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.

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.

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 $0.070 < \xi^- < 0.138$.

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.