CMS-PAS-HIG-22-009

CMS-PAS-HIG-22-009
Measurement of the signal strength of the Higgs boson decaying to bottom quarks and produced from Vector Boson Fusion using proton-proton collision data at $\sqrt{s}=$ 13 TeV
CMS Collaboration
8 November 2022

Abstract: A measurement of the signal strength of Higgs boson production via the vector boson fusion (VBF) process and its subsequent decay into a pair of bottom quarks is presented. The analysis uses the proton-proton collision data recorded by the CMS experiment at a center-of-mass energy of 13 TeV and corresponding to an integrated luminosity of 91 fb $^{-1}$ . Treating gluon-gluon fusion as a background and constraining its rate within the theoretical and the experimental uncertainties to the standard model prediction (SM), the signal strength of the VBF process, defined as the ratio of the observed signal rate to that predicted in the SM, is measured to be $\mu_{\mathrm{qqH}}=$ 0.97 $^{+0.53}_{-0.45}$ . The VBF signal is observed with a significance of 2.4 $\sigma$ relative to the background prediction, while the expected significance is 2.7 $\sigma$ . The inclusive measurement of the Higgs boson production followed by the Higgs boson decay into bottom quarks yields the best-fit value for the signal strength of $\mu_{\mathrm{Hb\bar{b}}}=$ 0.92 $^{+0.45}_{-0.39}$ , corresponding to an observed (expected) significance of 2.5 (2.9) $\sigma$ .
Links: CDS record (PDF) ; CADI line (restricted) ; These preliminary results are superseded in this paper, Submitted to JHEP. The superseded preliminary plots can be found here.

Figures & Tables	Summary	References	CMS Publications

Figures
png pdf	Figure 1: Representative Feynman diagram of the VBF production of Higgs boson and subsequently decaying to a pair of b quarks.
png pdf	Figure 2: The invariant mass $m_{\rm bb}$ of the b-jet pair in simulated $\rm{qqH\rightarrow qqb\bar{b}}$ events before (in orange) and after (in blue) the application of the b-jet energy regression in the Tight 2016 (left) and Loose 2016 (right) analysis samples. A single sided Crystal Ball (CB) function is used to fit the distributions.
png pdf	Figure 2-a: The invariant mass $m_{\rm bb}$ of the b-jet pair in simulated $\rm{qqH\rightarrow qqb\bar{b}}$ events before (in orange) and after (in blue) the application of the b-jet energy regression in the Tight 2016 (left) and Loose 2016 (right) analysis samples. A single sided Crystal Ball (CB) function is used to fit the distributions.
png pdf	Figure 2-b: The invariant mass $m_{\rm bb}$ of the b-jet pair in simulated $\rm{qqH\rightarrow qqb\bar{b}}$ events before (in orange) and after (in blue) the application of the b-jet energy regression in the Tight 2016 (left) and Loose 2016 (right) analysis samples. A single sided Crystal Ball (CB) function is used to fit the distributions.
png pdf	Figure 3: The 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), ggF (blue dashed line) and Z + jets (green hatched area) processes.
png pdf	Figure 3-a: The 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), ggF (blue dashed line) and Z + jets (green hatched area) processes.
png pdf	Figure 3-b: The 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), ggF (blue dashed line) and Z + jets (green hatched area) processes.
png pdf	Figure 4: The distributions of the BDT outputs: $D_{\rm{ggF}}$ (upper plots), $D_{\rm{VBF}}$ (middle plots) and $D_{\rm{Z}}$ (lower plots) in data and simulated samples in the Loose 2016 (left plots) and Loose 2018 (right plots) analysis samples. Data events (points), dominated by the QCD multijet background, are compared to the VBF (red solid line), ggF (blue dashed line) and Z + jets (green hatched area) processes.
png pdf	Figure 4-a: The distributions of the BDT outputs: $D_{\rm{ggF}}$ (upper plots), $D_{\rm{VBF}}$ (middle plots) and $D_{\rm{Z}}$ (lower plots) in data and simulated samples in the Loose 2016 (left plots) and Loose 2018 (right plots) analysis samples. Data events (points), dominated by the QCD multijet background, are compared to the VBF (red solid line), ggF (blue dashed line) and Z + jets (green hatched area) processes.
png pdf	Figure 4-b: The distributions of the BDT outputs: $D_{\rm{ggF}}$ (upper plots), $D_{\rm{VBF}}$ (middle plots) and $D_{\rm{Z}}$ (lower plots) in data and simulated samples in the Loose 2016 (left plots) and Loose 2018 (right plots) analysis samples. Data events (points), dominated by the QCD multijet background, are compared to the VBF (red solid line), ggF (blue dashed line) and Z + jets (green hatched area) processes.
png pdf	Figure 4-c: The distributions of the BDT outputs: $D_{\rm{ggF}}$ (upper plots), $D_{\rm{VBF}}$ (middle plots) and $D_{\rm{Z}}$ (lower plots) in data and simulated samples in the Loose 2016 (left plots) and Loose 2018 (right plots) analysis samples. Data events (points), dominated by the QCD multijet background, are compared to the VBF (red solid line), ggF (blue dashed line) and Z + jets (green hatched area) processes.
png pdf	Figure 4-d: The distributions of the BDT outputs: $D_{\rm{ggF}}$ (upper plots), $D_{\rm{VBF}}$ (middle plots) and $D_{\rm{Z}}$ (lower plots) in data and simulated samples in the Loose 2016 (left plots) and Loose 2018 (right plots) analysis samples. Data events (points), dominated by the QCD multijet background, are compared to the VBF (red solid line), ggF (blue dashed line) and Z + jets (green hatched area) processes.
png pdf	Figure 4-e: The distributions of the BDT outputs: $D_{\rm{ggF}}$ (upper plots), $D_{\rm{VBF}}$ (middle plots) and $D_{\rm{Z}}$ (lower plots) in data and simulated samples in the Loose 2016 (left plots) and Loose 2018 (right plots) analysis samples. Data events (points), dominated by the QCD multijet background, are compared to the VBF (red solid line), ggF (blue dashed line) and Z + jets (green hatched area) processes.
png pdf	Figure 4-f: The distributions of the BDT outputs: $D_{\rm{ggF}}$ (upper plots), $D_{\rm{VBF}}$ (middle plots) and $D_{\rm{Z}}$ (lower plots) in data and simulated samples in the Loose 2016 (left plots) and Loose 2018 (right plots) analysis samples. Data events (points), dominated by the QCD multijet background, are compared to the VBF (red solid line), ggF (blue dashed line) and Z + jets (green hatched area) processes.
png pdf	Figure 5: The $m_{\rm bb}$ distributions from simulations with overlaid parametric fits (blue solid lines) for the Tight 2016 analysis sample. Left: the fitted $m_{\rm bb}$ distribution in the signal combining the VBF (yellow histogram) and ggF (pink) contributions. Right: The $m_{\rm bb}$ distribution in simulated Z + jets background (black points) combining the electroweak (blue histogram) and Drell-Yan (green histogram) production. The dotted lines in each plot represents the component of the 2nd order Bernstein polynomial used to approximate contribution from the wrong pairing of jets.
png pdf	Figure 5-a: The $m_{\rm bb}$ distributions from simulations with overlaid parametric fits (blue solid lines) for the Tight 2016 analysis sample. Left: the fitted $m_{\rm bb}$ distribution in the signal combining the VBF (yellow histogram) and ggF (pink) contributions. Right: The $m_{\rm bb}$ distribution in simulated Z + jets background (black points) combining the electroweak (blue histogram) and Drell-Yan (green histogram) production. The dotted lines in each plot represents the component of the 2nd order Bernstein polynomial used to approximate contribution from the wrong pairing of jets.
png pdf	Figure 5-b: The $m_{\rm bb}$ distributions from simulations with overlaid parametric fits (blue solid lines) for the Tight 2016 analysis sample. Left: the fitted $m_{\rm bb}$ distribution in the signal combining the VBF (yellow histogram) and ggF (pink) contributions. Right: The $m_{\rm bb}$ distribution in simulated Z + jets background (black points) combining the electroweak (blue histogram) and Drell-Yan (green histogram) production. The dotted lines in each plot represents the component of the 2nd order Bernstein polynomial used to approximate contribution from the wrong pairing of jets.
png pdf	Figure 6: The $m_{\rm bb}$ distributions in three event categories: Tight 2016 1 (left), Tight 2016 2 (central) and Tight 2016 3 (right). The points indicate data, the blue solid curve corresponds to the fitted non-resonant component of the background, dominated by QCD multijets; the shaded (cyan) band represents 1 $\sigma$ uncertainty band. The total fitted signal+background model includes resonant contributions from $\rm{Z\rightarrow b\bar{b}}$ and $\rm{H\rightarrow b\bar{b}}$ and the non-resonant component; it is represented by the magenta curve. The lower panel compares the distribution of data after subtracting non-resonant component with the fitted resonant contribution of the $\rm{Z\rightarrow b\bar{b}}$ background (red curve) and $\rm{H\rightarrow b\bar{b}}$ signal (green curve).
png pdf	Figure 6-a: The $m_{\rm bb}$ distributions in three event categories: Tight 2016 1 (left), Tight 2016 2 (central) and Tight 2016 3 (right). The points indicate data, the blue solid curve corresponds to the fitted non-resonant component of the background, dominated by QCD multijets; the shaded (cyan) band represents 1 $\sigma$ uncertainty band. The total fitted signal+background model includes resonant contributions from $\rm{Z\rightarrow b\bar{b}}$ and $\rm{H\rightarrow b\bar{b}}$ and the non-resonant component; it is represented by the magenta curve. The lower panel compares the distribution of data after subtracting non-resonant component with the fitted resonant contribution of the $\rm{Z\rightarrow b\bar{b}}$ background (red curve) and $\rm{H\rightarrow b\bar{b}}$ signal (green curve).
png pdf	Figure 6-b: The $m_{\rm bb}$ distributions in three event categories: Tight 2016 1 (left), Tight 2016 2 (central) and Tight 2016 3 (right). The points indicate data, the blue solid curve corresponds to the fitted non-resonant component of the background, dominated by QCD multijets; the shaded (cyan) band represents 1 $\sigma$ uncertainty band. The total fitted signal+background model includes resonant contributions from $\rm{Z\rightarrow b\bar{b}}$ and $\rm{H\rightarrow b\bar{b}}$ and the non-resonant component; it is represented by the magenta curve. The lower panel compares the distribution of data after subtracting non-resonant component with the fitted resonant contribution of the $\rm{Z\rightarrow b\bar{b}}$ background (red curve) and $\rm{H\rightarrow b\bar{b}}$ signal (green curve).
png pdf	Figure 6-c: The $m_{\rm bb}$ distributions in three event categories: Tight 2016 1 (left), Tight 2016 2 (central) and Tight 2016 3 (right). The points indicate data, the blue solid curve corresponds to the fitted non-resonant component of the background, dominated by QCD multijets; the shaded (cyan) band represents 1 $\sigma$ uncertainty band. The total fitted signal+background model includes resonant contributions from $\rm{Z\rightarrow b\bar{b}}$ and $\rm{H\rightarrow b\bar{b}}$ and the non-resonant component; it is represented by the magenta curve. The lower panel compares the distribution of data after subtracting non-resonant component with the fitted resonant contribution of the $\rm{Z\rightarrow b\bar{b}}$ background (red curve) and $\rm{H\rightarrow b\bar{b}}$ signal (green curve).
png pdf	Figure 7: The $m_{\rm bb}$ distributions in three event categories: Tight 2018 1 (left), Tight 2018 2 (central) and Tight 2018 3 (right). The points indicate data, the blue solid curve corresponds to the fitted non-resonant component of the background, dominated by QCD multijets; the shaded (cyan) band represents 1 $\sigma$ uncertainty band. The total fitted signal+background model includes resonant contributions from $\rm{Z\rightarrow b\bar{b}}$ and $\rm{H\rightarrow b\bar{b}}$ and the non-resonant component; it is represented by the magenta curve. The lower panel compares the distribution of data after subtracting non-resonant component with the fitted resonant contribution of the $\rm{Z\rightarrow b\bar{b}}$ background (red curve) and $\rm{H\rightarrow b\bar{b}}$ signal (green curve).
png pdf	Figure 7-a: The $m_{\rm bb}$ distributions in three event categories: Tight 2018 1 (left), Tight 2018 2 (central) and Tight 2018 3 (right). The points indicate data, the blue solid curve corresponds to the fitted non-resonant component of the background, dominated by QCD multijets; the shaded (cyan) band represents 1 $\sigma$ uncertainty band. The total fitted signal+background model includes resonant contributions from $\rm{Z\rightarrow b\bar{b}}$ and $\rm{H\rightarrow b\bar{b}}$ and the non-resonant component; it is represented by the magenta curve. The lower panel compares the distribution of data after subtracting non-resonant component with the fitted resonant contribution of the $\rm{Z\rightarrow b\bar{b}}$ background (red curve) and $\rm{H\rightarrow b\bar{b}}$ signal (green curve).
png pdf	Figure 7-b: The $m_{\rm bb}$ distributions in three event categories: Tight 2018 1 (left), Tight 2018 2 (central) and Tight 2018 3 (right). The points indicate data, the blue solid curve corresponds to the fitted non-resonant component of the background, dominated by QCD multijets; the shaded (cyan) band represents 1 $\sigma$ uncertainty band. The total fitted signal+background model includes resonant contributions from $\rm{Z\rightarrow b\bar{b}}$ and $\rm{H\rightarrow b\bar{b}}$ and the non-resonant component; it is represented by the magenta curve. The lower panel compares the distribution of data after subtracting non-resonant component with the fitted resonant contribution of the $\rm{Z\rightarrow b\bar{b}}$ background (red curve) and $\rm{H\rightarrow b\bar{b}}$ signal (green curve).
png pdf	Figure 7-c: The $m_{\rm bb}$ distributions in three event categories: Tight 2018 1 (left), Tight 2018 2 (central) and Tight 2018 3 (right). The points indicate data, the blue solid curve corresponds to the fitted non-resonant component of the background, dominated by QCD multijets; the shaded (cyan) band represents 1 $\sigma$ uncertainty band. The total fitted signal+background model includes resonant contributions from $\rm{Z\rightarrow b\bar{b}}$ and $\rm{H\rightarrow b\bar{b}}$ and the non-resonant component; it is represented by the magenta curve. The lower panel compares the distribution of data after subtracting non-resonant component with the fitted resonant contribution of the $\rm{Z\rightarrow b\bar{b}}$ background (red curve) and $\rm{H\rightarrow b\bar{b}}$ signal (green curve).
png pdf	Figure 8: The $m_{\rm bb}$ distributions for the selected collision events (black points) for the $\rm{Z\rightarrow b\bar{b}}$ sensitive categories: Loose 2016 Z2 (left) and Loose 2018 Z2 (right). The blue solid curve corresponds to the expected non-resonant component of the background, dominated by QCD multijets; the shaded (cyan) band represents 1 $\sigma$ uncertainty in the prediction. The total signal+background model includes resonant contributions from Zbb and Hbb and the non-resonant component; it is represented by the magenta curve. The lower panel compares the distribution of data after subtracting the expected non-resonant component. The expectations from only $\rm{H\rightarrow b\bar{b}}$ signal and the $\rm{Z\rightarrow b\bar{b}}$ are presented by the green and red curves respectively.
png pdf	Figure 8-a: The $m_{\rm bb}$ distributions for the selected collision events (black points) for the $\rm{Z\rightarrow b\bar{b}}$ sensitive categories: Loose 2016 Z2 (left) and Loose 2018 Z2 (right). The blue solid curve corresponds to the expected non-resonant component of the background, dominated by QCD multijets; the shaded (cyan) band represents 1 $\sigma$ uncertainty in the prediction. The total signal+background model includes resonant contributions from Zbb and Hbb and the non-resonant component; it is represented by the magenta curve. The lower panel compares the distribution of data after subtracting the expected non-resonant component. The expectations from only $\rm{H\rightarrow b\bar{b}}$ signal and the $\rm{Z\rightarrow b\bar{b}}$ are presented by the green and red curves respectively.
png pdf	Figure 8-b: The $m_{\rm bb}$ distributions for the selected collision events (black points) for the $\rm{Z\rightarrow b\bar{b}}$ sensitive categories: Loose 2016 Z2 (left) and Loose 2018 Z2 (right). The blue solid curve corresponds to the expected non-resonant component of the background, dominated by QCD multijets; the shaded (cyan) band represents 1 $\sigma$ uncertainty in the prediction. The total signal+background model includes resonant contributions from Zbb and Hbb and the non-resonant component; it is represented by the magenta curve. The lower panel compares the distribution of data after subtracting the expected non-resonant component. The expectations from only $\rm{H\rightarrow b\bar{b}}$ signal and the $\rm{Z\rightarrow b\bar{b}}$ are presented by the green and red curves respectively.
png pdf	Figure 9: The $m_{\rm bb}$ distribution after weighted combination of all categories in the analysis weighted with S/(S+B). The blue solid curve corresponds to the non-resonant component of background, dominated by QCD multijets. The shaded band represent 1 $\sigma$ uncertainty in the non-resonant component. The total signal+background model, including $\rm{Z\rightarrow b\bar{b}}$ and $\rm{H\rightarrow b\bar{b}}$ resonant components and the non-resonant one is represented by the magenta curve. The lower panel compares distribution of data after subtracting the non-resonant component of the model with expectation from sum of the resonant components: $\rm{Z\rightarrow b\bar{b}}$ (red curve) and $\rm{H\rightarrow b\bar{b}}$ signal only expectation (green curve).

Tables
png pdf	Table 1: The HLT and offline selection requirement in the four analyzed samples.
png pdf	Table 2: Event categorization used in the analysis, a total of 18. The name 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.
png pdf	Table 3: Event yields for various categories of the analyzed 2016 data corresponding to ${\cal L}=$ 36.3 fb $^{-1}$ , in data compared to the expected numbers of events from the simulated samples of signal and background other than QCD multijets process. The quoted uncertainties are statistical only.
png pdf	Table 4: Event yields for various categories of the analyzed 2018 data corresponding to ${\cal L}=$ 54.5 fb $^{-1}$ , in data compared to the expected numbers of events from the simulated samples of signal and background other than QCD multijets process. The quoted uncertainties are statistical only.
png pdf	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)" denoted the product of an exponential function and a polynomial of the first (second) order.

Summary

A measurement of the Higgs boson produced in the vector boson fusion (VBF) process and decaying to bottom quarks has been performed on data sets collected by the CMS experiment at a center-of-mass energy of 13 TeV and corresponding to a total integrated luminosity of 91 fb

$^{-1}$ . The analysis employs boosted decision trees (BDT) to discriminate signal against major background processes - QCD multijet production and Z + jets events. The training of BDTs is performed exploiting kinematic properties of VBF jets, information on b-tagged jets assigned to the

$\rm{H\rightarrow b\bar{b}}$ decay and global event shape variables. Based on the BDT response, multiple event categories are introduced, targeting VBF, gluon-gluon fusion (ggF) and Z + jets processes to achieve maximum sensitivity for the signal. While VBF categories have the highest signal-to-background ratio, the Z + jets categories constrain the largest peaking background. Introduction of ggF categories enhanced the sensitivity to the inclusive production of the Higgs boson in association with two jets. The rate of VBF production followed by the

$\rm{H\rightarrow b\bar{b}}$ decay has been measured with the ggF contribution constrained within the theoretical and experimental uncertainties to the SM prediction. The signal has been observed with a significance of 2.4

$\sigma$ , compared to the expected significance of 2.7

$\sigma$ . The

$\rm{qqH\rightarrow qqb\bar{b}}$ signal strength, defined as the measured signal rate of the

$\rm{qqH\rightarrow qqb\bar{b}}$ process relative to the prediction in the SM, is

$\mu_{\mathrm{qqH}}=$ 0.97

$^{+0.53}_{-0.45}$ . The inclusive Higgs boson production in association with two jets, followed by

$\rm{H\rightarrow b\bar{b}}$ decay has been measured by treating the ggF contribution as a part of signal. The measured inclusive signal strength is

$\mu_{\mathrm{Hb\bar{b}}}=$ 0.92

$^{+0.45}_{-0.39}$ , corresponding to an observed (expected) significance of 2.5 (2.9)

$\sigma$ .

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