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Measurements of the Higgs boson production and decay rates and constraints on its couplings from a combined ATLAS and CMS analysis of the LHC $pp$ collision data at $\sqrt{s}=$ 7 and 8 TeV

ATLAS, CMS Collaborations

arXiv:1606.02266v2hep-ex

TL;DR

The paper addresses how Higgs production, decay, and couplings compare with Standard Model expectations. It combines ATLAS and CMS Run 1 measurements across production and decay channels using generic and more model-dependent parameterisations. The combined signal yield is 1.09 ± 0.11 relative to the Standard Model, with all considered parameterisations compatible with Standard Model predictions.

  • Problem

    The paper measures Higgs boson production and decay rates and tests its couplings to vector bosons and fermions against Standard Model predictions.

    Source: §1 · p. 2

  • Method

    ATLAS and CMS Run 1 measurements are combined across five production processes and six decay modes using cross-section, branching-fraction, and coupling-modifier parameterisations.

    Source: §1 · p. 2, §2.4 · p. 9, §3.2 · p. 13

  • Results

    1.09 ± 0.11 is the combined signal yield relative to the Standard Model, while vector-boson-fusion production and H → ττ have observed significances of 5.4σ and 5.5σ.

    Source: §7 · p. 51

  • Takeaways & Limitations

    The combined measurements are compatible with Standard Model predictions across the parameterisations considered, while constraining possible beyond-Standard-Model branching fractions to below 34% at 95% CL.

    Source: §7 · p. 51

    The results assume a single SM-like CP-even Higgs boson with narrow width and Standard Model signal modelling, which could matter for significant deviations from the Standard Model.

    Source: §1 · p. 2

Abstract

from arXiv · show

Combined ATLAS and CMS measurements of the Higgs boson production and decay rates, as well as constraints on its couplings to vector bosons and fermions, are presented. The combination is based on the analysis of five production processes, namely gluon fusion, vector boson fusion, and associated production with a $W$ or a $Z$ boson or a pair of top quarks, and of the six decay modes $H \to ZZ, WW$, $\gamma\gamma, \tau\tau, bb$, and $\mu\mu$. All results are reported assuming a value of 125.09 GeV for the Higgs boson mass, the result of the combined measurement by the ATLAS and CMS experiments. The analysis uses the CERN LHC proton--proton collision data recorded by the ATLAS and CMS experiments in 2011 and 2012, corresponding to integrated luminosities per experiment of approximately 5 fb$^{-1}$ at $\sqrt{s}=7$ TeV and 20 fb$^{-1}$ at $\sqrt{s} = 8$ TeV. The Higgs boson production and decay rates measured by the two experiments are combined within the context of three generic parameterisations: two based on cross sections and branching fractions, and one on ratios of coupling modifiers. Several interpretations of the measurements with more model-dependent parameterisations are also given. The combined signal yield relative to the Standard Model prediction is measured to be 1.09 $\pm$ 0.11. The combined measurements lead to observed significances for the vector boson fusion production process and for the $H \to \tau\tau$ decay of $5.4$ and $5.5$ standard deviations, respectively. The data are consistent with the Standard Model predictions for all parameterisations considered.

1. Introduction

This paper combines ATLAS and CMS Run 1 measurements of Higgs boson production, decay, and couplings across multiple processes and channels. The analysis uses a common 125.09 GeV mass assumption and model assumptions that may matter for significant deviations from the Standard Model.

  • The first ATLAS and CMS combination measures Higgs boson production and decay rates and constrains its couplings to Standard Model particles.Source: §1 · p. 2
  • The combination studies gluon fusion, vector boson fusion, WH, ZH, and ttH production, together with six bosonic and fermionic decay channels.Source: §1 · p. 2
  • The measurements use complete Run 1 data, corresponding to approximately 5 fb^-1 per experiment at 7 TeV and 20 fb^-1 at 8 TeV.Source: §1 · p. 2
  • Results assume a single CP-even, SM-like Higgs boson with Standard Model tensor coupling structure, narrow width, and factorised production and decay mechanisms.Source: §1 · p. 2
  • The model dependence has negligible impact for small deviations from the Standard Model but could become important for significant deviations.Source: §1 · p. 3
  • The combination incorporates correlated theoretical uncertainties and minor signal-parameterisation and systematic-treatment changes relative to earlier individual results.Source: §1 · p. 3

2. Higgs boson phenomenology and interpretation framework

The framework reviews Higgs production and decay, models signals with Monte Carlo simulation, and interprets combined measurements using signal strengths and coupling modifiers. It includes assumptions about unmeasured processes, higher-order theoretical predictions, and possible coupling deviations.

2. Higgs boson phenomenology and interpretation framework

  • The framework combines Higgs phenomenology, signal simulation, signal-strength fits, and coupling-modifier interpretations for the ATLAS and CMS measurements.These components cover production and decay predictions, Monte Carlo modelling, rate ratios, and parameterisations of deviations from Standard Model couplings.Source: §2 · p. 3

2.1. Higgs boson production and decay

  • Higgs production includes ggF, VBF, VH, ttH, bbH, and tH, while the studied decays include bosonic, fermionic, and loop-mediated photon channels.The H →WW and H →ZZ decays to vector bosons and decays to fermions proceed at tree level, whereas H →γγ is mediated by W-boson or heavy-quark loops.Source: §2.1 · pp. 3–4

2.2. Signal Monte Carlo simulation

  • Monte Carlo samples model Higgs-boson production and decay kinematics, estimate acceptance and selection efficiencies, and describe discriminating-variable distributions using process-specific event generators and shower simulations.Source: §2.2 · pp. 5, 7

2.3. Signal strengths

  • Signal strengths express measured Higgs rates relative to Standard Model predictions, but experiments measure only the product of production and decay modifiers without additional assumptions.The framework assumes equal signal strengths for several unmeasured or weakly constrained processes, including bbH with ggF and tH with ttH.Source: §2.3 · p. 8

2.4. Coupling modifiers

  • Coupling modifiers parameterise deviations in Higgs couplings, with effective modifiers for ggF and H →γγ and sensitivity to coupling signs through interference effects.Because the total Higgs width is not sufficiently constrained model-independently, the most generic κ-framework measures ratios of coupling strengths; tH interference can enhance its cross sections for κW · κt = −1.Source: §2.4 · pp. 9–10

3. Combination procedure and experimental inputs

The combination jointly fits ATLAS and CMS Run 1 Higgs analyses across production and decay channels, using profile likelihoods and correlated uncertainty models. Approximately 600 categories and updated analysis inputs support measurements of rates and coupling-related parameters.

3. Combination procedure and experimental inputs

  • Profile-likelihood fits combine ATLAS and CMS data while accounting for systematic-uncertainty correlations within and between experiments.Parameters of interest include signal strengths, coupling modifiers, cross sections, branching fractions, and their ratios.Source: §3 · p. 11, §3.2 · pp. 12–13

3.1. Overview of input analyses

  • Approximately 600 exclusive categories separate Higgs production signatures across five main production processes, while H →bb uses only VH and ttH categories.The input analyses cover H →γγ, ZZ, WW, ττ, bb, and µµ, together with ttH production studies.Source: §3.1 · pp. 11–12

3.2. Statistical treatment

  • The fits use observed data for measured results and Asimov data sets for Standard Model predictions, with confidence intervals derived from the profile-likelihood test statistic.The likelihood combines signal and background probability densities and nuisance parameters representing experimental and theoretical uncertainties.Source: §3.2 · p. 13

3.3. Treatment of systematic uncertainties

  • Systematic uncertainties are organized into statistical, signal-theory, background-theory, and other experimental categories, with correlations modeled selectively across channels and experiments.The combination incorporates approximately 4200 nuisance parameters; background-correlation choices generally have small effects, with the largest cited impact below 10% of the total uncertainty in the ttH, H →bb signal strength.Source: §3.3 · pp. 14–15

3.4. Analysis modifications for the combination

  • Updated signal models, background predictions, and correlation prescriptions change the combined inputs only modestly, with measurements differing from earlier individual combinations by less than approximately 10% of CMS total uncertainties and even less for ATLAS.Changes include revised jet-bin uncertainties, additional production processes, updated cross sections, unified ggF Higgs-boson pT treatment, and common signal-theory correlation schemes.Source: §3.4 · p. 16

4. Generic parameterisations of experimental results

The combination presents generic, increasingly structured parameterisations of Higgs production and decay measurements, from independent channel products to cross-section/branching-fraction ratios and coupling-modifier ratios. These fits provide largely model-independent tests of Standard Model compatibility while exposing precision limits, correlations, and deviations in selected ratios.

4. Generic parameterisations of experimental results

  • The analysis combines five production processes and five principal decay modes into generic parameterisations of channel products, ratios, and coupling modifiers.The independent-product fit uses 23 parameters in principle, with results quoted for 20 measurable parameters; ratio-based fits use a gg → H → ZZ reference.Source: §4 · pp. 16–17, §4.1.1 · p. 18, §4.1.2 · p. 20

4.1.1. Parameterisation using independent products of cross sections and branching fractions

  • Six σi · Bf products are measured more precisely than 40%, covering ggF decays to γγ, ZZ, and WW and VBF decays to γγ, WW, and ττ.The ggF and VBF results are significantly anticorrelated because of cross-contamination between their categories.Source: §4.1.1 · p. 19, Figure 7 · p. 21

4.1.2. Parameterisation using ratios of cross sections and branching fractions

  • Cross-section and branching-fraction ratios reduce dependence on inclusive theoretical predictions, while retaining assumptions about SM production and decay kinematics for acceptances and efficiencies.The reference σ(gg → H → ZZ) uncertainty is approximately 18%, and σVBF/σggF, BWW/BZZ, Bγγ/BZZ, and Bττ/BZZ have 30–40% relative uncertainties.Source: §4.1.2 · p. 22
  • The ratio fit yields a 16% data–SM compatibility p-value, with most measurements within 2σ but σttH/σggF and σZH/σggF showing approximately 3.0σ and similarly elevated deviations.The Bbb/BZZ ratio is measured at 0.19 relative to the SM prediction, with an approximately 2.5σ deficit anticorrelated with the elevated production ratios.Source: §4.1.2 · p. 22, Table 9 · p. 23

4.2. Parameterisation using ratios of coupling modifiers

  • The coupling-modifier fit gives a 13% data–SM compatibility p-value, with all results within 2σ except λtg and λbZ, whose deviations mirror the ttH/ggF and bb/ZZ ratio results.Negative solutions are allowed for λtg and λWZ, with combined 1σ intervals [−2.00, −1.59] ∪ [1.50, 2.07] and [−0.96, −0.82] ∪ [0.80, 0.98], respectively.Source: §4.2 · pp. 25–26, Table 10 · p. 26, Figure 10 · p. 27

5. Measurements of signal strengths

The combined ATLAS and CMS Run 1 measurements test Higgs signal strengths across production, decay, coupling-mediated production, and possible mass-degenerate states. Results are broadly compatible with the Standard Model, while the analyses provide evidence for several production and decay processes and no significant departure from a single Higgs state.

5.1. Global signal strength

  • The global signal strength is consistent with the Standard Model, with a 40% compatibility p-value; its systematic uncertainty exceeds the statistical uncertainty and is largest from the ggF cross section theory uncertainty.The fit uses one common signal-strength parameter for all production and decay channels.Source: §5.1 · p. 29

5.2. Signal strengths of individual production processes and decay channels

  • Independent production and decay signal-strength fits remain compatible with the Standard Model, with compatibility p-values of 24% and 75%, respectively.Production fits assume Standard Model branching fractions, while decay fits assume Standard Model production cross sections.Source: §5.2 · pp. 30, 32, Table 12 · p. 30
  • The combined significances exceed 5σ for VBF production and H →ττ, exceed 3σ for VH, and reach 4.4σ for ttH versus 2.0σ expected.The measured ttH excess corresponds to 2.3σ relative to the Standard Model prediction.Source: §5.2 · p. 32, Table 14 · p. 34

5.3. Boson- and fermion-mediated production processes

  • The six-parameter boson- versus fermion-mediated fit gives µV/µF = 1.09+0.36−0.28, consistent with the Standard Model, while the ten- and six-parameter fits have compatibility p-values of 90% and 75%.The ratio cancels the Higgs branching fraction separately for each decay channel.Source: §5.3 · p. 34

5.4. Search for mass-degenerate states with different coupling structures

  • The mass-degenerate analysis parameterises 25 production–decay combinations with either full freedom or a nine-parameter structure corresponding to yields from five production processes and five decay modes.The single-state parameterisation is nested within the general matrix parameterisation through constraints on its parameters.Source: §5.4 · pp. 36–37
  • The mass-degenerate-state test finds a single-state compatibility p-value of (29±2)%, showing no significant departure from the rank(M) = 1 hypothesis.The test compares a rank-one single-state matrix with a general rank-five matrix using a profile likelihood ratio and pseudo-data expectations.Source: §5.4 · pp. 36–38

6. Constraints on Higgs boson couplings

The combined fits constrain Higgs coupling modifiers under progressively restrictive assumptions about BSM loop contributions, BSM decays, fermion-sector symmetries, and vector–fermion relations. Across these parameterisations, the results are broadly compatible with Standard Model predictions while setting limits on possible deviations.

6.1. Parameterisations allowing contributions from BSM particles in loops and in decays

  • BBSM < 0.34 at 95% CL when |κV| ≤ 1 and BBSM ≥ 0, while the BBSM = 0 fit has an 11% SM-compatibility p-value.The fit allowing additional BSM contributions to the Higgs width gives an expected upper limit of 0.39.Source: §6.1 · p. 38, Table 17 · p. 40
  • The effective-coupling fit finds κγ = 1 and κg = 1 within the 68% CL region, with an 82% SM-compatibility p-value.All other coupling modifiers are fixed to their SM values and BBSM = 0.Source: §6.1 · pp. 38–39

6.2. Parameterisation assuming SM structure of the loops and no BSM decays

  • The SM-loop, BBSM = 0 fit yields coupling modifiers below SM predictions because the low κb reduces the dominant Γbb contribution to the total Higgs width.The resulting signal yields remain consistent with observations, and the SM-compatibility p-value is 74%.Source: §6.2 · pp. 41–42
  • Mass-scaled coupling parameters vary linearly with fermion mass and quadratically with weak-vector-boson mass, qualitatively matching the SM dependence.The parameterisation uses κF,i · mF,i/v for fermions and √κV,i · mV,i/v for weak vector bosons.Source: §6.2 · p. 42

6.3.1. Probing the up- and down-type fermion symmetry

  • The up-type versus down-type fermion fit has a 72% SM-compatibility p-value, and negative λVu values are excluded by more than 4σ.The ratios tested include λdu = κd/κu and λVu = κV/κu.Source: §6.3.1 · p. 44, §6.3 · p. 44

6.3.2. Probing the lepton and quark symmetry

  • The lepton-versus-quark fit has a 79% SM-compatibility p-value, while negative λVq values are excluded by more than 4σ.Because lepton–quark interference is negligible, the fit has sensitivity only to the absolute value of λlq.Source: §6.3.2 · p. 45, Table 19 · p. 46

6.4. Fermion and vector boson couplings

  • The global κF–κV fit agrees with the SM at κF = κV = 1 with a 59% compatibility p-value, and combining decay modes provides significant additional constraints.The opposite-sign coupling case is excluded by almost 5σ, driven mainly by the H → γγ interference pattern.Source: §6.4 · pp. 49–50

7. Summary

The combined Run 1 ATLAS and CMS analysis provides comprehensive Higgs production, decay, and coupling measurements across five production processes and six decay channels. Results are broadly compatible with the Standard Model while improving precision and constraining non-SM decays.

  • The combination uses approximately 600 event categories covering five production processes and six decay channels, assuming mH = 125.09 GeV and Run 1 luminosities of about 5 fb−1 at 7 TeV and 20 fb−1 at 8 TeV per experiment.Source: §7 · p. 50
  • The combined analysis improves precision over the individual experiment combinations by approximately a factor of 2 in most cases.Source: §7 · p. 51
  • 20 measurable products of production cross sections and branching fractions are compatible with a single Higgs boson hypothesis, which has a p-value of 29%.Source: §7 · p. 51
  • Ratios of coupling modifiers are measured with approximately 10–20% precision, while selected cross-section and branching-fraction ratios reach about 30–40% precision.Source: §7 · p. 51
  • The combined measurements are compatible with Standard Model predictions, and the overall branching fraction into BSM decays is constrained to less than 34% at 95% CL.Source: §7 · p. 51
  • The combined signal yield is 1.09±0.07 (stat) ±0.08 (syst) relative to the Standard Model, with observed significances of 5.4σ for VBF and 5.5σ for H →ττ.Source: §7 · p. 51

A. Correlation matrices

The correlation structure depends strongly on the chosen parameterisation: cross-section-times-branching-fraction products are mostly uncorrelated, whereas ratio-based fits exhibit broad correlations. The reported matrices have limitations for asymmetric uncertainties and cannot straightforwardly reproduce results under additional assumptions.

  • Most parameters in the 23-product cross-section-times-branching-fraction fit are uncorrelated, with anticorrelations arising from cross-contamination between production and decay categories.Notable anticorrelations occur between ggF and VBF, WH and ZH in H →γγ, and H →WW and H →ττ in ttH.Source: A. Correlation matrices · p. 55
  • Ratio-based parameterisations show correlations between all parameter pairs because the parameters share cross-section, branching-fraction, or coupling-modifier denominators.Source: A. Correlation matrices · p. 55
  • The matrices are symmetric around the observed best fit and therefore do not fully represent asymmetric uncertainties in some parameterisations.Consequently, deriving more constrained parameterisations directly from a generic fit and covariance matrix is not straightforward.Source: A. Correlation matrices · p. 55

B. Breakdown of systematic uncertainties

The paper reports ratio-based and coupling-modifier results using multiple reference channels and parameterisations, with tables and figures documenting combined and experiment-specific fits. These results include uncertainty breakdowns and correlation summaries.

  • The ratio parameterisations report σ(gg →H →ZZ) or σ(gg →H →WW) together with production-cross-section and branching-fraction ratios, while the coupling framework reports κgZ and coupling-modifier ratios.Source: B. Breakdown of systematic uncertainties · p. 55
  • Figures 27–29 provide correlation matrices for the 23-, nine-, and seven-parameter generic fits.Source: Figure 27 · p. 56, Figure 28 · p. 57, Figure 29 · p. 57
  • Tables 20 and 21 give combined and experiment-specific best fits with total uncertainties and four-component uncertainty breakdowns for the two reference channels.Source: Table 20 · p. 58, Table 21 · p. 59
  • Figure 30 visualizes the combined and individual-experiment best-fit values for gg →H →WW and related cross-section and branching-fraction ratios, normalized to Standard Model predictions.Source: Figure 30 · p. 60
  • Table 22 reports combined and experiment-specific coupling-modifier ratios, including disjoint intervals for λtg and λWZ when negative solutions are allowed.Source: Table 22 · p. 61

C. Likelihood scans for coupling modifier parameterisations

Likelihood scans account for multiple coupling-sign hypotheses when interference affects production or decay rates. This procedure identifies global minima across sign combinations and can widen confidence intervals or weaken upper limits.

The ATLAS Collaboration

This section lists the members of the ATLAS Collaboration and their institutional affiliations worldwide.

The ATLAS Collaboration

  • The section provides the ATLAS Collaboration author list, including contributors from G. Aad through W. Vandelli.The supplied passages consist solely of author names and affiliation markers.Source: The ATLAS Collaboration · pp. 72–77

Authors

  • The ATLAS Collaboration includes a large roster of authors identified by name and institutional superscripts.The author list continues across this section, covering surnames from Vanguri through Zwalinski and others.Source: The ATLAS Collaboration · p. 81

Affiliations

  • The listed affiliations span universities, laboratories, and research institutes across many countries.Affiliation entries include institutions in Europe, North and South America, Asia, Africa, Australia, and the Middle East.Source: The ATLAS Collaboration · pp. 82, 84, 86

Yerevan Physics Institute, Yerevan, Armenia

The supplied passages list contributors and institutional affiliations spanning Armenia, Austria, Belarus, Belgium, Brazil, Bulgaria, China, and Colombia.

University of Split, Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture, Split, Croatia

This section lists collaborating institutions across Croatia, Cyprus, Ecuador, Estonia, Finland, France, and Germany.

Institut für Experimentelle Kernphysik, Karlsruhe, Germany

This section lists collaborating institutions across Europe, Asia, North America, and the Middle East.

Laboratório de Instrumentação e Física Experimental de Partículas, Lisboa, Portugal

This section lists collaborating institutions in Portugal and Russia.

Institute for Theoretical and Experimental Physics, Moscow, Russia

This section identifies authors affiliated with the Institute for Theoretical and Experimental Physics in Moscow, Russia.

Institute for Theoretical and Experimental Physics, Moscow, Russia

  • V. Epshteyn, V. Gavrilov, N. Lychkovskaya, V. Popov, I. Pozdnyakov, G. Safronov, A. Spiridonov, M. Toms, E. Vlasov, and A. Zhokin are listed under the Institute for Theoretical and Experimental Physics, Moscow, Russia.Source: Institute for Theoretical and… · p. 96

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