Dependence of the parameter $A$ on $(t_1, t_2)$.

Dependence of the parameter $R$ on $(t_1, t_2)$.

Dependence of the parameter $c$ on $(t_1, t_2)$.

Dependence of the parameter $R$ on the two scattered proton transverse momenta.

Correlation coefficients among values of best parameters for the two-channel model, in the case of the exponential parametrisation of the proton-pomeron form factor.

Correlation coefficients among values of best parameters for the two-channel model, in the case of the Orear-type parametrisation of the proton-pomeron form factor.

Correlation coefficients among values of best parameters for the two-channel model, in the case of the power-law parametrisation of the proton-pomeron form factor.

The ratios between the hydrodynamic probes and their Taylor expansions. The ratios are plotted as functions of centrality in PbPb collisions at $\sqrt{s_{NN}}=5.02~\textrm{Te}\textrm{V}$. The measurement is performed with charged particles within the acceptance region.

The ratios between the hydrodynamic probes and their Taylor expansions. The ratios are plotted as functions of centrality in PbPb collisions at $\sqrt{s_{NN}}=5.02~\textrm{Te}\textrm{V}$. The measurement is performed with charged particles within the acceptance region.

The magnitudes of the measured skewness $\gamma_1^\textrm{exp}$ and "corrected" skewness $\gamma_{1,\textrm{corr}}^\textrm{exp}$ as functions of centrality in PbPb collisions at $\sqrt{s_{NN}}=5.02~\textrm{Te}\textrm{V}$. The measurement is performed with charged particles within the acceptance region.

The magnitudes of the measured kurtosis $\gamma_2^\textrm{exp}$ and "corrected" kurtosis $\gamma_{2,\textrm{corr}}^\textrm{exp}$ as functions of centrality in PbPb collisions at $\sqrt{s_{NN}}=5.02~\textrm{Te}\textrm{V}$. The measurement is performed with charged particles within the acceptance region.

The magnitudes of the measured superskewness $\gamma_3^\textrm{exp}$ and "corrected" superskewness $\gamma_{3,\textrm{corr}}^\textrm{exp}$ as functions of centrality in PbPb collisions at $\sqrt{s_{NN}}=5.02~\textrm{Te}\textrm{V}$. The measurement is performed with charged particles within the acceptance region.

Transverse dilepton-$p_{T}^{miss}$ mass pre-fit distribution for selected events in SR2 of the di-leptonic channel for the full dataset. The error bars on the data points represent the statistical uncertainty of the data, and the error bars on the predicted yields represent the combined systematic and statistical uncertainty in each bin. The signal prediction represents the mass point: $m_s = 160 GeV, m_{\chi} = 100 GeV, m_{Z'} = 500 GeV$. The last bin includes the overflow.

Dilepton mass pre-fit distribution for selected events in SR3 of the di-leptonic channel for the full dataset. The error bars on the data points represent the statistical uncertainty of the data, and the error bars on the predicted yields represent the combined systematic and statistical uncertainty in each bin. The signal prediction represents the mass point: $m_s = 160 GeV, m_{\chi} = 100 GeV, m_{Z'} = 500 GeV$. The last bin includes the overflow.

Dilepton $p_T$ pre-fit distribution for selected events in SR3 of the di-leptonic channel for the full dataset. The error bars on the data points represent the statistical uncertainty of the data, and the error bars on the predicted yields represent the combined systematic and statistical uncertainty in each bin. The signal prediction represents the mass point: $m_s = 160 GeV, m_{\chi} = 100 GeV, m_{Z'} = 500 GeV$. The last bin includes the overflow.

Dijet $p_T$ pre-fit distribution for selected events in the semi-leptonic channel for the full dataset. The error bars on the data points represent the statistical uncertainty of the data, and the error bars on the predicted yields represent the combined systematic and statistical uncertainty in each bin. The signal prediction represents the mass point: $m_s = 160 GeV, m_{\chi} = 100 GeV, m_{Z'} = 500 GeV$. The last bin includes the overflow.

Lepton-dijet $p_T$ pre-fit distribution for selected events in the semi-leptonic channel for the full dataset. The error bars on the data points represent the statistical uncertainty of the data, and the error bars on the predicted yields represent the combined systematic and statistical uncertainty in each bin. The signal prediction represents the mass point: $m_s = 160 GeV, m_{\chi} = 100 GeV, m_{Z'} = 500 GeV$. The last bin includes the overflow.

Maximum $p_T$ of the visible particles divided by the missing $p_T$, for selected events in the semi-leptonic channel for the full dataset. The error bars on the data points represent the statistical uncertainty of the data, and the error bars on the predicted yields represent the combined systematic and statistical uncertainty in each bin. The signal prediction represents the mass point: $m_s = 160 GeV, m_{\chi} = 100 GeV, m_{Z'} = 500 GeV$. The last bin includes the overflow.

Pre-fit distribution of the $\Delta \phi$ angle between jets, for selected events in the semi-leptonic channel for the full dataset. The error bars on the data points represent the statistical uncertainty of the data, and the error bars on the predicted yields represent the combined systematic and statistical uncertainty in each bin. The signal prediction represents the mass point: $m_s = 160 GeV, m_{\chi} = 100 GeV, m_{Z'} = 500 GeV$. The last bin includes the overflow.

Pre-fit distribution of the $\Delta \phi$ angle between the lepton and missing $p_T$, for selected events in the semi-leptonic channel for the full dataset. The error bars on the data points represent the statistical uncertainty of the data, and the error bars on the predicted yields represent the combined systematic and statistical uncertainty in each bin. The signal prediction represents the mass point: $m_s = 160 GeV, m_{\chi} = 100 GeV, m_{Z'} = 500 GeV$. The last bin includes the overflow.

Pre-fit distribution of the $\Delta \phi$ angle between the lepton and the dijet system, for selected events in the semi-leptonic channel for the full dataset. The error bars on the data points represent the statistical uncertainty of the data, and the error bars on the predicted yields represent the combined systematic and statistical uncertainty in each bin. The signal prediction represents the mass point: $m_s = 160 GeV, m_{\chi} = 100 GeV, m_{Z'} = 500 GeV$. The last bin includes the overflow.

Pre-fit distribution of the $\Delta R$ distance between the leptons, for selected events in the non-prompt validation region of the di-leptonic channel for the full dataset. The error bars on the data points represent the statistical uncertainty of the data, and the error bars on the predicted yields represent the combined systematic and statistical uncertainty in each bin. The signal prediction represents the mass point: $m_s = 160 GeV, m_{\chi} = 100 GeV, m_{Z'} = 500 GeV$. The last bin includes the overflow.

Pre-fit distribution of the $\Delta \phi$ angle between the di-lepton system and the missing $p_T$, for selected events in the non-prompt validation region of the di-leptonic channel for the full dataset. The error bars on the data points represent the statistical uncertainty of the data, and the error bars on the predicted yields represent the combined systematic and statistical uncertainty in each bin. The signal prediction represents the mass point: $m_s = 160 GeV, m_{\chi} = 100 GeV, m_{Z'} = 500 GeV$. The last bin includes the overflow.

Pre-fit distribution of the $\Delta \phi$ angle between the lepton and the di-jet system, for selected events in the non-prompt validation region of the semi-leptonic channel for the full dataset. The error bars on the data points represent the statistical uncertainty of the data, and the error bars on the predicted yields represent the combined systematic and statistical uncertainty in each bin. The signal prediction represents the mass point: $m_s = 160 GeV, m_{\chi} = 100 GeV, m_{Z'} = 500 GeV$. The last bin includes the overflow.

Pre-fit distribution of the $\Delta \phi$ angle between the lepton-dijet system and the missing $p_T$, for selected events in the non-prompt validation region of the semi-leptonic channel for the full dataset. The error bars on the data points represent the statistical uncertainty of the data, and the error bars on the predicted yields represent the combined systematic and statistical uncertainty in each bin. The signal prediction represents the mass point: $m_s = 160 GeV, m_{\chi} = 100 GeV, m_{Z'} = 500 GeV$. The last bin includes the overflow.

Leading lepton $p_T$ pre-fit distribution for selected events in the top control region of the di-leptonic channel for the full dataset. The error bars on the data points represent the statistical uncertainty of the data, and the error bars on the predicted yields represent the combined systematic and statistical uncertainty in each bin. The signal prediction represents the mass point: $m_s = 160 GeV, m_{\chi} = 100 GeV, m_{Z'} = 500 GeV$. The last bin includes the overflow.

Trailing lepton $p_T$ pre-fit distribution for selected events in the top control region of the di-leptonic channel for the full dataset. The error bars on the data points represent the statistical uncertainty of the data, and the error bars on the predicted yields represent the combined systematic and statistical uncertainty in each bin. The signal prediction represents the mass point: $m_s = 160 GeV, m_{\chi} = 100 GeV, m_{Z'} = 500 GeV$. The last bin includes the overflow.

Dilepton mass pre-fit distribution for selected events in the Drell-Yan control region of the di-leptonic channel for the full dataset. The error bars on the data points represent the statistical uncertainty of the data, and the error bars on the predicted yields represent the combined systematic and statistical uncertainty in each bin. The signal prediction represents the mass point: $m_s = 160 GeV, m_{\chi} = 100 GeV, m_{Z'} = 500 GeV$. The last bin includes the overflow.

Missing $p_T$ pre-fit distribution for selected events in the Drell-Yan control region of the di-leptonic channel for the full dataset. The error bars on the data points represent the statistical uncertainty of the data, and the error bars on the predicted yields represent the combined systematic and statistical uncertainty in each bin. The signal prediction represents the mass point: $m_s = 160 GeV, m_{\chi} = 100 GeV, m_{Z'} = 500 GeV$. The last bin includes the overflow.

Missing $p_T$ pre-fit distribution for selected events in the $WW$ control region of the di-leptonic channel for the full dataset. The error bars on the data points represent the statistical uncertainty of the data, and the error bars on the predicted yields represent the combined systematic and statistical uncertainty in each bin. The signal prediction represents the mass point: $m_s = 160 GeV, m_{\chi} = 100 GeV, m_{Z'} = 500 GeV$. The last bin includes the overflow.

Dilepton $p_T$ pre-fit distribution for selected events in the $WW$ control region of the di-leptonic channel for the full dataset. The error bars on the data points represent the statistical uncertainty of the data, and the error bars on the predicted yields represent the combined systematic and statistical uncertainty in each bin. The signal prediction represents the mass point: $m_s = 160 GeV, m_{\chi} = 100 GeV, m_{Z'} = 500 GeV$. The last bin includes the overflow.

Minimum $p_T$ of the visible particles divided by the missing $p_T$, for selected events in the top control region of the semi-leptonic channel for the full dataset. The error bars on the data points represent the statistical uncertainty of the data, and the error bars on the predicted yields represent the combined systematic and statistical uncertainty in each bin. The signal prediction represents the mass point: $m_s = 160 GeV, m_{\chi} = 100 GeV, m_{Z'} = 500 GeV$. The last bin includes the overflow.

Pre-fit distribution of the $\Delta \phi$ angle between jets, for selected events in the top control region of the semi-leptonic channel for the full dataset. The error bars on the data points represent the statistical uncertainty of the data, and the error bars on the predicted yields represent the combined systematic and statistical uncertainty in each bin. The signal prediction represents the mass point: $m_s = 160 GeV, m_{\chi} = 100 GeV, m_{Z'} = 500 GeV$. The last bin includes the overflow.

Pre-fit distribution of the $\Delta \phi$ angle between the lepton and missing $p_T$, for selected events in the $W$+jets control region of the semi-leptonic channel for the full dataset. The error bars on the data points represent the statistical uncertainty of the data, and the error bars on the predicted yields represent the combined systematic and statistical uncertainty in each bin. The signal prediction represents the mass point: $m_s = 160 GeV, m_{\chi} = 100 GeV, m_{Z'} = 500 GeV$. The last bin includes the overflow.

Pre-fit distribution of the $\Delta \phi$ angle between the lepton and the dijet system, for selected events in the $W$+jets control region of the semi-leptonic channel for the full dataset. The error bars on the data points represent the statistical uncertainty of the data, and the error bars on the predicted yields represent the combined systematic and statistical uncertainty in each bin. The signal prediction represents the mass point: $m_s = 160 GeV, m_{\chi} = 100 GeV, m_{Z'} = 500 GeV$. The last bin includes the overflow.

Unrolled $m_{ll}-m_{T}^{l min, p_{T}^{miss}}$ post-fit distributions in the di-leptonic channel in SR1 for the full data set. The histogram bins are spaced uniformly. Each group of five bins (from left to right) corresponds to $m_{T}^{l min, p_{T}^{miss}}$ distribution in a $m_{ll}$ region, placed in ascending order. The signal prediction represents the mass point: $m_s = 160 GeV, m_{\chi} = 100 GeV, m_{Z'} = 500 GeV$.

Unrolled $m_{ll}-m_{T}^{l min, p_{T}^{miss}}$ post-fit distributions in the di-leptonic channel in SR2 for the full data set. The histogram bins are spaced uniformly. Each group of five bins (from left to right) corresponds to $m_{T}^{l min, p_{T}^{miss}}$ distribution in a $m_{ll}$ region, placed in ascending order. The signal prediction represents the mass point: $m_s = 160 GeV, m_{\chi} = 100 GeV, m_{Z'} = 500 GeV$.

Unrolled $m_{ll}-m_{T}^{l min, p_{T}^{miss}}$ post-fit distributions in the di-leptonic channel in SR3 for the full data set. The histogram bins are spaced uniformly. Each group of five bins (from left to right) corresponds to $m_{T}^{l min, p_{T}^{miss}}$ distribution in a $m_{ll}$ region, placed in ascending order. The signal prediction represents the mass point: $m_s = 160 GeV, m_{\chi} = 100 GeV, m_{Z'} = 500 GeV$.

Post-fit BDT distributions in the semi-leptonic channel for the full data set in the top control region. The signal prediction represents the mass point: $m_{s} = 160$ GeV, $m_{\chi} = 100$ GeV, $m_{Z'} = 500$ GeV

Post-fit BDT distributions in the semi-leptonic channel for the full data set in the $W$+jets control region. The signal prediction represents the mass point: $m_{s} = 160$ GeV, $m_{\chi} = 100$ GeV, $m_{Z'} = 500$ GeV

Post-fit BDT distributions in the semi-leptonic channel in the 2016 signal region. The signal prediction represents the mass point: $m_{s} = 160$ GeV, $m_{\chi} = 100$ GeV, $m_{Z'} = 500$ GeV

Post-fit BDT distributions in the semi-leptonic channel in the 2017+2018 signal region. The signal prediction represents the mass point: $m_{s} = 160$ GeV, $m_{\chi} = 100$ GeV, $m_{Z'} = 500$ GeV

Contour of the 95% CL observed upper limits representing $\sigma / \sigma_{theory} = 1$ for the dark Higgs model in the ($m_{s}$, $m_{Z'}$) plane for $m_{\chi} = 100 GeV$.

Contour of the 95% CL expected + 2 std. upper limits representing $\sigma / \sigma_{theory} = 1$ for the dark Higgs model in the ($m_{s}$, $m_{Z'}$) plane for $m_{\chi} = 100 GeV$.

Contour of the 95% CL expected + 1 std. upper limits representing $\sigma / \sigma_{theory} = 1$ for the dark Higgs model in the ($m_{s}$, $m_{Z'}$) plane for $m_{\chi} = 100 GeV$.

Contour of the 95% CL expected upper limits representing $\sigma / \sigma_{theory} = 1$ for the dark Higgs model in the ($m_{s}$, $m_{Z'}$) plane for $m_{\chi} = 100 GeV$.

Contour of the 95% CL expected - 1 std. upper limits representing $\sigma / \sigma_{theory} = 1$ for the dark Higgs model in the ($m_{s}$, $m_{Z'}$) plane for $m_{\chi} = 100 GeV$.

Contour of the 95% CL expected - 2 std. upper limits representing $\sigma / \sigma_{theory} = 1$ for the dark Higgs model in the ($m_{s}$, $m_{Z'}$) plane for $m_{\chi} = 100 GeV$.

Contour of the 95% CL observed upper limits representing $\sigma / \sigma_{theory} = 1$ for the dark Higgs model in the ($m_{s}$, $m_{Z'}$) plane for $m_{\chi} = 150 GeV$.

Contour of the 95% CL expected + 2 std. upper limits representing $\sigma / \sigma_{theory} = 1$ for the dark Higgs model in the ($m_{s}$, $m_{Z'}$) plane for $m_{\chi} = 150 GeV$.

Contour of the 95% CL expected + 1 std. upper limits representing $\sigma / \sigma_{theory} = 1$ for the dark Higgs model in the ($m_{s}$, $m_{Z'}$) plane for $m_{\chi} = 150 GeV$.

Contour of the 95% CL expected upper limits representing $\sigma / \sigma_{theory} = 1$ for the dark Higgs model in the ($m_{s}$, $m_{Z'}$) plane for $m_{\chi} = 150 GeV$.

Contour of the 95% CL expected - 1 std. upper limits representing $\sigma / \sigma_{theory} = 1$ for the dark Higgs model in the ($m_{s}$, $m_{Z'}$) plane for $m_{\chi} = 150 GeV$.

Contour of the 95% CL expected - 2 std. upper limits representing $\sigma / \sigma_{theory} = 1$ for the dark Higgs model in the ($m_{s}$, $m_{Z'}$) plane for $m_{\chi} = 150 GeV$.

Contour of the 95% CL observed upper limits representing $\sigma / \sigma_{theory} = 1$ for the dark Higgs model in the ($m_{s}$, $m_{Z'}$) plane for $m_{\chi} = 200 GeV$.

Contour of the 95% CL expected + 2 std. upper limits representing $\sigma / \sigma_{theory} = 1$ for the dark Higgs model in the ($m_{s}$, $m_{Z'}$) plane for $m_{\chi} = 200 GeV$.

Contour of the 95% CL expected + 1 std. upper limits representing $\sigma / \sigma_{theory} = 1$ for the dark Higgs model in the ($m_{s}$, $m_{Z'}$) plane for $m_{\chi} = 200 GeV$.

Contour of the 95% CL expected upper limits representing $\sigma / \sigma_{theory} = 1$ for the dark Higgs model in the ($m_{s}$, $m_{Z'}$) plane for $m_{\chi} = 200 GeV$.

Contour of the 95% CL expected - 1 std. upper limits representing $\sigma / \sigma_{theory} = 1$ for the dark Higgs model in the ($m_{s}$, $m_{Z'}$) plane for $m_{\chi} = 200 GeV$.

Contour of the 95% CL expected - 2 std. upper limits representing $\sigma / \sigma_{theory} = 1$ for the dark Higgs model in the ($m_{s}$, $m_{Z'}$) plane for $m_{\chi} = 200 GeV$.

Contour of the 95% CL observed upper limits representing $\sigma / \sigma_{theory} = 1$ for the dark Higgs model in the ($m_{s}$, $m_{Z'}$) plane for $m_{\chi} = 300 GeV$.

Contour of the 95% CL expected + 2 std. upper limits representing $\sigma / \sigma_{theory} = 1$ for the dark Higgs model in the ($m_{s}$, $m_{Z'}$) plane for $m_{\chi} = 300 GeV$.

Contour of the 95% CL expected + 1 std. upper limits representing $\sigma / \sigma_{theory} = 1$ for the dark Higgs model in the ($m_{s}$, $m_{Z'}$) plane for $m_{\chi} = 300 GeV$.

Contour of the 95% CL expected upper limits representing $\sigma / \sigma_{theory} = 1$ for the dark Higgs model in the ($m_{s}$, $m_{Z'}$) plane for $m_{\chi} = 300 GeV$.

Contour of the 95% CL expected - 1 std. upper limits representing $\sigma / \sigma_{theory} = 1$ for the dark Higgs model in the ($m_{s}$, $m_{Z'}$) plane for $m_{\chi} = 300 GeV$.

Contour of the 95% CL expected - 2 std. upper limits representing $\sigma / \sigma_{theory} = 1$ for the dark Higgs model in the ($m_{s}$, $m_{Z'}$) plane for $m_{\chi} = 300 GeV$.

The $\sigma / \sigma_{theory}$ 95% CL upper limit values for the dark Higgs model in the ($m_{s}$, $m_{Z'}$) plane for $m_{\chi} = 100 GeV$.

The $\sigma / \sigma_{theory}$ 95% CL upper limit values for the dark Higgs model in the ($m_{s}$, $m_{Z'}$) plane for $m_{\chi} = 150 GeV$.

The $\sigma / \sigma_{theory}$ 95% CL upper limit values for the dark Higgs model in the ($m_{s}$, $m_{Z'}$) plane for $m_{\chi} = 200 GeV$.

The $\sigma / \sigma_{theory}$ 95% CL upper limit values for the dark Higgs model in the ($m_{s}$, $m_{Z'}$) plane for $m_{\chi} = 300 GeV$.

Observed upper limits at 90% CL on the square of the kinetic mixing coefficient $\epsilon$ in the minimal model of a dark photon

Observed upper limits at 90% CL on the mixing angle $\theta_H$ for the type IV 2HDM+S scenario with fixed $tan\beta=0.5$

The combined efficiency of the dimuon scouting trigger and the MVA muon selection, averaged between 2017 and 2018, weighted by the integrated luminosity of each year. The trigger and selection efficiencies are also included in the table.

Theory cross-section times branching fraction to muons times acceptance for the dark photon and 2HDM+S models.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Bayesian upper exclusion limits on the ratio $g_{W'}/g_{W}$ for an SSM-like W$\prime$ boson are shown. The unity coupling ratio (blue dotted curve) corresponds to the SSM common benchmark. The 68 and 95% quantiles of the limits are represented by the green and yellow bands, respectively.

Bayesian lower exclusion limits on the NUGIM G(221) mixing angle $\cot(\theta_{E})$ are shown as a function of the W$\prime$ boson mass. The theoretically excluded region is shaded in grey. The 68 and 95% quantiles of the limits are represented by the green and yellow bands, respectively.

Bayesian upper exclusion limits at 95% CL on the product of the production cross section and branching fraction of a QBH in an associated $ au$ lepton and neutrino final state. Minimum threshold masses $m_{th}$ of up to 6.6 TeV are excluded at 95% CL. The observed limit (solid line) is obtained from the intersection with the LO QBH cross section (blue dotted curve). The 68 and 95% quantiles of the limits are represented by the green and yellow bands, respectively.

Bayesian upper limits at 95% CL on the cross section of the process $pp\rightarrow\tau\nu$ mediated via LQ exchange in the t-channel. The inner (green) band and the outer (yellow) band indicate the regions containing 68 and 95%, respectively, of the distribution of limits expected under the background-only hypothesis. The predicted LQ cross section at LO in the three coupling benchmark scenarios is depicted in different colors for $g_{U}=1$. The uncertainty bandy correspond to the sum in quadrature of PDF and scale variations. The first benchmark scenario considers only couplings to left-handed SM fermions (i.e. $\beta_{\text{R}}^{ij}=0$) and is referred to as "best fit LH". The second benchmark, referred to as "best fit LH+RH", considers $|\beta_{\text{R}}^{\text{b}\tau}|=1$ and all other $\beta_{\text{R}}^{ij}=0$. In the third "democratic" benchmark, equal couplings only to LH fermions are assumed, i.e. $\beta_{\text{L}}^{ij}=1$ and $\beta_{\text{R}}^{ij}=0$ for all $i$ and $j$.

Expected and observed lower limits of the LQ mass as a function of the coupling $g_{U}$ in the LH scenario. The blue band shows the 68% and 95% regions of $g_{U}$ preferred by the fit to the b anomalies data.

Expected and observed lower limits of the LQ mass as a function of the coupling $g_{U}$ in the LH+RH scenario. The blue band shows the 68% and 95% regions of $g_{U}$ preferred by the fit to the b anomalies data.

Expected and observed lower limits of the LQ mass as a function of the coupling $g_{U}$ in the democratic scenario. The blue band shows the 68% and 95% regions of $g_{U}$ preferred by the fit to the b anomalies data.

Bayesian upper exclusion limits at 95% CL on each of the Wilson coefficients described by the EFT model based on 2016-2018 data. The three different coupling types represent a left-handed vector coupling ($\epsilon^{cb}_{L}$), tensor-like coupling ($\epsilon^{cb}_{T}$), and scalar-tensor-like coupling ($\epsilon^{cb}_{S_{L}}$). The 68 and 95% quantiles of the limits are represented by the green and yellow bands, respectively.

Summary of exclusion limits (expected and observed) calculated at 95% CL for full Run-2 CMS data.

Background prediction and observed data yields in the signal region bins. The background yields are obtained from the background-only fit and serve as input to the simplified likelihood reinterpretation scheme. The naming of the bins is "year_binnumber", following the binning from Figure 4.

Matrix of covariance coefficients between signal region bins. The coefficients are obtained from the background-only fit and serve as input to the simplified likelihood reinterpretation scheme. The naming of the bins is "year_binnumber", following the binning used in Figure 4.

Predicted signal yields for the 2017 data-taking period, corresponding to 41.3 fb$^{-1}$, after the application of each search requirement (cumulative) for various signal hypothesis. The requirements listed are presented as total efficiencies w.r.t. the previous selection step.

Expected and observed upper limits on the AQGC operators $a^Z_C/\Lambda^2$, with no unitarization. The $y$ axis shows the limit on the ratio of the observed cross section to the cross section predicted for each anomalous coupling value ($\sigma_\mathrm{AQGC}$).

Limits on LEP-like dimension-6 anomalous quartic gauge coupling parameters, with and without unitarization via a clipping procedure.

Conversion of limits on $a^W_0$ to dimension-8 $f_{M,i}$ operators, using the assumption of vanishing $WWZ\gamma$ couplings to eliminate some parameters. When quoting limits on one of the operators, the other is fixed to zero. The results for $|f_{M,0}/\Lambda^{4}|$ and $|f_{M,4}/\Lambda^{4}|$ are shown with and without clipping of the signal model at 1.4 TeV, when the other parameter is fixed to the SM value of zero.

Conversion of limits on $a^W_0$ and $a^W_C$ to dimension-8 $f_{M,i}$ operators, using the assumption that all $f_{M,i}$ except one are equal to zero. The results are shown with and without clipping of the signal model at 1.4 TeV.

{Expected and observed limits in the two-dimensional plane of $a^W_0/\Lambda^2$ vs. $a^W_C/\Lambda^2$. The limits are described by analytical ellipses of equation $(x-x0)^2/a^2 + (y-y0)^2/b^2 = 1$ and rotated counter-clockwise by $\theta$ degrees, where $x$ and $y$ in the equation correspond to the $a_0^W$ and $a_C^W$ couplings, respectively.

{Expected and observed limits in the two-dimensional plane of $a^W_0/\Lambda^2$ vs. $a^W_C/\Lambda^2$ with unitarization imposed by clipping the signal model at 1.4 TeV. The limits are described by analytical ellipses of equation $(x-x0)^2/a^2 + (y-y0)^2/b^2 = 1$ and rotated counter-clockwise by $\theta$ degrees, where $x$ and $y$ in the equation correspond to the $a_0^W$ and $a_C^W$ couplings, respectively.

{Expected and observed limits in the two-dimensional plane of $a^Z_0/\Lambda^2$ vs. $a^Z_C/\Lambda^2$. The limits are described by analytical ellipses of equation $(x-x0)^2/a^2 + (y-y0)^2/b^2 = 1$ and rotated counter-clockwise by $\theta$ degrees, where $x$ and $y$ in the equation correspond to the $a_0^Z$ and $a_C^Z$ couplings, respectively.

Upper limits on the production cross section times branching fraction of the b* RH hypothesis at a 95% CL. Dashed colored lines show the expected limits from the l+jets and all-hadronic channels, where the latter start at resonance masses of 1.4 TeV. The observed and expected limits from the combination are shown as solid and dashed black lines, respectively. The green and yellow bands show the 68 and 95% confidence intervals on the combined expected limits.

Upper limits on the production cross section times branching fraction of the b* VL hypothesis at a 95% CL. Dashed colored lines show the expected limits from the l+jets and all-hadronic channels, where the latter start at resonance masses of 1.4 TeV. The observed and expected limits from the combination are shown as solid and dashed black lines, respectively. The green and yellow bands show the 68 and 95% confidence intervals on the combined expected limits.

Upper limits on the production cross section times branching fraction of the B+b hypothesis at a 95% CL. Dashed colored lines show the expected limits from the l+jets and all-hadronic channels, where the latter start at resonance masses of 1.4 TeV. The observed and expected limits from the combination are shown as solid and dashed black lines, respectively. The green and yellow bands show the 68 and 95% confidence intervals on the combined expected limits.

Upper limits on the production cross section times branching fraction of the B+t hypothesis at a 95% CL. Dashed colored lines show the expected limits from the l+jets and all-hadronic channels, where the latter start at resonance masses of 1.4 TeV. The observed and expected limits from the combination are shown as solid and dashed black lines, respectively. The green and yellow bands show the 68 and 95% confidence intervals on the combined expected limits.

Exclusion limit for BrHZX_BrXee

Exclusion limit for BrHZX_BrXmumu

Exclusion limit for BrHZX_BrXll

Exclusion limit for cah

Exclusion limit for cZh

Exclusion limit for kappa

Invariant mass distribution of the diphoton pairs for the elastic selection region with events satisfying a < 0.005 (signal contribution is magnified by a factor 5000).

Predicted number of events having an elastic diphoton pair in association with a pair of protons observed within the range where the proton detectors have a radiation inefficiency less than 10%. The yields where the two-photon and two-proton systems mass and rapidity are matching at 2 and 3$\sigma$ are also quoted. This corresponds to a search region of $m_{\gamma\gamma} > 350$ GeV, $0.070 < \xi^+ < 0.111$, and $0.070 < \xi^- < 0.138$.

Predicted number of events having an elastic diphoton pair in association with a pair of protons observed within the range where the proton detectors have a radiation inefficiency less than 10%. The yields where the two-photon and two-proton systems mass and rapidity are matching at 2 and 3$\sigma$ are also quoted. This corresponds to a search region of $m_{\gamma\gamma} > 350$ GeV, $0.070 < \xi^+ < 0.111$, and $0.070 < \xi^- < 0.138$.

95% CL expected and observed frequentist upper limit for the LbL cross section within the $m_{\gamma\gamma} > 350$ GeV, $0.070 < \xi^+ < 0.111$, and $0.070 < \xi^- < 0.138$ search region.

95% CL expected and observed frequentist upper limit for the LbL cross section within the $m_{\gamma\gamma} > 350$ GeV, $0.070 < \xi^+ < 0.111$, and $0.070 < \xi^- < 0.138$ search region.

95% expected and observed one-dimensional limits on $\zeta_1$ and $\zeta_2$ anomalous LbyL production parameters, when the other parameter is set to zero. This corresponds to a search region of $m_{\gamma\gamma} > 350$ GeV, $0.070 < \xi^+ < 0.111$, and $0.070 < \xi^- < 0.138$.

95% expected and observed one-dimensional limits on $\zeta_1$ and $\zeta_2$ anomalous LbyL production parameters, when the other parameter is set to zero. This corresponds to a search region of $m_{\gamma\gamma} > 350$ GeV, $0.070 < \xi^+ < 0.111$, and $0.070 < \xi^- < 0.138$.

95% expected and observed limits on $\zeta_1$ and $\zeta_2$ anomalous LbyL production parameters. The parametric elliptic form is assumed: $a_0\zeta_1^2+a_1\zeta_1\zeta_2+a_2\zeta_2^2=1$. This corresponds to a search region of $m_{\gamma\gamma} > 350$ GeV, $0.070 < \xi^+ < 0.111$, and $0.070 < \xi^- < 0.138$.

95% expected and observed limits on $\zeta_1$ and $\zeta_2$ anomalous LbyL production parameters. The parametric elliptic form is assumed: $a_0\zeta_1^2+a_1\zeta_1\zeta_2+a_2\zeta_2^2=1$. This corresponds to a search region of $m_{\gamma\gamma} > 350$ GeV, $0.070 < \xi^+ < 0.111$, and $0.070 < \xi^- < 0.138$.

The 95% CL observed and expected limits on the branching fraction B(H $\rightarrow$ SS) for 15 GeV mass and $ S \rightarrow d\bar{d}$ decay mode.

The 95% CL observed and expected limits on the branching fraction B(H $\rightarrow$ SS) for 40 GeV mass and $ S \rightarrow d\bar{d}$ decay mode.

The 95% CL observed and expected limits on the branching fraction B(H $\rightarrow$ SS) for 40 GeV mass and $ S \rightarrow d\bar{d}$ decay mode.

The 95% CL observed and expected limits on the branching fraction B(H $\rightarrow$ SS) for 55 GeV mass and $ S \rightarrow d\bar{d}$ decay mode.

The 95% CL observed and expected limits on the branching fraction B(H $\rightarrow$ SS) for 55 GeV mass and $ S \rightarrow d\bar{d}$ decay mode.

The 95% CL observed and expected limits on the branching fraction B(H $\rightarrow$ SS) for 7 GeV mass and $ S \rightarrow \tau^{+} \tau^{-}$ decay mode.

The 95% CL observed and expected limits on the branching fraction B(H $\rightarrow$ SS) for 7 GeV mass and $ S \rightarrow \tau^{+} \tau^{-}$ decay mode.

The 95% CL observed and expected limits on the branching fraction B(H $\rightarrow$ SS) for 15 GeV mass and $ S \rightarrow \tau^{+} \tau^{-}$ decay mode.

The 95% CL observed and expected limits on the branching fraction B(H $\rightarrow$ SS) for 15 GeV mass and $ S \rightarrow \tau^{+} \tau^{-}$ decay mode.

The 95% CL observed and expected limits on the branching fraction B(H $\rightarrow$ SS) for 40 GeV mass and $ S \rightarrow \tau^{+} \tau^{-}$ decay mode.

The 95% CL observed and expected limits on the branching fraction B(H $\rightarrow$ SS) for 40 GeV mass and $ S \rightarrow \tau^{+} \tau^{-}$ decay mode.

The 95% CL observed and expected limits on the branching fraction B(H $\rightarrow$ SS) for 55 GeV mass and $ S \rightarrow \tau^{+} \tau^{-}$ decay mode.

The 95% CL observed and expected limits on the branching fraction B(H $\rightarrow$ SS) for 55 GeV mass and $ S \rightarrow \tau^{+} \tau^{-}$ decay mode.

The 95% CL observed and expected limits on the branching fraction B(H $\rightarrow$ SS) for 15 GeV mass and $ S \rightarrow b\bar{b}$ decay mode.

The 95% CL observed and expected limits on the branching fraction B(H $\rightarrow$ SS) for 15 GeV mass and $ S \rightarrow b\bar{b}$ decay mode.

The 95% CL observed and expected limits on the branching fraction B(H $\rightarrow$ SS) for 40 GeV mass and $ S \rightarrow b\bar{b}$ decay mode.

The 95% CL observed and expected limits on the branching fraction B(H $\rightarrow$ SS) for 40 GeV mass and $ S \rightarrow b\bar{b}$ decay mode.

The 95% CL observed and expected limits on the branching fraction B(H $\rightarrow$ SS) for 55 GeV mass and $ S \rightarrow b\bar{b}$ decay mode.

The 95% CL observed and expected limits on the branching fraction B(H $\rightarrow$ SS) for 55 GeV mass and $ S \rightarrow b\bar{b}$ decay mode.

The cluster efficiency in bins of hadronic and EM energy in region A. Region A is defined as 391 cm $< r <$ 695.5 cm and 400 cm $< |z| <$ 671 cm. The cluster efficiency is estimated with LLPs decaying to $\tau^{+} \tau^{-}$. The sample contains equal fractions of events with LLP mass of 7, 15, 40, and 55 GeV and LLP lifetime of 0.1, 1, 10, and 100m. The first hadronic energy bins correspond to LLPs that decayed leptonically with 0 hadronic energy. The cluster efficiency includes all cluster-level selections described in the paper, except for the jet veto, time cut, and $\Delta\phi$ cut. The full simulation signal yield prediction for samples with various LLP mass between 7 - 55 GeV, lifetime between 0.1 - 100 m, and decay mode to $d\bar{d}$ and $\tau^{+} \tau^{-}$ can be reproduced using this parameterization to within 35% and 20% for region A and B, respectively.

The cluster efficiency in bins of hadronic and EM energy in region A. Region A is defined as 391 cm $< r <$ 695.5 cm and 400 cm $< |z| <$ 671 cm. The cluster efficiency is estimated with LLPs decaying to $\tau^{+} \tau^{-}$. The sample contains equal fractions of events with LLP mass of 7, 15, 40, and 55 GeV and LLP lifetime of 0.1, 1, 10, and 100m. The first hadronic energy bins correspond to LLPs that decayed leptonically with 0 hadronic energy. The cluster efficiency includes all cluster-level selections described in the paper, except for the jet veto, time cut, and $\Delta\phi$ cut. The full simulation signal yield prediction for samples with various LLP mass between 7 - 55 GeV, lifetime between 0.1 - 100 m, and decay mode to $d\bar{d}$ and $\tau^{+} \tau^{-}$ can be reproduced using this parameterization to within 35% and 20% for region A and B, respectively.

The cluster efficiency in bins of hadronic and EM energy in region B. Region B is defined as 671 cm $< |z| <$ 1100 cm, $r <$ 695.5 cm, and $|\eta| <$ 2. The cluster efficiency is estimated with LLPs decaying to $\tau^{+} \tau^{-}$. The sample contains equal fractions of events with LLP mass of 7, 15, 40, and 55 GeV and LLP lifetime of 0.1, 1, 10, and 100m. The first hadronic energy bins correspond to LLPs that decayed leptonically with 0 hadronic energy. The cluster efficiency includes all cluster-level selections described in the paper, except for the jet veto, time cut, and $\Delta\phi$ cut. The full simulation signal yield prediction for samples with various LLP mass between 7 - 55 GeV, lifetime between 0.1 - 100 m, and decay mode to $d\bar{d}$ and $\tau^{+} \tau^{-}$ can be reproduced using this parameterization to within 35% and 20% for region A and B, respectively.

The cluster efficiency in bins of hadronic and EM energy in region B. Region B is defined as 671 cm $< |z| <$ 1100 cm, $r <$ 695.5 cm, and $|\eta| <$ 2. The cluster efficiency is estimated with LLPs decaying to $\tau^{+} \tau^{-}$. The sample contains equal fractions of events with LLP mass of 7, 15, 40, and 55 GeV and LLP lifetime of 0.1, 1, 10, and 100m. The first hadronic energy bins correspond to LLPs that decayed leptonically with 0 hadronic energy. The cluster efficiency includes all cluster-level selections described in the paper, except for the jet veto, time cut, and $\Delta\phi$ cut. The full simulation signal yield prediction for samples with various LLP mass between 7 - 55 GeV, lifetime between 0.1 - 100 m, and decay mode to $d\bar{d}$ and $\tau^{+} \tau^{-}$ can be reproduced using this parameterization to within 35% and 20% for region A and B, respectively.

The efficiency of $N_{station} > 1$ requirement in bins of hadronic energy in region B. Region B is defined as 671 cm $< |z| <$ 1100 cm, $r <$ 695.5 cm, and $|\eta| <$ 2. The cluster efficiency is estimated with LLPs decaying to $\tau^{+} \tau^{-}$. The sample contains equal fractions of events with LLP mass of 7, 15, 40, and 55 GeV and LLP lifetime of 0.1, 1, 10, and 100m. The first hadronic energy bin corresponds to LLPs that decayed leptonically with 0 hadronic energy. The efficiency is calculated with respect to clusters that pass all cluster-level cuts described in the paper, except for the jet veto, time cut, and $\Delta\phi$ cut. The full simulation signal yield prediction for samples with various LLP mass between 7 - 55 GeV, lifetime between 0.1 - 100 m, and decay mode to $d\bar{d}$ and $\tau^{+} \tau^{-}$ can be reproduced using this parameterization to within 10%.

The efficiency of $N_{station} > 1$ requirement in bins of hadronic energy in region B. Region B is defined as 671 cm $< |z| <$ 1100 cm, $r <$ 695.5 cm, and $|\eta| <$ 2. The cluster efficiency is estimated with LLPs decaying to $\tau^{+} \tau^{-}$. The sample contains equal fractions of events with LLP mass of 7, 15, 40, and 55 GeV and LLP lifetime of 0.1, 1, 10, and 100m. The first hadronic energy bin corresponds to LLPs that decayed leptonically with 0 hadronic energy. The efficiency is calculated with respect to clusters that pass all cluster-level cuts described in the paper, except for the jet veto, time cut, and $\Delta\phi$ cut. The full simulation signal yield prediction for samples with various LLP mass between 7 - 55 GeV, lifetime between 0.1 - 100 m, and decay mode to $d\bar{d}$ and $\tau^{+} \tau^{-}$ can be reproduced using this parameterization to within 10%.

The geometric signal acceptance as a function of $c\tau$. The acceptance is shown for four different LLP mass hypotheses: 7, 15, 40, and 55 GeV. The acceptance is defined by requiring at least 1 LLP to decay in the region defined as 400 cm $< |z| <$ 1100 cm, $r < $ 695.5 cm, and $|\eta| <$ 2.4.

Dijet signal efficiencies as a function of the signal mass and lifetime for events satisfying all event and vertex requirements, with corrections based on systematic differences in the vertex reconstruction efficiency between data and simulation.

The distribution of $d_{\mathrm{BV}}$ for $\geq$5-track one-vertex events in data and three simulated multijet signal samples each with a mass of 1600 GeV. The production cross section for each signal model is assumed to be the lower limit excluded by CMS-EXO-17-018, corresponding to values of 0.8, 0.25, and 0.15 fb for the samples with $c\tau =$ 0.3, 1.0, and 10 mm, respectively. The last bin includes the overflow events. This bin includes one event in data with a vertex with large $d_{\mathrm{BV}}$ that appears to arise from tracks originating from separate pp interaction vertices, consistent with background.

Distribution of the $x$-$y$ distances between vertices, $d_{\mathrm{VV}}$, for 2017 and 2018 data. The background distribution $d_{\mathrm{VV}}^{\kern 0.15em\mathrm{C}}$ (blue continuous line) is constructed from one-vertex events in data, and is normalized to the number of two-vertex events in data with two 3-track vertices. The two vertical red dashed lines separate the regions used in the fit.

Distribution of the $x$-$y$ distances between vertices, $d_{\mathrm{VV}}$, for 2017 and 2018 data. The background distribution $d_{\mathrm{VV}}^{\kern 0.15em\mathrm{C}}$ (blue continuous line) is constructed from one-vertex events in data, and is normalized to the number of two-vertex events in data which have exactly one 4-track vertex and one 3-track vertex. The two vertical red dashed lines separate the regions used in the fit.

Distribution of the $x$-$y$ distances between vertices, $d_{\mathrm{VV}}$, for 2017 and 2018 data. The background distribution $d_{\mathrm{VV}}^{\kern 0.15em\mathrm{C}}$ (blue continuous line) is constructed from one-vertex events in data, and is normalized to the number of two-vertex events in data with two 4-track vertices. The two vertical red dashed lines separate the regions used in the fit.

Distribution of the $x$-$y$ distances between vertices, $d_{\mathrm{VV}}$, for 2017 and 2018 data. The background distribution $d_{\mathrm{VV}}^{\kern 0.15em\mathrm{C}}$ (blue continuous line) is constructed from one-vertex events in data, and is normalized using $\geq$5-track one-vertex event information. The two vertical red dashed lines separate the regions used in the fit.

Predicted yields for the background-only normalized template, predicted yields for three simulated multijet signals each with a mass of 1600 GeV, and the observed yield in each $d_{\mathrm{VV}}$ bin. The production cross section for each signal model is assumed to be the lower limit excluded by CMS-EXO-17-018, corresponding to values of 0.8, 0.25, and 0.15 fb for samples with $c\tau =$ 0.3, 1.0, and 10 mm, respectively. The uncertainties in the signal yields and the systematic uncertainties in the background prediction reflect the systematic uncertainties given in the text.

Observed 95% CL upper limits on the product of cross section and branching fraction squared for the multijet signals, as a function of mass and $c\tau$. The overlaid mass-lifetime exclusion curves assume pair-production cross sections for the neutralino (red) and gluino (purple) with 100% branching fraction to each model's respective decay mode specified. The solid black (dashed colored) lines represent the observed (median expected) limits at 95% CL. The thin black lines represent the variation of the observed limit within theoretical uncertainties of the signal cross section. The thin dashed colored lines represent the region containing 68% of the expected limit distribution under the background-only hypothesis. The observed limits from the CMS displaced jets search (CMS-EXO-19-021) are also shown in teal for comparison.

Observed 95% CL upper limits on the product of cross section and branching fraction squared for the multijet signals, as a function of mass and $c\tau$. The overlaid mass-lifetime exclusion curves assume pair-production cross sections for the neutralino (red) and gluino (purple) with 100% branching fraction to each model's respective decay mode specified. The solid black (dashed colored) lines represent the observed (median expected) limits at 95% CL. The thin black lines represent the variation of the observed limit within theoretical uncertainties of the signal cross section. The thin dashed colored lines represent the region containing 68% of the expected limit distribution under the background-only hypothesis. The observed limits from the CMS displaced jets search (CMS-EXO-19-021) are also shown in teal for comparison.

Observed 95% CL upper limits on the product of cross section and branching fraction squared for the multijet signals, as a function of mass and $c\tau$. The overlaid mass-lifetime exclusion curves assume pair-production cross sections for the neutralino (red) and gluino (purple) with 100% branching fraction to each model's respective decay mode specified. The solid black (dashed colored) lines represent the observed (median expected) limits at 95% CL. The thin black lines represent the variation of the observed limit within theoretical uncertainties of the signal cross section. The thin dashed colored lines represent the region containing 68% of the expected limit distribution under the background-only hypothesis. The observed limits from the CMS displaced jets search (CMS-EXO-19-021) are also shown in teal for comparison.

Observed 95% CL upper limits on the product of cross section and branching fraction squared for the dijet signals, as a function of mass and $c\tau$. The overlaid mass-lifetime exclusion curves assume pair-production cross sections for the top squark with 100% branching fraction to each model's respective decay mode specified. The solid black (dashed colored) lines represent the observed (median expected) limits at 95% CL. The thin black lines represent the variation of the observed limit within theoretical uncertainties of the signal cross section. The thin dashed colored lines represent the region containing 68% of the expected limit distribution under the background-only hypothesis. The observed limits from the CMS displaced jets search (CMS-EXO-19-021) are also shown in teal for comparison.

Observed 95% CL upper limits on the product of cross section and branching fraction squared for the dijet signals, as a function of mass and $c\tau$. The overlaid mass-lifetime exclusion curves assume pair-production cross sections for the top squark with 100% branching fraction to each model's respective decay mode specified. The solid black (dashed colored) lines represent the observed (median expected) limits at 95% CL. The thin black lines represent the variation of the observed limit within theoretical uncertainties of the signal cross section. The thin dashed colored lines represent the region containing 68% of the expected limit distribution under the background-only hypothesis. The observed limits from the CMS displaced jets search (CMS-EXO-19-021) are also shown in teal for comparison.

Observed and expected 95% CL upper limits on the product of cross section and branching fraction squared, as a function of mass for multijet signals, for a fixed $c\tau$ of 300um in the full Run-2 data set. The neutralino and gluino pair production cross sections are shown for the multijet signals.

Observed and expected 95% CL upper limits on the product of cross section and branching fraction squared, as a function of mass for dijet signals, for a fixed $c\tau$ of 300um in the full Run-2 data set. The top squark pair-production cross section is shown for the dijet signals.

Observed and expected 95% CL upper limits on the product of cross section and branching fraction squared, as a function of mass for multijet signals, for a fixed $c\tau$ of 1 mm in the full Run-2 data set. The neutralino and gluino pair production cross sections are shown for the multijet signals.

Observed and expected 95% CL upper limits on the product of cross section and branching fraction squared, as a function of mass for dijet signals, for a fixed $c\tau$ of 1 mm in the full Run-2 data set. The top squark pair-production cross section is shown for the dijet signals.

Observed and expected 95% CL upper limits on the product of cross section and branching fraction squared, as a function of mass for multijet signals, for a fixed $c\tau$ of 10 mm in the full Run-2 data set. The neutralino and gluino pair production cross sections are shown for the multijet signals.

Observed and expected 95% CL upper limits on the product of cross section and branching fraction squared, as a function of mass for dijet signals, for a fixed $c\tau$ of 10 mm in the full Run-2 data set. The top squark pair-production cross section is shown for the dijet signals.

Observed and expected 95% CL upper limits on the product of cross section and branching fraction squared, as a function of $c\tau$ for multijet signals, for a fixed mass of 800 GeV in the full Run-2 data set. The neutralino and gluino pair production cross sections are shown for the multijet signals.

Observed and expected 95% CL upper limits on the product of cross section and branching fraction squared, as a function of $c\tau$ for dijet signals, for a fixed mass of 800 GeV in the full Run-2 data set. The top squark pair-production cross section is shown for the dijet signals.

Observed and expected 95% CL upper limits on the product of cross section and branching fraction squared, as a function of $c\tau$ for multijet signals, for a fixed mass of 1600 GeV in the full Run-2 data set. The neutralino and gluino pair production cross sections are shown for the multijet signals.

Observed and expected 95% CL upper limits on the product of cross section and branching fraction squared, as a function of $c\tau$ for dijet signals, for a fixed mass of 1600 GeV in the full Run-2 data set. The top squark pair-production cross section is shown for the dijet signals.

Observed and expected 95% CL upper limits on the product of cross section and branching fraction squared, as a function of $c\tau$ for multijet signals, for a fixed mass of 2400 GeV in the full Run-2 data set. The neutralino and gluino pair production cross sections are shown for the multijet signals. For $m$ = 2400 GeV, the expected neutralino cross section is $\approx 8\times 10^{-5}$ fb and is not shown.

Observed and expected 95% CL upper limits on the product of cross section and branching fraction squared, as a function of $c\tau$ for dijet signals, for a fixed mass of 2400 GeV in the full Run-2 data set. The top squark pair-production cross section is shown for the dijet signals.

Data-to-simulation efficiency correction factors, shown for multijet and dijet signal topologies in several ranges of $c\tau$. Note that these correction factors account for the two long-lived particles in the simulated events, and are therefore the total correction factors used to scale event yields rather than the correction factors one would apply to individual vertices.

Distribution of the azimuthal angle between vertices, $\Delta\phi_{\mathrm{VV}}$, for 2017 and 2018 data. The background distribution (blue continuous line) is constructed from 3-track one-vertex events in data, and is normalized to the number of 3-track two-vertex events in data.

Distribution of the azimuthal angle between vertices, $\Delta\phi_{\mathrm{VV}}$, for 2017 and 2018 data. The background distribution (blue continuous line) is constructed from 4-track and 3-track one-vertex events in data, and is normalized to the number of two-vertex events in data which have exactly one 4-track vertex and one 3-track vertex.

Distribution of the azimuthal angle between vertices, $\Delta\phi_{\mathrm{VV}}$, for 2017 and 2018 data. The background distribution (blue continuous line) is constructed from 4-track one-vertex events in data, and is normalized to the number of 4-track two-vertex events in data.

Distribution of the azimuthal angle between vertices, $\Delta\phi_{\mathrm{VV}}$, for 2017 and 2018 data. The background distribution (blue continuous line) is constructed from $\geq$5-track one-vertex events in data, and is normalized using one-vertex event information. No $\geq$5-track two-vertex data events pass the selection.

Reconstructed VLQ mass distributions for simulated signal events with a generated VLQ mass $m_{B} = 1200\GeV$. A moderate requirement of $\chi^{2}$/ndf < 2$ is applied to the events. Mass distributions for 4-jet (left), 5-jet (center), and 6-jet (right) events are shown for the three decay modes: bHbH (upper row), bHbZ (middle row), and bZbZ (lower row).

Reconstructed VLQ mass distributions for simulated signal events with a generated VLQ mass $m_{B} = 1200\GeV$. A moderate requirement of $\chi^{2}$/ndf < 2$ is applied to the events. Mass distributions for 4-jet (left), 5-jet (center), and 6-jet (right) events are shown for the three decay modes: bHbH (upper row), bHbZ (middle row), and bZbZ (lower row).

Reconstructed VLQ mass distributions for simulated signal events with a generated VLQ mass $m_{B} = 1200\GeV$. A moderate requirement of $\chi^{2}$/ndf < 2$ is applied to the events. Mass distributions for 4-jet (left), 5-jet (center), and 6-jet (right) events are shown for the three decay modes: bHbH (upper row), bHbZ (middle row), and bZbZ (lower row).

Reconstructed VLQ mass distributions for simulated signal events with a generated VLQ mass $m_{B} = 1200\GeV$. A moderate requirement of $\chi^{2}$/ndf < 2$ is applied to the events. Mass distributions for 4-jet (left), 5-jet (center), and 6-jet (right) events are shown for the three decay modes: bHbH (upper row), bHbZ (middle row), and bZbZ (lower row).

Reconstructed VLQ mass distributions for simulated signal events with a generated VLQ mass $m_{B} = 1200\GeV$. A moderate requirement of $\chi^{2}$/ndf < 2$ is applied to the events. Mass distributions for 4-jet (left), 5-jet (center), and 6-jet (right) events are shown for the three decay modes: bHbH (upper row), bHbZ (middle row), and bZbZ (lower row).

Reconstructed VLQ mass distributions for simulated signal events with a generated VLQ mass $m_{B} = 1200\GeV$. A moderate requirement of $\chi^{2}$/ndf < 2$ is applied to the events. Mass distributions for 4-jet (left), 5-jet (center), and 6-jet (right) events are shown for the three decay modes: bHbH (upper row), bHbZ (middle row), and bZbZ (lower row).

Reconstructed VLQ mass distributions for simulated signal events with a generated VLQ mass $m_{B} = 1200\GeV$. A moderate requirement of $\chi^{2}$/ndf < 2$ is applied to the events. Mass distributions for 4-jet (left), 5-jet (center), and 6-jet (right) events are shown for the three decay modes: bHbH (upper row), bHbZ (middle row), and bZbZ (lower row).

Distribution of $\chi^{2}$/ndf for the best jet combination for simulated 1200\GeV VLQ events (red histogram) and data (black points), for 4-jet events (left), 5-jet events (center), and 6-jet events (right). The simulated signal events and data events are normalized to the same value within the displayed $\chi^{2}$/ndf range.

Distribution of $\chi^{2}$/ndf for the best jet combination for simulated 1200\GeV VLQ events (red histogram) and data (black points), for 4-jet events (left), 5-jet events (center), and 6-jet events (right). The simulated signal events and data events are normalized to the same value within the displayed $\chi^{2}$/ndf range.

Distribution of $\chi^{2}$/ndf for the best jet combination for simulated 1200\GeV VLQ events (red histogram) and data (black points), for 4-jet events (left), 5-jet events (center), and 6-jet events (right). The simulated signal events and data events are normalized to the same value within the displayed $\chi^{2}$/ndf range.

Distributions of the average reconstructed mass of VLQ candidates for the jet combination with the least $\chi^{2}$ in 4-jet (left), 5-jet (center), and 6-jet (right) multiplicity events. The red lines show the exponential fit in the range 1000-2000 GeV. The lower panels show the fractional difference, (data-fit)/fit

Distributions of the average reconstructed mass of VLQ candidates for the jet combination with the least $\chi^{2}$ in 4-jet (left), 5-jet (center), and 6-jet (right) multiplicity events. The red lines show the exponential fit in the range 1000-2000 GeV. The lower panels show the fractional difference, (data-fit)/fit

Distributions of the average reconstructed mass of VLQ candidates for the jet combination with the least $\chi^{2}$ in 4-jet (left), 5-jet (center), and 6-jet (right) multiplicity events. The red lines show the exponential fit in the range 1000-2000 GeV. The lower panels show the fractional difference, (data-fit)/fit

Dependence of the BJTF on the average reconstructed VLQ mass in the control region, 12 < $\chi^{2}$/ndf < 48 for 4-jet (left column), 5-jet (center column), and 6-jet (right column) multiplicities and for the bHbH (upper row), bHbZ (middle row), and bZbZ (lower row) event modes. The data is shown in black points, and the linear fit and its uncertainty are shown as the red line and the pale red band.

Dependence of the BJTF on the average reconstructed VLQ mass in the control region, 12 < $\chi^{2}$/ndf < 48 for 4-jet (left column), 5-jet (center column), and 6-jet (right column) multiplicities and for the bHbH (upper row), bHbZ (middle row), and bZbZ (lower row) event modes. The data is shown in black points, and the linear fit and its uncertainty are shown as the red line and the pale red band.

Dependence of the BJTF on the average reconstructed VLQ mass in the control region, 12 < $\chi^{2}$/ndf < 48 for 4-jet (left column), 5-jet (center column), and 6-jet (right column) multiplicities and for the bHbH (upper row), bHbZ (middle row), and bZbZ (lower row) event modes. The data is shown in black points, and the linear fit and its uncertainty are shown as the red line and the pale red band.

Dependence of the BJTF on the average reconstructed VLQ mass in the control region, 12 < $\chi^{2}$/ndf < 48 for 4-jet (left column), 5-jet (center column), and 6-jet (right column) multiplicities and for the bHbH (upper row), bHbZ (middle row), and bZbZ (lower row) event modes. The data is shown in black points, and the linear fit and its uncertainty are shown as the red line and the pale red band.

Dependence of the BJTF on the average reconstructed VLQ mass in the control region, 12 < $\chi^{2}$/ndf < 48 for 4-jet (left column), 5-jet (center column), and 6-jet (right column) multiplicities and for the bHbH (upper row), bHbZ (middle row), and bZbZ (lower row) event modes. The data is shown in black points, and the linear fit and its uncertainty are shown as the red line and the pale red band.

Dependence of the BJTF on the average reconstructed VLQ mass in the control region, 12 < $\chi^{2}$/ndf < 48 for 4-jet (left column), 5-jet (center column), and 6-jet (right column) multiplicities and for the bHbH (upper row), bHbZ (middle row), and bZbZ (lower row) event modes. The data is shown in black points, and the linear fit and its uncertainty are shown as the red line and the pale red band.

Dependence of the BJTF on the average reconstructed VLQ mass in the control region, 12 < $\chi^{2}$/ndf < 48 for 4-jet (left column), 5-jet (center column), and 6-jet (right column) multiplicities and for the bHbH (upper row), bHbZ (middle row), and bZbZ (lower row) event modes. The data is shown in black points, and the linear fit and its uncertainty are shown as the red line and the pale red band.

Dependence of the BJTF on the average reconstructed VLQ mass in the control region, 12 < $\chi^{2}$/ndf < 48 for 4-jet (left column), 5-jet (center column), and 6-jet (right column) multiplicities and for the bHbH (upper row), bHbZ (middle row), and bZbZ (lower row) event modes. The data is shown in black points, and the linear fit and its uncertainty are shown as the red line and the pale red band.

Dependence of the BJTF on the average reconstructed VLQ mass in the control region, 12 < $\chi^{2}$/ndf < 48 for 4-jet (left column), 5-jet (center column), and 6-jet (right column) multiplicities and for the bHbH (upper row), bHbZ (middle row), and bZbZ (lower row) event modes. The data is shown in black points, and the linear fit and its uncertainty are shown as the red line and the pale red band.

Dependence of the BJTF on $\chi^{2}$/ndf in the low-mass VLQ region, for 4-jet (left column), 5-jet, (center column) and 6-jet (right column) multiplicities and for the bHbH (upper row), bHbZ (middle row), and bZbZ (lower row) event modes. The data is shown in black points, and the linear fit and its uncertainty are shown as the red line and the pale red band.

Dependence of the BJTF on $\chi^{2}$/ndf in the low-mass VLQ region, for 4-jet (left column), 5-jet, (center column) and 6-jet (right column) multiplicities and for the bHbH (upper row), bHbZ (middle row), and bZbZ (lower row) event modes. The data is shown in black points, and the linear fit and its uncertainty are shown as the red line and the pale red band.

Dependence of the BJTF on $\chi^{2}$/ndf in the low-mass VLQ region, for 4-jet (left column), 5-jet, (center column) and 6-jet (right column) multiplicities and for the bHbH (upper row), bHbZ (middle row), and bZbZ (lower row) event modes. The data is shown in black points, and the linear fit and its uncertainty are shown as the red line and the pale red band.

Dependence of the BJTF on $\chi^{2}$/ndf in the low-mass VLQ region, for 4-jet (left column), 5-jet, (center column) and 6-jet (right column) multiplicities and for the bHbH (upper row), bHbZ (middle row), and bZbZ (lower row) event modes. The data is shown in black points, and the linear fit and its uncertainty are shown as the red line and the pale red band.

Dependence of the BJTF on $\chi^{2}$/ndf in the low-mass VLQ region, for 4-jet (left column), 5-jet, (center column) and 6-jet (right column) multiplicities and for the bHbH (upper row), bHbZ (middle row), and bZbZ (lower row) event modes. The data is shown in black points, and the linear fit and its uncertainty are shown as the red line and the pale red band.

Dependence of the BJTF on $\chi^{2}$/ndf in the low-mass VLQ region, for 4-jet (left column), 5-jet, (center column) and 6-jet (right column) multiplicities and for the bHbH (upper row), bHbZ (middle row), and bZbZ (lower row) event modes. The data is shown in black points, and the linear fit and its uncertainty are shown as the red line and the pale red band.

Dependence of the BJTF on $\chi^{2}$/ndf in the low-mass VLQ region, for 4-jet (left column), 5-jet, (center column) and 6-jet (right column) multiplicities and for the bHbH (upper row), bHbZ (middle row), and bZbZ (lower row) event modes. The data is shown in black points, and the linear fit and its uncertainty are shown as the red line and the pale red band.

Dependence of the BJTF on $\chi^{2}$/ndf in the low-mass VLQ region, for 4-jet (left column), 5-jet, (center column) and 6-jet (right column) multiplicities and for the bHbH (upper row), bHbZ (middle row), and bZbZ (lower row) event modes. The data is shown in black points, and the linear fit and its uncertainty are shown as the red line and the pale red band.

Dependence of the BJTF on $\chi^{2}$/ndf in the low-mass VLQ region, for 4-jet (left column), 5-jet, (center column) and 6-jet (right column) multiplicities and for the bHbH (upper row), bHbZ (middle row), and bZbZ (lower row) event modes. The data is shown in black points, and the linear fit and its uncertainty are shown as the red line and the pale red band.

The reduction factor in data events, for 4-jet (left column), 5-jet (center column), and 6-jet (right column) multiplicities, and for the bHbH (upper row), bHbZ (middle row), and bZbZ (lower row) event modes.

The reduction factor in data events, for 4-jet (left column), 5-jet (center column), and 6-jet (right column) multiplicities, and for the bHbH (upper row), bHbZ (middle row), and bZbZ (lower row) event modes.

The reduction factor in data events, for 4-jet (left column), 5-jet (center column), and 6-jet (right column) multiplicities, and for the bHbH (upper row), bHbZ (middle row), and bZbZ (lower row) event modes.

The reduction factor in data events, for 4-jet (left column), 5-jet (center column), and 6-jet (right column) multiplicities, and for the bHbH (upper row), bHbZ (middle row), and bZbZ (lower row) event modes.

The reduction factor in data events, for 4-jet (left column), 5-jet (center column), and 6-jet (right column) multiplicities, and for the bHbH (upper row), bHbZ (middle row), and bZbZ (lower row) event modes.

The reduction factor in data events, for 4-jet (left column), 5-jet (center column), and 6-jet (right column) multiplicities, and for the bHbH (upper row), bHbZ (middle row), and bZbZ (lower row) event modes.

The reduction factor in data events, for 4-jet (left column), 5-jet (center column), and 6-jet (right column) multiplicities, and for the bHbH (upper row), bHbZ (middle row), and bZbZ (lower row) event modes.

The reduction factor in data events, for 4-jet (left column), 5-jet (center column), and 6-jet (right column) multiplicities, and for the bHbH (upper row), bHbZ (middle row), and bZbZ (lower row) event modes.

The reduction factor in data events, for 4-jet (left column), 5-jet (center column), and 6-jet (right column) multiplicities, and for the bHbH (upper row), bHbZ (middle row), and bZbZ (lower row) event modes.

The reduction factor in $m_B$ = 1200 GeV VLQ signal events, for 4-jet (left column), 5-jet (center column), and 6-jet (right column) multiplicities, and for the bHbH (upper row), bHbZ (middle row), and bZbZ (lower row) event modes.

The reduction factor in $m_B$ = 1200 GeV VLQ signal events, for 4-jet (left column), 5-jet (center column), and 6-jet (right column) multiplicities, and for the bHbH (upper row), bHbZ (middle row), and bZbZ (lower row) event modes.

The reduction factor in $m_B$ = 1200 GeV VLQ signal events, for 4-jet (left column), 5-jet (center column), and 6-jet (right column) multiplicities, and for the bHbH (upper row), bHbZ (middle row), and bZbZ (lower row) event modes.

The reduction factor in $m_B$ = 1200 GeV VLQ signal events, for 4-jet (left column), 5-jet (center column), and 6-jet (right column) multiplicities, and for the bHbH (upper row), bHbZ (middle row), and bZbZ (lower row) event modes.

The reduction factor in $m_B$ = 1200 GeV VLQ signal events, for 4-jet (left column), 5-jet (center column), and 6-jet (right column) multiplicities, and for the bHbH (upper row), bHbZ (middle row), and bZbZ (lower row) event modes.

The reduction factor in $m_B$ = 1200 GeV VLQ signal events, for 4-jet (left column), 5-jet (center column), and 6-jet (right column) multiplicities, and for the bHbH (upper row), bHbZ (middle row), and bZbZ (lower row) event modes.

The reduction factor in $m_B$ = 1200 GeV VLQ signal events, for 4-jet (left column), 5-jet (center column), and 6-jet (right column) multiplicities, and for the bHbH (upper row), bHbZ (middle row), and bZbZ (lower row) event modes.

The reduction factor in $m_B$ = 1200 GeV VLQ signal events, for 4-jet (left column), 5-jet (center column), and 6-jet (right column) multiplicities, and for the bHbH (upper row), bHbZ (middle row), and bZbZ (lower row) event modes.

The reduction factor in $m_B$ = 1200 GeV VLQ signal events, for 4-jet (left column), 5-jet (center column), and 6-jet (right column) multiplicities, and for the bHbH (upper row), bHbZ (middle row), and bZbZ (lower row) event modes.

Data (black points), expected background (solid blue histogram), and expected background plus a VLQ signal for different VLQ masses (colored lines). Left column: 4-jet events, center column: 5-jet events, right column: 6-jet events; upper row: bHbH, middle row: bHbZ,lower row: bZbZ. For the signal, a 100% B -> bH branching fraction is assumed. The hatched regions for the background and background plus signal distributions indicate the systematic uncertainties. All three data-taking years are combined.

Data (black points), expected background (solid blue histogram), and expected background plus a VLQ signal for different VLQ masses (colored lines). Left column: 4-jet events, center column: 5-jet events, right column: 6-jet events; upper row: bHbH, middle row: bHbZ,lower row: bZbZ. For the signal, a 100% B -> bH branching fraction is assumed. The hatched regions for the background and background plus signal distributions indicate the systematic uncertainties. All three data-taking years are combined.

Data (black points), expected background (solid blue histogram), and expected background plus a VLQ signal for different VLQ masses (colored lines). Left column: 4-jet events, center column: 5-jet events, right column: 6-jet events; upper row: bHbH, middle row: bHbZ,lower row: bZbZ. For the signal, a 100% B -> bH branching fraction is assumed. The hatched regions for the background and background plus signal distributions indicate the systematic uncertainties. All three data-taking years are combined.

Data (black points), expected background (solid blue histogram), and expected background plus a VLQ signal for different VLQ masses (colored lines). Left column: 4-jet events, center column: 5-jet events, right column: 6-jet events; upper row: bHbH, middle row: bHbZ,lower row: bZbZ. For the signal, a 100% B -> bH branching fraction is assumed. The hatched regions for the background and background plus signal distributions indicate the systematic uncertainties. All three data-taking years are combined.

Data (black points), expected background (solid blue histogram), and expected background plus a VLQ signal for different VLQ masses (colored lines). Left column: 4-jet events, center column: 5-jet events, right column: 6-jet events; upper row: bHbH, middle row: bHbZ,lower row: bZbZ. For the signal, a 100% B -> bH branching fraction is assumed. The hatched regions for the background and background plus signal distributions indicate the systematic uncertainties. All three data-taking years are combined.

Data (black points), expected background (solid blue histogram), and expected background plus a VLQ signal for different VLQ masses (colored lines). Left column: 4-jet events, center column: 5-jet events, right column: 6-jet events; upper row: bHbH, middle row: bHbZ,lower row: bZbZ. For the signal, a 100% B -> bH branching fraction is assumed. The hatched regions for the background and background plus signal distributions indicate the systematic uncertainties. All three data-taking years are combined.

Data (black points), expected background (solid blue histogram), and expected background plus a VLQ signal for different VLQ masses (colored lines). Left column: 4-jet events, center column: 5-jet events, right column: 6-jet events; upper row: bHbH, middle row: bHbZ,lower row: bZbZ. For the signal, a 100% B -> bH branching fraction is assumed. The hatched regions for the background and background plus signal distributions indicate the systematic uncertainties. All three data-taking years are combined.

Data (black points), expected background (solid blue histogram), and expected background plus a VLQ signal for different VLQ masses (colored lines). Left column: 4-jet events, center column: 5-jet events, right column: 6-jet events; upper row: bHbH, middle row: bHbZ,lower row: bZbZ. For the signal, a 100% B -> bH branching fraction is assumed. The hatched regions for the background and background plus signal distributions indicate the systematic uncertainties. All three data-taking years are combined.

Data (black points), expected background (solid blue histogram), and expected background plus a VLQ signal for different VLQ masses (colored lines). Left column: 4-jet events, center column: 5-jet events, right column: 6-jet events; upper row: bHbH, middle row: bHbZ,lower row: bZbZ. For the signal, a 100% B -> bH branching fraction is assumed. The hatched regions for the background and background plus signal distributions indicate the systematic uncertainties. All three data-taking years are combined.

Expected limits on the VLQ mass at 95% CL as a function of the branching fractions $\mathcal{B}$( B -> bH ) and $\mathcal{B}$( B -> bZ)

Observed limits on the VLQ mass at 95% CL as a function of the branching fractions $\mathcal{B}$( B -> bH ) and $\mathcal{B}$( B -> bZ)

The 95% confidence limit on the cross section for VLQ pair production as a function of VLQ mass for three branching fraction hypotheses: B( B -> bH ) = 100% (upper left), B( B -> bZ ) = 100% (upper right), and and B( B -> bH ) = B( B -> bZ ) = 50% (lower). The solid black line indicates the observed limit and the dashed line indicates the expected limit with 1 sigma (green band) and 2 sigma (yellow band) uncertainties. The theoretical cross section and its uncertainty are shown as the red line and pale red band.

The 95% confidence limit on the cross section for VLQ pair production as a function of VLQ mass for three branching fraction hypotheses: B( B -> bH ) = 100% (upper left), B( B -> bZ ) = 100% (upper right), and and B( B -> bH ) = B( B -> bZ ) = 50% (lower). The solid black line indicates the observed limit and the dashed line indicates the expected limit with 1 sigma (green band) and 2 sigma (yellow band) uncertainties. The theoretical cross section and its uncertainty are shown as the red line and pale red band.

The 95% confidence limit on the cross section for VLQ pair production as a function of VLQ mass for three branching fraction hypotheses: B( B -> bH ) = 100% (upper left), B( B -> bZ ) = 100% (upper right), and and B( B -> bH ) = B( B -> bZ ) = 50% (lower). The solid black line indicates the observed limit and the dashed line indicates the expected limit with 1 sigma (green band) and 2 sigma (yellow band) uncertainties. The theoretical cross section and its uncertainty are shown as the red line and pale red band.

Differential cross section of J/psi mesons from b hadrons as a function of dimuon pT in pp and PbPb collisions. The PbPb cross sections are normalised by TAA for direct comparison. Global uncertainties arise from the integrated luminosity uncertainty in pp collisions, and the number of minimum bias events and TAA uncertainties for PbPb collisions.

Differential cross section of prompt J/psi mesons as a function of dimuon rapidty in pp and PbPb collisions. The PbPb cross sections are normalised by TAA for direct comparison. Global uncertainties arise from the integrated luminosity uncertainty in pp collisions, and the number of minimum bias events and TAA uncertainties for PbPb collisions.

Differential cross section of J/psi mesons from b hadrons as a function of dimuon rapidty in pp and PbPb collisions. The PbPb cross sections are normalised by TAA for direct comparison. Global uncertainties arise from the integrated luminosity uncertainty in pp collisions, and the number of minimum bias events and TAA uncertainties for PbPb collisions.

Nuclear modification factor of prompt J/psi mesons as a function of dimuon rapidity. Global uncertainties arise from the integrated luminosity uncertainty of the pp data, and the number of minimum bias events and TAA uncertainties of the PbPb data.

Nuclear modification factor of prompt J/psi mesons as a function of collision centrality. Global uncertainties arise from the full pp statistical and systematic uncertainties (including integrated luminosity uncertainty), and the number of minimum bias events uncertainty of the PbPb data.

Nuclear modification factor of prompt J/psi mesons as a function of dimuon pT. Global uncertainties arise from the integrated luminosity uncertainty of the pp data, and the number of minimum bias events and TAA uncertainties of the PbPb data.

Nuclear modification factor of prompt J/psi mesons as a function of dimuon pT in the mid-rapidity interval. Global uncertainties arise from the integrated luminosity uncertainty of the pp data, and the number of minimum bias events and TAA uncertainties of the PbPb data.

Nuclear modification factor of prompt J/psi mesons as a function of dimuon pT in the most forward rapidity interval. Global uncertainties arise from the integrated luminosity uncertainty of the pp data, and the number of minimum bias events and TAA uncertainties of the PbPb data.

Nuclear modification factor of prompt J/psi mesons as a function of collision centrality in the mid- and most forward rapidity intervals. Global uncertainties arise from the full pp statistical and systematic uncertainties (including integrated luminosity uncertainty), and the number of minimum bias events uncertainty of the PbPb data.

Nuclear modification factor of prompt J/psi mesons as a function of pT in three centrality bins. Global uncertainties arise from the integrated luminosity uncertainty of the pp data, and the number of minimum bias events and TAA uncertainties of the PbPb data.

Nuclear modification factor of prompt J/psi mesons as a function of collision centrality in the most forward rapidity range at moderate and high pT. Global uncertainties arise from the full pp statistical and systematic uncertainties (including integrated luminosity uncertainty), and the number of minimum bias events uncertainty of the PbPb data.

Nuclear modification factor of prompt J/psi mesons as a function of collision centrality in the mid-rapidity range. Global uncertainties arise from the full pp statistical and systematic uncertainties (including integrated luminosity uncertainty), and the number of minimum bias events uncertainty of the PbPb data.

Nuclear modification factor of prompt psi(2S) mesons as a function of collision centrality in the mid-rapidity range. Global uncertainties arise from the full pp statistical and systematic uncertainties (including integrated luminosity uncertainty), and the number of minimum bias events uncertainty of the PbPb data.

95% CL intervals on the nuclear modification factor of prompt psi(2S) mesons as a function of collision centrality in the mid-rapidity range. Global uncertainties arise from the full pp statistical and systematic uncertainties (including integrated luminosity uncertainty), and the number of minimum bias events uncertainty of the PbPb data.

Nuclear modification factor of prompt J/psi and psi(2S) mesons as a function of dimuon pT in the mid-rapidity range. Global uncertainties arise from the integrated luminosity uncertainty of the pp data, and the number of minimum bias events and TAA uncertainties of the PbPb data.

Nuclear modification factor of prompt J/psi mesons as a function of collision centrality in the forward rapidity range. Global uncertainties arise from the full pp statistical and systematic uncertainties (including integrated luminosity uncertainty), and the number of minimum bias events uncertainty of the PbPb data.

Nuclear modification factor of prompt psi(2S) mesons as a function of collision centrality in the forward rapidity range. Global uncertainties arise from the full pp statistical and systematic uncertainties (including integrated luminosity uncertainty), and the number of minimum bias events uncertainty of the PbPb data.

95% CL intervals on the nuclear modification factor of prompt psi(2S) mesons as a function of collision centrality in the forward rapidity range. Global uncertainties arise from the full pp statistical and systematic uncertainties (including integrated luminosity uncertainty), and the number of minimum bias events uncertainty of the PbPb data.

Nuclear modification factor of prompt J/psi mesons as a function of dimuon pT in the forward rapidity range. Global uncertainties arise from the integrated luminosity uncertainty of the pp data, and the number of minimum bias events and TAA uncertainties of the PbPb data.

Nuclear modification factor of prompt psi(2S) mesons as a function of dimuon pT in the forward rapidity range. Global uncertainties arise from the integrated luminosity uncertainty of the pp data, and the number of minimum bias events and TAA uncertainties of the PbPb data.

95% CL intervals on the nuclear modification factor of prompt psi(2S) mesons as a function of dimuon pT in the forward rapidity range. Global uncertainties arise from the integrated luminosity uncertainty of the pp data, and the number of minimum bias events and TAA uncertainties of the PbPb data.

Nuclear modification factor of nonprompt J/psi mesons as a function of dimuon rapidity. Global uncertainties arise from the integrated luminosity uncertainty of the pp data, and the number of minimum bias events and TAA uncertainties of the PbPb data.

Nuclear modification factor of nonprompt J/psi mesons as a function of collision centrality. Global uncertainties arise from the full pp statistical and systematic uncertainties (including integrated luminosity uncertainty), and the number of minimum bias events uncertainty of the PbPb data.

Nuclear modification factor of nonprompt J/psi mesons as a function of dimuon pT. Global uncertainties arise from the integrated luminosity uncertainty of the pp data, and the number of minimum bias events and TAA uncertainties of the PbPb data.

Nuclear modification factor of nonprompt J/psi mesons as a function of dimuon pT in the mid-rapidity interval. Global uncertainties arise from the integrated luminosity uncertainty of the pp data, and the number of minimum bias events and TAA uncertainties of the PbPb data.

Nuclear modification factor of nonprompt J/psi mesons as a function of dimuon pT in the most forward rapidity interval. Global uncertainties arise from the integrated luminosity uncertainty of the pp data, and the number of minimum bias events and TAA uncertainties of the PbPb data.

Nuclear modification factor of nonprompt J/psi mesons as a function of collision centrality in the mid- and most forward rapidity intervals. Global uncertainties arise from the full pp statistical and systematic uncertainties (including integrated luminosity uncertainty), and the number of minimum bias events uncertainty of the PbPb data.

Nuclear modification factor of nonprompt J/psi mesons as a function of pT in three centrality bins. Global uncertainties arise from the integrated luminosity uncertainty of the pp data, and the number of minimum bias events and TAA uncertainties of the PbPb data.

Nuclear modification factor of nonprompt J/psi mesons as a function of collision centrality in the most forward rapidity range at moderate and high pT. Global uncertainties arise from the full pp statistical and systematic uncertainties (including integrated luminosity uncertainty), and the number of minimum bias events uncertainty of the PbPb data.