Precise determination of the mass of the Higgs boson and tests of compatibility of its couplings with the standard model predictions using proton collisions at 7 and 8 TeV

This is a condensed description with plots for the analysis CMS-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. Comprehensive sets of production and decay measurements are combined. The decay channels include $\gamma\gamma$, ZZ, WW, $\tau\tau$, bb, and $\mu\mu$ pairs. 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. From the high-resolution $\gamma\gamma$ and ZZ channels, the mass of the Higgs boson is determined to be $125.02 \,^{+0.26}_{-0.27}\,\text{(stat.)} \,^{+0.14}_{-0.15}\,\text{(syst.)}$ GeV. For this mass value, the event yields obtained in the different analyses tagging specific decay channels and production mechanisms are consistent with those expected for the standard model Higgs boson. The combined best-fit signal relative to the standard model expectation is $1.00 \,\pm0.09\,\text{(stat.)} \,^{+0.08}_{-0.07}\,\text{(theo.)} \,\pm0.07\,\text{(syst.)}$ at the measured mass. The couplings of the Higgs boson are probed for deviations in magnitude from the standard model predictions in multiple ways, including searches for invisible and undetected decays. No significant deviations are found.

\( \def\MX{\mathrm{m}_\mathrm{H}} \def\MH{\mathrm{m}_\mathrm{H}} \def\hgg{\mathrm{H}\rightarrow\mathrm{\gamma\gamma}} \def\hzzllll{\mathrm{H}\rightarrow\mathrm{ZZ}\rightarrow\mathrm{4\ell}} \def\ggh{\mathrm{ggH}} \def\tth{\mathrm{ttH}} \def\vh{\mathrm{VH}} \def\vbf{\mathrm{VBF}} \def\to{\rightarrow} \def\gg{\mathrm{\gamma\gamma}} \def\PH{\mathrm{H}} \def\GSM{\mathrm{\Gamma}_{\mathrm{SM}}} \def\GammaObsComb{1.7} \def\GammaExpComb{2.3} \def\muggh{\mu_{\mathrm{ggH}}} \def\mutth{\mu_{\mathrm{ttH}}} \def\muvh{\mu_{\mathrm{VH}}} \def\muvbf{\mu_{\mathrm{VBF}}} \)

Mass measurement and direct limits on the natural width

Plot	Caption
	The 68% CL confidence regions for the signal strength $\sigma /\sigma_{\text{SM}}$ versus the mass of the boson $\MH$ for the $\hgg$ and $\hzzllll$ final states, and their combination. The symbol $\sigma / \sigma_{\text{SM}}$ denotes the production cross section times the relevant branching fractions, relative to the SM expectation. In this combination, the relative signal strength for the two decay modes is set to the expectation for the SM Higgs boson.
	Scan of the test statistic $q(\MX)=-2 \, \Delta \ln \mathcal{L} $ versus the mass of the boson $\MX$ for the $\hgg$ and $\hzzllll$ final states separately and for their combination. Three independent signal strengths, $(\ggh,\tth)\to \gg$, $(\vbf,\vh)\to \gg$, and $\text{pp}\to\hzzllll$, are profiled together with all other nuisance parameters. 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 $\hgg$ 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.
	Scan of the test statistic $q(m_{\PH}^{\gg} - m_{\PH}^{4\ell})$ versus the difference between two individual mass measurements for the same model of signal strengths used in the left panel.
	Likelihood scan as a function of the width of the boson. The continuous (dashed) lines show the observed (expected) results for the $\hgg$ analysis, the $\hzzllll$ analysis, and their combination. The data are consistent with $\GSM \sim$ 4 MeV and for the combination of the two channels the observed (expected) upper limit on the width at the 95% CL is $\GammaObsComb (\GammaExpComb)$ GeV.

Significances of the observations in data

	Significance (mH = 125.0 GeV)
Combination	Expected (post-fit)	Observed
H→ZZ tagged	6.3 σ	6.5 σ
H→γγ tagged	5.3 σ	5.6 σ
H→WW tagged	5.4 σ	4.7 σ
H→ττ tagged	3.9 σ	3.8 σ
H→bb tagged	2.6 σ	2.0 σ
H→μμ tagged	<0.1 σ	0.4 σ

The observed and median expected significances of the excesses for each decay mode group, assuming $\MX=125.0$ GeV.

Compatibility of the observed yields with the SM Higgs boson hypothesis

Grouping by predominant decay mode and/or production tag

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 paper.

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/+0.954
H → ZZ (0/1 jet)	0.883	-0.272/+0.337
H → ττ (ttH tag)	-1.325	-3.600/+6.079
H → ττ (VH tag)	0.868	-0.884/+1.000
H → ττ (VBF tag)	0.949	-0.381/+0.432
H → ττ (0/1 jet)	0.845	-0.384/+0.423
H → WW (ttH tag)	3.939	-1.437/+1.704
H → WW (VH tag)	0.800	-0.934/+1.089
H → WW (VBF tag)	0.623	-0.479/+0.594
H → WW (0/1 jet)	0.766	-0.206/+0.229
H → γγ (ttH tag)	2.675	-1.729/+2.402
H → γγ (VH tag)	0.575	-0.807/+0.934
H → γγ (VBF tag)	1.514	-0.475/+0.545
H → γγ (untagged)	1.000	-0.257/+0.286
H → bb (ttH tag)	0.650	-1.809/+1.850
H → bb (VH tag)	0.890	-0.441/+0.469
by predominant decay mode	value	uncertainty
H → ZZ tagged	1.003	-0.264/+0.318
H → WW tagged	0.832	-0.201/+0.226
H → γγ tagged	1.121	-0.224/+0.251
H → ττ tagged	0.913	-0.264/+0.289
H → bb tagged	0.836	-0.429/+0.454
by production tag	value	uncertainty
ttH tagged	2.750	-0.911/+1.061
VH tagged	0.833	-0.345/+0.361
VBF tagged	1.150	-0.248/+0.287
Untagged	0.869	-0.146/+0.173

Fermion- and boson-mediated production processes and their ratio

Plot	Caption
	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,VH/μggH,ttH) scan vs the ratio of signal strength modifiers μVBF,VH/μggH,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 σVBF/σVH and σggH/σttH assumed to be as in the SM.

Numerical values

The best-fit values for the signal strength at m_H = 125.0 GeV, of the VBF and VH, and of the ggH and ttH production mechanisms, μ_VBF,VH and μ_ggH,ttH, respectively. The channels are grouped by decay mode tag. The observed and median expected results for the ratio of μ_VBF,VH to μ_ggH,ttH together with their uncertainties are also given for the full combination.

Channel grouping	Best fit (μggH,ttH, μVBF,VH)
H → γγ tagged	$(1.07,1.24)$
H → ZZ tagged	$(0.88,1.75)$
H → WW tagged	$(0.87,0.66)$
H → ττ tagged	$(0.52,1.21)$
H → bb tagged	$(0.55,0.85)$
Combined best fit μVBF,VH/μggH,ttH
Observed (expected)
$1.25_{-0.44}^{+0.62}$ ($1.00_{-0.35}^{+0.49}$)

Individual production modes

Plot	Caption
	Likelihood scan results for $\muggh, \muvbf, \muvh$, and $\mutth$. The inner bars represent the 68% CL confidence intervals while the outer bars represent the 95% CL confidence intervals. When scanning each individual parameter, the three other parameters are profiled. The SM values of the relative branching fractions are assumed for the different decay modes.

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	$0.85_{-0.16}^{+0.19}$	6.6	7.4	-0.8
μVBF	$1.16_{-0.34}^{+0.37}$	3.7	3.3	+0.4
μVH	$0.92_{-0.36}^{+0.38}$	2.7	2.9	-0.2
μttH	$2.90_{-0.94}^{+1.08}$	3.5	1.2	+2.2

Parameter	Best fit result (68% CL) for 7 TeV data	Best fit result (68% CL) for 8 TeV data
μggH	$1.03^{+0.37}_{-0.33}$	$0.79^{+0.19}_{-0.17}$
μVBF	$1.77^{+0.99}_{-0.90}$	$1.02^{+0.39}_{-0.36}$
μVH	$0.68^{+0.99}_{-0.68}$	$0.96^{+0.41}_{-0.39}$
μttH	< 2.19	$3.27^{+1.20}_{-1.04}$

Ratios between decay modes

\( \def\ensuremath{} \def\xspace{} \def\hzz{\mathrm{H}\rightarrow\mathrm{ZZ}} \def\hww{\mathrm{H}\rightarrow\mathrm{WW}} \def\htt{\mathrm{H}\rightarrow\mathrm{\tau\tau}} \def\hbb{\mathrm{H}\rightarrow\mathrm{bb}} \newcommand{\DRzzww}{\ensuremath{1.10^{+0.44}_{-0.33}}\xspace} \newcommand{\DRggww}{\ensuremath{1.21^{+0.41}_{-0.31}}\xspace} \newcommand{\DRttww}{\ensuremath{0.86^{+0.42}_{-0.32}}\xspace} \newcommand{\DRbbww}{\ensuremath{0.74^{+0.61}_{-0.41}}\xspace} \newcommand{\DRwwzz}{\ensuremath{0.88^{+0.38}_{-0.26}}\xspace} \newcommand{\DRggzz}{\ensuremath{1.06^{+0.44}_{-0.31}}\xspace} \newcommand{\DRttzz}{\ensuremath{0.76^{+0.43}_{-0.30}}\xspace} \newcommand{\DRbbzz}{\ensuremath{0.65^{+0.59}_{-0.37}}\xspace} \newcommand{\DRwwgg}{\ensuremath{0.83^{+0.27}_{-0.22}}\xspace} \newcommand{\DRzzgg}{\ensuremath{0.92^{+0.38}_{-0.27}}\xspace} \newcommand{\DRttgg}{\ensuremath{0.71^{+0.43}_{-0.25}}\xspace} \newcommand{\DRbbgg}{\ensuremath{0.63^{+0.44}_{-0.35}}\xspace} \newcommand{\DRwwtt}{\ensuremath{1.15^{+0.68}_{-0.44}}\xspace} \newcommand{\DRzztt}{\ensuremath{1.31^{+0.81}_{-0.48}}\xspace} \newcommand{\DRggtt}{\ensuremath{1.41^{+0.75}_{-0.45}}\xspace} \newcommand{\DRbbtt}{\ensuremath{0.87^{+0.69}_{-0.49}}\xspace} \newcommand{\DRwwbb}{\ensuremath{1.32^{+1.57}_{-0.59}}\xspace} \newcommand{\DRzzbb}{\ensuremath{1.48^{+1.85}_{-0.70}}\xspace} \newcommand{\DRggbb}{\ensuremath{1.60^{+1.86}_{-0.70}}\xspace} \newcommand{\DRttbb}{\ensuremath{1.14^{+1.34}_{-0.52}}\xspace} \newcommand{\DRzzwwTwoSig}{\ensuremath{[0.54,2.18]}\xspace} \newcommand{\DRggwwTwoSig}{\ensuremath{[0.67,2.22]}\xspace} \newcommand{\DRttwwTwoSig}{\ensuremath{[0.30,1.90]}\xspace} \newcommand{\DRbbwwTwoSig}{\ensuremath{[0,00,2.30]}\xspace} \newcommand{\DRwwzzTwoSig}{\ensuremath{[0.44,1.78]}\xspace} \newcommand{\DRggzzTwoSig}{\ensuremath{[0.54,2.16]}\xspace} \newcommand{\DRttzzTwoSig}{\ensuremath{[0.26,1.80]}\xspace} \newcommand{\DRbbzzTwoSig}{\ensuremath{[0.00,2.16]}\xspace} \newcommand{\DRwwggTwoSig}{\ensuremath{[0.44,1.48]}\xspace} \newcommand{\DRzzggTwoSig}{\ensuremath{[0.44,1.78]}\xspace} \newcommand{\DRttggTwoSig}{\ensuremath{[0.26,1.45]}\xspace} \newcommand{\DRbbggTwoSig}{\ensuremath{[0.00,1.76]}\xspace} \newcommand{\DRwwttTwoSig}{\ensuremath{[0.50,3.22]}\xspace} \newcommand{\DRzzttTwoSig}{\ensuremath{[0.54,3.79]}\xspace} \newcommand{\DRggttTwoSig}{\ensuremath{[0.67,3.76]}\xspace} \newcommand{\DRbbttTwoSig}{\ensuremath{[0.00,2.84]}\xspace} \newcommand{\DRwwbbTwoSig}{\ensuremath{[0.41,-]}\xspace} \newcommand{\DRzzbbTwoSig}{\ensuremath{[0.44,-]}\xspace} \newcommand{\DRggbbTwoSig}{\ensuremath{[0.54,-]}\xspace} \newcommand{\DRttbbTwoSig}{\ensuremath{[0.33,-]}\xspace} \)

\( \def\muf{\mu_\mathrm{ggH,ttH}} \def\muv{\mu_\mathrm{VBF,VH}} \)

Parameterization used to scale the expected SM Higgs boson yields of the different production and decay modes when obtaining the results presented in next table. The $\muf$ and $\muv$ parameters are introduced to reduce the dependency of the results on the SM expectation

\begin{array}{c|ccccc} \hline \text{Best-fit} ~\lambda_\text{col,row} & \hgg & \hzz & \hww & \htt & \hbb \\\hline \hgg & 1 & \DRzzgg & \DRwwgg & \DRttgg & \DRbbgg \\\hzz & \DRggzz & 1 & \DRwwzz & \DRttzz & \DRbbzz \\\hww & \DRggww & \DRzzww & 1 & \DRttww & \DRbbww \\\htt & \DRggtt & \DRzztt & \DRwwtt & 1 & \DRbbtt \\\hbb & \DRggbb & \DRzzbb & \DRwwbb & \DRttbb & 1 \\\hline \end{array}

The best-fit results and 68% CL confidence intervals for signal strength ratios of the decay mode in each column and the decay mode in each row, as modelled by the parameterization in previous table. When the likelihood of the data is scanned as a function of each individual parameter, the three other parameters in the same row, as well the production cross sections modifiers $\muf$ and $\muv$, are profiled. Since each row corresponds to an independent fit to data, the relation $\lambda_{yy,xx}=1/\lambda_{xx,yy}$ is only approximately satisfied.

Search for mass-degenerate states with different coupling structures

Plot

Caption

Distribution of the profile likelihood ratio $q_\lambda$ between different assumptions for the structure of the matrix of signal strengths for the production processes and decay modes both for pseudo-data samples generated under the SM hypothesis and the value observed in data. The likelihood in the numerator is that for the data under a model of a general rank 1 matrix, expected if the observations are due to a single particle and of which the SM is a particular case. The likelihood in the denominator is that for the data under a "saturated model'' with as many parameters as there are matrix elements. The arrow represents the observed value in data, $q_\lambda^\text{obs}$. Under the SM hypothesis, the probability to find a value of $q_\lambda \geq q_\lambda^\text{obs}$ is $(7.9\pm0.3)\%$, where the uncertainty reflects only the finite number of pseudo-data samples generated.

Compatibility of the observed data with the SM Higgs boson couplings

Relation between the coupling to the W and Z bosons

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 the couplings to massive vector bosons and fermions

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.

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.

Test of the scaling of couplings with the masses of SM particles

The coupling scale factors to fermions and vector bosons are expressed in terms of a mass scaling parameter $\epsilon$ and a \u201cvacuum expectation value\u201d 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 $M=v$.

Plot	Caption
	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.
	2D test statistics q(M, ε) scan. The cross indicates the best-fit values. The solid, dashed, and dotted contours show the 68%, 95%, and 99.7% CL confidence regions, respectively. The diamond represents the SM expectation, (M,ε) = (v,0), where v is the SM Higgs vacuum expectation value, v = 246.22 GeV.
	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)=2.76 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 $(M,\epsilon)$.

Test for the presence of BSM particles in loops

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).
	1D test statistics q(BRinv) scan, profiling the modifier to the effective coupling to photons and gluons κγ, κg, also combining with data from the H(inv) searches, thus assuming that BRBSM = BRinv, i.e. that there are no undetected decays, BRundet = 0.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).
	1D test statistics q(BRinv) scan, further assuming the modifier to the effective coupling to photons and gluons κγ = κg = 1 and combining with the data from the H(inv) searches. 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).

Test of a model with scaling factors for SM particles

The search is performed with six independent coupling modifiers: κ_V, κ_b, κ_τ, κ_t, κ_g, κ_γ.

Plot

Caption

Likelihood scans for parameters in a model with coupling scaling factors for the SM particles, one coupling at a time while profiling the remaining five together with all other nuisance parameters; from top to bottom: $\kappa_{V}$ (W and Z bosons), $\kappa_{b}$ (bottom quarks), $\kappa_{\tau}$ (tau leptons), $\kappa_{t}$ (top quarks), $\kappa_{g}$ (gluons; effective coupling), and $\kappa_{\gamma}$ (photons; effective coupling). The inner bars represent the 68% CL confidence intervals while the outer bars represent the 95% CL confidence intervals.

Test of a general model without assumptions on the total width

The search is performed with following 7 free parameters: κ_gZ (= κ_g˙κ_Z/κ_H), λ_γZ (= κ_γ/κ_Z), λ_WZ (= κ_W/κ_Z), λ_bZ (= κ_b/κ_Z), λ_τZ (= κ_τ/κ_Z), λ_Zg (= κ_Z/κ_g), λ_tg (= κ_t/κ_g), allowing all gauge and third generation fermion couplings to float and allowing for invisible or undetectable widths.

Plot	Caption
	Summary of the fits for deviations in the coupling modifier 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.

Constraints on $\text{BR}_{\text{BSM}}$ in a scenario with free couplings

Plot	Caption
	The likelihood scan versus BRBSM = ΓBSM/Γtot. 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 bounded by the SM expectation (κV ≤ 1).
	The likelihood scan versus BRinv = Γinv/Γtot, also combining with data from the H(inv) searches, thus assuming that BRBSM = BRinv, i.e. BRundet = 0. 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 bounded by the SM expectation (κV ≤ 1).
	The 2D likelihood scan for the BRinv and BRundet parameters for a combined analysis of the H(inv) search data and visible decay channels. The cross indicates the best-fit values. The solid, dashed, and dotted contours show the 68%, 95%, and 99.7% CL confidence regions, respectively. The diamond represents the SM expectation, (BRinv, BRundet) = (0, 0).
	The likelihood scan versus BRundet = Γundet/Γtot. The solid curve is the data and the dashed line indicates the expected median results in the presence of the SM Higgs boson. BRinv is constrained by the data from the H(inv) searches and modifiers for both the tree-level and loop-induced couplings are profiled, but the couplings to the electroweak bosons are assumed to be bounded by the SM expectation (κV ≤ 1).

Summary of tests of the compatibility of the data with the SM Higgs boson couplings

Plot

Caption

Summary plot of likelihood scan results for the different parameters of interest in benchmark models from the LHC XS WG recommendations (arXiv:1307.1347) separated by dotted lines. The BRBSM value at the bottom is obtained for the model with three parameters (κg,κγ,BRBSM). The inner bars represent the 68% CL confidence intervals while the outer bars represent the 95% CL confidence intervals. The list of parameters for each model and the numerical values of the intervals are also provided in Table 12 of the paper.

Additional plots (not in paper)

Mass measurements

Plot	Caption
	Values of the best-fit $\MH$ for the combination (solid vertical line) and for H→γγ and H→ZZ→4ℓ final states separately. The vertical band shows the combined uncertainty. The horizontal bars indicate the ±1 standard deviation uncertainties in the best-fit $\MH$ values for the individual channels.

Signal strengths by predominant decay mode and production tag

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.

Ratio of fermion- and boson-mediated production processes for different decay channels

Plot	Caption
	1D test statistics q(μVBF,VH/μggH,ttH) scan vs the ratio of signal strength modifiers μVBF,VH/μggH,ttH, profiling all other nuisances, for the different decay channels considered and their combination. The cross-section ratios σVBF/σVH and σggH/σttH assumed to be as in the SM.

Individual production modes for 7 and 8 TeV separately

Plot	Caption
	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.

Likelihood scans for individual parameters in the test of a model with scaling factors for SM particles

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.

Likelihood scans for individual parameters in the test of a general model without assumptions on the total width

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.