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CMS-HIG-22-001 ; CERN-EP-2022-039
A portrait of the Higgs boson by the CMS experiment ten years after the discovery
Nature 607 (2022) 60-68
Abstract: In July 2012, the ATLAS and CMS Collaborations at the CERN Large Hadron Collider announced the observation of a Higgs boson at a mass of around 125 GeV. Ten years later, and with the data corresponding to the production of 30 times larger number of Higgs bosons, we have learnt much more about the properties of the Higgs boson. The CMS experiment has observed the Higgs boson in numerous fermionic and bosonic decay channels, established its spin-parity quantum numbers, determined its mass and measured its production cross sections in various modes. Here the CMS Collaboration reports the most up-to-date combination of results on the properties of the Higgs boson, including the most stringent limit on the cross section for the production of a pair of Higgs bosons, on the basis of data from proton-proton collisions at a centre-of-mass energy of 13 TeV. Within the uncertainties, all these observations are compatible with the predictions of the standard model of elementary particle physics. Much evidence points to the fact that the standard model is a low-energy approximation of a more comprehensive theory. Several of the standard model issues originate in the sector of Higgs boson physics. An order of magnitude larger number of Higgs bosons, expected to be examined over the next fifteen years, will help deepen our understanding of this crucial sector.
Figures & Tables Summary References CMS Publications
Figures

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Figure 1:
Feynman diagrams for the leading Higgs boson interactions. Higgs boson production in (a) gluon-gluon fusion (ggH), (b) vector boson fusion (VBF), (c) associated production with a W or Z (V) boson (VH), (d) associated production with a top or bottom quark pair (ttH or bbH), (e, f) associated production with a single top quark (tH); with Higgs boson decays into (g) heavy vector boson pairs, (h) fermion-antifermion pairs, and (i, j) photon pairs or Z$ \gamma $; Higgs boson pair production: (k, l) via gluon-gluon fusion, and (m, n, o) via vector boson fusion. The different Higgs boson interactions are labelled with the coupling modifiers $\kappa $, and highlighted in different colours for Higgs-fermion interactions (red), Higgs-gauge-boson interactions (blue), and multiple Higgs boson interactions (green). The distinction between a particle and its antiparticle is dropped.

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Figure 2:
The agreement with the SM predictions for production modes and decay channels. Signal strength parameters extracted for (left) various production modes $\mu _i$, assuming $\mathcal {B}^f= (\mathcal {B}^f)_\text {SM}$, and (right) decay channels $\mu ^f$, assuming $\sigma _i = (\sigma _i)_\text {SM}$. The thick (thin) black lines indicate the 1 (2) s.d. confidence intervals, with the systematic and statistical components of the 1 s.d. interval indicated by the red and blue bands, respectively. The vertical dashed line at unity represents the values of $\mu _i$ and $\mu ^f$ in the SM. The covariance matrices of the fitted signal strength parameters are shown in Extended Data Fig. B.5. The $p$-value with respect to the SM prediction are 3.1% and 30.1% for the left and right plot, respectively. The $p$-value corresponds to the probability that a result deviates as much, or more, from the SM prediction as the observed one.

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Figure 2-a:
Signal strength parameters extracted for various production modes $\mu _i$, assuming $\mathcal {B}^f= (\mathcal {B}^f)_\text {SM}$. The thick (thin) black lines indicate the 1 (2) s.d. confidence intervals, with the systematic and statistical components of the 1 s.d. interval indicated by the red and blue bands, respectively. The vertical dashed line at unity represents the values of $\mu _i$ in the SM. The covariance matrix of the fitted signal strength parameters is shown in Extended Data Fig. B.5-a. The $p$-value with respect to the SM prediction is 3.1%. The $p$-value corresponds to the probability that a result deviates as much, or more, from the SM prediction as the observed one.

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Figure 2-b:
Signal strength parameters extracted for decay channels $\mu ^f$, assuming $\sigma _i = (\sigma _i)_\text {SM}$. The thick (thin) black lines indicate the 1 (2) s.d. confidence intervals, with the systematic and statistical components of the 1 s.d. interval indicated by the red and blue bands, respectively. The vertical dashed line at unity represents the values of $\mu ^f$ in the SM. The covariance matrix of the fitted signal strength parameters is shown in Extended Data Fig. B.5-b. The $p$-value with respect to the SM prediction is 30.1%. The $p$-value corresponds to the probability that a result deviates as much, or more, from the SM prediction as the observed one.

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Figure 3:
A portrait of the Higgs boson couplings to fermions and vector bosons. (left) Constraints on the Higgs boson coupling modifiers to fermions ($ {\kappa _\mathrm {f}}$) and heavy gauge bosons ($ {\kappa _\mathrm {V}}$), in different data sets: discovery (red), the full LHC Run 1 (blue), and the data presented here (black). The SM prediction corresponds to $ {\kappa _\mathrm {V}}= {\kappa _\mathrm {f}}= $ 1 (diamond marker). (right) The measured coupling modifiers of the Higgs boson to fermions and heavy gauge bosons, as functions of fermion or gauge boson mass, where $\upsilon $ is the vacuum expectation value of the BEH field (cf. Methods section A.7). For gauge bosons, the square root of the coupling modifier is plotted, to keep a linear proportionality to the mass, as predicted in the SM. The $p$-value with respect to the SM prediction for the right plot is 37.5%.

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Figure 3-a:
Constraints on the Higgs boson coupling modifiers to fermions ($ {\kappa _\mathrm {f}}$) and heavy gauge bosons ($ {\kappa _\mathrm {V}}$), in different data sets: discovery (red), the full LHC Run 1 (blue), and the data presented here (black). The SM prediction corresponds to $ {\kappa _\mathrm {V}}= {\kappa _\mathrm {f}}= $ 1 (diamond marker).

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Figure 3-b:
The measured coupling modifiers of the Higgs boson to fermions and heavy gauge bosons, as functions of fermion or gauge boson mass, where $\upsilon $ is the vacuum expectation value of the BEH field (cf. Methods section A.7). For gauge bosons, the square root of the coupling modifier is plotted, to keep a linear proportionality to the mass, as predicted in the SM. The $p$-value with respect to the SM prediction is 37.5%.

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Figure 4:
Coupling modifiers measurements and their evolution in time. (left) Coupling modifiers resulting from the fit. The $p$-value with respect to the SM prediction is 28%. (right) Observed and projected values resulting from the fit in the $\kappa $-framework in different data sets: at the time of the Higgs boson discovery, using the full data from LHC Run 1, in the data set used in this paper, and the expected 1 s.d. uncertainty at the HL-LHC for $\mathcal {L}=$ 3000 fb$^{-1}$. The H $ \to \mu \mu $ and $\kappa _{\mathrm{t}}$ measurements were not available for earlier data sets due to the lack of sensitivity.

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Figure 4-a:
Coupling modifiers resulting from the fit. The $p$-value with respect to the SM prediction is 28%.

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Figure 4-b:
Observed and projected values resulting from the fit in the $\kappa $-framework in different data sets: at the time of the Higgs boson discovery, using the full data from LHC Run 1, in the data set used in this paper, and the expected 1 s.d. uncertainty at the HL-LHC for $\mathcal {L}=$ 3000 fb$^{-1}$. The H $ \to \mu \mu $ and $\kappa _{\mathrm{t}}$ measurements were not available for earlier data sets due to the lack of sensitivity.

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Figure 5:
Limits on the production of Higgs boson pairs and their time evolution. (left) The expected and observed limits on the ratio of experimentally estimated production cross section and the expectation from the SM ($\sigma _\text {Theory}$) in searches using different final states and their combination. The search modes are ordered, from upper to lower, by their expected sensitivities from the least to the most sensitive. The overall combination of all searches is shown by the lowest entry. (right) Expected and observed limits on HH production in different data sets: early LHC Run 2 data (35.9 fb$^{-1}$), present results using full LHC Run 2 data (138 fb$^{-1}$), and projections for the HL-LHC (3000 fb$^{-1}$).

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Figure 5-a:
The expected and observed limits on the ratio of experimentally estimated production cross section and the expectation from the SM ($\sigma _\text {Theory}$) in searches using different final states and their combination. The search modes are ordered, from upper to lower, by their expected sensitivities from the least to the most sensitive. The overall combination of all searches is shown by the lowest entry.

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Figure 5-b:
Expected and observed limits on HH production in different data sets: early LHC Run 2 data (35.9 fb$^{-1}$), present results using full LHC Run 2 data (138 fb$^{-1}$), and projections for the HL-LHC (3000 fb$^{-1}$).

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Figure 6:
Limits on the Higgs boson self-interaction and quartic coupling. Combined expected and observed 95% CL upper limits on the HH production cross section for different values of $\kappa _{\lambda}$ (left) and $ {\kappa _\mathrm {2V}}$ (right), assuming the SM values for the modifiers of Higgs boson couplings to top quarks and vector bosons. The green and yellow bands represent, respectively, the 1 and 2 s.d. extensions beyond the expected limit; the red solid line (band) shows the theoretical prediction for the HH production cross section (its 1 s.d. uncertainty). The areas to the left and to the right of the hatched regions are excluded at 95% CL.

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Figure 6-a:
Combined expected and observed 95% CL upper limits on the HH production cross section for different values of $\kappa _{\lambda}$, assuming the SM values for the modifiers of Higgs boson couplings to top quarks and vector bosons. The green and yellow bands represent, respectively, the 1 and 2 s.d. extensions beyond the expected limit; the red solid line (band) shows the theoretical prediction for the HH production cross section (its 1 s.d. uncertainty). The areas to the left and to the right of the hatched regions are excluded at 95% CL.

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Figure 6-b:
Combined expected and observed 95% CL upper limits on the HH production cross section for different values of $ {\kappa _\mathrm {2V}}$, assuming the SM values for the modifiers of Higgs boson couplings to top quarks and vector bosons. The green and yellow bands represent, respectively, the 1 and 2 s.d. extensions beyond the expected limit; the red solid line (band) shows the theoretical prediction for the HH production cross section (its 1 s.d. uncertainty). The areas to the left and to the right of the hatched regions are excluded at 95% CL.

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Figure B1:
The CMS detector at the CERN LHC. Schematic longitudinal cut-away view of the CMS detector, showing the different layers around the LHC beam axis, with the collision point in the centre.

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Figure B2:
Higgs boson candidate events. (upper) An event display of a candidate H $ \to $ ZZ $ \to $ ee$\mu \mu $. (lower) An event display of an H $ \to $ bb candidate produced in association with a Z boson decaying into an electron-positron pair, in pp collisions at $\sqrt {s} = $ 13 TeV recorded by CMS. The charged-particle tracks, as reconstructed in the inner tracker, are shown in yellow; the electrons are shown in green, the energy deposited by the electrons in the ECAL is shown as large green towers, the size of which is proportional of the amount of energy deposited; the blue towers are indicative of the energy deposits in the HCAL, while the red boxes are the muon chambers crossed by the muons (red tracks); the yellow cones represent the reconstructed jets. (lower, inset) The zoom into the collision region shows the displaced secondary vertices (in red) of the two b quarks decaying away from the primary vertex (in yellow). One of the bottom hadrons decays into a charm hadron that moves away from the secondary vertex before decaying (b $ \to $ c $\to$ X; vertex in cyan).

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Figure B2-a:
An event display of a candidate H $ \to $ ZZ $ \to $ ee$\mu \mu $. The charged-particle tracks, as reconstructed in the inner tracker, are shown in yellow; the electrons are shown in green, the energy deposited by the electrons in the ECAL is shown as large green towers, the size of which is proportional of the amount of energy deposited; the red boxes are the muon chambers crossed by the muons (red tracks).

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Figure B2-b:
An event display of an H $ \to $ bb candidate produced in association with a Z boson decaying into an electron-positron pair, in pp collisions at $\sqrt {s} = $ 13 TeV recorded by CMS. The charged-particle tracks, as reconstructed in the inner tracker, are shown in yellow; the electrons are shown in green, the energy deposited by the electrons in the ECAL is shown as large green towers, the size of which is proportional of the amount of energy deposited; the blue towers are indicative of the energy deposits in the HCAL; the yellow cones represent the reconstructed jets. The zoom into the collision region shows the displaced secondary vertices (in red) of the two b quarks decaying away from the primary vertex (in yellow). One of the bottom hadrons decays into a charm hadron that moves away from the secondary vertex before decaying (b $ \to $ c $\to$ X; vertex in cyan).

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Figure B3:
Higgs boson mass peak in diboson decay channels. (upper left) The background-subtracted diphoton invariant mass distribution targeting the study of the decay channel H $ \to \gamma \gamma $. (upper right) The invariant mass distribution of four charged leptons targeting the study of the decay channel H $ \to $ ZZ $ \to $ 4$\ell$. (lower left) The background-subtracted transverse mass ${m_{\mathrm {T}}}$ distribution targeting the study of the decay channel H $ \to $ WW. (lower right) The background-subtracted $\ell \ell \gamma $ invariant mass distribution targeting the study of the decay channel H $ \to $ Z$ \gamma $. The SM prediction for the signal (red line) is scaled by the value of $\mu $, as estimated in the dedicated analysis for that channel, and computed for $m_\mathrm{H} = $ 125.38 GeV. The grey band around zero shows the 1 s.d. uncertainty in the background subtraction.

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Figure B3-a:
The background-subtracted diphoton invariant mass distribution targeting the study of the decay channel H $ \to \gamma \gamma $. The SM prediction for the signal (red line) is scaled by the value of $\mu $, as estimated in the dedicated analysis for that channel, and computed for $m_\mathrm{H} = $ 125.38 GeV. The grey band around zero shows the 1 s.d. uncertainty in the background subtraction.

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Figure B3-b:
The invariant mass distribution of four charged leptons targeting the study of the decay channel H $ \to $ ZZ $ \to $ 4$\ell$. The SM prediction for the signal (red line) is scaled by the value of $\mu $, as estimated in the dedicated analysis for that channel, and computed for $m_\mathrm{H} = $ 125.38 GeV.

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Figure B3-c:
The background-subtracted transverse mass ${m_{\mathrm {T}}}$ distribution targeting the study of the decay channel H $ \to $ WW. The SM prediction for the signal (red line) is scaled by the value of $\mu $, as estimated in the dedicated analysis for that channel, and computed for $m_\mathrm{H} = $ 125.38 GeV. The grey band around zero shows the 1 s.d. uncertainty in the background subtraction.

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Figure B3-d:
The background-subtracted $\ell \ell \gamma $ invariant mass distribution targeting the study of the decay channel H $ \to $ Z$ \gamma $. The SM prediction for the signal (red line) is scaled by the value of $\mu $, as estimated in the dedicated analysis for that channel, and computed for $m_\mathrm{H} = $ 125.38 GeV. The grey band around zero shows the 1 s.d. uncertainty in the background subtraction.

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Figure B4:
Higgs boson mass peak in difermion decay channels. The background-subtracted diparticle invariant mass distribution targeting the study of the decay channel (left) H $ \to {\tau \tau} $, (center) H $ \to $ bb, (right) H $ \to \mu \mu $. The SM prediction for the signal (red line) is scaled by the value of $\mu $, as estimated in the dedicated analysis for that channel, and computed for $m_\mathrm{H} = $ 125.38 GeV. The grey band around zero shows the 1 s.d. uncertainty in the background subtraction.

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Figure B4-a:
The background-subtracted diparticle invariant mass distribution targeting the study of the decay channel H $ \to {\tau \tau} $. The SM prediction for the signal (red line) is scaled by the value of $\mu $, as estimated in the dedicated analysis for that channel, and computed for $m_\mathrm{H} = $ 125.38 GeV. The grey band around zero shows the 1 s.d. uncertainty in the background subtraction.

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Figure B4-b:
The background-subtracted diparticle invariant mass distribution targeting the study of the decay channel H $ \to $ bb. The SM prediction for the signal (red line) is scaled by the value of $\mu $, as estimated in the dedicated analysis for that channel, and computed for $m_\mathrm{H} = $ 125.38 GeV. The grey band around zero shows the 1 s.d. uncertainty in the background subtraction.

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Figure B4-c:
The background-subtracted diparticle invariant mass distribution targeting the study of the decay channel H $ \to \mu \mu $. The SM prediction for the signal (red line) is scaled by the value of $\mu $, as estimated in the dedicated analysis for that channel, and computed for $m_\mathrm{H} = $ 125.38 GeV. The grey band around zero shows the 1 s.d. uncertainty in the background subtraction.

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Figure B5:
Correlations between the measurements of different couplings. Correlation matrices for the fits of the signal strength parameters per production mode $\mu _i$ (left) and per decay mode $\mu ^f$ (right). The values of the correlation coefficients, $\rho $, are indicated both in text and in the color scale.

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Figure B5-a:
Correlation matrix for the fit of the signal strength parameters per production mode $\mu _i$. The values of the correlation coefficients, $\rho $, are indicated both in text and in the color scale.

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Figure B5-b:
Correlation matrix for the fit of the signal strength parameters per decay mode $\mu ^f$. The values of the correlation coefficients, $\rho $, are indicated both in text and in the color scale.

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Figure B6:
The agreement with the SM predictions in Higgs boson production and decay. Signal strength parameters per individual production mode and decay channel $\mu _i^f$, and combined per production mode $\mu _i$ and decay channel $\mu ^f$. In this fit, ttH and tH are considered together and the $\mu _i$ results are slightly different from those of Fig. 2 (left). The dashed vertical lines at 1 represent the SM value. Light grey shading indicates that $\mu $ is contained to be positive. Dark grey shading indicates the absence of measurement. The $p$-value with respect to the SM prediction is 5.8%.

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Figure B7:
Time evolution of the signal strength measurements and their precision. Comparison of the signal strength parameter $\mu $ fit results in different data sets; in each panel, from left to right: at the time of the Higgs boson discovery, using the full data from LHC Run 1, in the data set analyzed for this paper, and the expected 1 s.d. uncertainty for HL-LHC for $\mathcal {L}=$ 3000 fb$^{-1}$. The H $ \to \mu \mu $ measurements were not available for the earlier data sets due to the lack of sensitivity.

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Figure B8:
Time evolution of the coupling measurements and their precision. (left) Comparison of the expected 1 s.d. uncertainties in the $\kappa $-framework fit including coupling modifiers for both tree-level and loop-induced Higgs boson interactions, in different data sets: at the time of the Higgs boson discovery, using the full data from LHC Run 1, in the data set used in this paper, and the expected 1 s.d. uncertainty for HL-LHC for $\mathcal {L}=$ 3000 fb$^{-1}$. (right) Results of a fit to the coupling modifiers $\kappa $ allowing both invisible and the undetected decay modes, with the SM value used as an upper bound on both $\kappa _\mathrm{W} $ and $\kappa _\mathrm{Z} $. The thick (thin) black lines indicate the 1 (2) s.d. confidence intervals, with the systematic and statistical components of the 1 s.d. interval indicated by the red and blue bands, respectively. The $p$-value with respect to the SM prediction is 33%.

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Figure B8-a:
Comparison of the expected 1 s.d. uncertainties in the $\kappa $-framework fit including coupling modifiers for both tree-level and loop-induced Higgs boson interactions, in different data sets: at the time of the Higgs boson discovery, using the full data from LHC Run 1, in the data set used in this paper, and the expected 1 s.d. uncertainty for HL-LHC for $\mathcal {L}=$ 3000 fb$^{-1}$.

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Figure B8-b:
Results of a fit to the coupling modifiers $\kappa $ allowing both invisible and the undetected decay modes, with the SM value used as an upper bound on both $\kappa _\mathrm{W} $ and $\kappa _\mathrm{Z} $. The thick (thin) black lines indicate the 1 (2) s.d. confidence intervals, with the systematic and statistical components of the 1 s.d. interval indicated by the red and blue bands, respectively. The $p$-value with respect to the SM prediction is 33%.

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Figure B9:
Constraints on Higgs boson self-interaction and quartic coupling. (left) Constraints on $ {\kappa _\lambda}$ and $ {\kappa _\mathrm {2V}}$ from the production of Higgs boson pairs. (right) Constraint on the Higgs boson self-coupling modifier $ {\kappa _\lambda}$ from single and pair production of Higgs boson(s).

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Figure B9-a:
Constraints on Higgs boson self-interaction and quartic coupling. (left) Constraints on $ {\kappa _\lambda}$ and $ {\kappa _\mathrm {2V}}$ from the production of Higgs boson pairs. (right) Constraint on the Higgs boson self-coupling modifier $ {\kappa _\lambda}$ from single and pair production of Higgs boson(s).

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Figure B9-b:
Constraints on Higgs boson self-interaction and quartic coupling. (left) Constraints on $ {\kappa _\lambda}$ and $ {\kappa _\mathrm {2V}}$ from the production of Higgs boson pairs. (right) Constraint on the Higgs boson self-coupling modifier $ {\kappa _\lambda}$ from single and pair production of Higgs boson(s).
Tables

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Table B1:
The SM Higgs production cross sections and branching fractions. Theoretical cross sections for each production mode and branching fractions for the decay channels, at $\sqrt {s}=$ 13 TeV and for $m_{\mathrm{H}} = $ 125.38 GeV [39].

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Table B2:
Summary of the Higgs boson analyses included in this paper. The analysis and decay channels are indicated in the first two columns, with the third column containing the production mechanism and kinematic regions targeted by each analysis. All analyses, apart from ttH in the H $ \to $ bb final state (2016 data only) and VH in the H $ \to $ bb final state (2016-2017 data), use the full data set collected in Run 2. The various symbols are as follows: $\ell $ is e or $\mu $, jet (j), di-jet mass ($m_\text {jj}$), number of jets ($N_\text {j}$), same-sign (SS) of electric charge, hadronic decay of the tau lepton ($ {\tau _\mathrm {h}} $).

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Table B3:
Summary of the event selections. Some of the typical selection criteria used in the trigger (online selection) and in offline analysis for some of the final states and for leading (1) and subleading (2) particles. The ${{p_{\mathrm {T}}} ^\text {miss}}$ is a measure of the imbalance in energy in the plane transverse to the colliding proton beams.
Summary
The discovery of the Higgs boson in 2012 completed the particle content of the standard model (SM) of elementary particle physics, a theory that explains visible matter and its interactions in exquisite detail. The completion of the SM spanned 60 years of theoretical and experimental work. In the ten years following the discovery, great progress has been made in painting a clearer portrait of the Higgs boson.

In this paper, the CMS Collaboration reports the most up-to-date combination of results on the properties of the Higgs boson, based on data corresponding to an $\mathcal{L}$ of up to 138 fb$^{-1}$, recorded at 13 TeV. Many of its properties have been determined with accuracies better than 10%. All measurements made so far are found to be consistent with the expectations of the SM. In particular, the overall signal strength parameter has been measured to be $\mu=$ 1.002 $\pm$ 0.057. It has been shown that the Higgs boson directly couples to bottom quarks, tau leptons, and muons, which had not been observed at the time of the discovery, and also proven that it is indeed a scalar particle. The CMS experiment is approaching the sensitivity necessary to probe Higgs boson couplings to charm quarks [74]. The observed (expected) 95% CL value for $\kappa_\mathrm{c}$ is found to be 1.1 $ < |{\kappa_\mathrm{c}}| < $ 5.5 ($|{\kappa_\mathrm{c}}| < $ 3.40), the most stringent result to date. Moreover, the recent progress in searches for the pair production of Higgs bosons has allowed the setting of tight constraints on the Higgs boson self-interaction strength, and the setting of limits on the Higgs boson pair production cross section not much above twice the expected SM value.

Much evidence points to the fact that the SM is a low-energy approximation of a more comprehensive theory. In connection with the mechanism of spontaneous symmetry breaking, several puzzles appear: the so-called naturalness, a technical issue related to the fact that the Higgs boson mass is close to the electroweak scale; in relation with cosmology, the metastability of the vacuum state of the SM and the conjectured period of inflation in the early universe; the dynamics of electroweak phase transition and its connection to the matter-antimatter asymmetry of our universe. These issues motivate attempts at obtaining a deeper understanding of the physics of the Higgs boson. The impressive progress made over the last decade is foreseen to continue into the next one. The current data set is expected to be doubled in size by the middle of this decade, enabling the establishment of rare decays channels such as H $ \to \mu\mu$ and H $ \to \mathrm{Z} \gamma$. Operation with the high-luminosity LHC is expected during the next decade and should yield ten times more data then originally foreseen. This should allow the ATLAS and CMS experiments to establish the SM Higgs boson pair production with a significance of 4 s.d., as well as the Higgs boson coupling to charm quarks, and to search for any exotic decays. Improvements in experimental techniques and theoretical calculations are also anticipated to continue. The CMS experiment is entering the era of precision Higgs physics that will shed light on the physics beyond the SM.
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