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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

The 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.

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.