A portrait of the Higgs boson by the CMS experiment ten years after the discovery

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 gigaelectronvolts. Ten years later, and with the data corresponding to the production of a 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 teraelectronvolts. 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 15 years, will help deepen our understanding of this crucial sector.

Fig. 1. Feynman diagrams for the leading Higgs boson interactions.

a–f, Higgs boson production in ggH (a) and VBF (b), associated production with a W or Z (V) boson (VH; c), associated production with a top or bottom quark pair (ttH or bbH; d) and associated production with a single top quark (tH; e,f). g–j, Higgs boson decays into heavy vector boson pairs (g), fermion–antifermion pairs (h) and photon pairs or Zγ (i,j). k–o, Higgs boson pair production through ggH (k,l) and through VBF (m,n,o). The different Higgs boson interactions are labelled with the coupling modifiers κ, 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.

Fig. 2. The agreement with the SM predictions for production modes and decay channels.

Signal-strength parameters extracted for various production modes μ_i, assuming ${ℬ}^f={\left({ℬ}^f\right)}_{\mathrm{SM}}$ (left), and decay channels μ^f, assuming σ_i = (σ_i)_SM (right). The thick and thin black lines indicate the 1-s.d. and 2-s.d. confidence intervals, respectively, with the systematic (syst) and statistical (stat) 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 μ_i and μ^f in the SM. The covariance matrices of the fitted signal-strength parameters are shown in Extended Data Fig. 5. The P values with respect to the SM prediction are 3.1% and 30.1% for the left plot and the 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.

Fig. 3. A portrait of the Higgs boson couplings to fermions and vector bosons.

Left: constraints on the Higgs boson coupling modifiers to fermions (κ_f) and heavy gauge bosons (κ_V), in different datasets: discovery (red), the full LHC Run 1 (blue) and the data presented here (black). The SM prediction corresponds to κ_V = κ_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 υ is the vacuum expectation value of the BEH field (‘Notes on self-interaction strength’ in Methods). 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%.

Fig. 4. Coupling modifier 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 κ framework in different datasets: at the time of the Higgs boson discovery, using the full data from LHC Run 1, in the dataset used in this paper and the expected 1-s.d. uncertainty at the HL-LHC for $\mathcal{L}=3,000{\mathrm{fb}}^{-1}$. The H → μμ and κ_t measurements were not available for earlier datasets owing to the lack of sensitivity.

Fig. 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 (σ_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 datasets: 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 (3,000 fb⁻¹).

Fig. 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 κ_λ (left) and κ_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 the 1-s.d. and 2-s.d. extensions beyond the expected limit, respectively; 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 the 95% CL.

Extended Data Fig. 1. 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.

Extended Data Fig. 2. Higgs boson candidate events.

(upper) An event display of a candidate H → ZZ → eeμμ. (lower) An event display of an H → bb candidate produced in association with a boson decaying into an electron–positron pair, in pp collisions at $\sqrt{s}=13\mathrm{TeV}$ 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 → c → X; vertex in cyan).

Extended Data Fig. 3. 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 → γγ. (upper right) The invariant mass distribution of four charged leptons targeting the study of the decay channel H → ZZ → 4l. (lower left) The background-subtracted transverse mass m_T distribution targeting the study of the decay channel H → WW. (lower right) The background-subtracted $\mathit{\ell }\mathit{\ell }\gamma$ invariant mass distribution targeting the study of the decay channel H → Zγ. The SM prediction for the signal (red line) is scaled by the value of μ, as estimated in the dedicated analysis for that channel, and computed for m_H = 125.38 GeV. The grey band around zero shows the 1 s.d. uncertainty in the background subtraction.

Extended Data Fig. 4. Higgs boson mass peak in difermion decay channels.

The background-subtracted diparticle invariant mass distribution targeting the study of the decay channel (left) H → ττ, (center) H → bb, (right) H → μμ. The SM prediction for the signal (red line) is scaled by the value of μ, as estimated in the dedicated analysis for that channel, and computed for m_H = 125.38 GeV. The grey band around zero shows the 1 s.d. uncertainty in the background subtraction.

Extended Data Fig. 5. Correlations between the measurements of different couplings.

Covariance matrices for the fits of the signal-strength parameters per production mode μ_i (left) and per decay mode μ^f (right). The values of the correlation coefficients, ρ, are indicated both in text and in the color scale.

Extended Data Fig. 6. 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 μ_i and decay channel μ^f. In this fit, ttH and tH are considered together and the μ_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 μ 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%.

Extended Data Fig. 7. Time evolution of the signal-strength measurements and their precision.

Comparison of the signal-strength parameter μ fit results in different datasets; 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 dataset analyzed for this paper, and the expected 1 s.d. uncertainty for HL-LHC for $ℒ=3000{\mathrm{fb}}^{-1}$. The H → μμ measurements were not available for the earlier datasets due to the lack of sensitivity.

Extended Data Fig. 8. Time evolution of the coupling measurements and their precision.

(left) Comparison of the expected 1 SD uncertainties in the κ-framework fit including coupling modifiers for both tree-level and loop-induced Higgs boson interactions, in different datasets: at the time of the Higgs boson discovery, using the full data from LHC Run 1, in the dataset used in this paper, and the expected 1SD uncertainty for HL-LHC for $ℒ=3000{\mathrm{fb}}^{-1}$. (right) Results of a fit to the coupling modifiers κ allowing both invisible and the undetected decay modes, with the SM value used as an upper bound on both κ_W and κ_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%.

Extended Data Fig. 9. Constrains on Higgs boson self-interaction and quartic coupling.

(left) Constraints on κ_λ and κ_2V from the production of Higgs boson pairs. (right) Constraint on the Higgs boson self-coupling modifier κ_λ from single and pair production of Higgs boson(s).