CMSHIG22009 ; CERNEP2023110  
Measurement of the Higgs boson production via vector boson fusion and its decay into bottom quarks in protonproton collisions at $ \sqrt{s}= $ 13 TeV  
CMS Collaboration  
2 August 2023  
JHEP 01 (2024) 173  
Abstract: A measurement of the Higgs boson (H) production via vector boson fusion (VBF) and its decay into a bottom quarkantiquark pair ($ \mathrm{b} \overline{\mathrm{b}} $) is presented using protonproton collision data recorded by the CMS experiment at $ \sqrt{s}= $ 13 TeV and corresponding to an integrated luminosity of 90.8 fb$ ^{1} $. Treating the gluongluon fusion process as a background and constraining its rate to the value expected in the standard model (SM) within uncertainties, the signal strength of the VBF process, defined as the ratio of the observed signal rate to that predicted by the SM, is measured to be $ {\mu^{\mathrm{q}\mathrm{q}\mathrm{H}}_{\mathrm{H}\mathrm{b}\overline{\mathrm{b}}}}= $ 1.01$ ^{+0.55}_{0.46} $. The VBF signal is observed with a significance of 2.4 standard deviations relative to the background prediction, while the expected significance is 2.7 standard deviations. Considering inclusive Higgs boson production and decay into bottom quarks, the signal strength is measured to be $ {\mu^\text{incl.}_{\mathrm{H}\mathrm{b}\overline{\mathrm{b}}}}= $ 0.99$ ^{+0.48}_{0.41} $, corresponding to an observed (expected) significance of 2.6 (2.9) standard deviations.  
Links: eprint arXiv:2308.01253 [hepex] (PDF) ; CDS record ; inSPIRE record ; HepData record ; CADI line (restricted) ; 
Figures  
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Figure 1:
Representative Feynman diagram of the LO VBF production of a Higgs boson, followed by its decay to a pair of b quarks. 
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Figure 2:
The invariant mass $ m_{\mathrm{b}\overline{\mathrm{b}}} $ of the b jet pair in simulated $ \mathrm{q}\mathrm{q}\mathrm{H}\to\mathrm{q}\mathrm{q}\mathrm{b}\overline{\mathrm{b}} $ events before (orange dashed line) and after (blue dashed line) the application of the b jet energy regression in the Tight 2016 (left) and Loose 2016 (right) samples. A onesided Crystal Ball function [50] is used to fit the distributions. 
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Figure 2a:
The invariant mass $ m_{\mathrm{b}\overline{\mathrm{b}}} $ of the b jet pair in simulated $ \mathrm{q}\mathrm{q}\mathrm{H}\to\mathrm{q}\mathrm{q}\mathrm{b}\overline{\mathrm{b}} $ events before (orange dashed line) and after (blue dashed line) the application of the b jet energy regression in the Tight 2016 sample. A onesided Crystal Ball function [50] is used to fit the distributions. 
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Figure 2b:
The invariant mass $ m_{\mathrm{b}\overline{\mathrm{b}}} $ of the b jet pair in simulated $ \mathrm{q}\mathrm{q}\mathrm{H}\to\mathrm{q}\mathrm{q}\mathrm{b}\overline{\mathrm{b}} $ events before (orange dashed line) and after (blue dashed line) the application of the b jet energy regression in the Loose 2016 sample. A onesided Crystal Ball function [50] is used to fit the distributions. 
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Figure 3:
The unit normalized distributions of the VBF BDT outputs in data and simulated samples in the Tight 2016 (left) and Tight 2018 (right) analysis samples. Data events (points), dominated by the QCD multijet background, are compared to the VBF (red solid line), ggH (blue dashed line), and Z+jets (green hatched area) processes. 
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Figure 3a:
The unit normalized distributions of the VBF BDT outputs in data and simulated samples in the Tight 2016 analysis sample. Data events (points), dominated by the QCD multijet background, are compared to the VBF (red solid line), ggH (blue dashed line), and Z+jets (green hatched area) processes. 
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Figure 3b:
The unit normalized distributions of the VBF BDT outputs in data and simulated samples in the Tight 2018 analysis sample. Data events (points), dominated by the QCD multijet background, are compared to the VBF (red solid line), ggH (blue dashed line), and Z+jets (green hatched area) processes. 
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Figure 4:
The unit normalized distributions of the BDT outputs: $ D_{\mathrm{g}\mathrm{g}\mathrm{H}} $ (upper), $ D_{\text{VBF}} $ (middle), and $ D_{\mathrm{Z}} $ (lower) in data and simulated samples in the Loose 2016 (left) and Loose 2018 (right) analysis samples. Data events (points), dominated by the QCD multijet background, are compared to the VBF (red solid line), ggH (blue dashed line), and Z+jets (green hatched area) processes. 
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Figure 4a:
The unit normalized distribution of the $ D_{\mathrm{g}\mathrm{g}\mathrm{H}} $ BDT output in data and simulated samples in the Loose 2016 analysis sample. Data events (points), dominated by the QCD multijet background, are compared to the VBF (red solid line), ggH (blue dashed line), and Z+jets (green hatched area) processes. 
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Figure 4b:
The unit normalized distribution of the $ D_{\mathrm{g}\mathrm{g}\mathrm{H}} $ BDT output in data and simulated samples in the Loose 2018 analysis sample. Data events (points), dominated by the QCD multijet background, are compared to the VBF (red solid line), ggH (blue dashed line), and Z+jets (green hatched area) processes. 
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Figure 4c:
The unit normalized distribution of the $ D_{\text{VBF}} $ BDT output in data and simulated samples in the Loose 2016 analysis sample. Data events (points), dominated by the QCD multijet background, are compared to the VBF (red solid line), ggH (blue dashed line), and Z+jets (green hatched area) processes. 
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Figure 4d:
The unit normalized distribution of the $ D_{\text{VBF}} $ BDT output in data and simulated samples in the Loose 2018 analysis sample. Data events (points), dominated by the QCD multijet background, are compared to the VBF (red solid line), ggH (blue dashed line), and Z+jets (green hatched area) processes. 
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Figure 4e:
The unit normalized distribution of the $ D_{\mathrm{Z}} $ BDT output in data and simulated samples in the Loose 2016 analysis sample. Data events (points), dominated by the QCD multijet background, are compared to the VBF (red solid line), ggH (blue dashed line), and Z+jets (green hatched area) processes. 
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Figure 4f:
The unit normalized distribution of the $ D_{\mathrm{Z}} $ BDT output in data and simulated samples in the Loose 2018 analysis sample. Data events (points), dominated by the QCD multijet background, are compared to the VBF (red solid line), ggH (blue dashed line), and Z+jets (green hatched area) processes. 
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Figure 5:
The $ m_{\mathrm{b}\overline{\mathrm{b}}} $ distributions from simulation with overlaid parametric fits (solid blue lines) for the Tight 2016 analysis sample. Left: The fitted $ m_{\mathrm{b}\overline{\mathrm{b}}} $ distribution in the signal combining the VBF (yellow histogram) and ggH (orange) contributions. The black points refer to the total Higgs bosom contribution from VBF and ggH production modes. Right: The fitted $ m_{\mathrm{b}\overline{\mathrm{b}}} $ distribution in simulated Z+jets background (black points) combining the $ \mathrm{W}\mathrm{W}\to\mathrm{Z} $ (dark green histogram) and $ \mathrm{q}\overline{\mathrm{q}}\to\mathrm{Z} $ (light green histogram) production modes. The black points refer to the total Z+jets contribution from $ \mathrm{q}\overline{\mathrm{q}}\to\mathrm{Z} $ and $ \mathrm{W}\mathrm{W}\to\mathrm{Z} $ modes. The dotted lines represent the secondorder Bernstein polynomial components used to approximate the contributions from the wrong jet pairing. 
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Figure 5a:
The $ m_{\mathrm{b}\overline{\mathrm{b}}} $ distributions from simulation with overlaid parametric fits (solid blue lines) for the Tight 2016 analysis sample. The fitted $ m_{\mathrm{b}\overline{\mathrm{b}}} $ distribution in the signal combining the VBF (yellow histogram) and ggH (orange) contributions. The black points refer to the total Higgs bosom contribution from VBF and ggH production modes. 
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Figure 5b:
The $ m_{\mathrm{b}\overline{\mathrm{b}}} $ distributions from simulation with overlaid parametric fits (solid blue lines) for the Tight 2016 analysis sample. The fitted $ m_{\mathrm{b}\overline{\mathrm{b}}} $ distribution in simulated Z+jets background (black points) combining the $ \mathrm{W}\mathrm{W}\to\mathrm{Z} $ (dark green histogram) and $ \mathrm{q}\overline{\mathrm{q}}\to\mathrm{Z} $ (light green histogram) production modes. The black points refer to the total Z+jets contribution from $ \mathrm{q}\overline{\mathrm{q}}\to\mathrm{Z} $ and $ \mathrm{W}\mathrm{W}\to\mathrm{Z} $ modes. The dotted lines represent the secondorder Bernstein polynomial components used to approximate the contributions from the wrong jet pairing. 
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Figure 6:
The $ m_{\mathrm{b}\overline{\mathrm{b}}} $ distributions in three event categories: Tight 2016 1 (left), Tight 2016 2 (center), and Tight 2016 3 (right). The points indicate data, the blue solid curve corresponds to the fitted nonresonant component of the background, dominated by QCD multijet events; the shaded (cyan) band represents the $ \pm $1$ \sigma $ uncertainty band. The total signalplusbackground model includes contributions from $ \mathrm{Z}\to\mathrm{b}\overline{\mathrm{b}} $, $ \mathrm{H}\to\mathrm{b}\overline{\mathrm{b}} $, and the nonresonant component; it is represented by the magenta curve. The lower panel compares the distribution of the data after subtracting the nonresonant component with the resonant contributions of the $ \mathrm{Z}\to\mathrm{b}\overline{\mathrm{b}} $ background (red curve) and $ \mathrm{H}\to\mathrm{b}\overline{\mathrm{b}} $ signal (green curve). 
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Figure 6a:
The $ m_{\mathrm{b}\overline{\mathrm{b}}} $ distributions in the Tight 2016 1 category. The points indicate data, the blue solid curve corresponds to the fitted nonresonant component of the background, dominated by QCD multijet events; the shaded (cyan) band represents the $ \pm $1$ \sigma $ uncertainty band. The total signalplusbackground model includes contributions from $ \mathrm{Z}\to\mathrm{b}\overline{\mathrm{b}} $, $ \mathrm{H}\to\mathrm{b}\overline{\mathrm{b}} $, and the nonresonant component; it is represented by the magenta curve. The lower panel compares the distribution of the data after subtracting the nonresonant component with the resonant contributions of the $ \mathrm{Z}\to\mathrm{b}\overline{\mathrm{b}} $ background (red curve) and $ \mathrm{H}\to\mathrm{b}\overline{\mathrm{b}} $ signal (green curve). 
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Figure 6b:
The $ m_{\mathrm{b}\overline{\mathrm{b}}} $ distributions in the Tight 2016 2 category. The points indicate data, the blue solid curve corresponds to the fitted nonresonant component of the background, dominated by QCD multijet events; the shaded (cyan) band represents the $ \pm $1$ \sigma $ uncertainty band. The total signalplusbackground model includes contributions from $ \mathrm{Z}\to\mathrm{b}\overline{\mathrm{b}} $, $ \mathrm{H}\to\mathrm{b}\overline{\mathrm{b}} $, and the nonresonant component; it is represented by the magenta curve. The lower panel compares the distribution of the data after subtracting the nonresonant component with the resonant contributions of the $ \mathrm{Z}\to\mathrm{b}\overline{\mathrm{b}} $ background (red curve) and $ \mathrm{H}\to\mathrm{b}\overline{\mathrm{b}} $ signal (green curve). 
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Figure 6c:
The $ m_{\mathrm{b}\overline{\mathrm{b}}} $ distributions in the Tight 2016 3 category. The points indicate data, the blue solid curve corresponds to the fitted nonresonant component of the background, dominated by QCD multijet events; the shaded (cyan) band represents the $ \pm $1$ \sigma $ uncertainty band. The total signalplusbackground model includes contributions from $ \mathrm{Z}\to\mathrm{b}\overline{\mathrm{b}} $, $ \mathrm{H}\to\mathrm{b}\overline{\mathrm{b}} $, and the nonresonant component; it is represented by the magenta curve. The lower panel compares the distribution of the data after subtracting the nonresonant component with the resonant contributions of the $ \mathrm{Z}\to\mathrm{b}\overline{\mathrm{b}} $ background (red curve) and $ \mathrm{H}\to\mathrm{b}\overline{\mathrm{b}} $ signal (green curve). 
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Figure 7:
The $ m_{\mathrm{b}\overline{\mathrm{b}}} $ distributions in three event categories: Tight 2018 1 (left), Tight 2018 2 (center), and Tight 2018 3 (right). A complete description is given in Fig. 6. 
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Figure 7a:
The $ m_{\mathrm{b}\overline{\mathrm{b}}} $ distributions in three event categories: Tight 2018 1. A complete description is given in Fig. 6. 
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Figure 7b:
The $ m_{\mathrm{b}\overline{\mathrm{b}}} $ distributions in three event categories: Tight 2018 2. A complete description is given in Fig. 6. 
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Figure 7c:
The $ m_{\mathrm{b}\overline{\mathrm{b}}} $ distributions in three event categories: Tight 2018 3. A complete description is given in Fig. 6. 
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Figure 8:
The $ m_{\mathrm{b}\overline{\mathrm{b}}} $ distributions in two event categories: Loose 2016 Z2 (left) and Loose 2018 Z2 (right). A complete description is given in Fig. 6. 
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Figure 8a:
The $ m_{\mathrm{b}\overline{\mathrm{b}}} $ distributions in two event categories: Loose 2016 Z2. A complete description is given in Fig. 6. 
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Figure 8b:
The $ m_{\mathrm{b}\overline{\mathrm{b}}} $ distributions in two event categories: Loose 2018 Z2. A complete description is given in Fig. 6. 
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Figure 9:
The $ m_{\mathrm{b}\overline{\mathrm{b}}} $ distribution after weighted combination of all categories in the analysis weighted with $ S/(S+B) $. A complete description is given in Fig. 6. 
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Figure 10:
The best fit values of the signal strength modifier for the different processes. The horizontal bars in blue and red colors represent the $ \pm$1$\sigma $ total uncertainty and its systematic component. The vertical dashed line shows the standard model prediction. 
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Figure 11:
The best fit values of the signal strength modifier for the different processes, the horizontal bars in blue and red colors represent the $ \pm1\,\sigma $ total uncertainty and its systematic component and the vertical dashed line shows the SM prediction (left). The twodimensional likelihood scan of $ \mu^{\mathrm{q}\mathrm{q}\mathrm{H}}_{\mathrm{H}\mathrm{b}\overline{\mathrm{b}}} $ and $ \mu^{\mathrm{g}\mathrm{g}\mathrm{H}}_{\mathrm{H}\mathrm{b}\overline{\mathrm{b}}} $, the red (blue) solid and dashed lines correspond to the observed (expected) 68 and 95% CL contours in the $ (\mu^{\mathrm{q}\mathrm{q}\mathrm{H}}_{\mathrm{H}\mathrm{b}\overline{\mathrm{b}}}, \mu^{\mathrm{g}\mathrm{g}\mathrm{H}}_{\mathrm{H}\mathrm{b}\overline{\mathrm{b}}}) $ plane (right). The SM predicted and observed best fit values are indicated by the blue and red crosses. 
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Figure 11a:
The best fit values of the signal strength modifier for the different processes, the horizontal bars in blue and red colors represent the $ \pm1\,\sigma $ total uncertainty and its systematic component and the vertical dashed line shows the SM prediction. 
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Figure 11b:
The twodimensional likelihood scan of $ \mu^{\mathrm{q}\mathrm{q}\mathrm{H}}_{\mathrm{H}\mathrm{b}\overline{\mathrm{b}}} $ and $ \mu^{\mathrm{g}\mathrm{g}\mathrm{H}}_{\mathrm{H}\mathrm{b}\overline{\mathrm{b}}} $, the red (blue) solid and dashed lines correspond to the observed (expected) 68 and 95% CL contours in the $ (\mu^{\mathrm{q}\mathrm{q}\mathrm{H}}_{\mathrm{H}\mathrm{b}\overline{\mathrm{b}}}, \mu^{\mathrm{g}\mathrm{g}\mathrm{H}}_{\mathrm{H}\mathrm{b}\overline{\mathrm{b}}}) $ plane (right). The SM predicted and observed best fit values are indicated by the blue and red crosses. 
Tables  
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Table 1:
The HLT and offline selection requirements in the four analyzed samples. 
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Table 2:
Event categorization used in the analysis for a total of 18 categories. The names of the categories are given in the first column. The BDT score boundaries defining each category are given in the second column and the targeted process is indicated in the third column. 
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Table 3:
Event yields for various categories of the analyzed 2016 data corresponding to 36.3 fb$ ^{1} $, compared to the expected number of events from the simulated samples of signal and background other than the QCD multijet process. The quoted uncertainties are statistical only. 
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Table 4:
Event yields for various categories of the analyzed 2018 data corresponding to 54.5 fb$ ^{1} $, compared to the expected number of events from the simulated samples of signal and background other than the QCD multijet process. The quoted uncertainties are statistical only. 
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Table 5:
The functional forms used to fit the continuum component of the background in various analysis categories. The notation ``exp'' stands for the exponential function, ``exp$ \cdot $pol1 (pol2)" denotes the product of an exponential function and a firstorder (secondorder) polynomial. 
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Table 6:
The impact of the dominant systematic uncertainties on the observed signal strength for inclusive Higgs boson production followed by decay to bottom quarks. 
Summary 
A measurement of the Higgs boson (H) production via vector boson fusion (VBF) process and its decay to a bottom quarkantiquark pair ($ \mathrm{b} \overline{\mathrm{b}} $) was performed on protonproton collision data sets collected by the CMS experiment at $ \sqrt{s}= $ 13 TeV corresponding to a total integrated luminosity of 90.8 fb$ ^{1} $. The analysis employs boosted decision trees (BDTs) to discriminate the signal against major background processesQCDinduced multijet production and Z+jets events. The BDTs exploit kinematic properties of the VBF jets, information of the btagged jets assigned to the $ \mathrm{H}\to\mathrm{b}\overline{\mathrm{b}} $ decay, and global event shape variables. Based on the BDT response, multiple event categories are introduced, targeting the VBF, gluongluon fusion (ggH), and Z+jets processes to achieve a maximum sensitivity for the signal. While the VBF categories have the highest signaltobackground ratio, the Z+jets categories constrain the largest resonant background. The ggH categories enhance the sensitivity to the inclusive production of the Higgs boson in association with two jets. The VBF Higgs boson production rate has been measured in its decay to bottom quarkantiquark pairs with the ggH contribution constrained within the theoretical and experimental uncertainties to the standard model prediction. The signal strength of the VBF Higgs production, followed by the $ \mathrm{H}\to\mathrm{b}\overline{\mathrm{b}} $ decay, defined as the rate of the signal process relative to the value predicted in the standard model, is measured to be, $ {\mu^{\mathrm{q}\mathrm{q}\mathrm{H}}_{\mathrm{H}\mathrm{b}\overline{\mathrm{b}}}}= $ 1.01$ ^{+0.55}_{0.46} $. The signal was observed with a significance of 2.4 standard deviations, compared to the expected significance of 2.7 standard deviations. In addition, inclusive Higgs boson production in association with two jets, followed by $ \mathrm{H}\to\mathrm{b}\overline{\mathrm{b}} $ decay, was measured by treating the ggH contribution as part of the signal. The inclusive signal strength was measured to be $ {\mu^\text{incl.}_{\mathrm{H}\mathrm{b}\overline{\mathrm{b}}}}= $ 0.99$ ^{+0.48}_{0.41} $, corresponding to an observed (expected) significance of 2.6 (2.9) standard deviations. The measurements are consistent within uncertainties with the prediction from the standard model. 
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