = 0.5$ for the single-tau one-bin SR. The simulated sample contains 210,000 raw MC events. Weighted event yields are reported, normalized to an integrated luminosity of 139 fb$^{-1}$. 'Preselection' refers to the preselection for the single-tau channel.

Cutflow for the benchmark signal model $m(\text{LQ}_{3}^{\text{d}}) = 1.2$ TeV, $\beta = 0.5$ for the single-tau multi-bin SR. The simulated sample contains 210,000 raw MC events. Weighted event yields are reported, normalized to an integrated luminosity of 139 fb$^{-1}$. 'Preselection' refers to the preselection for the single-tau channel.

Cutflow for the benchmark signal model $m(\text{LQ}_{3}^{\text{v}}) = 1.4$ TeV, $\beta = 0.5$ in the minimal-coupling scenario for the di-tau SR. The simulated sample contains 50,000 raw MC events. Weighted event yields are reported, normalized to an integrated luminosity of 139 fb$^{-1}$. 'Preselection' refers to the preselection for the di-tau channel.

Cutflow for the benchmark signal model $m(\text{LQ}_{3}^{\text{v}}) = 1.4$ TeV, $\beta = 0.5$ in the minimal-coupling scenario for the single-tau one-bin SR. The simulated sample contains 50,000 raw MC events. Weighted event yields are reported, normalized to an integrated luminosity of 139 fb$^{-1}$. 'Preselection' refers to the preselection for the single-tau channel.

Cutflow for the benchmark signal model $m(\text{LQ}_{3}^{\text{v}}) = 1.4$ TeV, $\beta = 0.5$ in the minimal-coupling scenario for the single-tau multi-bin SR. The simulated sample contains 50,000 raw MC events. Weighted event yields are reported, normalized to an integrated luminosity of 139 fb$^{-1}$. 'Preselection' refers to the preselection for the single-tau channel.

Cutflow for the benchmark signal model $m(\text{LQ}_{3}^{\text{v}}) = 1.4$ TeV, $\beta = 0.5$ in the Yang--Mills scenario for the di-tau SR. The simulated sample contains 50,000 raw MC events. Weighted event yields are reported, normalized to an integrated luminosity of 139 fb$^{-1}$. 'Preselection' refers to the preselection for the di-tau channel.

Cutflow for the benchmark signal model $m(\text{LQ}_{3}^{\text{v}}) = 1.4$ TeV, $\beta = 0.5$ in the Yang--Mills scenario for the single-tau one-bin SR. The simulated sample contains 50,000 raw MC events. Weighted event yields are reported, normalized to an integrated luminosity of 139 fb$^{-1}$. 'Preselection' refers to the preselection for the single-tau channel.

Cutflow for the benchmark signal model $m(\text{LQ}_{3}^{\text{v}}) = 1.4$ TeV, $\beta = 0.5$ in the Yang--Mills scenario for the single-tau multi-bin SR. The simulated sample contains 50,000 raw MC events. Weighted event yields are reported, normalized to an integrated luminosity of 139 fb$^{-1}$. 'Preselection' refers to the preselection for the single-tau channel.

Expected and observed candidates for $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to K^+K^-$) as a function of the reduced mediator candidate mass.

Expected and observed candidates for $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to e^+e^-$) as a function of the reduced mediator candidate mass.

Expected and observed candidates for $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to \mu^+\mu^-$) as a function of the reduced mediator candidate mass.

Expected and observed candidates for $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to \pi^+\pi^-$) as a function of the reduced mediator candidate mass.

Expected and observed candidates for $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to K^+K^-$) as a function of the reduced mediator candidate mass.

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to e^+e^-$) for a lifetime of $c\tau=$0.001cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to e^+e^-$) for a lifetime of $c\tau=$0.003cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to e^+e^-$) for a lifetime of $c\tau=$0.005cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to e^+e^-$) for a lifetime of $c\tau=$0.007cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to e^+e^-$) for a lifetime of $c\tau=$0.01cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to e^+e^-$) for a lifetime of $c\tau=$0.025cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to e^+e^-$) for a lifetime of $c\tau=$0.05cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to e^+e^-$) for a lifetime of $c\tau=$0.1cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to e^+e^-$) for a lifetime of $c\tau=$0.25cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to e^+e^-$) for a lifetime of $c\tau=$0.5cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to e^+e^-$) for a lifetime of $c\tau=$1.0cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to e^+e^-$) for a lifetime of $c\tau=$2.5cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to e^+e^-$) for a lifetime of $c\tau=$5.0cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to e^+e^-$) for a lifetime of $c\tau=$10.0cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to e^+e^-$) for a lifetime of $c\tau=$25.0cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to e^+e^-$) for a lifetime of $c\tau=$50.0cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to e^+e^-$) for a lifetime of $c\tau=$100.0cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to e^+e^-$) for a lifetime of $c\tau=$200.0cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to e^+e^-$) for a lifetime of $c\tau=$400.0cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to \mu^+\mu^-$) for a lifetime of $c\tau=$0.001cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to \mu^+\mu^-$) for a lifetime of $c\tau=$0.003cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to \mu^+\mu^-$) for a lifetime of $c\tau=$0.005cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to \mu^+\mu^-$) for a lifetime of $c\tau=$0.007cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to \mu^+\mu^-$) for a lifetime of $c\tau=$0.01cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to \mu^+\mu^-$) for a lifetime of $c\tau=$0.025cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to \mu^+\mu^-$) for a lifetime of $c\tau=$0.05cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to \mu^+\mu^-$) for a lifetime of $c\tau=$0.1cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to \mu^+\mu^-$) for a lifetime of $c\tau=$0.25cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to \mu^+\mu^-$) for a lifetime of $c\tau=$0.5cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to \mu^+\mu^-$) for a lifetime of $c\tau=$1.0cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to \mu^+\mu^-$) for a lifetime of $c\tau=$2.5cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to \mu^+\mu^-$) for a lifetime of $c\tau=$5.0cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to \mu^+\mu^-$) for a lifetime of $c\tau=$10.0cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to \mu^+\mu^-$) for a lifetime of $c\tau=$25.0cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to \mu^+\mu^-$) for a lifetime of $c\tau=$50.0cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to \mu^+\mu^-$) for a lifetime of $c\tau=$100.0cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to \mu^+\mu^-$) for a lifetime of $c\tau=$200.0cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to \mu^+\mu^-$) for a lifetime of $c\tau=$400.0cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to \pi^+\pi^-$) for a lifetime of $c\tau=$0.001cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to \pi^+\pi^-$) for a lifetime of $c\tau=$0.003cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to \pi^+\pi^-$) for a lifetime of $c\tau=$0.005cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to \pi^+\pi^-$) for a lifetime of $c\tau=$0.007cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to \pi^+\pi^-$) for a lifetime of $c\tau=$0.01cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to \pi^+\pi^-$) for a lifetime of $c\tau=$0.025cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to \pi^+\pi^-$) for a lifetime of $c\tau=$0.05cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to \pi^+\pi^-$) for a lifetime of $c\tau=$0.1cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to \pi^+\pi^-$) for a lifetime of $c\tau=$0.25cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to \pi^+\pi^-$) for a lifetime of $c\tau=$0.5cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to \pi^+\pi^-$) for a lifetime of $c\tau=$1.0cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to \pi^+\pi^-$) for a lifetime of $c\tau=$2.5cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to \pi^+\pi^-$) for a lifetime of $c\tau=$5.0cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to \pi^+\pi^-$) for a lifetime of $c\tau=$10.0cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to \pi^+\pi^-$) for a lifetime of $c\tau=$25.0cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to \pi^+\pi^-$) for a lifetime of $c\tau=$50.0cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to \pi^+\pi^-$) for a lifetime of $c\tau=$100.0cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to \pi^+\pi^-$) for a lifetime of $c\tau=$200.0cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to \pi^+\pi^-$) for a lifetime of $c\tau=$400.0cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to K^+K^-$) for a lifetime of $c\tau=$0.001cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to K^+K^-$) for a lifetime of $c\tau=$0.003cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to K^+K^-$) for a lifetime of $c\tau=$0.005cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to K^+K^-$) for a lifetime of $c\tau=$0.007cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to K^+K^-$) for a lifetime of $c\tau=$0.01cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to K^+K^-$) for a lifetime of $c\tau=$0.025cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to K^+K^-$) for a lifetime of $c\tau=$0.05cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to K^+K^-$) for a lifetime of $c\tau=$0.1cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to K^+K^-$) for a lifetime of $c\tau=$0.25cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to K^+K^-$) for a lifetime of $c\tau=$0.5cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to K^+K^-$) for a lifetime of $c\tau=$1.0cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to K^+K^-$) for a lifetime of $c\tau=$2.5cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to K^+K^-$) for a lifetime of $c\tau=$5.0cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to K^+K^-$) for a lifetime of $c\tau=$10.0cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to K^+K^-$) for a lifetime of $c\tau=$25.0cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to K^+K^-$) for a lifetime of $c\tau=$50.0cm

Expected and observed limits on $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to K^+K^-$) for a lifetime of $c\tau=$100.0cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to e^+e^-$) for a lifetime of $c\tau=$0.001cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to e^+e^-$) for a lifetime of $c\tau=$0.003cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to e^+e^-$) for a lifetime of $c\tau=$0.005cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to e^+e^-$) for a lifetime of $c\tau=$0.007cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to e^+e^-$) for a lifetime of $c\tau=$0.01cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to e^+e^-$) for a lifetime of $c\tau=$0.025cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to e^+e^-$) for a lifetime of $c\tau=$0.05cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to e^+e^-$) for a lifetime of $c\tau=$0.1cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to e^+e^-$) for a lifetime of $c\tau=$0.25cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to e^+e^-$) for a lifetime of $c\tau=$0.5cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to e^+e^-$) for a lifetime of $c\tau=$1.0cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to e^+e^-$) for a lifetime of $c\tau=$2.5cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to e^+e^-$) for a lifetime of $c\tau=$5.0cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to e^+e^-$) for a lifetime of $c\tau=$10.0cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to e^+e^-$) for a lifetime of $c\tau=$25.0cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to e^+e^-$) for a lifetime of $c\tau=$50.0cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to e^+e^-$) for a lifetime of $c\tau=$100.0cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to e^+e^-$) for a lifetime of $c\tau=$200.0cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to e^+e^-$) for a lifetime of $c\tau=$400.0cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to \mu^+\mu^-$) for a lifetime of $c\tau=$0.001cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to \mu^+\mu^-$) for a lifetime of $c\tau=$0.003cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to \mu^+\mu^-$) for a lifetime of $c\tau=$0.005cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to \mu^+\mu^-$) for a lifetime of $c\tau=$0.007cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to \mu^+\mu^-$) for a lifetime of $c\tau=$0.01cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to \mu^+\mu^-$) for a lifetime of $c\tau=$0.025cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to \mu^+\mu^-$) for a lifetime of $c\tau=$0.05cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to \mu^+\mu^-$) for a lifetime of $c\tau=$0.1cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to \mu^+\mu^-$) for a lifetime of $c\tau=$0.25cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to \mu^+\mu^-$) for a lifetime of $c\tau=$0.5cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to \mu^+\mu^-$) for a lifetime of $c\tau=$1.0cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to \mu^+\mu^-$) for a lifetime of $c\tau=$2.5cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to \mu^+\mu^-$) for a lifetime of $c\tau=$5.0cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to \mu^+\mu^-$) for a lifetime of $c\tau=$10.0cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to \mu^+\mu^-$) for a lifetime of $c\tau=$25.0cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to \mu^+\mu^-$) for a lifetime of $c\tau=$50.0cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to \mu^+\mu^-$) for a lifetime of $c\tau=$100.0cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to \mu^+\mu^-$) for a lifetime of $c\tau=$200.0cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to \mu^+\mu^-$) for a lifetime of $c\tau=$400.0cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to \pi^+\pi^-$) for a lifetime of $c\tau=$0.001cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to \pi^+\pi^-$) for a lifetime of $c\tau=$0.003cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to \pi^+\pi^-$) for a lifetime of $c\tau=$0.005cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to \pi^+\pi^-$) for a lifetime of $c\tau=$0.007cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to \pi^+\pi^-$) for a lifetime of $c\tau=$0.01cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to \pi^+\pi^-$) for a lifetime of $c\tau=$0.025cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to \pi^+\pi^-$) for a lifetime of $c\tau=$0.05cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to \pi^+\pi^-$) for a lifetime of $c\tau=$0.1cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to \pi^+\pi^-$) for a lifetime of $c\tau=$0.25cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to \pi^+\pi^-$) for a lifetime of $c\tau=$0.5cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to \pi^+\pi^-$) for a lifetime of $c\tau=$1.0cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to \pi^+\pi^-$) for a lifetime of $c\tau=$2.5cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to \pi^+\pi^-$) for a lifetime of $c\tau=$5.0cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to \pi^+\pi^-$) for a lifetime of $c\tau=$10.0cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to \pi^+\pi^-$) for a lifetime of $c\tau=$25.0cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to \pi^+\pi^-$) for a lifetime of $c\tau=$50.0cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to \pi^+\pi^-$) for a lifetime of $c\tau=$100.0cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to \pi^+\pi^-$) for a lifetime of $c\tau=$200.0cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to \pi^+\pi^-$) for a lifetime of $c\tau=$400.0cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to K^+K^-$) for a lifetime of $c\tau=$0.001cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to K^+K^-$) for a lifetime of $c\tau=$0.003cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to K^+K^-$) for a lifetime of $c\tau=$0.005cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to K^+K^-$) for a lifetime of $c\tau=$0.007cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to K^+K^-$) for a lifetime of $c\tau=$0.01cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to K^+K^-$) for a lifetime of $c\tau=$0.025cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to K^+K^-$) for a lifetime of $c\tau=$0.05cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to K^+K^-$) for a lifetime of $c\tau=$0.1cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to K^+K^-$) for a lifetime of $c\tau=$0.25cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to K^+K^-$) for a lifetime of $c\tau=$0.5cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to K^+K^-$) for a lifetime of $c\tau=$1.0cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to K^+K^-$) for a lifetime of $c\tau=$2.5cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to K^+K^-$) for a lifetime of $c\tau=$5.0cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to K^+K^-$) for a lifetime of $c\tau=$10.0cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to K^+K^-$) for a lifetime of $c\tau=$25.0cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to K^+K^-$) for a lifetime of $c\tau=$50.0cm

Expected and observed limits on $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to K^+K^-$) for a lifetime of $c\tau=$100.0cm

Efficiencies for $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to e^+e^-$)

Efficiencies for $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to \mu^+\mu^-$)

Efficiencies for $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to \pi^+\pi^-$)

Efficiencies for $\mathcal{B}($$B^+\to K^+S$$) \times$ $\mathcal{B}($$S\to K^+K^-$)

Efficiencies for $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to e^+e^-$)

Efficiencies for $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to \mu^+\mu^-$)

Efficiencies for $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to \pi^+\pi^-$)

Efficiencies for $\mathcal{B}($$B^0\to K^{*0}(\to K^+\pi^-)S$$) \times$ $\mathcal{B}($$S\to K^+K^-$)

Summary of the total efficiencies. Quoted uncertainties correspond to statistical uncertainties of the simulated samples used. For the $B_c^+\to J/\psi \pi^+$ channel, the efficiency $\epsilon_{B_c^+\to J/\psi \pi^+}$ entering the equations for $R_{D_s^{(*)+}/\pi^+}$ is shown, while the efficiency for the full dataset is not defined.