Combined measurements of Higgs boson couplings in proton-proton collisions at $\sqrt{s} =$ 13 TeV

1 Introduction

• Precision Higgs-boson measurements test the standard-model description of electroweak symmetry breaking and probe possible beyond-the-standard-model effects.The motivation includes unexplained Yukawa-coupling patterns and the Higgs-mass hierarchy problem.Source: §1 · p. 3
• The paper combines Higgs decays to bb, ττ, µµ, ZZ, WW, and γγ, with representative leading-order diagrams shown for these channels.The selected decay samples are combined with production-mode analyses described in the introduction.Source: §1 · p. 3, Figure 1 · p. 3
• The combination uses 13 TeV CMS data across gluon fusion, vector-boson fusion, vector-boson-associated, and top-quark-associated production modes.Single-top-associated tH production is also included where analyses have sensitivity.Source: §1 · pp. 3–4
• The analyses account for interference in selected processes, making tH production sensitive to the relative sign of the HWW and ttH couplings.The tH cross section is small in the standard model because the relevant interference is destructive, but becomes constructive for a negative relative coupling sign.Source: §1 · p. 4
• The 2016 dataset provides larger luminosity and higher 13 TeV signal cross sections than Run 1, improving precision for several parameters.The predicted ggH and ttH cross sections increase by approximately factors of 2.3 and 3.8, respectively, from 8 to 13 TeV.Source: §1 · p. 5

2 The CMS detector

• A 3.8 T superconducting solenoid with 6 m internal diameter is the central feature of the CMS apparatus.The detector includes silicon tracking, electromagnetic and hadron calorimetry, and muon chambers surrounding the solenoid.Source: §2 · p. 5
• The detector's barrel, endcap, and forward systems provide measurements of charged particles, electromagnetic and hadronic energy, and muons.The cited detector description identifies the tracker, calorimeters, forward calorimeters, and gas-ionization muon chambers.Source: §2 · p. 5

3 Analyses included in the combination

• The combination targets production mechanisms through additional leptons, jets, b-tagged jets, missing transverse momentum, and distinctive VBF kinematics.Large jet separation and invariant mass identify VBF-like topologies, while missing transverse momentum can target ZH production with invisible Z decay.Source: §3 · p. 6
• Up to 265 event categories and more than 5500 nuisance parameters cover production and decay signatures while enforcing negligible event overlap.Categories use synchronized object definitions, strict multiplicity requirements, or opposing requirements on higher-level observables.Source: §3 · p. 6

3.1 H →γγ

• The H →γγ analysis separates production mechanisms with exclusive categories for ttH, ZH, WH, VBF, VH, and untagged events.The VBF category is subdivided by increasing purity against ggH, and untagged events are divided by signal purity.Source: §3.1 · p. 6
• The H →γγ signal is extracted as a narrow diphoton-mass peak over a smoothly falling continuum background.The dominant experimental uncertainties concern photon-identification shower-shape modeling and background-shape parametrization.Source: §3.1 · pp. 6, 8

3 Analyses included in the combination

• Table 1 summarizes each category's decay channel, targeted production mechanism, category count, expected signal composition, and approximate mass resolution.Control regions are excluded from the reported category counts.Source: Table 1 · p. 7

3.2 H →ZZ

• H →ZZ →4ℓ has the lowest branching fraction among the considered modes but very low background, giving strong sensitivity to high-rate production and the HZZ coupling.Separate 4e, 4µ, and 2e2µ/2µ2e channels model differing mass resolutions and background rates.Source: §3.2 · p. 8
• The H →ZZ analysis separates production modes using jet, b-tag, lepton, missing-momentum, and matrix-element-discriminant categories.The categories include VBF, hadronic and leptonic VH, ttH, missing-momentum VH, and untagged selections.Source: §3.2 · p. 8
• The dominant H →ZZ experimental uncertainties arise from lepton efficiencies and determining the Z+jets background from data.These uncertainties define an important experimental limitation of the channel.Source: §3.2 · p. 8

3.3 H →WW

• H →WW →ℓνℓν has a large branching fraction and relatively low-background final state, providing strong sensitivity to most production processes, especially ggH and VBF.The different-flavor eµ channel dominates sensitivity, while same-flavor channels are more affected by Drell–Yan contamination.Source: §3.3 · p. 8
• The H →WW analysis uses jet-multiplicity, subleading-lepton-pT, and multilepton categories to suppress backgrounds and enhance VBF, WH, and ZH sensitivity.Dedicated two-jet categories enhance VBF and VH sensitivity, while three- and four-lepton categories target WH and ZH.Source: §3.3 · p. 8
• The main H →WW experimental uncertainties come from data-driven top-pair, WW, and Drell–Yan background determinations and lepton reconstruction efficiencies.The uncertainties depend on lepton transverse momentum and pseudorapidity.Source: §3.3 · p. 9

3.4 H →ττ

• The H →ττ analysis provides competitive sensitivity to ggH and VBF production and the best sensitivity for directly measuring a fermionic Higgs coupling.Source: §3.4 · p. 9
• Events in the H →ττ analysis are categorized into 0-jet, boosted, and VBF classes, with VBF selections enhancing purity and boosted bins targeting ggH sensitivity.Source: §3.4 · p. 9
• The dominant H →ττ experimental uncertainties arise from τ-related energy scales and the Z(ττ)+jets background determination.Source: §3.4 · p. 9

3.5 VH production with H →bb

• The VH(bb) analysis provides the best sensitivity to WH and ZH production and the bbH coupling by requiring associated vector-boson production and categorizing b-tagged final states.Source: §3.5 · p. 9
• The VH(bb) analysis uses lepton-count and boost categories, including a pmiss_T > 170 GeV requirement for Z(νν)H(bb) events.Source: §3.5 · p. 9
• Background determination and b-tagging discriminator shapes and efficiencies dominate the VH(bb) experimental uncertainties.Source: §3.5 · p. 9

3.6 Boosted H production with H →bb

• The boosted H →bb analysis reconstructs high-pT Higgs candidates as AK8 jets using soft-drop jet mass and divides selected events into six jet-pT bins from 450 GeV to 1 TeV.Source: §3.6 · pp. 9–10
• The boosted H →bb analysis estimates QCD multijet backgrounds from a signal-depleted control region, with dominant uncertainties from extrapolating QCD and tt backgrounds.Source: §3.6 · p. 10

3.7 ttH production

• The ttH leptonic analysis is mainly sensitive to H decays into ττ, WW, or ZZ and provides the best sensitivity to ttH production.Source: §3.7 · p. 10
• The dominant ttH uncertainties arise from lepton reconstruction and reducible-background estimates in leptonic channels, and from ttbb, b tagging, and QCD multijet backgrounds in H →bb channels.Source: §3.7 · pp. 10–11
• The ttH H →bb analyses use leptonic and all-hadronic final states and improve the precision of the bbH coupling measurement.Source: §3.7 · pp. 10–11
• The ttH analyses categorize events using lepton content, jet and b-jet multiplicities, and multivariate or final-state selections across leptonic and all-hadronic channels.Source: §3.7 · pp. 10–11

• The H →µµ search is the only combination analysis sensitive to the Higgs coupling to second-generation fermions.Source: §3.8 · p. 11
• Events are categorized using mass-uncorrelated variables that distinguish ggH and VBF signals from Drell–Yan and tt backgrounds while exploiting dimuon mass resolution.Source: §3.8 · p. 11
• The observed upper limit on σ(H →µµ) × B(H →µµ) is 2.93 times the SM value, with background-fit function parameters dominating the uncertainty.Source: §3.8 · p. 11

• The search targets VBF, leptonic and hadronic VH, and ggH production using events with large missing transverse momentum and associated reconstructed objects.Source: §3.9 · pp. 11–12
• VBF, VH hadronic, and ggH categories use jet-based selections, with Z(νν)+jets and W(ℓν)+jets as dominant backgrounds estimated from lepton and photon control regions.Source: §3.9 · p. 12
• The ZH leptonic category selects opposite-sign electron or muon pairs consistent with Z decay, with dominant backgrounds from ZZ and WZ diboson production.Source: §3.9 · p. 12
• The observed upper limit on the invisible Higgs branching fraction is 26% assuming SM Higgs production rates.Source: §3.9 · p. 12
• The invisible analyses are included only in models allowing a nonzero invisible Higgs branching fraction.Source: §3.9 · p. 12

4 Modifications to the input analyses

• The section documents modifications made to input analyses so their signal predictions and uncertainty treatments can be combined consistently.These changes include common theoretical predictions, updated ggH uncertainty schemes, and revised treatment of limited Monte Carlo statistics.Source: §4 · p. 12, §4.1 · p. 13, §4.3 · p. 13

4.1 Gluon fusion modeling

• A common signal model is enforced by reweighting gluon-fusion samples to NNLOPS predictions across jet bins.The procedure normalizes samples to the inclusive N3LO cross section and applies NNLOPS-to-generator pT(H) ratios; validation in H →γγ and H →ττ found statistical compatibility.Source: §4.1 · p. 12

4.2 Theoretical uncertainties in gluon fusion

• Nine nuisance parameters represent ggH uncertainties from exclusive jet-bin migrations, VBF phase spaces, pT(H) regions, and missing higher-order finite-top-mass corrections.The boosted H →bb analysis uses a dedicated high-pT(H) prediction with uncertainties treated as uncorrelated from the other analyses.Source: §4.2 · p. 13

4.3 Statistical uncertainties in simulation

• The Barlow-Beeston lite approach assigns one nuisance parameter per bin, reducing minimization time while reproducing the full treatment within 1%.Each parameter scales the total bin yield and can be solved analytically because its maximum likelihood estimator is independent of the others.Source: §4.3 · p. 13

5 Combination procedure

• Parameters of interest are estimated with a profile likelihood ratio, while experimental and theoretical uncertainties enter through nuisance parameters.The likelihood combines signal and background probability densities with constraint terms for selected nuisance parameters.Source: §5 · p. 13
• Signal strengths, coupling modifiers, production cross sections, branching fractions, or their ratios serve as parameters of interest depending on the model.Remaining parameters are treated as nuisance parameters, with each systematic source correlated across the input analyses.Source: §5 · p. 13
• One-dimensional 1σ and 2σ intervals use q(α) < 1 and q(α) < 4, while two-dimensional regions use q(α) < 2.30 and q(α) < 6.18.Physical boundaries can truncate intervals, in which case coverage is not expected to be maintained.Source: §5 · p. 14
• Observed results use the collision data, whereas expected results use an SM Asimov data set constructed from expected parameter values.Observed and expected intervals can differ because of fluctuations in the observed data.Source: §5 · p. 14
• The SM production and decay predictions are evaluated at mH = 125.09 ± 0.21(stat) ± 0.11(syst) GeV.This mass comes from the combined ATLAS and CMS Run 1 measurement using H →γγ and H →ZZ(*) → 4ℓ channels.Source: §5 · p. 14

6 Systematic uncertainties

• Theoretical uncertainties are correlated across input analyses for total cross sections and branching fractions, but kinematic-shape migration uncertainties are largely uncorrelated.ggH normalization and shape uncertainties follow the dedicated correlation scheme described for gluon fusion.Source: §6 · p. 14
• Systematic uncertainties are often as large as or larger than statistical uncertainties for many parameters of interest.Theoretical signal uncertainties are among the most important systematic contributions.Source: §6 · p. 14
• Experimental correlations are applied selectively: luminosity and pileup are correlated across analyses, while many object-related uncertainties remain analysis-dependent.Jet-energy-scale and b-tagging uncertainties receive specialized correlation structures for analyses sharing sensitivities or reconstruction methods.Source: §6 · pp. 14–15
• Background-model shape and normalization parameters are determined directly from data and assigned to the statistical uncertainty.Other uncertainty sources are grouped as systematic uncertainties.Source: §6 · p. 15

7 Signal strength and cross section fits

• Production and decay modifiers are fitted separately, while the most generic model assigns one parameter to each production–decay combination.With five production and six decay modes, the generic model contains 30 parameters, although some are fixed or constrained because dedicated sensitivity is unavailable or negative yields would result.Source: §7 · pp. 15, 16, 18
• Only the product μ_iμ_f is experimentally extracted because production cross sections and decay branching fractions cannot be separated without additional assumptions.The production–decay products use the narrow-width approximation, whose reliability was found adequate for global fits.Source: §7 · p. 15
• At mH = 125.09 GeV, the combined measurement of the common signal strength modifier is reported.Its total uncertainty is decomposed into statistical, signal theoretical systematic, and other systematic components; integrated luminosity contributes Δμ/μ = 2.5%.Source: §7 · p. 15
• The ggH production-rate precision improves from approximately 20% to 10% versus Ref. [55] and from approximately 15% to 10% versus Ref. [56].The improvement is attributed to the increased ggH cross section and reduced associated theoretical uncertainties.Source: §7 · p. 16

7.1 Ratios of cross sections and branching fractions, relative to ggH →ZZ

• Ratios relative to ggH →ZZ measure decay and production relationships while canceling some systematic or theoretical uncertainties common to numerator and denominator.The fitted ratios include μγγ/μZZ, μWW/μZZ, μττ/μZZ, μμμ/μZZ, μbb/μZZ, and production ratios for VBF, WH, ZH, and ttH relative to ggH.Source: §7.1 · p. 18, Figure 7 · p. 19, Table 4 · p. 20

7.2 Stage 0 simplified template cross sections

• Stage 0 simplified-template measurements use the fiducial region |yH| < 2.5 to reduce theoretical uncertainty from extrapolation to inclusive phase space.Seven production processes are measured with experimentally motivated mergers, including ggH+bbH and ttH+tH; branching fractions enter as ratios to BZZ.Source: §7.2 · pp. 20–21, Figure 8 · p. 21, Table 5 · p. 21

8.1 Generic model within κ-framework assuming resolved loops

• The resolved-loop model fits six coupling modifiers, with ggH and H →γγ rates expressed through the underlying W, Z, top, tau, and bottom modifiers.Both positive and negative κW, κZ, and κb values are allowed, while κt is restricted positive.Source: §8.1 · pp. 22–23, Table 6 · p. 23
• The resolved-loop fit prefers positive κZ, while negative κZ remains allowed and the preference for negative κb is weak because the q difference is below 0.1.H →ZZ and ZH depend only on |κZ|, with gg →ZH interference providing sign sensitivity.Source: §8.1 · p. 23, Figure 9 · p. 24

8.2 Generic model within κ-framework with effective loops

• 95% CL limits are Binv < 0.22 and Bundet < 0.38 when invisible and undetected branching fractions float.The model imposes |κW|, |κZ| ≤1 to avoid a total-width degeneracy; the κt uncertainty improves by nearly 40% relative to Ref. [56].Source: §8.2 · pp. 24, 28, Figure 12 · p. 28
• Negative κW is preferred in both generic effective-loop models because destructive or constructive interference changes tH production, helping explain an excess in ttH-tagged H →γγ categories.The effective H →γγ coupling removes direct κW dependence in this interpretation.Source: §8.2 · p. 28, Figure 13 · p. 29

8.3 Generic model with effective loops and coupling modifier ratios

• The coupling-ratio model avoids assumptions about the total width by using κgZ = κgκZ/κH and ratios including λZg, λtg, λWZ, λγZ, λτZ, and λbZ.The results are summarized in Fig. 16 and Table 9.Source: §8.3 · p. 30, Figure 16 · p. 30, Table 9 · p. 31

8.4 Fits of vector boson and fermion coupling modifiers

• Common-scaling fits constrain vector-boson and fermion modifiers through κV and κF, while large κF values produce an essentially flat likelihood with κF ∈ [1.22, ∞] at 68% CL.The best-fit points and confidence regions are shown in Fig. 17.Source: §8.4 · p. 31, Figure 17 · p. 31

8.5 Benchmark models with resolved loops to test the symmetry of fermion couplings

• Fermion-symmetry benchmarks separately fit up- versus down-type and lepton versus quark coupling ratios, including λdu, λVu, λlq, and λVq.These resolved-loop parametrizations are summarized in Table 11 and Fig. 18.Source: §8.5 · p. 32, Figure 18 · p. 32, Table 11 · p. 33

8.6 Compatibility of measurements with the SM

• All tested parametrizations have p-values above 5% for compatibility with the SM prediction.This includes the signal parametrizations considered in Sections 7 and 8.Source: §8.6 · p. 33

9 Constraints on benchmark two Higgs doublet models

• The four considered 2HDM types differ in which Higgs doublet couples to up-type fermions, down-type fermions, quarks, and right-handed leptons.All models modify vector-boson couplings by sin(β−α), with production and decay rates depending at leading order on cos(β−α) and tan β.Source: §9 · p. 33, Table 13 · p. 35
• The allowed 95% confidence regions are obtained from interpolated likelihood scans, retaining points with Δq < 5.99 in the relevant cos(β−α)–tan β or mA–tan β planes.The threshold corresponds to a χ2 distribution with two degrees of freedom.Source: §9 · pp. 35–36
• Lobe features in the Type II, III, and IV constraints arise from negative κd, κτ, and κb values that current sensitivity does not exclude.For every considered 2HDM, the SM couplings are recovered at cos(β−α) = 0.Source: §9 · p. 36
• Observed hMSSM constraints are stronger than expected because the fitted λdu is below 1, whereas hMSSM predicts λdu > 1 for tan β > 1.The resulting data disfavors small mA values.Source: §9 · p. 36
• The 2HDM and hMSSM constraints complement direct searches for additional Higgs bosons.The hMSSM is treated as an effective Type II MSSM scenario with parameters mA and tan β.Source: §9 · pp. 33, 35, 36

• The combination uses six Higgs decay channels and targets gluon fusion, vector boson fusion, and associated production with a vector boson or top-quark pair.It uses 13 TeV proton-proton collision data collected by CMS in 2016, corresponding to 35.9 fb−1.Source: §10 · p. 36
• 1.17 ± 0.10 is the measured combined signal yield relative to the standard model prediction at mH = 125.09 GeV.Source: §10 · p. 36
• Results are compatible with standard model predictions across the considered parametrizations, including cross-section, branching-fraction, and coupling-modifier frameworks.Source: §10 · p. 36
• The invisible Higgs branching fraction is constrained to be less than 22 (38%) at 95% confidence level.Source: §10 · p. 36
• The combined constraints on the two-Higgs-doublet and minimal supersymmetric model parameter spaces complement direct searches for additional Higgs bosons.Source: §10 · p. 36
• Figure 19 presents 95% confidence-level constraints on Types I–IV two-Higgs-doublet models and the hMSSM, with observed allowed regions compared against standard-model expectations.Source: Figure 19 · p. 37