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CMS-B2G-18-002 ; CERN-EP-2019-107
A multi-dimensional search for new heavy resonances decaying to boosted WW, WZ, or ZZ boson pairs in the dijet final state at 13 TeV
Eur. Phys. J. C 80 (2020) 237
Abstract: A search in an all-jet final state for new massive resonances decaying to WW, WZ, or ZZ boson pairs using a novel analysis method is presented. The analysis is performed on data corresponding to an integrated luminosity of 77.3 fb$^{-1}$ recorded with the CMS experiment at the LHC at a centre-of-mass energy of 13 TeV. The search is focussed on potential resonances with masses above 1.2 TeV, where the decay products of each W or Z boson are expected to be collimated into a single, large-radius jet. The signal is extracted using a three-dimensional maximum likelihood fit of the two jet masses and the dijet invariant mass, yielding an improvement in sensitivity of up to 30% relative to previous search methods. No excess is observed above the estimated standard model background. In a heavy vector triplet model, spin-1 Z' and W' resonances with masses below 3.5 and 3.8 TeV, respectively, are excluded at 95% confidence level. In a narrow-width bulk graviton model, upper limits on cross sections are set between 27 and 0.2 fb for resonance masses between 1.2 and 5.2 TeV, respectively. The limits presented in this paper are the best to date in the dijet final state.
Figures & Tables Summary References CMS Publications
Figures

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Figure 1:
The ${\tau _{21}}$ (left) and ${\tau _{21}^\text {DDT}}$ (right) profile dependencies on $\rho '=\ln({m_\mathrm {jet}} ^2/({p_{\mathrm {T}}} \mu))$ examined in QCD multijet events. A fit to the linear part of the spectrum for $ {p_{\mathrm {T}}} > $ 200 GeV yields the slope $M=-0.080$, which is used to define the mass- and ${p_{\mathrm {T}}} $-decorrelated variable $ {\tau _{21}^\text {DDT}} = {\tau _{21}} -M\rho '$.

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Figure 1-a:
The ${\tau _{21}}$ profile dependency on $\rho '=\ln({m_\mathrm {jet}} ^2/({p_{\mathrm {T}}} \mu))$ examined in QCD multijet events. A fit to the linear part of the spectrum for $ {p_{\mathrm {T}}} > $ 200 GeV yields the slope $M=-0.080$, which is used to define the mass- and ${p_{\mathrm {T}}} $-decorrelated variable $ {\tau _{21}^\text {DDT}} = {\tau _{21}} -M\rho '$.

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Figure 1-b:
The ${\tau _{21}^\text {DDT}}$ profile dependency on $\rho '=\ln({m_\mathrm {jet}} ^2/({p_{\mathrm {T}}} \mu))$ examined in QCD multijet events. A fit to the linear part of the spectrum for $ {p_{\mathrm {T}}} > $ 200 GeV yields the slope $M=-0.080$, which is used to define the mass- and ${p_{\mathrm {T}}} $-decorrelated variable $ {\tau _{21}^\text {DDT}} = {\tau _{21}} -M\rho '$.

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Figure 2:
Performance of the $N$-subjettiness discriminants (${\tau _{21}}$ and ${\tau _{21}^\text {DDT}}$) in the background-signal efficiency plane (left). Distribution of ${\tau _{21}}$ and ${\tau _{21}^\text {DDT}}$ for W -jets and quark/gluon jets from QCD multijet events (right). The analysis selections applied to derive these distributions are specified in the figures. For this analysis the working point (WP) of ${\tau _{21}^\text {DDT}} {\leq}0.43$ is chosen.

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Figure 2-a:
Performance of the $N$-subjettiness discriminants (${\tau _{21}}$ and ${\tau _{21}^\text {DDT}}$) in the background-signal efficiency plane. The analysis selections applied to derive this distribution are specified in the figures. For this analysis the working point (WP) of ${\tau _{21}^\text {DDT}} {\leq}0.43$ is chosen.

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Figure 2-b:
Distribution of ${\tau _{21}}$ and ${\tau _{21}^\text {DDT}}$ for W -jets and quark/gluon jets from QCD multijet events. The analysis selections applied to derive this distribution are specified in the figures. For this analysis the working point (WP) of ${\tau _{21}^\text {DDT}} {\leq}0.43$ is chosen.

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Figure 3:
The trigger efficiency as a function of the dijet invariant mass for a combination of all triggers used in this analysis (left) and as a function of the jet mass for triggers requiring an online trimmed mass of at least 30 GeV (right). The solid yellow circles correspond to the trigger efficiencies for the full 2017 data set and do not reach 100% efficiency because the jet mass based triggers were unavailable for a period at the beginning of data taking (corresponding to 4.8 fb$^{-1}$). The open yellow circles are the corresponding efficiencies excluding this period. The uncertainties shown are statistical only.

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Figure 3-a:
The trigger efficiency as a function of the jet mass for triggers requiring an online trimmed mass of at least 30 GeV. The solid yellow circles correspond to the trigger efficiencies for the full 2017 data set and do not reach 100% efficiency because the jet mass based triggers were unavailable for a period at the beginning of data taking (corresponding to 4.8 fb$^{-1}$). The open yellow circles are the corresponding efficiencies excluding this period. The uncertainties shown are statistical only.

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Figure 3-b:
The trigger efficiency as a function of the jet mass for triggers requiring an online trimmed mass of at least 30 GeV. The solid yellow circles correspond to the trigger efficiencies for the full 2017 data set and do not reach 100% efficiency because the jet mass based triggers were unavailable for a period at the beginning of data taking (corresponding to 4.8 fb$^{-1}$). The open yellow circles are the corresponding efficiencies excluding this period. The uncertainties shown are statistical only.

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Figure 4:
Jet mass (upper left) and ${\tau _{21}^\text {DDT}}$ (upper right) distributions for selected jets (one random jet per event), and dijet invariant mass distribution (lower), for events with a jet mass between 55 and 215 GeV. For the QCD multijet simulation, several alternative predictions are shown, scaled to the data minus the other background processes, which are scaled to their SM expectation as described in the text. The different signal distributions are scaled to be visible. No selection on ${\tau _{21}^\text {DDT}}$ is applied. The ratio plots show the fraction of data over QCD multijet simulation for PYTHIA 8 (black markers), HERWIG++ (dotted line), and MadGraph+PYTHIA 8 (dashed line).

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Figure 4-a:
Jet mass distribution for selected jets (one random jet per event), for events with a jet mass between 55 and 215 GeV. For the QCD multijet simulation, several alternative predictions are shown, scaled to the data minus the other background processes, which are scaled to their SM expectation as described in the text. The different signal distributions are scaled to be visible. No selection on ${\tau _{21}^\text {DDT}}$ is applied. The ratio plot shows the fraction of data over QCD multijet simulation for PYTHIA 8 (black markers), HERWIG++ (dotted line), and MadGraph+PYTHIA 8 (dashed line).

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Figure 4-b:
${\tau _{21}^\text {DDT}}$ distribution for selected jets (one random jet per event), for events with a jet mass between 55 and 215 GeV. For the QCD multijet simulation, several alternative predictions are shown, scaled to the data minus the other background processes, which are scaled to their SM expectation as described in the text. The different signal distributions are scaled to be visible. No selection on ${\tau _{21}^\text {DDT}}$ is applied. The ratio plot shows the fraction of data over QCD multijet simulation for PYTHIA 8 (black markers), HERWIG++ (dotted line), and MadGraph+PYTHIA 8 (dashed line).

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Figure 4-c:
Dijet invariant mass distribution, for events with a jet mass between 55 and 215 GeV. For the QCD multijet simulation, several alternative predictions are shown, scaled to the data minus the other background processes, which are scaled to their SM expectation as described in the text. The different signal distributions are scaled to be visible. No selection on ${\tau _{21}^\text {DDT}}$ is applied. The ratio plot shows the fraction of data over QCD multijet simulation for PYTHIA 8 (black markers), HERWIG++ (dotted line), and MadGraph+PYTHIA 8 (dashed line).

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Figure 5:
The jet mass distribution for events that pass (left) and fail (right) the $ {\tau _{21}^\text {DDT}} \leq 0.43$ selection in the ${\mathrm{t} {}\mathrm{\bar{t}}}$ control sample. The results of the fits to data and to simulation are shown by the dash-dotted blue and solid red lines, respectively. The background components of the fits are shown as dashed and dash-dotted lines. The fit to 2016 data is shown in the upper panels and the fit to 2017 data in the lower panels.

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Figure 5-a:
The jet mass distribution for events that pass the $ {\tau _{21}^\text {DDT}} \leq 0.43$ selection in the ${\mathrm{t} {}\mathrm{\bar{t}}}$ control sample. The results of the fits to data and to simulation are shown by the dash-dotted blue and solid red lines, respectively. The background components of the fits are shown as dashed and dash-dotted lines. The fit to 2016 data is shown.

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Figure 5-b:
The jet mass distribution for events that fail the $ {\tau _{21}^\text {DDT}} \leq 0.43$ selection in the ${\mathrm{t} {}\mathrm{\bar{t}}}$ control sample. The results of the fits to data and to simulation are shown by the dash-dotted blue and solid red lines, respectively. The background components of the fits are shown as dashed and dash-dotted lines. The fit to 2016 data is shown.

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Figure 5-c:
The jet mass distribution for events that pass the $ {\tau _{21}^\text {DDT}} \leq 0.43$ selection in the ${\mathrm{t} {}\mathrm{\bar{t}}}$ control sample. The results of the fits to data and to simulation are shown by the dash-dotted blue and solid red lines, respectively. The background components of the fits are shown as dashed and dash-dotted lines. The fit to 2017 data is shown.

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Figure 5-d:
The jet mass distribution for events that fail the $ {\tau _{21}^\text {DDT}} \leq 0.43$ selection in the ${\mathrm{t} {}\mathrm{\bar{t}}}$ control sample. The results of the fits to data and to simulation are shown by the dash-dotted blue and solid red lines, respectively. The background components of the fits are shown as dashed and dash-dotted lines. The fit to 2017 data is shown.

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Figure 6:
Total signal efficiency as a function of ${m_\mathrm {X}}$ after all selections are applied, for signal models with a Z' decaying to WW, $ {\mathrm{G} _{\text {bulk}}} $ decaying to WW, W' decaying to WZ, and $ {\mathrm{G} _{\text {bulk}}} $ decaying to ZZ. The denominator is the number of generated events. The solid and dashed lines show the signal efficiencies for the HPHP and HPLP categories, respectively. The decrease in efficiency between 5.0 and 5.5 TeV is due to the requirement $ {m_\mathrm {jj}} < $ 5500 GeV.

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Figure 7:
The final ${m_\mathrm {jj}}$ (left) and ${m_\text {jet1}}$ (right) signal shapes extracted from the parameterization of the dCB function. The same ${m_\mathrm {jj}}$ shapes are used for both purity categories. The jet mass distributions are shown for a range of resonance masses between 1.2 and 5.2 TeV for one of the two jets in the events in the HPHP category. Because the jets are labelled randomly, the jet mass distributions for the second jet are essentially the same as the one shown. The distributions for a $ {\mathrm{G} _{\text {bulk}}} $ decaying to WW have the same shapes as those for the Z' signal and are therefore not visible.

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Figure 7-a:
The final ${m_\mathrm {jj}}$ signal shapes extracted from the parameterization of the dCB function. The same ${m_\mathrm {jj}}$ shapes are used for both purity categories.

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Figure 7-b:
The final ${m_\text {jet1}}$ signal shapes extracted from the parameterization of the dCB function. The jet mass distributions are shown for a range of resonance masses between 1.2 and 5.2 TeV for one of the two jets in the events in the HPHP category. Because the jets are labelled randomly, the jet mass distributions for the second jet are essentially the same as the one shown. The distributions for a $ {\mathrm{G} _{\text {bulk}}} $ decaying to WW have the same shapes as those for the Z' signal and are therefore not visible.

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Figure 8:
The mass scale (left) and resolution (right) of the jet as a function of ${m_\mathrm {X}}$, obtained from the mean and width of the dCB function used to fit the jet mass spectrum. The HPHP (solid lines) and HPLP (dotted lines) categories are shown for different signal models. The distributions are only shown for one of the two jets in the event, since the distributions for the second jet are essentially the same.

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Figure 8-a:
The mass scale of the jet as a function of ${m_\mathrm {X}}$, obtained from the mean and width of the dCB function used to fit the jet mass spectrum. The HPHP (solid lines) and HPLP (dotted lines) categories are shown for different signal models. The distributions are only shown for one of the two jets in the event, since the distributions for the second jet are essentially the same.

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Figure 8-b:
The mass resolution of the jet as a function of ${m_\mathrm {X}}$, obtained from the mean and width of the dCB function used to fit the jet mass spectrum. The HPHP (solid lines) and HPLP (dotted lines) categories are shown for different signal models. The distributions are only shown for one of the two jets in the event, since the distributions for the second jet are essentially the same.

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Figure 9:
Nominal QCD multijet simulation using PYTHIA 8 (data points) and three-dimensional pdfs derived using a forward-folding kernel approach (black solid line), shown together with the five alternate shapes that are added to the multi-dimensional fit as shape nuisance parameters. The shapes for the high-purity (left) and low-purity (right) categories obtained with the 2017 simulation are shown for the projection on ${m_\text {jet1}}$ (upper) and ${m_\mathrm {jj}}$ (lower). The projection on ${m_\text {jet2}}$ is omitted since it is equivalent to the ${m_\text {jet1}}$ projection except for statistical fluctuations. The distributions for 2016 simulations are similar.

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Figure 9-a:
Nominal QCD multijet simulation using PYTHIA 8 (data points) and three-dimensional pdfs derived using a forward-folding kernel approach (black solid line), shown together with the five alternate shapes that are added to the multi-dimensional fit as shape nuisance parameters. The shapes for the high-purity category obtained with the 2017 simulation are shown for the projection on ${m_\text {jet1}}$. The projection on ${m_\text {jet2}}$ is omitted since it is equivalent to the ${m_\text {jet1}}$ projection except for statistical fluctuations.

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Figure 9-b:
Nominal QCD multijet simulation using PYTHIA 8 (data points) and three-dimensional pdfs derived using a forward-folding kernel approach (black solid line), shown together with the five alternate shapes that are added to the multi-dimensional fit as shape nuisance parameters. The shapes for the low-purity category obtained with the 2017 simulation are shown for the projection on ${m_\text {jet1}}$. The projection on ${m_\text {jet2}}$ is omitted since it is equivalent to the ${m_\text {jet1}}$ projection except for statistical fluctuations.

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Figure 9-c:
Nominal QCD multijet simulation using PYTHIA 8 (data points) and three-dimensional pdfs derived using a forward-folding kernel approach (black solid line), shown together with the five alternate shapes that are added to the multi-dimensional fit as shape nuisance parameters. The shapes for the high-purity category obtained with the 2017 simulation are shown for the projection on ${m_\mathrm {jj}}$.

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Figure 9-d:
Nominal QCD multijet simulation using PYTHIA 8 (data points) and three-dimensional pdfs derived using a forward-folding kernel approach (black solid line), shown together with the five alternate shapes that are added to the multi-dimensional fit as shape nuisance parameters. The shapes for the low-purity category obtained with the 2017 simulation are shown for the projection on ${m_\mathrm {jj}}$.

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Figure 10:
For the HPHP category: comparison between the fitted result and the data distributions of ${m_\text {jet1}}$ (upper left), ${m_\text {jet2}}$ (upper right), and ${m_\mathrm {jj}}$ (lower). The background shape uncertainty is shown as a gray shaded band, and the statistical uncertainties of the data are shown as vertical bars. An example of a signal distribution is overlaid, where the number of expected events is scaled by a factor of 5. Shown below each mass plot is the corresponding pull distribution (Data-fit)/$\sigma $, where $\sigma =\sqrt {\sigma _\mathrm {data}^2-\sigma _\mathrm {fit}^2}$ for each bin to ensure a Gaussian pull-distribution, as defined in Ref. [83].

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Figure 10-a:
For the HPHP category: comparison between the fitted result and the data distributions of ${m_\text {jet1}}$. The background shape uncertainty is shown as a gray shaded band, and the statistical uncertainties of the data are shown as vertical bars. An example of a signal distribution is overlaid, where the number of expected events is scaled by a factor of 5. Shown below the mass plot is the corresponding pull distribution (Data-fit)/$\sigma $, where $\sigma =\sqrt {\sigma _\mathrm {data}^2-\sigma _\mathrm {fit}^2}$ for each bin to ensure a Gaussian pull-distribution, as defined in Ref. [83].

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Figure 10-b:
For the HPHP category: comparison between the fitted result and the data distributions of ${m_\text {jet2}}$. The background shape uncertainty is shown as a gray shaded band, and the statistical uncertainties of the data are shown as vertical bars. An example of a signal distribution is overlaid, where the number of expected events is scaled by a factor of 5. Shown below the mass plot is the corresponding pull distribution (Data-fit)/$\sigma $, where $\sigma =\sqrt {\sigma _\mathrm {data}^2-\sigma _\mathrm {fit}^2}$ for each bin to ensure a Gaussian pull-distribution, as defined in Ref. [83].

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Figure 10-c:
For the HPHP category: comparison between the fitted result and the data distributions of ${m_\mathrm {jj}}$. The background shape uncertainty is shown as a gray shaded band, and the statistical uncertainties of the data are shown as vertical bars. An example of a signal distribution is overlaid, where the number of expected events is scaled by a factor of 5. Shown below the mass plot is the corresponding pull distribution (Data-fit)/$\sigma $, where $\sigma =\sqrt {\sigma _\mathrm {data}^2-\sigma _\mathrm {fit}^2}$ for each bin to ensure a Gaussian pull-distribution, as defined in Ref. [83].

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Figure 11:
For the HPLP category: comparison between the fitted result and the data distributions of ${m_\text {jet1}}$ (upper left), ${m_\text {jet2}}$ (upper right), and ${m_\mathrm {jj}}$ (lower). The background shape uncertainty is shown as a gray shaded band, and the statistical uncertainties of the data are shown as vertical bars. An example of a signal distribution is overlaid, where the number of expected events is scaled by a factor of 5. Shown below each mass plot is the corresponding pull distribution (Data-fit)/$\sigma $, where $\sigma =\sqrt {\sigma _\mathrm {data}^2-\sigma _\mathrm {fit}^2}$ for each bin to ensure a Gaussian pull-distribution, as defined in Ref. [83].

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Figure 11-a:
For the HPLP category: comparison between the fitted result and the data distributions of ${m_\text {jet1}}$. The background shape uncertainty is shown as a gray shaded band, and the statistical uncertainties of the data are shown as vertical bars. An example of a signal distribution is overlaid, where the number of expected events is scaled by a factor of 5. Shown below the mass plot is the corresponding pull distribution (Data-fit)/$\sigma $, where $\sigma =\sqrt {\sigma _\mathrm {data}^2-\sigma _\mathrm {fit}^2}$ for each bin to ensure a Gaussian pull-distribution, as defined in Ref. [83].

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Figure 11-b:
For the HPLP category: comparison between the fitted result and the data distributions of ${m_\text {jet2}}$. The background shape uncertainty is shown as a gray shaded band, and the statistical uncertainties of the data are shown as vertical bars. An example of a signal distribution is overlaid, where the number of expected events is scaled by a factor of 5. Shown below the mass plot is the corresponding pull distribution (Data-fit)/$\sigma $, where $\sigma =\sqrt {\sigma _\mathrm {data}^2-\sigma _\mathrm {fit}^2}$ for each bin to ensure a Gaussian pull-distribution, as defined in Ref. [83].

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Figure 11-c:
For the HPLP category: comparison between the fitted result and the data distributions of ${m_\mathrm {jj}}$. The background shape uncertainty is shown as a gray shaded band, and the statistical uncertainties of the data are shown as vertical bars. An example of a signal distribution is overlaid, where the number of expected events is scaled by a factor of 5. Shown below the mass plot is the corresponding pull distribution (Data-fit)/$\sigma $, where $\sigma =\sqrt {\sigma _\mathrm {data}^2-\sigma _\mathrm {fit}^2}$ for each bin to ensure a Gaussian pull-distribution, as defined in Ref. [83].

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Figure 12:
Observed and expected 95% CL upper limits on the product of the production cross section ($\sigma $) and the branching fraction, obtained after combining categories of all purities with 77.3 fb$^{-1}$ of 13 TeV data, for $ {\mathrm{G} _{\text {bulk}}} \to \mathrm{W} \mathrm{W} $ (upper left), $ {\mathrm{G} _{\text {bulk}}} \to \mathrm{Z} \mathrm{Z} $ (upper right), $\mathrm{W'} \to \mathrm{W} \mathrm{Z} $ (lower left), and $\mathrm{Z'} \to \mathrm{W} \mathrm{W} $ (lower right) signals. For each signal scenario the theoretical prediction (red line) and its uncertainty associated with the choice of PDF set (red hashed band) is shown. The theory cross sections (red line) are calculated at LO in QCD [34,6].

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Figure 12-a:
Observed and expected 95% CL upper limits on the product of the production cross section ($\sigma $) and the branching fraction, obtained after combining categories of all purities with 77.3 fb$^{-1}$ of 13 TeV data, for the$ {\mathrm{G} _{\text {bulk}}} \to \mathrm{W} \mathrm{W} $ signal. The theoretical prediction (red line) and its uncertainty associated with the choice of PDF set (red hashed band) is shown. The theory cross section (red line) is calculated at LO in QCD [34,6].

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Figure 12-b:
Observed and expected 95% CL upper limits on the product of the production cross section ($\sigma $) and the branching fraction, obtained after combining categories of all purities with 77.3 fb$^{-1}$ of 13 TeV data, for the $ {\mathrm{G} _{\text {bulk}}} \to \mathrm{Z} \mathrm{Z} $ signal. The theoretical prediction (red line) and its uncertainty associated with the choice of PDF set (red hashed band) is shown. The theory cross section (red line) is calculated at LO in QCD [34,6].

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Figure 12-c:
Observed and expected 95% CL upper limits on the product of the production cross section ($\sigma $) and the branching fraction, obtained after combining categories of all purities with 77.3 fb$^{-1}$ of 13 TeV data, for the $\mathrm{W'} \to \mathrm{W} \mathrm{Z} $ signal. The theoretical prediction (red line) and its uncertainty associated with the choice of PDF set (red hashed band) is shown. The theory cross section (red line) is calculated at LO in QCD [34,6].

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Figure 12-d:
Observed and expected 95% CL upper limits on the product of the production cross section ($\sigma $) and the branching fraction, obtained after combining categories of all purities with 77.3 fb$^{-1}$ of 13 TeV data, for the $\mathrm{Z'} \to \mathrm{W} \mathrm{W} $ signal. The theoretical prediction (red line) and its uncertainty associated with the choice of PDF set (red hashed band) is shown. The theory cross section (red line) is calculated at LO in QCD [34,6].

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Figure 13:
Expected 95% CL upper limits on the product of the production cross section ($\sigma $) and the branching fraction for a $ {\mathrm{G} _{\text {bulk}}} \to \mathrm{W} \mathrm{W} $ signal using 35.9 fb$^{-1}$ of data collected in 2016 obtained using the multi-dimensional fit method presented here (red solid line), compared to the result obtained with previous methods (black dash-dotted line) [29]. The final limit obtained when combining data collected in 2016 and 2017 is also shown (blue dashed line).
Tables

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Table 1:
The W jet mass peak position (m) and resolution ($\sigma $), and the W-tagging efficiencies, as extracted from top quark enriched data and from simulation, together with the corresponding data-to-simulation scale factors. The uncertainties in the scale factors include systematic uncertainties estimated as described in Ref. [62].

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Table 2:
Summary of the systematic uncertainties and the quantities they affect. Numbers in parentheses correspond to uncertainties for the 2016 analysis if these differ from those for 2017. Dashes indicate shape variations that cannot be described by a single parameter, and are discussed in the text.

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Table 3:
Observed yield and background yields extracted from the multi-dimensional fit together with post-fit uncertainties, in the two purity categories.
Summary
A search is presented for resonances with masses above 1.2 TeV that decay to WW, ZZ, or WZ boson pairs. Each of the two bosons decays into one large-radius jet, yielding dijet final states. The search is conducted using a novel approach based on a three-dimensional maximum likelihood fit in the dijet invariant mass as well as the two jet masses, thus taking advantage of the fact that the expected signal is resonant in all three mass dimensions. This method yields an improvement in sensitivity of up to 30% relative to previous search methods. The new method places additional constraints on systematic uncertainties affecting the signal by measuring the standard model background from W or Z production with associated jets. Decays of W and Z bosons are identified using jet substructure observables that reduce the background from quantum chromodynamics multijet production. No evidence is found for a signal, and upper limits on the resonance production cross section are set as a function of the resonance mass. The limits presented in this paper are the best to date in the dijet final state, and have a similar sensitivity as the combination of different VV, VH, and HH decay channels using the 2016 data set. The results are interpreted within bulk graviton models, and as limits on the production of the W' and Z' bosons within the heavy vector triplet framework. For the heavy vector triplet model B, we exclude at 95% confidence level W' and Z' spin-1 resonances with masses below 3.8 and 3.5 TeV, respectively. In the narrow-width bulk graviton model, upper limits on the production cross sections for ${\mathrm{G}_{\text{bulk}}} \to\mathrm{WW} (\mathrm{ZZ})$ are set in the range of 20 (27) fb to 0.2 fb for resonance masses between 1.2 and 5.2 TeV.
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