Precise determination of the mass of the Higgs boson and studies of the compatibility of its couplings with the standard model

This is a condensed description with plots for the analysis CMS-PAS-HIG-14-009.

Abstract

Properties of the Higgs boson with mass near 125 GeV are measured in proton-proton collisions with the CMS experiment at the LHC. A comprehensive set of production and decay measurements are combined. The decays to $\gamma\gamma$, ZZ, WW, $\tau\tau$, and bb pairs are exploited, including studies targeting Higgs bosons produced in association with a pair of top quarks. The data samples were collected in 2011 and 2012 and correspond to integrated luminosities of up to 5.1 fb$^{-1}$ at 7 TeV and up to 19.7 fb$^{-1}$ at 8 TeV; the final detector calibration and alignment are used in the event reconstruction. From the high-resolution $\gamma\gamma$ and ZZ channels, the mass of this Higgs boson is measured to be $125.03 \,^{+0.26}_{-0.27}\,\text{(stat.)} \,^{+0.13}_{-0.15}\,\text{(syst.)}$ GeV, with the precision dominated by the statistical uncertainty. For this mass, the event yields obtained in the different analyses tagging specific decay modes and production mechanisms are consistent with those expected for the standard model Higgs boson. The combined best-fit signal strength, relative to the standard model expectation, is found to be $1.00 \,\pm0.09\,\text{(stat.)} \,^{+0.08}_{-0.07}\,\text{(theo.)} \,\pm0.07\,\text{(syst.)}$ at the measured mass. Various searches for deviations in the magnitudes of the Higgs boson scalar couplings from those predicted for the standard model are performed. No significant deviations are found.

Mass of the observed state

Plot Caption
(Left) 1D test statistics q(mH) scan vs hypothesized Higgs boson mass mH for the γγ (green) and 4l (red) final states separately and for their combination (black). In this combination, three independent signal strengths (ggH, ttH) → γγ, (VBF, VH) → H → γγ, and pp → H → ZZ(*) → 4l are profiled together with all other nuisance parameters.
(Right) 2D 68% CL contours for a hypothesized Higgs boson mass mH and signal strength σ/σSM for the γγ (green) and 4l (red), and their combination (black). In this combination, the relative signal strength for the two decay modes is set to the expectation for the SM Higgs boson.
1D test statistics q(mH) scan vs hypothesized Higgs boson mass mH for the combination of the γγ and 4l analyses. 1D-scans of the test statistic q(mH) versus hypothesized boson mass mH for the combination of the γγ and 4l final states. The solid curve is obtained by profiling all nuisance parameters and thus includes both statistical and systematic uncertainties. The dashed curve is obtained by fixing all nuisance parameters to their best-fit values, except for those related to the H → γγ background description, thus including only statistical uncertainties. The crossings with the thick (thin) horizontal lines define the 68% (95%) CL interval for the measured mass.
1D test statistics q($\mathrm{m}_\mathrm{H}^{\gamma\gamma}-\mathrm{m}_\mathrm{H}^\mathrm{4l}$) scan vs the difference between two individual mass measurements. 1D test statistics q($\mathrm{m}_\mathrm{H}^{\gamma\gamma}-\mathrm{m}_\mathrm{H}^\mathrm{4l}$) scan versus the difference between two individual mass measurements from γγ and 4l final states. The crossings with the thick (thin) horizontal lines define the 68% (95%) CL interval for the measured difference.

Additional plots

Plot Caption
2D test statistics –2 ln Q vs hypothesized Higgs boson mass mH and signal strength σ/σSM for the combination of the high resolution channels. The cross indicates the best-fit values. The solid, dashed, and dotted contours show the 68%, 95%, and 99.7% CL ranges, respectively. In this combination, the relative signal strengths for the various final states are constrained by the expectations for the SM Higgs boson.
2D test statistics –2 ln Q vs hypothesized Higgs boson mass mH and signal strength σ/σSM for the diphoton final state. The cross indicates the best-fit values. The solid, dashed, and dotted contours show the 68%, 95%, and 99.7% CL ranges, respectively. In this combination, the relative signal strengths for the various production modes are constrained by the expectations for the SM Higgs boson.
2D test statistics –2 ln Q vs hypothesized Higgs boson mass mH and signal strength σ/σSM for the four-lepton final state. The cross indicates the best-fit values. The solid, dashed, and dotted contours show the 68%, 95%, and 99.7% CL ranges, respectively.

Sensitivities to and significances of the observed excess by decay mode groups

  Significance (mH = 125.0 GeV)
Combination Expected (pre-fit) Expected (post-fit) Observed
H→ZZ tagged 6.3 σ 6.3 σ 6.5 σ
H→γγ tagged 5.1 σ 5.3 σ 5.6 σ
H→WW tagged 5.7 σ 5.4 σ 4.7 σ
H→bb tagged 2.2 σ 2.3 σ 2.0 σ
H→ττ tagged 4.1 σ 3.9 σ 3.8 σ

The expected significance is computed for the background + SM Higgs signal hypothesis (with μ=σ/σSM=1). The pre-fit expected significance is computed for the nominal value of the nuisance parameters, while the post-fit expected significance is computed setting the nuisance parameters to their best-fit values.

Compatibility of the observed state with the SM Higgs boson hypothesis: signal strengths

Plot Caption
Values of the best-fit σ/σSM for the combination (solid vertical line) and for subcombinations by predominant decay mode and additional tags targeting a particular production mechanism. The vertical band shows the overall σ/σSM uncertainty. The σ/σSM ratio denotes the production cross section times the relevant branching fractions, relative to the SM expectation. The horizontal bars indicate the ±1 standard deviation uncertainties in the best-fit σ/σSM values for the individual modes; they include both statistical and systematic uncertainties.
Values of the best-fit σ/σSM for the combination (solid vertical line) and for subcombinations by predominant decay mode. The vertical band shows the overall σ/σSM uncertainty. The σ/σSM ratio denotes the production cross section times the relevant branching fractions, relative to the SM expectation. The horizontal bars indicate the ±1 standard deviation uncertainties in the best-fit σ/σSM values for the individual modes; they include both statistical and systematic uncertainties.
Values of the best-fit σ/σSM for the combination (solid vertical line) and for subcombinations by analysis tags targeting individual production mechanisms. The vertical band shows the overall σ/σSM uncertainty. The σ/σSM ratio denotes the production cross section times the relevant branching fractions, relative to the SM expectation. The horizontal bars indicate the ±1 standard deviation uncertainties in the best-fit σ/σSM values for the individual modes; they include both statistical and systematic uncertainties.

Numeric values

The tables below contain the same information that is shown in Figure 4 of the HIG-14-009 PAS.

Grouping μ̂ = σ/σSM (mH = 125.0 GeV)
by production tag and predominant decay mode value uncertainty
H → ZZ (2 jets) 1.549 -0.661/+ 0.953
H → ZZ (0/1 jet) 0.883 -0.272/+ 0.336
H → ττ (ttH tag) -1.325 -3.600/+ 6.078
H → ττ (VH tag) 0.867 -0.883/+ 0.998
H → ττ (VBF tag) 0.948 -0.379/+ 0.431
H → ττ (0/1 jet) 0.843 -0.382/+ 0.423
H → WW (ttH tag) 3.939 -1.435/+ 1.698
H → WW (VH tag) 0.800 -0.934/+ 1.088
H → WW (VBF tag) 0.623 -0.479/+ 0.593
H → WW (0/1 jet) 0.766 -0.205/+ 0.228
H → γγ (ttH tag) 2.671 -1.726/+ 2.414
H → γγ (VH tag) 0.574 -0.806/+ 0.935
H → γγ (VBF tag) 1.514 -0.476/+ 0.551
H → γγ (untagged) 1.007 -0.259/+ 0.293
H → bb (ttH tag) 0.650 -1.809/+ 1.849
H → bb (VH tag) 1.008 -0.499/+ 0.527
by predominant decay mode value uncertainty
H → ZZ tagged 1.003 -0.263/+ 0.317
H → WW tagged 0.832 -0.200/+ 0.224
H → γγ tagged 1.126 -0.228/+ 0.259
H → ττ tagged 0.912 -0.263/+ 0.286
H → bb tagged 0.932 -0.482/+ 0.506
by production tag value uncertainty
ttH tagged 2.762 -0.923/+ 1.052
VH tagged 0.890 -0.372/+ 0.387
VBF tagged 1.140 -0.251/+ 0.282
Untagged 0.865 -0.139/+ 0.176

Production modes

Two independent signal strengths corresponding to two groups of production mechanisms: (ggH,ttH) and (VBF,VH)

The 68% CL regions (bounded by the solid curves) for signal strength of the ggH and ttH, and of the VBF and VH production mechanisms: μggH,ttH and μ VBF,VH, respectively. The different colors show the results obtained by combining data from each of the five analyzed decay mode groups: γγ (green), WW (blue), ZZ(red), ττ (violet), bb (cyan). The crosses indicate the best-fit values. The diamond at (1,1) indicates the expected values for the SM Higgs boson.
1D test statistics q(μVBF,VHggH,ttH) scan vs the ratio of signal strength modifiers μVBF,VHggH,ttH combined for all channels. The solid curve represents the observed result in data while the dashed curve indicates the expected median result in the presence of the SM Higgs boson. Crossings with the horizontal thick and thin red lines denote the 68% CL and 95% CL confidence intervals.The cross-section ratios σVBFVH and σggHttH assumed to be as in the SM.
Numerical values
The best-fit values for the signal strength at mH = 125.0 GeV, of the VBF and VH, and of the ggH and ttH production mechanisms, μVBF,VH and μggH,ttH, respectively. The channels are grouped by decay mode tag. The observed and median expected results for the ratio of μVBF,VH to μggH,ttH together with their uncertainties are also given for the full combination.
Channel grouping Best fit (μggH,ttH, μVBF,VH)
H → ZZ tagged $(0.88,1.75)$
H → γγ tagged $(1.07,1.24)$
H → WW tagged $(0.87,0.66)$
H → ττ tagged $(0.52,1.21)$
H → bb tagged $(0.57,0.96)$
Combined best fit μVBF,VHggH,ttH
Observed (expected)
$1.25_{-0.45}^{+0.63}$ ($1.00_{-0.35}^{+0.49}$)

Four independent signal strengths corresponding to the four SM main production modes

Likelihood scan results for a fit to the data assuming independent signal strengths for each of the four production modes, while the decay branching fractions are assumed to be as in the SM.

Plot Caption
1D test statistics q(μggH) scan vs the signal strength modifier for gluon-fusion production μggH, profiling the signal strength modifiers for the other production modes μVBFVHttH and all other nuisances. The decay branching fractions are assumed to be as in the SM.
1D test statistics q(μVBF) scan vs the signal strength modifier for vector-boson-fusion production μVBF, profiling the signal strength modifiers for the other production modes μggHVHttH and all other nuisances. The decay branching fractions are assumed to be as in the SM.
1D test statistics q(μVH) scan vs the signal strength modifier for associated VH production μVH, profiling the signal strength modifiers for the other production modes μggHVBFttH and all other nuisances. The decay branching fractions are assumed to be as in the SM.
1D test statistics q(μttH) scan vs the signal strength modifier for associated ttH production μttH, profiling the signal strength modifiers for the other production modes μggHVBFVH and all other nuisances. The decay branching fractions are assumed to be as in the SM.

Numerical values
The best-fit results for independent signal strengths corresponding to the four main production processes, ggH, VBF, VH, and ttH; the expected sensitivities and observed significances with respect to background-only hypothesis ($\mu = 0$), and the pull of the observation with respect to the SM hypothesis ($\mu=1$). These results assume that the relative values of the branching fractions are those predicted by the SM.
Parameter Best fit result (68% CL)
for full combination
Observed significance ($\sigma$) Expected sensitivity ($\sigma$) Pull to SM hypothesis ($\sigma$)
μggH $0.85_{-0.17}^{+0.19}$ 6.5 7.5 -0.8
μVBF $1.15_{-0.35}^{+0.37}$ 3.6 3.3 0.4
μVH $1.00_{-0.40}^{+0.40}$ 2.7 2.7 0.0
μttH $2.93_{-0.97}^{+1.04}$ 3.5 1.2 2.1

Additional plots (not in PAS)

Plot Caption
1D test statistics q(μVBF,VHggH,ttH) scan vs the ratio of signal strength modifiers μVBF,VHggH,ttH, profiling all other nuisances, for the different decay channels considered and their combination. The cross-section ratios σVBFVH and σggHttH assumed to be as in the SM.
Summary of the fits to the full data assuming independent signal strengths for each of the four production modes, while the decay branching fractions are assumed to be as in the SM. The best fit of the signal strengths are shown, with the corresponding 68% and 95% CL intervals.
Summary of the fits to the 7 TeV data assuming independent signal strengths for each of the four production modes, while the decay branching fractions are assumed to be as in the SM. The best fit of the signal strengths are shown, with the corresponding 68% and 95% CL intervals.
Summary of the fits to the 8 TeV data assuming independent signal strengths for each of the four production modes, while the decay branching fractions are assumed to be as in the SM. The best fit of the signal strengths are shown, with the corresponding 68% and 95% CL intervals.

Numerical values
The best-fit results for independent signal strengths corresponding to the four main production processes, ggH, VBF, VH, and ttH, for 7 TeV and 8 TeV data separately. These results assume the relative values of the branching fractions to be those of the SM.
Parameter Best fit result (68% CL) for 7 TeV data Best fit result (68% CL) for 8 TeV data
μggH $1.00^{+0.36}_{-0.32}$ $0.80^{+0.19}_{-0.17}$
μVBF $1.78^{+0.97}_{-0.91}$ $1.02^{+0.39}_{-0.36}$
μVH $0.69^{+0.98}_{-0.66}$ $1.06^{+0.45}_{-0.43}$
μttH $0.00^{+2.13}_{-0.00}$ $3.22^{+1.14}_{-1.00}$

The observed results for the ratio of μ(VBF,VH) to μ(ggH,ttH) are given for the individual channels and the full combination.

Channel grouping Best fit μVBF,VHggH,ttH
H → ZZ tagged 2.00
H → γγ tagged 1.15
H → WW tagged 0.65
H → ττ tagged 2.55
Combined 1.25

Compatibility of the observed data with the SM Higgs boson couplings

Test of Custodial Symmetry

Using only untagged pp → H → WW and pp → H → ZZ events and assuming SM couplings to fermions

Plot Caption
1D test statistics q($\lambda_{\mathrm{WZ}}$) scan vs $\lambda_{\mathrm{WZ}}$, the ratio of the couplings to W and Z bosons, profiling the coupling modifier κZ and all other nuisances. The coupling to fermions is taken to be the SM one (κF = 1).

Using all channels, and without assumption on the couplings to fermions (except their universality)

Plot Caption
1D test statistics q($\lambda_{\mathrm{WZ}}$) scan vs $\lambda_{\mathrm{WZ}}$, the ratio of the couplings to W and Z bosons, profiling the coupling modifiers κZ and κF and all other nuisances.

Test of Fermion and Vector Boson Couplings

Plot Caption
2D test statistics q(κV, κF) scan. The cross indicates the best-fit values. The solid, dashed, and dotted contours show the 68%, 95%, and 99.7% CL regions, respectively. The yellow diamond shows the SM point (κV, κf) = (1, 1). The left plot shows the likelihood scan in two quadrants, $(+, +)$ and $(+,-)$. The right plot shows the likelihood scan constrained to the $(+, +)$ quadrant.
2D test statistics q(κV, κF) scan for individual channels (colored swaths) and for the overall combination (thick curve). The cross indicates the global best-fit values. The dashed contour bounds the 95% CL region for the combination. The yellow diamond shows the SM point (κV, κf) = (1, 1). The left plot shows the likelihood scan in two quadrants, $(+, +)$ and $(+,-)$. The right plot shows the positive quadrant only.

Additional plots (not in PAS)

1D test statistics q(κV) scan, profiling κF.
1D test statistics q(κF) scan, profiling κV.

Test for the presence of BSM particles

Plot Caption
2D test statistics q(κg, κγ) scan, assuming that ΓBSM = 0. The cross indicates the best-fit values. The solid, dashed, and dotted contours show the 68%, 95%, and 99.7% CL regions, respectively. The yellow diamond represents the SM expectation, (κγ, κg) = (1, 1). The partial widths associated with the tree-level production processes and decay modes are assumed to be unaltered (κ = 1).
1D test statistics q(BRBSM) scan, profiling the modifier to the effective coupling to photons and gluons κγ, κg. The solid curve represents the observation and the dashed curve indicates the expected median results in the presence of the SM Higgs boson. The partial widths associated with the tree-level production processes and decay modes are assumed to be unaltered (κ = 1).
2D test statistics q(κg, BRBSM) scan, profiling the modifier to the effective coupling to photons κγ. The solid, dashed, and dotted contours show the 68%, 95%, and 99.7% CL regions, respectively. The partial widths associated with the tree-level production processes and decay modes are assumed to be unaltered (κ = 1).

Additional plots (not in PAS)

Plot Caption
1D test statistics q(κg) scan, assuming that ΓBSM = 0, profiling the modifier to the effective coupling to photons κγ.
1D test statistics q(κγ) scan, assuming that ΓBSM = 0, profiling the modifier to the effective coupling to gluons κg.

Test for asymmetries in the couplings to fermions

Up-type vs Down-type Fermions

Plot Caption
1D test statistics q(λdu) scan vs the coupling modifier ratio λdu, profiling the coupling modifiers κu and κV and all other nuisances.

Leptons vs Quarks

Plot Caption
1D test statistics q(λlq) scan vs the coupling modifier ratio λlq, profiling the coupling modifiers κq and κV and all other nuisances.

Generic search for deviations in the couplings (with effective photon and gluon couplings)

The search is performed with six independent coupling modifiers: κV, κb, κτ, κt, κg, κγ.
Plot Caption
1D test statistics q(κV) scan, profiling the other five coupling modifiers.
1D test statistics q(κb) scan, profiling the other five coupling modifiers.
1D test statistics q(κτ) scan, profiling the other five coupling modifiers.
1D test statistics q(κt) scan, profiling the other five coupling modifiers.
1D test statistics q(κγ) scan, profiling the other five coupling modifiers.
1D test statistics q(κg) scan, profiling the other five coupling modifiers.

Including BSM decays

Plot Caption
The likelihood scan versus BRBSM = ΓBSMtot. The solid curve is the data and the dashed line indicates the expected median results in the presence of the SM Higgs boson. The modifiers for both the tree-level and loop-induced couplings are profiled, but the couplings to the electroweak bosons are assumed to be bound by the SM expectation (κV ≤ 1)

Generic search for deviations in the couplings (assuming SM loop structure) (not in PAS)

The search is performed with five independent coupling modifiers: κW, κZ, κb, κτ, κt.

Plot Caption
1D test statistics q(κW) scan, profiling the other four coupling modifiers.
1D test statistics q(κZ) scan, profiling the other four coupling modifiers.
1D test statistics q(κb) scan, profiling the other four coupling modifiers.
1D test statistics q(κτ) scan, profiling the other four coupling modifiers.
1D test statistics q(κt) scan, profiling the other four coupling modifiers.

Generic search for deviations in the coupling ratios (with effective photon and gluon couplings) (not in PAS)

The search is performed with following 7 free parameters: κgZ (= κκZH), λγZ (= κγZ), λWZ (= κWZ), λbZ (= κbZ), λτZ (= κτZ), λZg (= κZg), λtg (= κtg), allowing all gauge and third generation fermion couplings to float and allowing for invisible or undetectable widths.

Plot Caption
1D test statistics q(κgZ) scan, profiling the other 6 parameters.
1D test statistics q(κgZ) scan, profiling the other 6 parameters.
1D test statistics q(κgZ) scan, profiling the other 6 parameters.
1D test statistics q(κgZ) scan, profiling the other 6 parameters.
1D test statistics q(κgZ) scan, profiling the other 6 parameters.
1D test statistics q(κgZ) scan, profiling the other 6 parameters.
1D test statistics q(κgZ) scan, profiling the other 6 parameters.

Search for deviation on the mass scaling factor ε and the vacuum expectation value parameter M (not in PAS)

The coupling scale factors to fermions and vector bosons are expressed in terms of a mass scaling parameter $\epsilon$ and a “vacuum expectation value” parameter $M$, described in arXiv:1207.1693. The coupling scale factors to fermions are $\kappa_{f,i}=v\cdot m_{f,i}^{\epsilon} / M^{1+\epsilon}$ and the coupling scale factors to vector bosons are $\kappa_{V,j}=v\cdot m_{V,j}^{2\epsilon} / M^{1+2\epsilon}$, where $v\approx246$ GeV is the SM vacuum expectation value, $m_{f,i}$ are the fermion masses, and $m_{V,i}$ are the vector boson masses. The SM expectation of $\kappa_{f,i}=\kappa_{V,i}=1$ is recovered in the double limit of $\epsilon=0$ and $M=v$.

2D test statistics q(M, ε) scan.

Summary plots of couplings (not in PAS)

Plot Caption
Summary of the fits for deviations in the coupling for the LHC XS WG benchmark models (arXiv:1307.1347). For each model, the best fit values of the most interesting parameters are shown, with the corresponding 68% and 95% CL intervals. The list of parameters for each model and the numerical values of the intervals are provided in Table 3 of the PAS.
Summary of the fits for deviations in the coupling for the generic six-parameter model including effective loop couplings. The best fit of the parameters are shown, with the corresponding 68% and 95% CL intervals. The result of the fit when extending the model to allow for beyond-SM decays while restricting the effective coupling to vector bosons to not exceed unity (κV ≤ 1.0) is also shown.
Summary of the fits for deviations in the coupling ratios for the general seven-parameter model with effective loop couplings. The best fit of the parameters are shown, with the corresponding 68% and 95% CL intervals.
Summary of the fits for deviations in the coupling for the generic five-parameter model not effective loop couplings. In this model, loop-induced couplings are assumed to follow the SM structure as in arXiv:1307.1347. The best fit values of the parameters are shown, with the corresponding 68% and 95% CL intervals.
Summary of the fits for deviations in the coupling for the generic five-parameter model not effective loop couplings, expressed as function of the particle mass. For the fermions, the values of the fitted yukawa couplings hff are shown, while for vector bosons the square-root of the coupling for the hVV vertex divided by twice the vacuum expectation value of the Higgs boson field. Particle masses for leptons and weak boson, and the vacuum expectation value of the Higgs boson are taken from the PDG. For the top quark the same mass used in theoretical calculations is used (172.5 GeV) and for the bottom quark the running mass mb(mH=125.0 GeV)=2.763 GeV is used. In this model, loop-induced couplings are assumed to follow the SM structure as in arXiv:1307.1347.
Summary of the fits for deviations in the coupling for the generic five-parameter model not effective loop couplings, expressed as function of the particle mass. For the fermions, the values of the fitted yukawa couplings hff are shown, while for vector bosons the square-root of the coupling for the hVV vertex divided by twice the vacuum expectation value of the Higgs boson field. Particle masses for leptons and weak boson, and the vacuum expectation value of the Higgs boson are taken from the PDG. For the top quark the same mass used in theoretical calculations is used (172.5 GeV) and for the bottom quark the running mass mb(mH=125.0 GeV)=2.763 GeV is used. In this model, loop-induced couplings are assumed to follow the SM structure as in arXiv:1307.1347. The solid black line with 68% and 95% CL bands are taken from the fit to data with the model $(M,\epsilon)$.
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