$\xi$ distributions for different jet $p_T$ bins.

$\xi$ distributions for different jet $p_T$ bins.

The $j_T/p_{T}^{\rm jet}$ distributions for different jet $p_T$ bins.

The $j_T/p_{T}^{\rm jet}$ distributions for different jet $p_T$ bins.

$r$ distributions for different jet $p_T$ bins.

Distribution of $E_{\text{T}}^{\text{miss}}$ in SROS-on-b-$e\mu\mu$. The SR selections are applied for each distribution, except for the variable shown, for which the selection is indicated by a black arrow. The last bin includes the overflow. The `Others' category contains the production of Higgs boson, 3-top, 4-top, and single-top processes. Distributions for SBH signals are overlaid. The bottom panels show the ratio of the observed data to the predicted total background yields. The hatched band includes all statistical and systematic uncertainties.

Distribution of $m_{\text{T}}^{\text{min}}$ in SROS-on-b-$e\mu\mu$. The SR selections are applied for each distribution, except for the variable shown, for which the selection is indicated by a black arrow. The last bin includes the overflow. The `Others' category contains the production of Higgs boson, 3-top, 4-top, and single-top processes. Distributions for SBH signals are overlaid. The bottom panels show the ratio of the observed data to the predicted total background yields. The hatched band includes all statistical and systematic uncertainties.

Distribution of $E_{\text{T}}^{\text{miss}}$ in SRSS-$2\mu$. The SR selections are applied for each distribution, except for the variable shown, for which the selection is indicated by a black arrow. The last bin includes the overflow. The `Others' category contains the production of Higgs boson, 3-top, 4-top, and single-top processes. Distributions for SBH signals are overlaid. The bottom panels show the ratio of the observed data to the predicted total background yields. The hatched band includes all statistical and systematic uncertainties.

Observed ($N_{\text{obs}}$) and expected ($N_{\text{exp}}$) yields after the background-only fit for the flavor-merged inclusive SRs. The third and fourth columns list the 95\% CL upper limits on the visible cross-section ($\sigma_{\text{vis}}^{95}$) and on the number of signal events ($S_\text{obs}^{95}$). The fifth column ($S_\text{exp}^{95}$) shows the 95\% CL upper limit on the number of signal events, given the expected number of background events and its $\pm 1\sigma$ variations. The last two columns indicate the CL$_{\text{b}}$ value, i.e. the confidence level observed for the background-only hypothesis, and the discovery $p$-value ($p(s = 0)$) with its associated statistical significance $Z$. If the observed yield is below the expected yield, the $p$-value is capped at 0.5.

Observed and expected exclusion limits on the SBH model where mass-degenerate $\tilde{e}_{\text{L}}$, $\tilde{\mu}_{\text{L}}$ and $\tilde{\nu}$ are considered. The expected 95% CL exclusion limit is shown as a dashed black line, with the yellow band indicating $\pm1\sigma_{\text{exp}}$ including all uncertainties except for the signal cross-section uncertainty. The observed 95% CL exclusion limit is shown as a red solid line, with the dotted red lines indicating $\pm1\sigma_{\text{theory}}$ due to the signal cross-section uncertainty. The limits are shown projected onto the $m(\tilde{\ell}_{\text{L}}^{\pm})$ vs $m(\tilde{\chi}^0_3)$ plane, with $m(\tilde{\chi}^0_1)$ assumed to be 100~GeV.

Observed and expected exclusion limits on the SBH model where mass-degenerate $\tilde{e}_{\text{L}}$, $\tilde{\mu}_{\text{L}}$ and $\tilde{\nu}$ are considered. The expected 95% CL exclusion limit is shown as a dashed black line, with the yellow band indicating $\pm1\sigma_{\text{exp}}$ including all uncertainties except for the signal cross-section uncertainty. The observed 95% CL exclusion limit is shown as a red solid line, with the dotted red lines indicating $\pm1\sigma_{\text{theory}}$ due to the signal cross-section uncertainty. The limits are shown projected onto the $m(\tilde{\ell}_{\text{L}}^{\pm})$ vs $m(\tilde{\chi}^0_3)$ plane, with $m(\tilde{\chi}^0_1)$ assumed to be 100~GeV.

Observed and expected exclusion limits on the SBH model where mass-degenerate $\tilde{e}_{\text{L}}$, $\tilde{\mu}_{\text{L}}$ and $\tilde{\nu}$ are considered. The expected 95% CL exclusion limit is shown as a dashed black line, with the yellow band indicating $\pm1\sigma_{\text{exp}}$ including all uncertainties except for the signal cross-section uncertainty. The observed 95% CL exclusion limit is shown as a red solid line, with the dotted red lines indicating $\pm1\sigma_{\text{theory}}$ due to the signal cross-section uncertainty. The limits are shown projected onto the $m(\tilde{\ell}_{\text{L}}^{\pm})$ vs $m(\tilde{\chi}^0_3)$ plane, with $m(\tilde{\chi}^0_1)$ assumed to be 100~GeV.

Observed and expected exclusion limits on the SBH model where mass-degenerate $\tilde{e}_{\text{L}}$, $\tilde{\mu}_{\text{L}}$ and $\tilde{\nu}$ are considered. The expected 95% CL exclusion limit is shown as a dashed black line, with the yellow band indicating $\pm1\sigma_{\text{exp}}$ including all uncertainties except for the signal cross-section uncertainty. The observed 95% CL exclusion limit is shown as a red solid line, with the dotted red lines indicating $\pm1\sigma_{\text{theory}}$ due to the signal cross-section uncertainty. The limits are shown projected onto the $m(\tilde{\ell}_{\text{L}}^{\pm})$ vs $m(\tilde{\chi}^0_3)$ plane, with $m(\tilde{\chi}^0_1)$ assumed to be 100~GeV.

Observed and expected exclusion limits on the SBH model where mass-degenerate $\tilde{e}_{\text{L}}$, $\tilde{\mu}_{\text{L}}$ and $\tilde{\nu}$ are considered. The expected 95% CL exclusion limit is shown as a dashed black line, with the yellow band indicating $\pm1\sigma_{\text{exp}}$ including all uncertainties except for the signal cross-section uncertainty. The observed 95% CL exclusion limit is shown as a red solid line, with the dotted red lines indicating $\pm1\sigma_{\text{theory}}$ due to the signal cross-section uncertainty. The limits are shown projected onto the $m(\tilde{\ell}_{\text{L}}^{\pm})$ vs $m(\tilde{\chi}^0_3)$ plane, with $m(\tilde{\chi}^0_1)$ assumed to be 100~GeV.

Observed and expected exclusion limits on the SBH model where mass-degenerate $\tilde{e}_{\text{L}}$, $\tilde{\mu}_{\text{L}}$ and $\tilde{\nu}$ are considered. The expected 95% CL exclusion limit is shown as a dashed black line, with the yellow band indicating $\pm1\sigma_{\text{exp}}$ including all uncertainties except for the signal cross-section uncertainty. The observed 95% CL exclusion limit is shown as a red solid line, with the dotted red lines indicating $\pm1\sigma_{\text{theory}}$ due to the signal cross-section uncertainty. The limits are shown projected onto the $m(\tilde{\ell}_{\text{L}}^{\pm})$ vs $m(\tilde{\chi}^0_3)$ plane, with $m(\tilde{\chi}^0_1)$ assumed to be 100~GeV.

Observed and expected exclusion limits on the SBH model where only $\tilde{e}_{\text{L}}$ is considered. The expected 95% CL exclusion limit is shown as a dashed black line, with the yellow band indicating $\pm1\sigma_{\text{exp}}$ including all uncertainties except for the signal cross-section uncertainty. The observed 95% CL exclusion limit is shown as a red solid line, with the dotted red lines indicating $\pm1\sigma_{\text{theory}}$ due to the signal cross-section uncertainty. The limits are shown projected onto the $m(\tilde{\ell}_{\text{L}}^{\pm})$ vs $m(\tilde{\chi}^0_3)$ plane, with $m(\tilde{\chi}^0_1)$ assumed to be 100~GeV.

Observed and expected exclusion limits on the SBH model where only $\tilde{e}_{\text{L}}$ is considered. The expected 95% CL exclusion limit is shown as a dashed black line, with the yellow band indicating $\pm1\sigma_{\text{exp}}$ including all uncertainties except for the signal cross-section uncertainty. The observed 95% CL exclusion limit is shown as a red solid line, with the dotted red lines indicating $\pm1\sigma_{\text{theory}}$ due to the signal cross-section uncertainty. The limits are shown projected onto the $m(\tilde{\ell}_{\text{L}}^{\pm})$ vs $m(\tilde{\chi}^0_3)$ plane, with $m(\tilde{\chi}^0_1)$ assumed to be 100~GeV.

Observed and expected exclusion limits on the SBH model where only $\tilde{e}_{\text{L}}$ is considered. The expected 95% CL exclusion limit is shown as a dashed black line, with the yellow band indicating $\pm1\sigma_{\text{exp}}$ including all uncertainties except for the signal cross-section uncertainty. The observed 95% CL exclusion limit is shown as a red solid line, with the dotted red lines indicating $\pm1\sigma_{\text{theory}}$ due to the signal cross-section uncertainty. The limits are shown projected onto the $m(\tilde{\ell}_{\text{L}}^{\pm})$ vs $m(\tilde{\chi}^0_3)$ plane, with $m(\tilde{\chi}^0_1)$ assumed to be 100~GeV.

Observed and expected exclusion limits on the SBH model where only $\tilde{e}_{\text{L}}$ is considered. The expected 95% CL exclusion limit is shown as a dashed black line, with the yellow band indicating $\pm1\sigma_{\text{exp}}$ including all uncertainties except for the signal cross-section uncertainty. The observed 95% CL exclusion limit is shown as a red solid line, with the dotted red lines indicating $\pm1\sigma_{\text{theory}}$ due to the signal cross-section uncertainty. The limits are shown projected onto the $m(\tilde{\ell}_{\text{L}}^{\pm})$ vs $m(\tilde{\chi}^0_3)$ plane, with $m(\tilde{\chi}^0_1)$ assumed to be 100~GeV.

Observed and expected exclusion limits on the SBH model where only $\tilde{e}_{\text{L}}$ is considered. The expected 95% CL exclusion limit is shown as a dashed black line, with the yellow band indicating $\pm1\sigma_{\text{exp}}$ including all uncertainties except for the signal cross-section uncertainty. The observed 95% CL exclusion limit is shown as a red solid line, with the dotted red lines indicating $\pm1\sigma_{\text{theory}}$ due to the signal cross-section uncertainty. The limits are shown projected onto the $m(\tilde{\ell}_{\text{L}}^{\pm})$ vs $m(\tilde{\chi}^0_3)$ plane, with $m(\tilde{\chi}^0_1)$ assumed to be 100~GeV.

Observed and expected exclusion limits on the SBH model where only $\tilde{e}_{\text{L}}$ is considered. The expected 95% CL exclusion limit is shown as a dashed black line, with the yellow band indicating $\pm1\sigma_{\text{exp}}$ including all uncertainties except for the signal cross-section uncertainty. The observed 95% CL exclusion limit is shown as a red solid line, with the dotted red lines indicating $\pm1\sigma_{\text{theory}}$ due to the signal cross-section uncertainty. The limits are shown projected onto the $m(\tilde{\ell}_{\text{L}}^{\pm})$ vs $m(\tilde{\chi}^0_3)$ plane, with $m(\tilde{\chi}^0_1)$ assumed to be 100~GeV.

Observed and expected exclusion limits on the SBH model where only $\tilde{\mu}_{\text{L}}$ is considered. The expected 95% CL exclusion limit is shown as a dashed black line, with the yellow band indicating $\pm1\sigma_{\text{exp}}$ including all uncertainties except for the signal cross-section uncertainty. The observed 95% CL exclusion limit is shown as a red solid line, with the dotted red lines indicating $\pm1\sigma_{\text{theory}}$ due to the signal cross-section uncertainty. The limits are shown projected onto the $m(\tilde{\ell}_{\text{L}}^{\pm})$ vs $m(\tilde{\chi}^0_3)$ plane, with $m(\tilde{\chi}^0_1)$ assumed to be 100~GeV.

Observed and expected exclusion limits on the SBH model where only $\tilde{\mu}_{\text{L}}$ is considered. The expected 95% CL exclusion limit is shown as a dashed black line, with the yellow band indicating $\pm1\sigma_{\text{exp}}$ including all uncertainties except for the signal cross-section uncertainty. The observed 95% CL exclusion limit is shown as a red solid line, with the dotted red lines indicating $\pm1\sigma_{\text{theory}}$ due to the signal cross-section uncertainty. The limits are shown projected onto the $m(\tilde{\ell}_{\text{L}}^{\pm})$ vs $m(\tilde{\chi}^0_3)$ plane, with $m(\tilde{\chi}^0_1)$ assumed to be 100~GeV.

Observed and expected exclusion limits on the SBH model where only $\tilde{\mu}_{\text{L}}$ is considered. The expected 95% CL exclusion limit is shown as a dashed black line, with the yellow band indicating $\pm1\sigma_{\text{exp}}$ including all uncertainties except for the signal cross-section uncertainty. The observed 95% CL exclusion limit is shown as a red solid line, with the dotted red lines indicating $\pm1\sigma_{\text{theory}}$ due to the signal cross-section uncertainty. The limits are shown projected onto the $m(\tilde{\ell}_{\text{L}}^{\pm})$ vs $m(\tilde{\chi}^0_3)$ plane, with $m(\tilde{\chi}^0_1)$ assumed to be 100~GeV.

Observed and expected exclusion limits on the SBH model where only $\tilde{\mu}_{\text{L}}$ is considered. The expected 95% CL exclusion limit is shown as a dashed black line, with the yellow band indicating $\pm1\sigma_{\text{exp}}$ including all uncertainties except for the signal cross-section uncertainty. The observed 95% CL exclusion limit is shown as a red solid line, with the dotted red lines indicating $\pm1\sigma_{\text{theory}}$ due to the signal cross-section uncertainty. The limits are shown projected onto the $m(\tilde{\ell}_{\text{L}}^{\pm})$ vs $m(\tilde{\chi}^0_3)$ plane, with $m(\tilde{\chi}^0_1)$ assumed to be 100~GeV.

Observed and expected exclusion limits on the SBH model where only $\tilde{\mu}_{\text{L}}$ is considered. The expected 95% CL exclusion limit is shown as a dashed black line, with the yellow band indicating $\pm1\sigma_{\text{exp}}$ including all uncertainties except for the signal cross-section uncertainty. The observed 95% CL exclusion limit is shown as a red solid line, with the dotted red lines indicating $\pm1\sigma_{\text{theory}}$ due to the signal cross-section uncertainty. The limits are shown projected onto the $m(\tilde{\ell}_{\text{L}}^{\pm})$ vs $m(\tilde{\chi}^0_3)$ plane, with $m(\tilde{\chi}^0_1)$ assumed to be 100~GeV.

Observed and expected exclusion limits on the SBH model where only $\tilde{\mu}_{\text{L}}$ is considered. The expected 95% CL exclusion limit is shown as a dashed black line, with the yellow band indicating $\pm1\sigma_{\text{exp}}$ including all uncertainties except for the signal cross-section uncertainty. The observed 95% CL exclusion limit is shown as a red solid line, with the dotted red lines indicating $\pm1\sigma_{\text{theory}}$ due to the signal cross-section uncertainty. The limits are shown projected onto the $m(\tilde{\ell}_{\text{L}}^{\pm})$ vs $m(\tilde{\chi}^0_3)$ plane, with $m(\tilde{\chi}^0_1)$ assumed to be 100~GeV.

Distribution of $E_{\text{T}}^{\text{miss}}$ in SROS-off-b-$e\mu\mu$. The SR selections are applied for each distribution, except for the variable shown, for which the selection is indicated by a black arrow. The last bin includes the overflow. The `Others' category contains the production of Higgs boson, 3-top, 4-top, and single-top processes. Distributions for SBH signals are overlaid. The bottom panels show the ratio of the observed data to the predicted total background yields. Ratio values outside the graph range are indicated by brown arrows. The hatched band includes all statistical and systematic uncertainties.

Distribution of $m_{\text{T}}^{\text{min}}$ in SROS-off-b-$e\mu\mu$. The SR selections are applied for each distribution, except for the variable shown, for which the selection is indicated by a black arrow. The last bin includes the overflow. The `Others' category contains the production of Higgs boson, 3-top, 4-top, and single-top processes. Distributions for SBH signals are overlaid. The bottom panels show the ratio of the observed data to the predicted total background yields. Ratio values outside the graph range are indicated by brown arrows. The hatched band includes all statistical and systematic uncertainties.

Distribution of $E_{\text{T}}^{\text{miss}}$ in SRSS-$eee$. The SR selections are applied for each distribution, except for the variable shown, for which the selection is indicated by a black arrow. The last bin includes the overflow. The `Others' category contains the production of Higgs boson, 3-top, 4-top, and single-top processes. Distributions for SBH signals are overlaid. The bottom panels show the ratio of the observed data to the predicted total background yields. Ratio values outside the graph range are indicated by brown arrows. The hatched band includes all statistical and systematic uncertainties.

Distribution of $E_{\text{T}}^{\text{miss}}$ in SRSS-$ee\mu$. The SR selections are applied for each distribution, except for the variable shown, for which the selection is indicated by a black arrow. The last bin includes the overflow. The `Others' category contains the production of Higgs boson, 3-top, 4-top, and single-top processes. Distributions for SBH signals are overlaid. The bottom panels show the ratio of the observed data to the predicted total background yields. Ratio values outside the graph range are indicated by brown arrows. The hatched band includes all statistical and systematic uncertainties.

Observed and expected exclusion limits on the SBH model where mass-degenerate $\tilde{e}_{\text{L}}$, $\tilde{\mu}_{\text{L}}$ and $\tilde{\nu}$ is considered. The expected 95% CL exclusion limit is shown as a dashed black line, with the yellow band indicating $\pm1\sigma_{\text{exp}}$ including all uncertainties except for the signal cross-section uncertainty. The observed 95% CL exclusion limit is shown as a red solid line, with the dotted red lines indicating $\pm1\sigma_{\text{theory}}$ due to the signal cross-section uncertainty. The limits are shown projected onto the $m(\tilde{\ell}_{\text{L}}^{\pm})$ vs $m(\tilde{\chi}^0_3)$ plane, with $m(\tilde{\chi}^0_1)$ assumed to be 150 GeV.

Observed and expected exclusion limits on the SBH model where mass-degenerate $\tilde{e}_{\text{L}}$, $\tilde{\mu}_{\text{L}}$ and $\tilde{\nu}$ is considered. The expected 95% CL exclusion limit is shown as a dashed black line, with the yellow band indicating $\pm1\sigma_{\text{exp}}$ including all uncertainties except for the signal cross-section uncertainty. The observed 95% CL exclusion limit is shown as a red solid line, with the dotted red lines indicating $\pm1\sigma_{\text{theory}}$ due to the signal cross-section uncertainty. The limits are shown projected onto the $m(\tilde{\ell}_{\text{L}}^{\pm})$ vs $m(\tilde{\chi}^0_3)$ plane, with $m(\tilde{\chi}^0_1)$ assumed to be 150 GeV.

Observed and expected exclusion limits on the SBH model where mass-degenerate $\tilde{e}_{\text{L}}$, $\tilde{\mu}_{\text{L}}$ and $\tilde{\nu}$ is considered. The expected 95% CL exclusion limit is shown as a dashed black line, with the yellow band indicating $\pm1\sigma_{\text{exp}}$ including all uncertainties except for the signal cross-section uncertainty. The observed 95% CL exclusion limit is shown as a red solid line, with the dotted red lines indicating $\pm1\sigma_{\text{theory}}$ due to the signal cross-section uncertainty. The limits are shown projected onto the $m(\tilde{\ell}_{\text{L}}^{\pm})$ vs $m(\tilde{\chi}^0_3)$ plane, with $m(\tilde{\chi}^0_1)$ assumed to be 150 GeV.

Observed and expected exclusion limits on the SBH model where mass-degenerate $\tilde{e}_{\text{L}}$, $\tilde{\mu}_{\text{L}}$ and $\tilde{\nu}$ is considered. The expected 95% CL exclusion limit is shown as a dashed black line, with the yellow band indicating $\pm1\sigma_{\text{exp}}$ including all uncertainties except for the signal cross-section uncertainty. The observed 95% CL exclusion limit is shown as a red solid line, with the dotted red lines indicating $\pm1\sigma_{\text{theory}}$ due to the signal cross-section uncertainty. The limits are shown projected onto the $m(\tilde{\ell}_{\text{L}}^{\pm})$ vs $m(\tilde{\chi}^0_3)$ plane, with $m(\tilde{\chi}^0_1)$ assumed to be 150 GeV.

Observed and expected exclusion limits on the SBH model where mass-degenerate $\tilde{e}_{\text{L}}$, $\tilde{\mu}_{\text{L}}$ and $\tilde{\nu}$ is considered. The expected 95% CL exclusion limit is shown as a dashed black line, with the yellow band indicating $\pm1\sigma_{\text{exp}}$ including all uncertainties except for the signal cross-section uncertainty. The observed 95% CL exclusion limit is shown as a red solid line, with the dotted red lines indicating $\pm1\sigma_{\text{theory}}$ due to the signal cross-section uncertainty. The limits are shown projected onto the $m(\tilde{\ell}_{\text{L}}^{\pm})$ vs $m(\tilde{\chi}^0_3)$ plane, with $m(\tilde{\chi}^0_1)$ assumed to be 150 GeV.

Observed and expected exclusion limits on the SBH model where mass-degenerate $\tilde{e}_{\text{L}}$, $\tilde{\mu}_{\text{L}}$ and $\tilde{\nu}$ is considered. The expected 95% CL exclusion limit is shown as a dashed black line, with the yellow band indicating $\pm1\sigma_{\text{exp}}$ including all uncertainties except for the signal cross-section uncertainty. The observed 95% CL exclusion limit is shown as a red solid line, with the dotted red lines indicating $\pm1\sigma_{\text{theory}}$ due to the signal cross-section uncertainty. The limits are shown projected onto the $m(\tilde{\ell}_{\text{L}}^{\pm})$ vs $m(\tilde{\chi}^0_3)$ plane, with $m(\tilde{\chi}^0_1)$ assumed to be 150 GeV.

Observed and expected exclusion limits on the SBH model where mass-degenerate $\tilde{e}_{\text{L}}$, $\tilde{\mu}_{\text{L}}$ and $\tilde{\nu}$ are considered. The expected 95% CL exclusion limit is shown as a dashed black line, with the yellow band indicating $\pm1\sigma_{\text{exp}}$ including all uncertainties except for the signal cross-section uncertainty. The observed 95% CL exclusion limit is shown as a red solid line, with the dotted red lines indicating $\pm1\sigma_{\text{theory}}$ due to the signal cross-section uncertainty. The limits are shown projected onto the $\Delta m(\tilde{\chi}^0_3, \tilde{\chi}^0_1)$ vs $\Delta m(\tilde{\ell}_{\text{L}}, \tilde{\chi}^0_3)$ plane, with $m(\tilde{\chi}^0_1)$ assumed to be 100 GeV.

Observed and expected exclusion limits on the SBH model where mass-degenerate $\tilde{e}_{\text{L}}$, $\tilde{\mu}_{\text{L}}$ and $\tilde{\nu}$ are considered. The expected 95% CL exclusion limit is shown as a dashed black line, with the yellow band indicating $\pm1\sigma_{\text{exp}}$ including all uncertainties except for the signal cross-section uncertainty. The observed 95% CL exclusion limit is shown as a red solid line, with the dotted red lines indicating $\pm1\sigma_{\text{theory}}$ due to the signal cross-section uncertainty. The limits are shown projected onto the $\Delta m(\tilde{\chi}^0_3, \tilde{\chi}^0_1)$ vs $\Delta m(\tilde{\ell}_{\text{L}}, \tilde{\chi}^0_3)$ plane, with $m(\tilde{\chi}^0_1)$ assumed to be 100 GeV.

Observed and expected exclusion limits on the SBH model where mass-degenerate $\tilde{e}_{\text{L}}$, $\tilde{\mu}_{\text{L}}$ and $\tilde{\nu}$ are considered. The expected 95% CL exclusion limit is shown as a dashed black line, with the yellow band indicating $\pm1\sigma_{\text{exp}}$ including all uncertainties except for the signal cross-section uncertainty. The observed 95% CL exclusion limit is shown as a red solid line, with the dotted red lines indicating $\pm1\sigma_{\text{theory}}$ due to the signal cross-section uncertainty. The limits are shown projected onto the $\Delta m(\tilde{\chi}^0_3, \tilde{\chi}^0_1)$ vs $\Delta m(\tilde{\ell}_{\text{L}}, \tilde{\chi}^0_3)$ plane, with $m(\tilde{\chi}^0_1)$ assumed to be 100 GeV.

Observed and expected exclusion limits on the SBH model where mass-degenerate $\tilde{e}_{\text{L}}$, $\tilde{\mu}_{\text{L}}$ and $\tilde{\nu}$ are considered. The expected 95% CL exclusion limit is shown as a dashed black line, with the yellow band indicating $\pm1\sigma_{\text{exp}}$ including all uncertainties except for the signal cross-section uncertainty. The observed 95% CL exclusion limit is shown as a red solid line, with the dotted red lines indicating $\pm1\sigma_{\text{theory}}$ due to the signal cross-section uncertainty. The limits are shown projected onto the $\Delta m(\tilde{\chi}^0_3, \tilde{\chi}^0_1)$ vs $\Delta m(\tilde{\ell}_{\text{L}}, \tilde{\chi}^0_3)$ plane, with $m(\tilde{\chi}^0_1)$ assumed to be 100 GeV.

Observed and expected exclusion limits on the SBH model where mass-degenerate $\tilde{e}_{\text{L}}$, $\tilde{\mu}_{\text{L}}$ and $\tilde{\nu}$ are considered. The expected 95% CL exclusion limit is shown as a dashed black line, with the yellow band indicating $\pm1\sigma_{\text{exp}}$ including all uncertainties except for the signal cross-section uncertainty. The observed 95% CL exclusion limit is shown as a red solid line, with the dotted red lines indicating $\pm1\sigma_{\text{theory}}$ due to the signal cross-section uncertainty. The limits are shown projected onto the $\Delta m(\tilde{\chi}^0_3, \tilde{\chi}^0_1)$ vs $\Delta m(\tilde{\ell}_{\text{L}}, \tilde{\chi}^0_3)$ plane, with $m(\tilde{\chi}^0_1)$ assumed to be 100 GeV.

Observed and expected exclusion limits on the SBH model where mass-degenerate $\tilde{e}_{\text{L}}$, $\tilde{\mu}_{\text{L}}$ and $\tilde{\nu}$ are considered. The expected 95% CL exclusion limit is shown as a dashed black line, with the yellow band indicating $\pm1\sigma_{\text{exp}}$ including all uncertainties except for the signal cross-section uncertainty. The observed 95% CL exclusion limit is shown as a red solid line, with the dotted red lines indicating $\pm1\sigma_{\text{theory}}$ due to the signal cross-section uncertainty. The limits are shown projected onto the $\Delta m(\tilde{\chi}^0_3, \tilde{\chi}^0_1)$ vs $\Delta m(\tilde{\ell}_{\text{L}}, \tilde{\chi}^0_3)$ plane, with $m(\tilde{\chi}^0_1)$ assumed to be 100 GeV.

The expected upper limits on the cross-section for each signal point. The gray numbers represent the values. The expected (dashed) and observed (solid) 95% CL exclusion limits are overlaid. An asymptotic approximation is employed in the CL$_{\text{s}}$ calculation instead of the full calculation using pseudo-experiments.

The observed upper limits on the cross-section for each signal point. The gray numbers represent the values. The expected (dashed) and observed (solid) 95% CL exclusion limits are overlaid. An asymptotic approximation is employed in the CL$_{\text{s}}$ calculation instead of the full calculation using pseudo-experiments.

Acceptance for signals with $m(\tilde{\chi}^0_1)=100$ GeV in flavored-merged SRs. The acceptance is given by the ratio of weighted selected events in the SR to the weighted total number of generated events. The selection is based on generator-level particle information.

Acceptance for signals with $m(\tilde{\chi}^0_1)=100$ GeV in flavored-merged SRs. The acceptance is given by the ratio of weighted selected events in the SR to the weighted total number of generated events. The selection is based on generator-level particle information.

Acceptance for signals with $m(\tilde{\chi}^0_1)=100$ GeV in flavored-merged SRs. The acceptance is given by the ratio of weighted selected events in the SR to the weighted total number of generated events. The selection is based on generator-level particle information.

Acceptance for signals with $m(\tilde{\chi}^0_1)=100$ GeV in flavored-merged SRs. The acceptance is given by the ratio of weighted selected events in the SR to the weighted total number of generated events. The selection is based on generator-level particle information.

Acceptance for signals with $m(\tilde{\chi}^0_1)=100$ GeV in flavored-merged SRs. The acceptance is given by the ratio of weighted selected events in the SR to the weighted total number of generated events. The selection is based on generator-level particle information.

Acceptance for signals with $m(\tilde{\chi}^0_1)=100$ GeV in flavored-merged SRs. The acceptance is given by the ratio of weighted selected events in the SR to the weighted total number of generated events. The selection is based on generator-level particle information.

Acceptance for signals with $m(\tilde{\chi}^0_1)=100$ GeV in flavored-merged SRs. The acceptance is given by the ratio of weighted selected events in the SR to the weighted total number of generated events. The selection is based on generator-level particle information.

Efficiencies for signals with $m(\tilde{\chi}^0_1)=100$ GeV in the $m_{3\ell}$ merged SRSFOS and SRSS. The efficiency is defined by the number of events of reconstructed-level signal simulation divided by the number of events obtained at generator level. Efficiencies below 0.002% are rounded to 0. The efficiency values are affected by statistical fluctuations due to the limited number of events.

Efficiencies for signals with $m(\tilde{\chi}^0_1)=100$ GeV in the $m_{3\ell}$ merged SRSFOS and SRSS. The efficiency is defined by the number of events of reconstructed-level signal simulation divided by the number of events obtained at generator level. Efficiencies below 0.002% are rounded to 0. The efficiency values are affected by statistical fluctuations due to the limited number of events.

Efficiencies for signals with $m(\tilde{\chi}^0_1)=100$ GeV in the $m_{3\ell}$ merged SRSFOS and SRSS. The efficiency is defined by the number of events of reconstructed-level signal simulation divided by the number of events obtained at generator level. Efficiencies below 0.002% are rounded to 0. The efficiency values are affected by statistical fluctuations due to the limited number of events.

Efficiencies for signals with $m(\tilde{\chi}^0_1)=100$ GeV in the $m_{3\ell}$ merged SRSFOS and SRSS. The efficiency is defined by the number of events of reconstructed-level signal simulation divided by the number of events obtained at generator level. Efficiencies below 0.002% are rounded to 0. The efficiency values are affected by statistical fluctuations due to the limited number of events.

Efficiencies for signals with $m(\tilde{\chi}^0_1)=100$ GeV in the $m_{3\ell}$ merged SRSFOS and SRSS. The efficiency is defined by the number of events of reconstructed-level signal simulation divided by the number of events obtained at generator level. Efficiencies below 0.002% are rounded to 0. The efficiency values are affected by statistical fluctuations due to the limited number of events.

Efficiencies for signals with $m(\tilde{\chi}^0_1)=100$ GeV in the $m_{3\ell}$ merged SRSFOS and SRSS. The efficiency is defined by the number of events of reconstructed-level signal simulation divided by the number of events obtained at generator level. Efficiencies below 0.002% are rounded to 0. The efficiency values are affected by statistical fluctuations due to the limited number of events.

Efficiencies for signals with $m(\tilde{\chi}^0_1)=100$ GeV in the $m_{3\ell}$ merged SRSFOS and SRSS. The efficiency is defined by the number of events of reconstructed-level signal simulation divided by the number of events obtained at generator level. Efficiencies below 0.002% are rounded to 0. The efficiency values are affected by statistical fluctuations due to the limited number of events.

Efficiencies for signals with $m(\tilde{\chi}^0_1)=100$ GeV in the $m_{3\ell}$ merged SRSFOS and SRSS. The efficiency is defined by the number of events of reconstructed-level signal simulation divided by the number of events obtained at generator level. Efficiencies below 0.002% are rounded to 0. The efficiency values are affected by statistical fluctuations due to the limited number of events.

Efficiencies for signals with $m(\tilde{\chi}^0_1)=100$ GeV in the $m_{3\ell}$ merged SRSFOS and SRSS. The efficiency is defined by the number of events of reconstructed-level signal simulation divided by the number of events obtained at generator level. Efficiencies below 0.002% are rounded to 0. The efficiency values are affected by statistical fluctuations due to the limited number of events.

Efficiencies for signals with $m(\tilde{\chi}^0_1)=100$ GeV in the $m_{3\ell}$ merged SRSFOS and SRSS. The efficiency is defined by the number of events of reconstructed-level signal simulation divided by the number of events obtained at generator level. Efficiencies below 0.002% are rounded to 0. The efficiency values are affected by statistical fluctuations due to the limited number of events.

Efficiencies for signals with $m(\tilde{\chi}^0_1)=100$ GeV in the $m_{3\ell}$ merged SRSFOS and SRSS. The efficiency is defined by the number of events of reconstructed-level signal simulation divided by the number of events obtained at generator level. Efficiencies below 0.002% are rounded to 0. The efficiency values are affected by statistical fluctuations due to the limited number of events.

Summary of the number of events passing each selection for the $m(\tilde{\ell}_{\text{L}}^{\pm},\tilde{\chi}^0_3,\tilde{\chi}^0_1)=(300, 200, 100)$, $(550, 300, 100)$, $(450, 180, 100)$ GeV signal points, including all production processes. After the initial selections, the table is split into row blocks per inclusive region, and then further for each SR channel. Flavor-binned SRs are shown for SROS-on-b for reference. The generator level selections require to have two or more leptons.

Summary of the number of events passing each selection for the $m(\tilde{\ell}_{\text{L}}^{\pm},\tilde{\chi}^0_3,\tilde{\chi}^0_1)=(300, 200, 100)$, $(550, 300, 100)$, $(450, 180, 100)$ GeV signal points, including all production processes. After the initial selections, the table is split into row blocks per inclusive region, and then further for each SR channel. Flavor-binned SRs are shown for SROS-off-b for reference. The generator level selections require to have two or more leptons.

Summary of the number of events passing each selection for the $m(\tilde{\ell}_{\text{L}}^{\pm},\tilde{\chi}^0_3,\tilde{\chi}^0_1)=(300, 200, 100)$, $(550, 300, 100)$, $(450, 180, 100)$ GeV signal points, including all production processes. After the initial selections, the table is split into row blocks per inclusive region, and then further for each SR channel. Flavor-binned SRs are shown. The generator level selections require to have two or more leptons.

The Charged-hadron yields as a function of pT in different y selections in p+Pb collisions.

The K^{0}_{S} yields as a function of pT in different y selections in Pb+Pb photo-nuclear collisions.

The #Lambda yields as a function of pT in different y selections in Pb+Pb photo-nuclear collisions.

The #Xi^{-} yields as a function of pT in different y selections in Pb+Pb photo-nuclear collisions.

The K^{0}_{S} yields as a function of pT in different y selections in p+Pb collisions.

The #Lambda yields as a function of pT in different y selections in p+Pb collisions.

The #Xi^{-} yields as a function of pT in different y selections in p+Pb collisions.

The Charged-hadron and identified-hadron yields as a function of y in Pb+Pb photo-nuclear collisions.

The Charged-hadron and identified-hadron yields as a function of y in Pb+Pb photo-nuclear collisions.

The Charged-hadron and identified-hadron yields as a function of y in p+Pb collisions.

The Charged-hadron and identified-hadron yields as a function of y in p+Pb collisions.

The meanpT of charged hadrons and identified hadrons as a function of Nchrec in Pb+Pb photo-nuclear collisions.

The meanpT of charged hadrons and identified hadrons as a function of Nchrec in Pb+Pb photo-nuclear collisions.

The meanpT of charged hadrons and identified hadrons as a function of Nchrec in Pb+Pb photo-nuclear collisions.

The meanpT of charged hadrons and identified hadrons as a function of Nchrec in p+Pb collisions.

The meanpT of charged hadrons and identified hadrons as a function of Nchrec in p+Pb collisions.

The baryon to meson ratio as a function of pT in Pb+Pb photo-nuclear collisions.

The baryon to meson ratio as a function of pT in Pb+Pb photo-nuclear collisions.

The baryon to meson ratio as a function of pT in p+Pb collisions.

The baryon to meson ratio as a function of pT in p+Pb collisions.

The ratios of identified-strange-hadron yield to charged-hadron yields as a function of Nchrec in Pb+Pb photo-nuclear collisions.

The ratios of identified-strange-hadron yield to charged-hadron yields as a function of Nchrec in Pb+Pb photo-nuclear collisions.

The ratios of identified-strange-hadron yield to charged-hadron yields as a function of Nchrec in Pb+Pb photo-nuclear collisions.

The ratios of identified-strange-hadron yield to charged-hadron yields as a function of Nchrec in p+Pb collisions.

The ratios of identified-strange-hadron yield to charged-hadron yields as a function of Nchrec in p+Pb collisions.

Suppl. Fig. 7. The reconstructed shower angle for all single photon events. The individual signal and background event type categories added together form the unconstrained prediction.

Suppl. Fig. 7. The constrained covariance matrix for the reconstructed shower angle for all single-photon events. The matrix shows uncertainties and correlations between bins due to flux uncertainties, cross-section uncertainties, hadron reinteraction uncertainties, detector systematic uncertainties, Monte-Carlo statistical uncertainties, and dirt (outside cryostat) uncertainties. Data statistical uncertainties are not included. An example of how to add Pearson data statistical uncertainties can be found in the example code repository.

Suppl. Fig. 7. The unconstrained covariance matrix for reconstructed shower angle for all single-photon events. The matrix shows uncertainties and correlations between bins due to flux uncertainties, cross-section uncertainties, hadron reinteraction uncertainties, detector systematic uncertainties, Monte-Carlo statistical uncertainties, and dirt (outside cryostat) uncertainties. Data statistical uncertainties are not included. An example of how to add Pearson data statistical uncertainties can be found in the example code repository.

Fig. 3. The reconstructed number of protons, with a proton KE energy threshold of 35 MeV, for all single-photon events. The individual signal and background event type categories added together form the unconstrained prediction.

Fig. 4, Suppl. Fig. 8. The reconstructed shower energy for zero proton events binned from 0 to 600 MeV. The individual signal and background event type categories added together form the unconstrained prediction.

Fig. 4. The constrained covariance matrix for the reconstructed shower energy for zero proton events binned from 0 to 600 MeV. The matrix shows uncertainties and correlations between bins due to flux uncertainties, cross-section uncertainties, hadron reinteraction uncertainties, detector systematic uncertainties, Monte-Carlo statistical uncertainties, and dirt (outside cryostat) uncertainties. Data statistical uncertainties are not included. An example of how to add Pearson data statistical uncertainties can be found in the example code repository.

Fig. 4. The unconstrained covariance matrix for reconstructed shower energy for zero proton events binned from 0 to 600 MeV. The matrix shows uncertainties and correlations between bins due to flux uncertainties, cross-section uncertainties, hadron reinteraction uncertainties, detector systematic uncertainties, Monte-Carlo statistical uncertainties, and dirt (outside cryostat) uncertainties. Data statistical uncertainties are not included. An example of how to add Pearson data statistical uncertainties can be found in the example code repository.

Fig. 6. The reconstructed shower energy for zero proton events binned from 150 to 1250 MeV, with LEE prediction. The individual signal and background event type categories added together form the unconstrained prediction. The "LEE" category is the unfolded MiniBooNE LEE model prediction scaled under the neutrino-target nucleon interaction assumption.

Fig. 6. The constrained covariance matrix for the reconstructed shower energy for zero proton events binned from 150 to 1250 MeV. Both with and without the LEE model added. The matrix shows uncertainties and correlations between bins due to flux uncertainties, cross-section uncertainties, hadron reinteraction uncertainties, detector systematic uncertainties, Monte-Carlo statistical uncertainties, and dirt (outside cryostat) uncertainties. Data statistical uncertainties are not included. An example of how to add Pearson data statistical uncertainties can be found in the example code repository.

Fig. 6. The unconstrained covariance matrix for reconstructed shower energy for zero proton events binned from 150 to 1250 MeV. Both with and without the LEE model added. The matrix shows uncertainties and correlations between bins due to flux uncertainties, cross-section uncertainties, hadron reinteraction uncertainties, detector systematic uncertainties, Monte-Carlo statistical uncertainties, and dirt (outside cryostat) uncertainties. Data statistical uncertainties are not included. An example of how to add Pearson data statistical uncertainties can be found in the example code repository.

Suppl. Fig. 10. The reconstructed shower backwards projected distance for zero proton events. The individual signal and background event type categories added together form the unconstrained prediction.

Suppl. Fig. 9. The reconstructed shower angle for zero proton events. Includes LEE model prediction. The individual signal and background event type categories added together form the unconstrained prediction. The "LEE" category is the unfolded MiniBooNE LEE model prediction scaled under the neutrino-target nucleon interaction assumption.

Suppl. Fig. 9. The constrained covariance matrix for the reconstructed shower angle for zero proton events. The matrix shows uncertainties and correlations between bins due to flux uncertainties, cross-section uncertainties, hadron reinteraction uncertainties, detector systematic uncertainties, Monte-Carlo statistical uncertainties, and dirt (outside cryostat) uncertainties. Data statistical uncertainties are not included. An example of how to add Pearson data statistical uncertainties can be found in the example code repository.

Suppl. Fig. 9. The unconstrained covariance matrix for reconstructed shower angle for zero proton events. The matrix shows uncertainties and correlations between bins due to flux uncertainties, cross-section uncertainties, hadron reinteraction uncertainties, detector systematic uncertainties, Monte-Carlo statistical uncertainties, and dirt (outside cryostat) uncertainties. Data statistical uncertainties are not included. An example of how to add Pearson data statistical uncertainties can be found in the example code repository.

1$\gamma$Xp shower energy and angle selection efficiencies for true 1$\gamma$Xp events. NaN values indicate a "divide by zero" case where zero events were present in the bin before any selection was applied. Energy and Angle values represent bin lower edges.

1$\gamma$0p shower energy and angle selection efficiencies for true single-photon events with no other true particles of any energy. NaN values indicate a "divide by zero" case where zero events were present in the bin before any selection was applied. Energy and Angle values represent bin lower edges.

Covariance matrix showing uncertainties and correlations between bins due to flux uncertainties, cross-section uncertainties, hadron reinteraction uncertainties, detector systematic uncertainties, Monte-Carlo statistical uncertainties, and dirt (outside cryostat) uncertainties. Pearson data statistical uncertainties have been included, and include small correlations due to events which can be selected by both WC and Pandora. The first four bins are the WC $1\gamma Np$, WC $1\gamma 0p$, Pandora $1\gamma 1p$, and Pandora $1\gamma 0p$ channels, and the next four sets of 16 bins are the NC $\pi^0 Np$, NC $\pi^0 0p$, $\nu_\mu$CC $Np$, and $\nu_\mu$CC $0p$ channels. This corresponds to Fig. 1 of the paper and Fig. 6 of the Supplemental Material.

Constrained WC $1\gamma Np$ energy distribution. There are 6 bins from 0 to 600 MeV of reconstructed shower energy, with an additional overflow bin. Constrained systematic uncertainties on the predictions are illustrated, and a more detailed covariance matrix is included in the Constrained Energy Distributions Covariance Matrix tab. This corresponds to Fig. 2 of the paper.

Constrained WC $1\gamma 0p$ energy distribution. There are 14 bins from 0 to 700 MeV of reconstructed shower energy, with an additional overflow bin. Constrained systematic uncertainties on the predictions are illustrated, and a more detailed covariance matrix is included in the Constrained Energy Distributions Covariance Matrix tab. This corresponds to Fig. 2 of the paper.

Constrained Pandora $1\gamma 1p$ energy distribution. There are 6 bins from 0 to 600 MeV of reconstructed shower energy, with an additional overflow bin. Constrained systematic uncertainties on the predictions are illustrated, and a more detailed covariance matrix is included in the Constrained Energy Distributions Covariance Matrix tab. This corresponds to Fig. 2 of the paper.

Constrained Pandora $1\gamma 0p$ energy distribution. There are 14 bins from 0 to 700 MeV of reconstructed shower energy, with an additional overflow bin. Constrained systematic uncertainties on the predictions are illustrated, and a more detailed covariance matrix is included in the Constrained Energy Distributions Covariance Matrix tab. This corresponds to Fig. 2 of the paper.

Constrained covariance matrix showing constrained uncertainties and correlations between bins due to flux uncertainties, cross-section uncertainties, hadron reinteraction uncertainties, detector systematic uncertainties, Monte-Carlo statistical uncertainties, and dirt (outside cryostat) uncertainties. Pearson data statistical uncertainties have been included, and include small correlations due to events which can be selected by both WC and Pandora. The first seven bins are the WC $1\gamma Np$ reconstructed shower energy from 0-600 MeV with an overflow bin, the next 15 bins are the WC $1\gamma 0p$ reconstructed shower energy from 0-700 MeV with an overflow bin, the next seven bins are the Pandora $1\gamma 1p$ reconstructed shower energy from 0-600 MeV with an overflow bin, and the last 15 bins are the Pandora $1\gamma 0p$ reconstructed shower energy from 0-700 MeV with an overflow bin. This corresponds to Fig. 2 of the paper.

2D efficiency matrix showing the efficiency of the WC $1\gamma Np$ selection with respect to all true NC Delta Radiative Decay events which interact in the fiducial volume. The efficiency is shown as a function of true photon energy and angle. There are 10 bins from -1 to 1 in true photon $\cos \theta$ and 15 bins from 0 to 1500 MeV in true photon energy. NaN values indicate a "divide by zero" case where zero events were present in the bin before any selection was applied. This corresponds to Fig. 9 of the Supplemental Material.

2D efficiency matrix showing the efficiency of the WC $1\gamma 0p$ selection with respect to all true NC Delta Radiative Decay events which interact in the fiducial volume. The efficiency is shown as a function of true photon energy and angle. There are 10 bins from -1 to 1 in true photon $\cos \theta$ and 30 bins from 0 to 1500 MeV in true photon energy. NaN values indicate a "divide by zero" case where zero events were present in the bin before any selection was applied. This corresponds to Fig. 9 of the Supplemental Material.

2D efficiency matrix showing the efficiency of the Pandora $1\gamma 1p$ selection with respect to all true NC Delta Radiative Decay events which interact in the fiducial volume. The efficiency is shown as a function of true photon energy and angle. There are 10 bins from -1 to 1 in true photon $\cos \theta$ and 15 bins from 0 to 1500 MeV in true photon energy, with lower bin edges indicated in the table. NaN values indicate a "divide by zero" case where zero events were present in the bin before any selection was applied. This corresponds to Fig. 9 of the Supplemental Material.

2D efficiency matrix showing the efficiency of the Pandora $1\gamma 0p$ selection with respect to all true NC Delta Radiative Decay events which interact in the fiducial volume. The efficiency is shown as a function of true photon energy and angle. There are 10 bins from -1 to 1 in true photon $\cos \theta$ and 30 bins from 0 to 1500 MeV in true photon energy, with lower bin edges indicated in the table. NaN values indicate a "divide by zero" case where zero events were present in the bin before any selection was applied. This corresponds to Fig. 9 of the Supplemental Material.

2D efficiency matrix showing the efficiency of the WC $1\gamma 0p$ selection with respect to all true zero-primary-final-state-proton NC Delta Radiative Decay events which interact in the fiducial volume. The efficiency is shown as a function of true photon energy and angle. There are 10 bins from -1 to 1 in true photon $\cos \theta$ and 30 bins from 0 to 1500 MeV in true photon energy, with lower bin edges indicated in the table. NaN values indicate a "divide by zero" case where zero events were present in the bin before any selection was applied.

2D efficiency matrix showing the efficiency of the Pandora $1\gamma 0p$ selection with respect to all true zero-primary-final-state-proton NC Delta Radiative Decay events which interact in the fiducial volume. The efficiency is shown as a function of true photon energy and angle. There are 10 bins from -1 to 1 in true photon $\cos \theta$ and 30 bins from 0 to 1500 MeV in true photon energy, with lower bin edges indicated in the table. NaN values indicate a "divide by zero" case where zero events were present in the bin before any selection was applied.

$a_2(1320)$ differential cross section in the m=-2 projection split into different reflectivity components, $\frac{d\sigma^+_{-2}}{dt}$ and $\frac{d\sigma^-_{-2}}{dt}$, in bins of four-momentum transfer. The first uncertainty is statistical, the second systematic.

$a_2(1320)$ differential cross section in the m=0 projection split into different reflectivity components, $\frac{d\sigma^+_{0}}{dt}$ and $\frac{d\sigma^-_{0}}{dt}$, in bins of four-momentum transfer. The first uncertainty is statistical, the second systematic.

$a_2(1320)$ differential cross section in the m=+1 projection split into different reflectivity components, $\frac{d\sigma^+_{+1}}{dt}$ and $\frac{d\sigma^-_{+1}}{dt}$, in bins of four-momentum transfer. The first uncertainty is statistical, the second systematic.

$a_2(1320)$ differential cross section in the m=+2 projection split into different reflectivity components, $\frac{d\sigma^+_{+2}}{dt}$ and $\frac{d\sigma^-_{+2}}{dt}$, in bins of four-momentum transfer. The first uncertainty is statistical, the second systematic.

Observed and expected 95 % CL exclusion limits on $\tan\beta$ as a function of $m_{H^{\pm}}$, shown in the context of the mh125 scenario, for $m_{H^{\pm}}>150$ GeV and $(1 \leq \tan\beta \leq 60)$. The surrounding shaded bands correspond to the 1$\sigma$ and 2$\sigma$ confidence intervals around the expected limit.

Observed and expected 95 % CL exclusions on $\tan\beta$ as a function of $m_{H^{\pm}}$ derived from exclusion limits on $\mathrm{\cal{B}}(t\to bH^+)\times \mathrm{\cal{B}}(H^+ \to \tau \nu)$, for Type I 2HDM low mass scenario. The surrounding shaded bands correspond to the 1$\sigma$ and 2$\sigma$ confidence intervals around the expected limit.

Observed and expected 95 % CL exclusions on $\tan\beta$ as a function of $m_{H^{\pm}}$ derived from exclusion limits on $\mathrm{\cal{B}}(t\to bH^+)\times \mathrm{\cal{B}}(H^+ \to \tau \nu)$, for Lepton Specific 2HDM low mass scenario. The surrounding shaded bands correspond to the 1$\sigma$ and 2$\sigma$ confidence intervals around the expected limit.

The measured differential cross-sections and the predictions from the GM-VFNS calculation for the $D_s^\pm$ meson in bins of $p_T$ for $|\eta| < 2.5$. The statistical, systematic (excluding branching ratio) and branching ratio uncertainties are shown separately for data, while the total theory uncertainties are shown for GM-VFNS.

Inclusive $D^\pm$ meson production cross-sections in different fiducial volumes defined by $|\eta|<2.5$ and different $p_T$ regions. For the ATLAS measurements, the statistical, systematic (excluding branching ratio) and branching ratio uncertainties are shown separately; for the theoretical predictions, the total theoretical uncertainties are shown.

Inclusive $D_s^\pm$ meson production cross-sections in different fiducial volumes defined by $|\eta|<2.5$ and different $p_T$ regions. For the ATLAS measurements, the statistical, systematic (excluding branching ratio) and branching ratio uncertainties are shown separately; for the theoretical predictions, the total theoretical uncertainties are shown.

The distribution of the $p_\mathrm{T}{}_{\mu\mathrm{-had}}^\mathrm{col}$ in the VR. `$Z(\rightarrow\tau\tau)+\text{jets}$' represents the contributions from the signal process. `Diboson' indicates the contributions from $WW$, $WZ$, and $ZZ$ processes. `Top' represents the predicted contributions from the $t\bar{t}$, single-top-quark, and $tW$ processes. `Other' includes the contributions from the $Z(\rightarrow\ell\ell)$+jets, $W$+jets, and Higgs boson processes. The uncertainties shown include both statistical and systematic sources.

The distributions of $m_{\mu\mathrm{-had}}^\mathrm{col}$ corresponding to the SR selection criteria defined in the text. `$Z(\rightarrow\tau\tau)+\text{jets}$' represents the contributions from the signal process. `Diboson' indicates the contributions from $WW$, $WZ$, and $ZZ$ processes. `Top' represents the predicted contributions from the $t\bar{t}$, single-top-quark, and $tW$ processes. `Other' includes the contributions from the $Z(\rightarrow\ell\ell)$+jets, $W$+jets, and Higgs boson processes. The uncertainties shown include both statistical and systematic sources.

The distributions of $m_{\mu\mathrm{-had}}^\mathrm{col}$ corresponding to the SR_\text{std} selection criteria defined in the text. `$Z(\rightarrow\tau\tau)+\text{jets}$' represents the contributions from the signal process. `Diboson' indicates the contributions from $WW$, $WZ$, and $ZZ$ processes. `Top' represents the predicted contributions from the $t\bar{t}$, single-top-quark, and $tW$ processes. `Other' includes the contributions from the $Z(\rightarrow\ell\ell)$+jets, $W$+jets, and Higgs boson processes. The uncertainties shown include both statistical and systematic sources.

The distributions of $m_{\mu\mathrm{-had}}^\mathrm{col}$ corresponding to the SR_\text{tight} selection criteria defined in the text. `$Z(\rightarrow\tau\tau)+\text{jets}$' represents the contributions from the signal process. `Diboson' indicates the contributions from $WW$, $WZ$, and $ZZ$ processes. `Top' represents the predicted contributions from the $t\bar{t}$, single-top-quark, and $tW$ processes. `Other' includes the contributions from the $Z(\rightarrow\ell\ell)$+jets, $W$+jets, and Higgs boson processes. The uncertainties shown include both statistical and systematic sources.

The distributions of $m_{\mu\mathrm{-had}}^\mathrm{col}$ corresponding to the SR_\text{tight}^\text{std} selection criteria defined in the text. `$Z(\rightarrow\tau\tau)+\text{jets}$' represents the contributions from the signal process. `Diboson' indicates the contributions from $WW$, $WZ$, and $ZZ$ processes. `Top' represents the predicted contributions from the $t\bar{t}$, single-top-quark, and $tW$ processes. `Other' includes the contributions from the $Z(\rightarrow\ell\ell)$+jets, $W$+jets, and Higgs boson processes. The uncertainties shown include both statistical and systematic sources.

The distribution of $\Delta\phi^\mathrm{signed}_{\mu-MET}$ with all other event selection criteria applied in the SR; the straight lines indicate the positions of the selection requirements. `$Z(\rightarrow\tau\tau)+\text{jets}$' represents the contributions from the signal process. `Diboson' indicates the contributions from $WW$, $WZ$, and $ZZ$ processes. `Top' represents the predicted contributions from the $t\bar{t}$, single-top, and $tW$ processes. `Other' includes the contributions from the $Z(\rightarrow\ell\ell)$+jets, $W$+jets, and Higgs boson processes. The uncertainties shown include both statistical and systematic errors.

The distribution of $\Delta\phi^\mathrm{signed}_{\mu-MET}$ with all other event selection criteria applied in the VR; the straight lines indicate the positions of the selection requirements. `$Z(\rightarrow\tau\tau)+\text{jets}$' represents the contributions from the signal process. `Diboson' indicates the contributions from $WW$, $WZ$, and $ZZ$ processes. `Top' represents the predicted contributions from the $t\bar{t}$, single-top, and $tW$ processes. `Other' includes the contributions from the $Z(\rightarrow\ell\ell)$+jets, $W$+jets, and Higgs boson processes. The uncertainties shown include both statistical and systematic errors.

The distribution of the $m_{\mu\mathrm{-had}}^\mathrm{col}$ in the SR. `$Z(\rightarrow\tau\tau)+\text{jets}$' represents the contributions from the signal process. `Diboson' indicates the contributions from $WW$, $WZ$, and $ZZ$ processes. `Top' represents the predicted contributions from the $t\bar{t}$, single-top, and $tW$ processes. `Other' includes the contributions from the $Z(\rightarrow\ell\ell)$+jets, $W$+jets, and Higgs boson processes. The uncertainties shown include both statistical and systematic errors.

The distribution of the $m_{\mu\mathrm{-had}}^\mathrm{col}$ in the VR. `$Z(\rightarrow\tau\tau)+\text{jets}$' represents the contributions from the signal process. `Diboson' indicates the contributions from $WW$, $WZ$, and $ZZ$ processes. `Top' represents the predicted contributions from the $t\bar{t}$, single-top, and $tW$ processes. `Other' includes the contributions from the $Z(\rightarrow\ell\ell)$+jets, $W$+jets, and Higgs boson processes. The uncertainties shown include both statistical and systematic errors.

The distribution of the $p_\mathrm{T}$ of the $\tau_\mathrm{had}^{\mu\mkern-10mu\backslash}$ in the SR. `$Z(\rightarrow\tau\tau)+\text{jets}$' represents the contributions from the signal process. `Diboson' indicates the contributions from $WW$, $WZ$, and $ZZ$ processes. `Top' represents the predicted contributions from the $t\bar{t}$, single-top, and $tW$ processes. `Other' includes the contributions from the $Z(\rightarrow\ell\ell)$+jets, $W$+jets, and Higgs boson processes. The uncertainties shown include both statistical and systematic errors.

The distribution of the $p_\mathrm{T}$ of the $\tau_\mathrm{had}^{\mu\mkern-10mu\backslash}$ in the VR. `$Z(\rightarrow\tau\tau)+\text{jets}$' represents the contributions from the signal process. `Diboson' indicates the contributions from $WW$, $WZ$, and $ZZ$ processes. `Top' represents the predicted contributions from the $t\bar{t}$, single-top, and $tW$ processes. `Other' includes the contributions from the $Z(\rightarrow\ell\ell)$+jets, $W$+jets, and Higgs boson processes. The uncertainties shown include both statistical and systematic errors.

The distribution of the $p_\mathrm{T}$ of the muon removed from the $\tau_\mathrm{had}^{\mu\mkern-10mu\backslash}$ in the SR `$Z(\rightarrow\tau\tau)+\text{jets}$' represents the contributions from the signal process. `Diboson' indicates the contributions from $WW$, $WZ$, and $ZZ$ processes. `Top' represents the predicted contributions from the $t\bar{t}$, single-top, and $tW$ processes. `Other' includes the contributions from the $Z(\rightarrow\ell\ell)$+jets, $W$+jets, and Higgs boson processes. The uncertainties shown include both statistical and systematic errors.

The distribution of the $p_\mathrm{T}$ of the muon removed from the $\tau_\mathrm{had}^{\mu\mkern-10mu\backslash}$ in the VR `$Z(\rightarrow\tau\tau)+\text{jets}$' represents the contributions from the signal process. `Diboson' indicates the contributions from $WW$, $WZ$, and $ZZ$ processes. `Top' represents the predicted contributions from the $t\bar{t}$, single-top, and $tW$ processes. `Other' includes the contributions from the $Z(\rightarrow\ell\ell)$+jets, $W$+jets, and Higgs boson processes. The uncertainties shown include both statistical and systematic errors.

The distribution of the $p_\mathrm{T}$ of the leading jet in the SR. `$Z(\rightarrow\tau\tau)+\text{jets}$' represents the contributions from the signal process. `Diboson' indicates the contributions from $WW$, $WZ$, and $ZZ$ processes. `Top' represents the predicted contributions from the $t\bar{t}$, single-top, and $tW$ processes. `Other' includes the contributions from the $Z(\rightarrow\ell\ell)$+jets, $W$+jets, and Higgs boson processes. The uncertainties shown include both statistical and systematic errors.

The distribution of the $p_\mathrm{T}$ of the leading jet in the VR. `$Z(\rightarrow\tau\tau)+\text{jets}$' represents the contributions from the signal process. `Diboson' indicates the contributions from $WW$, $WZ$, and $ZZ$ processes. `Top' represents the predicted contributions from the $t\bar{t}$, single-top, and $tW$ processes. `Other' includes the contributions from the $Z(\rightarrow\ell\ell)$+jets, $W$+jets, and Higgs boson processes. The uncertainties shown include both statistical and systematic errors.

The distribution of the $\Delta{R}_{\tau\tau}^\mathrm{reco}$ between the muon and the $\tau_\mathrm{had}^{\mu\mkern-10mu\backslash}$ in the SR `$Z(\rightarrow\tau\tau)+\text{jets}$' represents the contributions from the signal process. `Diboson' indicates the contributions from $WW$, $WZ$, and $ZZ$ processes. `Top' represents the predicted contributions from the $t\bar{t}$, single-top, and $tW$ processes. `Other' includes the contributions from the $Z(\rightarrow\ell\ell)$+jets, $W$+jets, and Higgs boson processes. The uncertainties shown include both statistical and systematic errors.

The distribution of the $\Delta{R}_{\tau\tau}^\mathrm{reco}$ between the muon and the $\tau_\mathrm{had}^{\mu\mkern-10mu\backslash}$ in the VR `$Z(\rightarrow\tau\tau)+\text{jets}$' represents the contributions from the signal process. `Diboson' indicates the contributions from $WW$, $WZ$, and $ZZ$ processes. `Top' represents the predicted contributions from the $t\bar{t}$, single-top, and $tW$ processes. `Other' includes the contributions from the $Z(\rightarrow\ell\ell)$+jets, $W$+jets, and Higgs boson processes. The uncertainties shown include both statistical and systematic errors.

The distribution of the reconstructed $E_\mathrm{T}^\mathrm{miss}$ in the SR `$Z(\rightarrow\tau\tau)+\text{jets}$' represents the contributions from the signal process. `Diboson' indicates the contributions from $WW$, $WZ$, and $ZZ$ processes. `Top' represents the predicted contributions from the $t\bar{t}$, single-top, and $tW$ processes. `Other' includes the contributions from the $Z(\rightarrow\ell\ell)$+jets, $W$+jets, and Higgs boson processes. The uncertainties shown include both statistical and systematic errors.

The distribution of the reconstructed $E_\mathrm{T}^\mathrm{miss}$ in the VR `$Z(\rightarrow\tau\tau)+\text{jets}$' represents the contributions from the signal process. `Diboson' indicates the contributions from $WW$, $WZ$, and $ZZ$ processes. `Top' represents the predicted contributions from the $t\bar{t}$, single-top, and $tW$ processes. `Other' includes the contributions from the $Z(\rightarrow\ell\ell)$+jets, $W$+jets, and Higgs boson processes. The uncertainties shown include both statistical and systematic errors.

The observed and expected ($\pm2\sigma$) upper limits at 95% CL on the branching ratio for $H\rightarrow aa\rightarrow \gamma\gamma\tau\tau$ as a function of the resonance mass hypothesis $m_{a}$.

The polynomial parameterisation of the total signal selection efficiency as a function of $m_{a}$, defined as the fraction of the reconstructed and selected events out of the total number of events in the signal simulated samples.