ATLAS NOTE - CERN...ATLAS NOTE ATLAS-CONF-2013-034 March 13, 2013 Combined coupling measurements of the Higgs-like boson with the ATLAS detector using up to 25fb 1 of proton-proton

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ATLAS NOTEATLAS-CONF-2013-034

March 13, 2013

Combined coupling measurements of the Higgs-like boson with theATLAS detector using up to 25 fb−1 of proton-proton collision data

The ATLAS Collaboration

Abstract

This note presents an update of the measurements of the properties of the newly dis-covered boson using the full pp collision data sample recorded by the ATLAS experi-ment at the LHC for the channels H→ γγ, H→ZZ(∗)→ 4` and H→WW (∗)→ `ν`ν, cor-responding to integrated luminosities of up to 4.8 fb−1 at

√s = 7 TeV and 20.7 fb−1 at√

s = 8 TeV. The combination also includes results from the H → ττ and H → bb̄ channelsbased on pp collision data corresponding to an integrated luminosity of up to 4.7 fb−1 at√

s = 7 TeV and 13 fb−1 at√

s = 8 TeV. The combined signal strength is determined tobe µ = 1.30 ± 0.13 (stat) ± 0.14 (sys) at a mass of 125.5 GeV. The cross section ratio be-tween vector boson mediated and gluon (top) initiated Higgs boson production processes isfound to be µVBF+VH/µggF+tt̄H = 1.2+0.7

−0.5, giving more than 3σ evidence for Higgs-like bosonproduction through vector-boson fusion. Measurements of relative branching fraction ratiosbetween the H→ γγ, H→ ZZ(∗)→ 4` and H→WW (∗)→ `ν`ν channels, as well as combinedfits testing the fermion and vector coupling sector, couplings to W and Z and loop inducedprocesses of the Higgs-like boson show no significant deviation from the Standard Modelexpectation.

c© Copyright 2013 CERN for the benefit of the ATLAS Collaboration.Reproduction of this article or parts of it is allowed as specified in the CC-BY-3.0 license.

1 Introduction

The observation of a new particle in the search for the Standard Model (SM) Higgs boson at the LHC,reported by the ATLAS [1] and CMS [2] Collaborations, is a milestone in the quest to understand elec-troweak symmetry breaking. In Refs. [1] and [3] the ATLAS Collaboration reported first measurementsof the mass of the particle and its coupling properties. The combined signal strength value for the chan-nels H→WW (∗)→ `ν`ν, H → ττ and H → bb̄ was reported in Ref. [4]. The mass and signal strengthmeasurements were updated in Refs. [5, 6] based on 13 fb−1 of data at

√s = 8 TeV and 20.7 fb−1 at√

s = 8 TeV respectively for the high mass resolution channels.This document presents an update of the measurements of signal strength and couplings of the ob-

served new particle using 4.8 fb−1 of pp collision data at√

s = 7 TeV and 20.7 fb−1 at√

s = 8 TeV forthe three most sensitive channels H→ γγ [7], H→ZZ(∗)→ 4` [8] and H→WW (∗)→ `ν`ν [9].

The results are based on the same statistical model as in Refs. [1, 3]. The aspects of the individualchannels relevant for these measurements are briefly summarized in Section 2. The statistical proce-dure and the treatment of systematic uncertainties are outlined in Section 3. In Section 4 the measuredyields are analysed in terms of the signal strengths, for different production and decays modes, and theircombinations.

Finally, in Section 5 the couplings of the newly discovered boson are tested through fits to the ob-served data. These studies aim to probe, under the assumptions described in the text, the Lagrangianstructure in the vector boson and fermion sectors, the ratio of couplings to the W and Z bosons and theloop induced couplings to gluons and photons.

2 Input Channels

For the H→ γγ, H → ZZ(∗) and H → WW (∗) channels, the updated analyses based on the full 2011and 2012 datasets as presented in Refs. [7–9] are used. For the H → ττ and H → bb̄ channels, theanalyses [10, 11] are applied to the full 2011 data sample at

√s = 7 TeV and a subsample of the 2012

data corresponding to 13 fb−1 at√

s = 8 TeV . The different final states and channel categories consideredin this analysis are summarized in Table 1.

3 Statistical Procedure

The statistical modelling of the data is described in Refs. [12–16]. Systematic uncertainties on observ-ables are handled by introducing nuisance parameters. When these parameters are related to observablesthat are estimated externally an additional constraint is added to the model as a probability density func-tion (pdf) associated with the uncertainty on the corresponding parameter. The typical constraints usedare Gaussian, log-normal or gamma distributions. Rectangular pdfs are also used in specific cases whichwill be detailed in this note. The latter give a flat a priori likelihood in the range of the ±1σ Gaussianuncertainty intervals for the corresponding sources of systematic uncertainties. The use of such a pdfmodel for systematic uncertainties could lead to a coherent shift of the nuisance parameters within theirallowed range to values which reduce the tension between measurements.

The number of signal events in the likelihood function is parametrized in terms of scale factors forthe cross section σi,SM of each SM Higgs boson production mode i, the branching ratios B f ,SM of the SMHiggs boson decay modes f , and the mass of the Higgs boson mH . For each production mode, a signalstrength factor µi = σi/σi,SM is introduced. Similarly, for each decay final state, a factor µ f = B f /B f ,SM

2

is introduced. For each analysis category (k) the number of signal events (nksignal) is parametrized as:

nksignal =

∑i

µiσi,SM × Aki f × ε

ki f

× µ f × B f ,SM × Lk (1)

where A represents the detector acceptance, ε the reconstruction efficiency and L the integrated lumi-nosity. The number of signal events expected from each combination of production and decay modeis scaled by the corresponding product µiµ f , with no change to the distribution of kinematic or otherproperties. This parametrization generalizes the dependence of the signal yields on the production crosssections and decay branching fractions, allowing for a coherent variation across several channels. Thisapproach is also general in the sense that it is not restricted by any relationship between production crosssections and branching ratios. The relationship between production and decay in the context of a specifictheory or benchmark is achieved via a parametrization of µi, µ f → f (κ), where κ are the parameters of

Table 1: Summary of the individual channels entering the combined results presented here. In channelssensitive to associated production of the Higgs boson, V indicates a W or Z boson. The symbols ⊗ and ⊕represent direct products and sums over sets of selection requirements, respectively. The abbreviationslisted here are described in the corresponding References indicated in the last column. For the determi-nation of the combined signal strength µ, reported in Section 4, the inclusive H→ ZZ(∗)→ 4` analysis [8]is used.

Higgs Boson SubsequentSub-Channels

∫L dt

Ref.Decay Decay [fb−1]

2011√

s =7 TeVH → ZZ(∗) 4` {4e, 2e2µ, 2µ2e, 4µ, 2-jet VBF, `-tag} 4.6 [8]

H → γγ –10 categories

4.8 [7]{pTt ⊗ ηγ ⊗ conversion} ⊕ {2-jet VBF}H → WW (∗) `ν`ν {ee, eµ, µe, µµ} ⊗ {0-jet, 1-jet, 2-jet VBF} 4.6 [9]

H → ττ

τlepτlep {eµ} ⊗ {0-jet} ⊕ {``} ⊗ {1-jet, 2-jet, pT,ττ > 100 GeV, VH} 4.6τlepτhad {e, µ} ⊗ {0-jet, 1-jet, pT,ττ > 100 GeV, 2-jet} 4.6 [10]τhadτhad {1-jet, 2-jet} 4.6

VH → VbbZ → νν Emiss

T ∈ {120 − 160, 160 − 200,≥ 200 GeV} ⊗ {2-jet, 3-jet} 4.6W → `ν pW

T ∈ {< 50, 50 − 100, 100 − 150, 150 − 200,≥ 200 GeV} 4.7 [11]Z → `` pZ

T ∈ {< 50, 50 − 100, 100 − 150, 150 − 200,≥ 200 GeV} 4.7

2012√

s =8 TeVH → ZZ(∗) 4` {4e, 2e2µ, 2µ2e, 4µ, 2-jet VBF, `-tag}} 20.7 [8]

H → γγ –14 categories

20.7 [7]{pTt ⊗ ηγ ⊗ conversion} ⊕ {2-jet VBF} ⊕ {`-tag, EmissT -tag, 2-jet VH}

H → WW (∗) `ν`ν {ee, eµ, µe, µµ} ⊗ {0-jet, 1-jet, 2-jet VBF} 20.7 [9]

H → ττ

τlepτlep {``} ⊗ {1-jet, 2-jet, pT,ττ > 100 GeV, VH} 13τlepτhad {e, µ} ⊗ {0-jet, 1-jet, pT,ττ > 100 GeV, 2-jet} 13 [10]τhadτhad {1-jet, 2-jet} 13

VH → VbbZ → νν Emiss

T ∈ {120 − 160, 160 − 200,≥ 200 GeV} ⊗ {2-jet, 3-jet} 13W → `ν pW

T ∈ {< 50, 50 − 100, 100 − 150, 150 − 200,≥ 200 GeV} 13 [11]Z → `` pZ

T ∈ {< 50, 50 − 100, 100 − 150, 150 − 200,≥ 200 GeV} 13

3

the theory or benchmark under consideration as defined in Section 5. In the simplest cases the productµiµ f is also represented by a single signal strength parameter µ j, where j is an index representing boththe production and decay indices i and f . For example, the global signal strength µ scales the total num-ber of events from all combinations of production and decay modes relative to their SM values, such thatµ = 0 corresponds to the background-only hypothesis and µ = 1 corresponds to the SM Higgs bosonsignal in addition to the background.

The likelihood is a function of a vector of signal strength factors µ, the mass mH and the nuisanceparameters θ. Hypothesis testing and confidence intervals are based on the profile likelihood ratio [17].The parameters of interest are different in the various tests, while the remaining parameters are profiled.

Hypothesized values of µ are tested with a statistic1

Λ(µ) =L(µ, ˆ̂θ(µ)

)L(µ̂, θ̂)

, (2)

where the single circumflex denotes the unconditional maximum likelihood estimate of a parameter andthe double circumflex (e.g. ˆ̂θ(µ)) denotes the conditional maximum likelihood estimate (e.g. of θ) forgiven fixed values of µ. This test statistic extracts the information on the parameters of interest from thefull likelihood function. When the signal strength parameters µ are reparametrized in terms of µ(κ), thesame equation is used for Λ(κ) with µ→ κ.

Asymptotically, a test statistic −2 lnΛ(µ) of several parameters of interest µ is distributed as a χ2

distribution with n degrees of freedom, where n is the dimensionality of the vector µ. In particular,the 100(1 − α)% confidence level (CL) contours are defined by −2 lnΛ(µ) < kα, where kα satisfiesP(χ2

n > kα) = α. For two degrees of freedom the 68% and 95% CL contours are given by −2 lnΛ(µ) = 2.3and 6.0, respectively. All contours shown in the following Sections are based on likelihood evaluationsand can therefore be translated into CL contours only if the asymptotic approximation is valid.2

4 Signal Production Strength in Individual Decay Modes

This section focuses on the global signal strength parameter µ and the individual signal strength param-eters µi, f which depend upon the production mode i and the decay mode f , for a fixed mass hypothesismH . Hypothesized values of µ and µi, f are tested with the statistic Λ(µ) as defined in Eqn. 2.

The best-fit signal strength parameter µ is a convenient observable to test the compatibility of thedata with the background-only hypothesis (µ = 0) and the SM Higgs hypothesis (µ = 1). The best-fit values of the signal strength parameter for each channel independently and for the combination areillustrated in Fig. 1 and in Table 2 for a mass of mH = 125.5 GeV, derived from the combination of theH→ γγ and H→ZZ(∗)→ 4` channels [6]. Checks allowing the Higgs boson mass hypothesis to float,using it as an additional nuisance parameter in measurements of µ, and thus taking into account theexperimental uncertainty on its estimate, were performed and no significant deviations from the resultspresented herein were observed.

The measured global signal yield is µ̂ = 1.30 ± 0.13 (stat) ± 0.14 (sys) for mH = 125.5 GeV with allchannels combined. This combined signal strength µ̂ is consistent with the SM Higgs boson hypothesisµ = 1 at the 9% level. The consistency with the SM Higgs boson hypothesis is also tested using rectan-gular pdfs for the dominant theory systematic uncertainties from gg→ H QCD scale and PDF variationsfollowing the recommendations in Refs. [19, 20]. With this treatment, the consistency of the observedsignal strength with the SM hypothesis increases to ∼40%. The global compatibilty between the signal

1Here Λ is used for the profile likelihood ratio to avoid confusion with the parameter λ used in Higgs boson coupling scalefactor benchmarks [18].

2Whenever probabilities are translated into number of Gaussian standard deviations the two-sided convention is chosen.

4

strengths of the five channels and the SM expectation of one is about 8%. The compatibility betweenthe combined best-fit signal strength µ̂ and the best-fit signal strengths of the five channels is 13%. Thedependence of the combined value of µ̂ on the assumed mH has been investigated and is relatively weak:changing the mass hypothesis between 124.5 and 126.5 GeV changes the value of µ̂ by about 4%.

Table 2: Summary of the best-fit values and uncertainties for the signal strength µ for the individualchannels and their combination at a Higgs boson mass of 125.5 GeV.

Higgs Boson Decayµ

(mH=125.5 GeV)VH → Vbb −0.4 ± 1.0

H → ττ 0.8 ± 0.7H → WW (∗) 1.0 ± 0.3

H → γγ 1.6 ± 0.3H → ZZ(∗) 1.5 ± 0.4Combined 1.30 ± 0.20

)µSignal strength ( -1 0 +1

Combined

4l→ (*) ZZ→H

γγ →H

νlν l→ (*) WW→H

ττ →H

bb→W,Z H

-1Ldt = 4.6 - 4.8 fb∫ = 7 TeV: s-1Ldt = 13 - 20.7 fb∫ = 8 TeV: s

-1Ldt = 4.6 fb∫ = 7 TeV: s-1Ldt = 20.7 fb∫ = 8 TeV: s



-1Ldt = 4.6 fb∫ = 7 TeV: s-1Ldt = 13 fb∫ = 8 TeV: s


= 125.5 GeVHm

0.20± = 1.30 µ

ATLAS Preliminary

Figure 1: Measurements of the signal strength parameter µ for mH =125.5 GeV for the individual chan-nels and their combination.

In the SM, the production cross sections are completely fixed once mH is specified. The best-fit valuefor the global signal strength factor µ does not give any direct information on the relative contributionsfrom different production modes. Furthermore, fixing the ratios of the production cross sections to theratios predicted by the SM may conceal tension between the data and the SM. Therefore, in addition tothe signal strength in different decay modes, the signal strengths of different Higgs production processescontributing to the same final state are determined. Such a separation avoids model assumptions needed

5

for a consistent parametrization of both production and decay modes in terms of Higgs boson couplings.Since several Higgs boson production modes are available at the LHC, results shown in two di-

mensional plots require either some µi to be fixed or several µi to be related. No direct tt̄H productionhas been observed yet, hence a common signal strength scale factor µggF+tt̄H has been assigned to bothgluon fusion production (ggF) and the very small tt̄H production mode, as they both scale dominantlywith the ttH coupling in the SM. Similarly, a common signal strength scale factor µVBF+VH has beenassigned to the VBF and VH production modes, as they scale with the WH/ZH gauge coupling in theSM. The resulting contours for the H→ γγ, H→WW (∗)→ `ν`ν, H→ZZ(∗)→ 4` and H → ττ channelsfor mH=125.5 GeV are shown in Fig. 2.

SM B/B× ggF+ttH

µ-2 -1 0 1 2 3 4 5 6 7 8

SM

B/B

× V

BF

+V

Hµ

-4

-2

0

2

4

6

8

10

Standard ModelBest fit68% CL95% CL

γγ →H

4l→ (*) ZZ→H


ττ →H

PreliminaryATLAS -1Ldt = 4.6-4.8 fb∫ = 7 TeV: s-1Ldt = 13-20.7 fb∫ = 8 TeV: s

= 125.5 GeVHm

Figure 2: Likelihood contours for the H→ γγ, H→ZZ(∗)→ 4`, H→WW (∗)→ `ν`ν and H → ττ channelsin the (µggF+tt̄H , µVBF+VH) plane for a Higgs boson mass hypothesis of mH = 125.5 GeV. Both µggF+tt̄Hand µVBF+VH are modified by the branching ratio factors B/BSM, which are different for the differentfinal states. The quantity µggF+tt̄H (µVBF+VH) is a common scale factor for the gluon fusion and tt̄H (VBFand VH) production cross sections. The best fit to the data (×) and 68% (full) and 95% (dashed) CLcontours are also indicated, as well as the SM expectation (+).

The factors µi are not constrained to be positive in order to account for a deficit of events from thecorresponding production process. As described in Ref. [12], while the signal strengths may be negative,the total probability density function must remain positive everywhere, and hence the total number ofexpected signal+background events has to be positive everywhere. This restriction is responsible forthe sharp cutoff in the H→ZZ(∗)→ 4` contour. It should be noted that each contour refers to a differentbranching fraction B/BSM, hence a direct combination of the contours from different final states is notpossible.

It is nevertheless possible to use the ratio of production modes channel by channel to eliminate thedependence on the branching fractions and illustrate the relative discriminating power between ggF+ tt̄Hand VBF + VH, and test the compatibility of the measurements among channels. The relevant channels

6

have the following proportionality:

σ(gg→ H) ∗ BR(H→ γγ) ∼ µggF+tt̄H;H→ γγ

σ(qq′ → qq′H) ∗ BR(H→ γγ) ∼ µggF+tt̄H;H→ γγ · µVBF+VH/µggF+tt̄H

σ(gg→ H) ∗ BR(H → ZZ(∗)) ∼ µggF+tt̄H;H→ZZ(∗)

σ(qq′ → qq′H) ∗ BR(H → ZZ(∗)) ∼ µggF+tt̄H;H→ZZ(∗) · µVBF+VH/µggF+tt̄H

σ(gg→ H) ∗ BR(H → WW (∗)) ∼ µggF+tt̄H;H→WW(∗) (3)

σ(qq′ → qq′H) ∗ BR(H → WW (∗)) ∼ µggF+tt̄H;H→WW(∗) · µVBF+VH/µggF+tt̄H

σ(gg→ H) ∗ BR(H → ττ) ∼ µggF+tt̄H;H→ττ

σ(qq′ → qq′H) ∗ BR(H → ττ) ∼ µggF+tt̄H;H→ττ · µVBF+VH/µggF+tt̄H

where µggF+tt̄H;H→XX is defined as

µggF+tt̄H;H→XX =σ(ggF) · BR(H → XX)

σSM(ggF) · BRSM(H → XX)=

σ(tt̄H) · BR(H → XX)σSM(tt̄H) · BRSM(H → XX)

(4)

and µVBF+VH/µggF+tt̄H is the parameter of interest giving the ratio between VBF + VH and ggF + tt̄Hscale factors.

The likelihood as a function of the common ratio µVBF+VH/µggF+tt̄H , while profiling over all pa-rameters µggF+tt̄H;H→XX , is shown in Fig. 3 for the H→ γγ, H→ZZ(∗)→ 4`, H→WW (∗)→ `ν`ν andH → ττ channels and their combination. For this combination it is only necessary to assume thatthe same boson H is responsible for all observed Higgs-like signals and that the separation of gluon-fusion-like events and VBF-like events within the individual analyses based on the event kinematicproperties is valid. The measurements in the four channels, as well as the observed combined ratioµVBF+VH/µggF+tt̄H = 1.2+0.7

−0.5 , are compatible with the SM expectation of unity. The p-value3 when test-ing the hypothesis µVBF+VH/µggF+tt̄H = 0 is 0.05% , corresponding to a significance against the vanishingvector boson mediated production assumption of 3.3σ. The ratio µVBF/µggF+tt̄H , where the signal strengthµVH of the VH Higgs production process is profiled instead of being treated together with µVBF, givesthe same result of µVBF/µggF+tt̄H = 1.2+0.7

−0.5. The p-value for µVBF/µggF+tt̄H = 0 is 0.09% correspondingto a significance against the vanishing VBF production assumption of 3.1σ.

In another approach the dependence on the individual production µi cancels out when taking theratio of µi × BR within the same production mode. For the example of the H→ γγ and H→ ZZ(∗)→ 4`channels, this results in a ratio of relative branching ratios ρ, defined as:

ργγ/ZZ =BR(H→ γγ)

BR(H → ZZ(∗))× BRSM(H → ZZ(∗))

BRSM(H→ γγ) , (5)

where the first term is the ratio of branching ratios and the second term rescales this ratio to the SMexpectations. The relevant channels have the following proportionality:

σ(gg→ H) ∗ BR(H→ γγ) ∼ µggF+tt̄H;H→ZZ(∗) · ργγ/ZZ

σ(qq′ → qq′H) ∗ BR(H→ γγ) ∼ µggF+tt̄H;H→ZZ(∗) · µVBF+VH/µggF+tt̄H · ργγ/ZZ

σ(gg→ H) ∗ BR(H → ZZ(∗)) ∼ µggF+tt̄H;H→ZZ(∗) (6)

σ(qq′ → qq′H) ∗ BR(H → ZZ(∗)) ∼ µggF+tt̄H;H→ZZ(∗) · µVBF+VH/µggF+tt̄H

3The p-value and significance are calculated for the test hypothesis µVBF+VH/µggF+tt̄H = 0 against the one-sided alternativeµVBF+VH/µggF+tt̄H > 0 using the profile likelihood test statistic.

7

ggF+ttHµ /

VBF+VHµ

-0.5 0 0.5 1 1.5 2 2.5 3 3.5

Λ-2

ln

0

2

4

6

8

10

12

14

combinedSM expected

γγ →H

4l→ (*) ZZ→H


ττ →H


= 125.5 GeVHm

(a)

ggF+ttHµ /

VBFµ

-0.5 0 0.5 1 1.5 2 2.5 3 3.5

Λ-2

ln

0

2

4

6

8

10

12

14

combinedSM expected


= 125.5 GeVHm

VHµprofiled

(b)

Figure 3: Likelihood curves for the ratio (a) µVBF+VH/µggF+tt̄H and (b) µVBF/µggF+tt̄H for the H→ γγ,H→ZZ(∗)→ 4`, H→WW (∗)→ `ν`ν and H → ττ channels and their combination for a Higgs bosonmass hypothesis of mH = 125.5 GeV. The branching ratios and possible non-SM effects coming fromthe branching ratios cancel in µVBF+VH/µggF+tt̄H and µVBF/µggF+tt̄H , hence the different measurementsfrom all four channels can be compared and combined. For the measurement of µVBF/µggF+tt̄H , thesignal strength µVH is profiled. The dashed curves show the SM expectation for the combination. Thehorizontal dashed lines indicate the 68% and 95% confidence levels.

Figure 4 shows the likelihood as a function of the ratios ρXX/YY for pairwise combinations of theH→ γγ, H→ZZ(∗)→ 4` and H→WW (∗)→ `ν`ν channels, while profiling over the parameters µggF+tt̄H;H→YYand µVBF+VH/µggF+tt̄H . The best-fit values are

ργγ/ZZ = 1.1+0.4−0.3

ργγ/WW = 1.7+0.7−0.5 (7)

ρZZ/WW = 1.6+0.8−0.5 ,

in agreement with the SM expectation of one.

5 Coupling fits

In the previous section signal strength scale factors µi, f for either the Higgs production or decay modeswere determined. However, for a consistent measurement of Higgs boson couplings, production and de-cay modes cannot be treated independently. Following the framework and benchmarks as recommendedin Ref. [18,21], measurements of coupling scale factors are implemented using a LO tree level motivatedframework. This framework makes the following assumptions:

• The signals observed in the different search channels originate from a single narrow resonancewith a mass near 125.5 GeV. The case of several, possibly overlapping, resonances in this massregion is not considered.

• The width of the assumed Higgs boson near 125.5 GeV is neglected, i.e. the zero-width approxi-mation for this state is used. Hence the product σ × BR(ii → H → ff ) can be decomposed in thefollowing way for all channels:

σ × BR(ii→ H → ff ) =σii · ΓffΓH

, (8)

8

/ ZZγγρ

0 0.5 1 1.5 2 2.5 3

Λ2

ln

0

1

2

3

4

5

6

observedSM expected

PreliminaryATLAS -1Ldt = 4.6-4.8 fb∫ = 7 TeV: s

-1Ldt = 20.7 fb∫ = 8 TeV: s

= 125.5 GeVHm

(a)

/ WWγγρ

0 0.5 1 1.5 2 2.5 3

Λ2

ln

0

1

2

3

4

5

6

observedSM expected

PreliminaryATLAS -1Ldt = 4.6-4.8 fb∫ = 7 TeV: s

-1Ldt = 20.7 fb∫ = 8 TeV: s

= 125.5 GeVHm

(b)

ZZ / WWρ

0 0.5 1 1.5 2 2.5 3

Λ2

ln

0

1

2

3

4

5

6

observedSM expected

PreliminaryATLAS -1Ldt = 4.6 fb∫ = 7 TeV: s

-1Ldt = 20.7 fb∫ = 8 TeV: s

= 125.5 GeVHm

(c)

Figure 4: Likelihood curves for pairwise ratios of branching ratios normalized to their SM expectations(a) ργγ/ZZ , (b) ργγ/WW and (c) ρZZ/WW of the H→ γγ, H→ ZZ(∗)→ 4` and H→WW (∗)→ `ν`ν channels,for a Higgs boson mass hypothesis of mH = 125.5 GeV. The dashed curves show the SM expectation.

where σii is the production cross section through the initial state ii, Γff the partial decay width intothe final state ff and ΓH the total width of the Higgs boson.

• Only modifications of couplings strengths, i.e. of absolute values of couplings, are taken into ac-count, while the tensor structure of the couplings is assumed to be the same as in the SM prediction.This means in particular that the observed state is assumed to be a CP-even scalar as in the SM.

The LO motivated coupling scale factors κ j are defined in such a way that the cross sections σ j andthe partial decay widths Γ j associated with the SM particle j scale with the factor κ2

j when compared tothe corresponding SM prediction. Details can be found in Refs. [3, 18]

Taking the process gg → H → γγ as an example, one would write the cross section as:

σ · BR (gg → H → γγ) = σSM(gg → H) · BRSM(H → γγ) ·κ2

g · κ2γ

κ2H

(9)

where the values and uncertainties for both σSM(gg → H) and BRSM(H → γγ) are taken from Refs. [19,20, 22] for a given Higgs boson mass hypothesis.

In some of the fits the effective scale factors κγ and κg for the processes H → γγ and gg → H, whichare loop induced in the SM, are treated as a function of the more fundamental coupling scale factors κt,

9

κb, κW, and similarly for all other particles that contribute to these SM loop processes. In these casesthe scaled fundamental couplings are propagted through the loop calculations, including all interferenceeffects, using the functional form derived from the SM [21].

5.1 Fermion versus vector (gauge) couplings

This benchmark is an extension of the single parameter µ fit, where different strengths for the fermionand vector couplings are probed. It assumes that only SM particles contribute to the H→ γγ and gg→ Hvertex loops, but any modification of the coupling strength factors for fermions and vector bosons arepropagated through the loop calculations. The fit is performed in two variants, with and without theassumption that the total width of the Higgs boson is given by the sum of the known SM Higgs bosondecay modes (modified in strength by the appropriate fermion and vector coupling scale factors).

5.1.1 Only SM contributions to the total width

The fit parameters are the coupling scale factors κF for all fermions and κV for all vector couplings:

κV = κW = κZ (10)

κF = κt = κb = κτ = κg (11)

As only SM particles are assumed to contribute to the gg → H vertex loop in this benchmark, thegluon fusion process measures directly the fermion scale factor κ2

F . For the most relevant Higgs bosonproduction and decay modes the following proportionality is found:

σ(gg→ H) ∗ BR(H→ γγ) ∼κ2

F · κ2γ (κF , κV )

0.75 · κ2F + 0.25 · κ2

V

σ(qq′ → qq′H) ∗ BR(H→ γγ) ∼κ2

V · κ2γ (κF , κV )

0.75 · κ2F + 0.25 · κ2

V

σ(gg→ H) ∗ BR(H → ZZ(∗),H → WW (∗)) ∼κ2

F · κ2V

0.75 · κ2F + 0.25 · κ2

V

(12)

σ(qq′ → qq′H) ∗ BR(H → ZZ(∗),H → WW (∗)) ∼κ2

V · κ2V

0.75 · κ2F + 0.25 · κ2

V

σ(qq′ → qq′H,VH) ∗ BR(H → ττ,H → bb̄) ∼κ2

V · κ2F

0.75 · κ2F + 0.25 · κ2

V

,

where κγ (κF , κV ) is the SM functional dependence of the effective scale factor κγ on the scale factors κF

and κV , which is to first approximation:4

κ2γ (κF , κV ) = 1.59 · κ2

V − 0.66 · κVκF + 0.07 · κ2F . (13)

The denominator is the total width scale factor κ2H expressed as a function of the scale factors κF and κV ,

where 0.75 is the SM branching ratio to fermion and gluon final states and 0.25 the SM branching ratiointo WW (∗), ZZ(∗) and γγ for mH = 125.5 GeV.

Figure 5 shows the results for this benchmark. Only the relative sign between κF and κV is physicaland hence in the following only κV > 0 is considered without loss of generality. Some sensitivity to thisrelative sign is gained from the negative interference between the W-loop and t-loop in the H→ γγ decay.

4The fit uses the full dependence of κγ on κW , κt , κb and κτ [21].

10

Vκ0.7 0.8 0.9 1 1.1 1.2 1.3

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Figure 5: Fits for 2-parameter benchmark models described in Equations (10-13) probing different cou-pling strength scale factors for fermions and vector bosons, assuming only SM contributions to the totalwidth: (a) Correlation of the coupling scale factors κF and κV ; (b) the same correlation, overlaying the68% CL contours derived from the individual channels and their combination; (c) coupling scale factorκV (κF is profiled); (d) coupling scale factor κF (κV is profiled). The dashed curves in (c) and (d) showthe SM expectation. The thin dotted lines in (c) indicate the continuation of the likelihood curve whenrestricting the parameters to either the positive or negative sector of κF .

As can be seen in Fig. 5(a) the fit prefers the SM minimum with a positive relative sign, but the localminimum with negative relative sign is also compatible at the ∼ 1σ level. The likelihood as a function ofκV when κF is profiled and as a function of κF when κV is profiled is presented in Fig. 5(c) and Fig. 5(d)respectively. Figure 5(d) shows in particular to what extent the sign degeneracy is resolved. Figure 5(b)illustrates how the H→ γγ, H → ZZ(∗), H → WW (∗), H → ττ and H → bb̄ channels contribute to thecombined measurement.

The 68% CL intervals of κF and κV when profiling over the other parameter are:

κF ∈ [−0.88,−0.75] ∪ [0.73, 1.07] (14)

κV ∈ [0.91, 0.97] ∪ [1.05, 1.21] . (15)

These intervals combine all experimental and theoretical systematic uncertainties. The two-dimensionalcompatibility of the SM hypothesis with the best fit point is 8%.

11

5.1.2 No assumption on the total width

The assumption on the total width gives a strong constraint on the fermion coupling scale factor κF inthe previous benchmark model, as the total width is dominated in the SM by the sum of the b, τ andgluon-decay widths. The fit is therefore repeated without the assumption on the total width.

In this case only ratios of coupling scale factors can be measured. Hence there are the following freeparameters:

λFV = κF/κV (16)

κVV = κV · κV/κH . (17)

λFV is the ratio of the fermion and vector coupling scale factors, and κVV an overall scale that includesthe total width and applies to all rates. For the most relevant Higgs boson production and decay modesthe following proportionality is found:

σ(gg→ H) ∗ BR(H→ γγ) ∼ λ2FV · κ2

VV · κ2γ (λFV , 1)

σ(qq′ → qq′H) ∗ BR(H→ γγ) ∼ κ2VV · κ2

γ (λFV , 1)

σ(gg→ H) ∗ BR(H → ZZ(∗),H → WW (∗)) ∼ λ2FV · κ2

VV (18)

σ(qq′ → qq′H) ∗ BR(H → ZZ(∗),H → WW (∗)) ∼ κ2VV

σ(qq′ → qq′H,VH) ∗ BR(H → ττ,H → bb̄) ∼ κ2VV · λ2

FV ,

where the second order polynomial form of κ2γ (κF , κV ), given in Equation (13), allows to factorize out

the scale factor κV into the common factor κVV and the ratio λFV as argument to the κγ function.Figure 6 shows the results of this fit. The 68% confidence interval of λFV and κVV when profiling

over the other parameter yield:

λFV ∈ [−0.94,−0.80] ∪ [0.67, 0.93] (19)

κVV ∈ [0.96, 1.12] ∪ [1.18, 1.49] . (20)

The two-dimensional compatibility of the SM hypothesis with the best fit point is 7%.

5.1.3 No assumption on the total width and on the H→ γγ loop content

As the H→ γγ decay is loop induced, it can be a very sensitive probe of beyond the SM physics. There-fore the H→ γγ decay is treated in the following benchmark as additional degree of freedom. This givesthe following benchmark model with the parameters of interest:

λFV = κF/κV (21)

λγV = κγ/κV (22)

κVV = κV · κV/κH , (23)

where λFV is the ratio of the fermion and heavy vector coupling scale factors, λγV the ratio between thephoton and vector coupling scale factors and κVV an overall scale that includes the total width and acts onall rates. For the most relevant Higgs boson production and decay modes the following proportionalityis found:

σ(gg→ H) ∗ BR(H→ γγ) ∼ λ2FV · κ2

VV · λ2γV

σ(qq′ → qq′H) ∗ BR(H→ γγ) ∼ κ2VV · λ2

γV

σ(gg→ H) ∗ BR(H → ZZ(∗),H → WW (∗)) ∼ λ2FV · κ2

VV (24)

σ(qq′ → qq′H) ∗ BR(H → ZZ(∗),H → WW (∗)) ∼ κ2VV

σ(qq′ → qq′H,VH) ∗ BR(H → ττ,H → bb̄) ∼ κ2VV · λ2

FV .

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Figure 6: Fits for a 2-parameter benchmark model described in Equations (16-18) probing differentcoupling strength scale factors for fermions and vector bosons without assumptions on the total width:(a) coupling scale factor ratio λFV (κVV is profiled); (b) correlation of the coupling scale factors λFV =

κF/κV and κVV = κV · κV/κH; (c) coupling scale factor ratio κVV (λFV is profiled). The dashed curvesin (a) and (c) show the SM expectation. The thin dotted lines in (c) indicate the continuation of thelikelihood curve when restricting the parameters to either the positive or negative sector of λFV .

FVλ

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Figure 7: Fits for a 3-parameter benchmark model described in Equations (21-24) probing differentcoupling strength scale factors for fermions, photons and heavy vector bosons without assumptions onthe total width: (a) coupling scale factor ratio λFV (λγV and κVV are profiled); (b) coupling scale factorratio λγV (λFV and κVV are profiled); (c) overall scale factor κVV (λFV and λγV are profiled). The dashedcurves show the SM expectation.

13

Figure 7 shows the results of this benchmark. As the effective photon scale factor ratio λγV is treatedas independent degree of freedom, this benchmark model has no sensitivity to the relative sign betweenfermion and vector couplings. The best fit values and uncertainties when profiling over the other param-eter are

λFV = 0.85+0.23−0.13 (25)

λγV = 1.22+0.18−0.14 (26)

κVV = 1.15 ± 0.21 (27)

at 68% CL. The three-dimensional compatibility of the SM hypothesis with the best fit point is 9%.

5.1.4 Summary

The non-vanishing value of the fitted coupling of the new particle to gauge bosons κV is both directly andindirectly constrained by several channels at the ∼20% level. The coupling to fermions can be directlyobserved in the H → ττ and H → bb̄ channels. However, this direct constraint is weak as both channelsare compatible with both the SM Higgs boson signal and the SM background hypothesis at the 95%CL level (see Fig. 1). A value of κF significantly deviating from zero is indirectly observed through theconstraints from the channels which are dominated by the main production process gg → H, which isassumed to be fermion mediated in this benchmark model.

The ratio between the fermion and vector coupling λFV is compatible with the SM hypothesis, inde-pendently of the inclusion of the H→ γγ channel in the measurement of the λFV ratio.

5.2 Probing the custodial symmetry of the W and Z couplings

Identical coupling scale factors for the W- and Z-boson are required within tight bounds by the SU(2)Lcustodial symmetry and the ρ parameter measurements at LEP [23]. To test this constraint directly in theHiggs sector, the ratio λWZ = κW/κZ is probed. Otherwise the same assumptions as in Section 5.1.2 onκF are made (κF = κt = κb = κτ). The free parameters are:

κZZ = κZ · κZ/κH (28)

λWZ = κW/κZ (29)

λFZ = κF/κZ . (30)

For the most relevant Higgs boson production and decay modes the following proportionality is found:

σ(gg→ H) ∗ BR(H→ γγ) ∼ λ2FZ · κ2

ZZ · κ2γ (λFZ , 1)

σ(qq′ → qq′H) ∗ BR(H→ γγ) ∼ κ2VBF(λWZ, 1) · κ2

ZZ · κ2γ (λFZ , 1)

σ(gg→ H) ∗ BR(H → ZZ(∗)) ∼ λ2FZ · κ2

ZZ

σ(qq′ → qq′H) ∗ BR(H → ZZ(∗)) ∼ κ2VBF(λWZ, 1) · κ2

ZZ (31)

σ(gg→ H) ∗ BR(H → WW (∗)) ∼ λ2FZ · κ2

ZZ · λ2WZ

σ(qq′ → qq′H) ∗ BR(H → WW (∗)) ∼ κ2VBF(λWZ, 1) · κ2

ZZ · λ2WZ

σ(qq′ → qq′H) ∗ BR(H → ττ) ∼ κ2VBF(λWZ, 1) · κ2

ZZ · λ2FZ ,

where κ2VBF(κW, κZ) is the second order polynomial functional dependence of the VBF cross section on

the coupling scale factors κW and κZ.

14

Figure 8 shows the likelihood distributions for this benchmark. In principle there is a relative signambiguity between the W and Z couplings. However, this relative sign is not accessible at the LHC5,hence the positive half of the λWZ distribution can be chosen without loss of generality. As can be seenin Fig. 8(b) the fit prefers the non-SM local minimum with a negative relative sign for λFZ, but the SMlocal minimum is compatible at the ∼ 1.5σ level.

The measurement of λWZ, λFZ and κZZ, when profiling the other parameters, is:

λWZ ∈ [0.64, 0.87] (32)

λFZ ∈ [−0.89,−0.55] (33)

κZZ ∈ [1.20, 2.08] (34)


5.2.1 Probing the custodial symmetry of the W and Z couplings independently of deviations inthe H→ γγ channel

The measurement of the ratio λWZ is dominated by the observed rates in the H → WW (∗) and H→ γγchannels (the H→ γγ event rate depends strongly on the κW coupling scale factor) on the one hand andthe H → ZZ(∗) channel on the other hand. However, as discussed before, potential contributions beyondthe SM could influence the observed event yield in the H→ γγ channel, producing apparent deviations ofthe ratio λWZ from unity, even if custodial symmetry is not broken. Hence it is desirable to decouple theobserved event rate in H→ γγ from the measurement of λWZ in an extended fit for the ratio λWZ, whereone extra degree of freedom absorbs possible deviations in the H→ γγ channel. The free parameters are:

κZZ = κZ · κZ/κH (35)

λWZ = κW/κZ (36)

λγZ = κγ/κZ (37)

λFZ = κF/κZ . (38)

For the most relevant Higgs boson production and decay modes the following proportionality isfound:

σ(gg→ H) ∗ BR(H→ γγ) ∼ λ2FZ · κ2

ZZ · λ2γZ

σ(qq′ → qq′H) ∗ BR(H→ γγ) ∼ κ2VBF(λWZ, 1) · κ2

ZZ · λ2γZ

σ(gg→ H) ∗ BR(H → ZZ(∗)) ∼ λ2FZ · κ2

ZZ

σ(qq′ → qq′H) ∗ BR(H → ZZ(∗)) ∼ κ2VBF(λWZ, 1) · κ2

ZZ (39)

σ(gg→ H) ∗ BR(H → WW (∗)) ∼ λ2FZ · κ2

ZZ · λ2WZ

σ(qq′ → qq′H) ∗ BR(H → WW (∗)) ∼ κ2VBF(λWZ, 1) · κ2

ZZ · λ2WZ

σ(qq′ → qq′H) ∗ BR(H → ττ) ∼ κ2VBF(λWZ, 1) · κ2

ZZ · λ2FZ .

Figure 9 shows the results of this benchmark. Similar to Section 5.1.3, the effective photon scalefactor ratio λγZ is treated as an independent degree of freedom. Hence this benchmark model has also nosensitivity to the relative sign between fermion and vector couplings.

5In principle the VBF process has some sensitivity to the W and Z interference, but the interference term is << 1% andhence too small to be discriminating.

15

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Figure 8: Fits for benchmark models described in Equations (28-31) probing the custodial symmetrythrough the ratio λWZ = κW/κZ: (a) coupling scale factor ratio λWZ (λFZ and κZZ are profiled); (b) cou-pling scale factor ratio λFZ (λWZ and κZZ are profiled); (c) overall scale factor κZZ (λWZ and λFZ areprofiled). The dashed curves show the SM expectation. The thin dotted lines in (a) indicate the contin-uation of the likelihood curve when restricting the parameters to either the positive or negative sector ofλFZ.

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Figure 9: Fits for benchmark models described in Equations (35-39) probing the custodial symmetrythrough the ratio λWZ = κW/κZ without assumptions on the H→ γγ loop content: (a) coupling scalefactor ratio λWZ (λγZ, λFZ and κZZ are profiled); (b) coupling scale factor ratio λFZ (λWZ, λγZ and κZZare profiled); (c) coupling scale factor ratio λγZ (λWZ, λFZ and κZZ are profiled); (d) overall scale factorκZZ (λWZ, λγZ and λFZ are profiled). The dashed curves show the SM expectation.

16

The measurement gives

λWZ = 0.80 ± 0.15 (40)

λγZ = 1.10 ± 0.18 (41)

λFZ = 0.74+0.21−0.17 (42)

κZZ = 1.5+0.5−0.4 (43)

at 68% CL. The four-dimensional compatibilty of the SM hypothesis with the best fit point is 9%.

5.2.2 Summary

The ratio λWZ probes the custodial symmetry through the relative couplings of the new particle to theW and Z bosons. This parameter is in part directly constrained by the decays in the H→WW (∗)→ `ν`νand H→ZZ(∗)→ 4` channels and the WH and ZH production processes. It is also indirectly constrainedby the VBF production process, which in the SM is roughly 75% W-fusion and 25% Z-fusion mediated.The κW part is also constrained by the H→ γγ channel since the decay branching ratio gets a dominantcontribution from κW . The measured value of λWZ is in agreement with the custodial symmetry valueλWZ = 1 within 95% CL, regardless of the inclusion of the H→ γγ channel as indirect constraint on κW .

5.3 Probing beyond the SM contributions

This case allows for new particle contributions either in loops or in new final states. All coupling scalefactors of known SM particles are assumed to be as in the SM, i.e. κi = 1. For the H→ γγ and gg → Hvertices, effective scale factors κg and κγ are introduced. They allow for extra contributions from newparticles. The potential new particles contributing to the H→ γγ and gg → H loops may or may notcontribute to the total width of the observed state through direct invisible decays or decays into finalstates that cannot be distinguished from the background. In these cases the resulting variation in thetotal width is parameterized in terms of the additional branching ratio BRinv.,undet.. Both aforementionedscenarios are addressed in this section.

5.3.1 Only SM contributions to the total width

In the first benchmark model it is assumed that there are no sizeable extra contributions to the total widthcaused by non-SM particles. The free parameters are κg and κγ . For the most relevant Higgs bosonproduction and decay modes the following proportionality is found:


g · κ2γ

0.085 · κ2g + 0.0023 · κ2

γ + 0.91


γ

0.085 · κ2g + 0.0023 · κ2

γ + 0.91

σ(gg→ H) ∗ BR(H → ZZ(∗),H → WW (∗)) ∼κ2

g

0.085 · κ2g + 0.0023 · κ2

γ + 0.91(44)

σ(qq′ → qq′H) ∗ BR(H → ZZ(∗),H → WW (∗)) ∼ 10.085 · κ2

g + 0.0023 · κ2γ + 0.91

σ(qq′ → qq′H,VH) ∗ BR(H → ττ,H → bb̄) ∼ 10.085 · κ2

g + 0.0023 · κ2γ + 0.91

.

17

Figure 10 shows the results for this benchmark. The best fit values and uncertainties when profilingover the other parameter are

κg = 1.08 ± 0.14 (45)

κγ = 1.23+0.16−0.13 (46)

at 68% CL. The two-dimensional compatibility of the SM hypothesis with the best fit point is 5%.

5.3.2 No assumption on the total width

By constraining some of the factors to be equal to their SM values, it is possible to probe for new non-SMdecay modes that might appear as invisible or undetectable final states6. The free parameters in this caseare κg, κγ and BRinv.,undet.. In this model the modification to the total width is parametrized as follows:

ΓH =κ2

H(κi)

(1 − BRinv.,undet.)ΓSM

H . (47)

For the most relevant Higgs boson production and decay modes the following proportionality is found:


g · κ2γ

0.085 · κ2g + 0.0023 · κ2

γ + 0.91· (1 − BRinv.,undet.)


γ

0.085 · κ2g + 0.0023 · κ2

γ + 0.91· (1 − BRinv.,undet.)

σ(gg→ H) ∗ BR(H → ZZ(∗),H → WW (∗)) ∼κ2

g

0.085 · κ2g + 0.0023 · κ2

γ + 0.91· (1 − BRinv.,undet.) (48)

σ(qq′ → qq′H) ∗ BR(H → ZZ(∗),H → WW (∗)) ∼ 10.085 · κ2

g + 0.0023 · κ2γ + 0.91

· (1 − BRinv.,undet.)

σ(qq′ → qq′H,VH) ∗ BR(H → ττ,H → bb̄) ∼ 10.085 · κ2

g + 0.0023 · κ2γ + 0.91

· (1 − BRinv.,undet.) .

Figure 11 shows the results from this benchmark. A possible BRinv.,undet. contribution can be limitedto < 0.6 at the 95% CL level under the conditions stated above. The best fit values and their uncertaintieswhen profiling over the other parameters are:

κg = 1.08+0.32−0.14 (49)

κγ = 1.24+0.16−0.14 (50)

BRinv.,undet. < 0.33 (51)


5.3.3 Summary

Under the hypothesis that all tree level couplings of the new boson to SM particles are fixed to their SMvalues, no significant deviations are observed in the effective couplings to photons and gluons (κγ andκg respectively) regardless of the assumption on the total width. Releasing the assumption on the totalwidth constrains BRinv.,undet. to < 0.6 at the 95% CL.

6Invisible final states can be directly searched for through the EmissT signature [24], while undetectable final states have a

signature that offers no discrimination from backgrounds. An example would be a decay mode to mulitple light jets, whichcannot be distinguished from multi-jet backgrounds.

18

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Figure 10: Fits for benchmark models described in Equation (44) probing contributions from non-SMparticles in the H→ γγ and gg → H loops, assuming no sizeable extra contributions to the total width:(a) correlation of the coupling scale factors κγ and κg; (b) coupling scale factor κγ (κg is profiled);(c) coupling scale factor κg (κγ is profiled). The dashed curves in (b) and (c) show the SM expectation.

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9

10]

i,u,Bgκ,γκ[


-1Ldt = 4.6-4.8 fb∫ = 7 TeV, s

ATLAS Preliminary

(c)

Figure 11: Fits for benchmark models described in Equations (47,48) probing contributions from non-SM particles in the H→ γγ and gg → H loops, while allowing for potential extra contributions to thetotal width: (a) branching fraction Bi,u = BRinv.,undet. to invisible or undetectable decay modes (κγ and κgare profiled); (b) coupling scale factor κγ (κg and BRinv.,undet. are profiled); (c) coupling scale factor κg(κγ and BRinv.,undet. are profiled). The dashed curves show the SM expectation.

19

6 Conclusion

An update of the couplings determination of the Higgs-like boson using a data set corresponding to4.8 fb−1 of pp collision data at

√s = 7 TeV and 20.7 fb−1 at

√s = 8 TeV for the three most sensitive

channels H→ γγ, H→ ZZ(∗)→ 4` and H→WW (∗)→ `ν`ν is presented. The combined measurement ofthe global signal strength for the final states H→ γγ, H→ ZZ(∗)→ 4`, H→WW (∗)→ `ν`ν, H → ττ andH → bb̄ results in a value of 1.30 ± 0.13 (stat) ± 0.14 (sys) obtained at the mass of 125.5 GeV. The crosssection ratio between vector-boson mediated and gluon (top) initiated Higgs boson production processesis determined to be µVBF+VH/µggF+tt̄H = 1.2+0.7

−0.5. A determination of µVBF/µggF+tt̄H provides evidence forVBF production at the 3.1σ level.

The compatibility of the measured yields for the studied channels with the prediction for the SMHiggs boson is tested under various benchmark assumptions probing salient features of the couplings. Asummary of all coupling scale factor measurements in all benchmark models is shown in Fig. 12. Forthe different tested benchmarks the compatibility with the SM Higgs expectation ranges between 5% and10%; hence, no significant deviation from the SM prediction is observed in any of the fits performed.

parameter value-1 0 1 2

i,u1-Bγκgκγκgκ

ZZκFZλ

ZγλWZλZZκFZλ

WZλVVκ

VγλFVλVVκFVλ

FκVκ

ATLAS Preliminary -1Ldt = 4.6-4.8 fb∫ = 7 TeV, s-1Ldt = 13-20.7 fb∫ = 8 TeV, s

= 125.5 GeVHm

σ 1± σ 2±

Figure 12: Summary of the coupling scale factor measurements for mH=125.5 GeV. The best-fit valuesare represented by the solid black vertical lines. The measurements in the different benchmark models,separated by double lines in the Figure, are strongly correlated, as they are obtained from fits to the sameexperimental data. Hence they should not be considered as independent measurements and an overallχ2-like compatibility test to the SM is not possible.

20

References

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[9] ATLAS Collaboration, Measurements of the properties of the Higgs-like boson in theWW (∗) → `ν`ν decay channel with the ATLAS detector using 25 fb−1 of proton-proton collisiondata, ATLAS-CONF-2013-030 (2013).

[10] ATLAS Collaboration, Search for the Standard Model Higgs boson in H→ ττ decays inproton-proton collisions with the ATLAS detector, ATLAS-CONF-2012-160 (2012).

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[12] ATLAS Collaboration, Combined search for the Standard Model Higgs boson in pp collisions at√s=7 TeV with the ATLAS detector, Phys. Rev. D86 (2012) 032003, arXiv:1207.0319[hep-ex].

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[14] L. Moneta, K. Belasco, K. S. Cranmer, S. Kreiss, A. Lazzaro, et al., The RooStats Project, PoSACAT2010 (2010) 057, arXiv:1009.1003 [physics.data-an].

21

[15] K. Cranmer, G. Lewis, L. Moneta, A. Shibata, and W. Verkerke, HistFactory: A tool for creatingstatistical models for use with RooFit and RooStats, CERN-OPEN-2012-016 (2012).http://cdsweb.cern.ch/record/1456844.

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[17] G. Cowan, K. Cranmer, E. Gross, and O. Vitells, Asymptotic formulae for likelihood-based tests ofnew physics, Eur. Phys. J. C71 (2011) 1554.

[18] LHC Higgs Cross Section Working Group, A. David et al., LHC HXSWG interimrecommendations to explore the coupling structure of a Higgs-like particle, arXiv:1209.0040[hep-ph].

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[23] ALEPH, CDF, D0, DELPHI, L3, OPAL, and SLD Collaborations, LEP Electroweak WorkingGroup, Tevatron Electroweak Working Group, SLD electroweak heavy flavour groups, PrecisionElectroweak Measurements and Constraints on the Standard Model, arXiv:1012.2367[hep-ex].

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22

Appendix

[GeV]Hm115 120 125 130 135

0p

-2410

-2110

-1810

-1510

-1210

-910

-610

-310

1

310

610

910

ObservedSM expected

ATLAS Preliminary

-1Ldt = 13-20.7 fb∫ = 8 TeV, s

-1Ldt = 4.6-4.8 fb∫ = 7 TeV, s

σ0σ2

σ4

σ6

σ8

σ10

Figure 13: The local probability p0 for a background-only experiment to be more signal-like than theobservation as a function of mH for the combination of all channels. The effect of mass scale systematicuncertainties is taken into account by an extrapolation of the sum of a chi-squared and a falling exponen-tial to the distribution of the likelihood ratio-based test statistic for a large number of pseudo-experiments,as described in Ref. [25]. The dashed curve shows the median expected local p0 under the hypothesis ofa Standard Model Higgs boson production at that mass (nuisance parameter values are taken from a fitto data with µ = 0). The horizontal dashed lines indicate the p-values corresponding to significances of0σ to 10σ.

ggF+ttHµ /

VBF+VHµ

0 1 2 3 4 5

Λ-2

ln

0

1

2

3

4

5

6

7



-1Ldt = 20.7 fb∫ = 8 TeV: s

= 125.5 GeVHm

Figure 14: Likelihood curve for the ratio µVBF+VH/µggF+tt̄H for the H→WW (∗)→ `ν`ν channel for aHiggs boson mass hypothesis of mH = 125.5 GeV. The corresponding curves for H→ γγ, H→ ZZ(∗)→ 4`and H → ττ are reported in Ref. [6]

23

SM B/B× ggF+ttH

µ-0.5 0 0.5 1 1.5 2 2.5

SM

B/B

× V

BF

+V

Hµ

0

1

2

3

4

5

6

7

8


Standard ModelBest fit68% CL95% CL


-1Ldt = 20.7 fb∫ = 8 TeV: s

= 125.5 GeVHm

Figure 15: Likelihood contours for the H→WW (∗)→ `ν`ν channel in the (µggF+tt̄H , µVBF+VH) plane fora Higgs boson mass hypothesis of mH = 125.5 GeV. Both µggF+tt̄H and µVBF+VH are modified by thebranching ratio factor B/BSM, which can be different for the different final states. The quantity µggF+tt̄H(µVBF+VH) is a common scale factor for the gluon fusion and tt̄H (VBF and VH) production cross sec-tions. The best-fit to the data (×) and 68% (full) and 95% (dashed) CL contours are indicated, as wellas the SM expectation (+). The corresponding contours for H→ γγ, H→ ZZ(∗)→ 4` and H → ττ arereported in Ref. [6].

parameter value-1 0 1

i,u1-B

γκ

gκ

WZλ

FVλ

Fκ

Vκ

ATLAS Preliminary -1Ldt = 4.6-4.8 fb∫ = 7 TeV, s-1Ldt = 13-20.7 fb∫ = 8 TeV, s

= 125.5 GeVHm

mod

el:

Fκ, Vκ

mod

el:

VV

κ, F

Vλ

mod

el: ,

FZ

λ, W

Zλ

ZZ

κ

mod

el: γκ, gκ

mod

el: i,u

, B γκ, gκ

σ 1± σ 2±

Figure 16: Summary of the coupling scale factor measurements for mH=125.5 GeV. The best-fit valuesare represented by the solid black vertical lines. The measurements in the different coupling benchmarkmodels are strongly correlated, as they are obtained from fits to the same experimental data. Hence theyshould not be considered as independent measurements and an overall χ2-like compatibility test to theSM is not possible. In this figure only a subset of the benchmark models presented in the note is shownand for each one only the main parameters of interest are plotted.

24


Combined

4l→ (*) ZZ→H

γγ →H


ττ →H

bb→W,Z H







= 124.5 GeVHm

0.21± = 1.36 µ

ATLAS Preliminary

(a)


Combined

4l→ (*) ZZ→H

γγ →H


ττ →H

bb→W,Z H







= 125 GeVHm

0.20± = 1.33 µ

ATLAS Preliminary

(b)


Combined

4l→ (*) ZZ→H

γγ →H


ττ →H

bb→W,Z H







= 125.5 GeVHm

0.20± = 1.30 µ

ATLAS Preliminary

(c)


Combined

4l→ (*) ZZ→H

γγ →H


ττ →H

bb→W,Z H







= 126 GeVHm

0.20± = 1.28 µ

ATLAS Preliminary

(d)


Combined

4l→ (*) ZZ→H

γγ →H


ττ →H

bb→W,Z H







= 126.5 GeVHm

0.19± = 1.25 µ

ATLAS Preliminary

(e)

Figure 17: Measurements of the signal strength parameter µ for mH between 124.5 GeV and 126.5 GeVfor the individual channels and their combination.

25

Documents

ATLAS NOTE - CERN...ATLAS NOTE ATLAS-CONF-2013-034 March 13, 2013 Combined coupling measurements of the Higgs-like boson with the ATLAS detector using up to 25fb 1 of proton-proton