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ATLAS NOTE

ATLAS-CONF-2011-161

December 11, 2011

Search for the Standard Model Higgs boson in the diphoton decay channel

with 4.9 fb−1 of ATLAS data at√s=7 TeV

The ATLAS collaboration

Abstract

This note presents a search for the Standard Model Higgs boson in the diphoton decay

channel in proton-proton collisions at a centre-of-mass energy of√s = 7TeV using data

corresponding to an integrated luminosity of 4.9 fb−1 collected with the ATLAS detectorat the LHC. Over the diphoton mass range 110 – 150 GeV the maximum deviation from

the background-only expectation is observed at 126 GeV with a local significance of 2.8

standard deviations. Taking the look-elsewhere effect into account, the significance is 1.5

standard deviations. The expected cross section exclusion at 95% confidence level varies

between 1.6 and 2.9 times the Standard Model cross section over the mass range 110 –

150 GeV. The observed exclusions lie between 0.9 and 4.0 times the Standard Model cross

section, and a Standard Model Higgs boson is excluded at 95% confidence level in the mass

range of 114 – 115 GeV and 135 – 136 GeV.

1 Introduction

The low mass region, in which the Standard Model (SM) Higgs boson [1–3] is not yet excluded, is

constrained from below at 114.4 GeV by the LEP experiments [4] and from above at 141 GeV by the

ATLAS and CMS experiments [5]. The diphoton decay mode is one of the most important channels

in the search for the Higgs boson in this region. This note presents the search for the Higgs boson in

the diphoton decay channel with an integrated luminosity of 4.9 fb−1, corresponding to the total proton-proton collision data sample recorded with the ATLAS detector [6] in 2011 at a centre-of-mass energy of

7 TeV. The general analysis strategy closely follows the one described in Ref. [7], but some refinements

have been introduced to the categorization of events, as described below.

This note is organized as follows. The photon reconstruction and event selection are described in

Section 2. The event categorization is illustrated in Section 3, and the signal and background modelling

are discussed in Section 4. The systematic uncertainties are summarized in Section 5. The statistical

methods and the results of the search are presented in Section 6. Conclusions are given in Section 7.

2 Photon Reconstruction, Event Selection and Sample Composition

2.1 Photon Reconstruction and Event Selection

The data used in this analysis were recorded using a diphoton trigger with a threshold on the transverse

energy ET on each photon of 20 GeV, seeded by a trigger that required two clusters in the electromagnetic

calorimeter with ET >12 or 14 GeV, depending on the data-taking period. The trigger has an efficiencyof approximately 99% for the signal after the final offline event selection. After applying data quality

requirements on the recorded data sample, the total integrated luminosity of the data set used in this

analysis amounts to 4.9 fb−1.Events are required to contain at least one primary vertex with at least three associated tracks, where

the transverse momentum, pT, of each track is required to be larger than 0.4 GeV. Photons are recon-

structed both in the converted and unconverted topologies. In both cases, photon candidates are seeded

by energy clusters in the electromagnetic calorimeter with ET > 2.5 GeV. In the case of converted photoncandidates, tracks reconstructed in the inner detector are matched to these calorimeter clusters. The pho-

ton energy is calibrated based on detailed Monte Carlo (MC) simulations, separately for converted and

unconverted photons [8]. A correction, dependent on pseudorapidity and typically of the order of ±1%,is applied to the photon calibrated energy, as obtained from studies using Z → ee decays in data [9].Photons are reconstructed in the fiducial region defined by the pseudorapidity1|η | < 2.37, excluding thecalorimeter barrel/endcap transition region, 1.37< |η | < 1.52.The ET of the leading (subleading) photon candidate must exceed 40 GeV (25 GeV). MC simulation

studies [8] have shown that this requirement leads to an optimal sensitivity in the mass region of interest.

Both candidates are required to pass tight identification criteria based on shower shape variables and on

the energy leakage into the hadronic calorimeter [10]. The tight photon identification efficiency ranges

typically from 65% to 95% for ET=25 – 80 GeV. These two photon candidates are required to be isolatedby having at most 5 GeV energy deposited in the calorimeter in a cone of ∆R=

√(∆η)2+(∆φ)2 = 0.4

around the candidate excluding the photon energy itself. The isolation variable is corrected for lateral

shower leakage and ambient energy from pileup, as explained in Ref. [11]. The isolation cut efficiency for

the diphoton candidate is ≈ 87% for the Higgs boson signal. If the reconstructed photon is a conversion,it is rejected if it has a track reconstructed in a region of the inner detector where the module traversed

1ATLAS uses a right-handed coordinate system with its origin at the nominal interaction point (IP) in the center of the

detector and the z-axis along the beam pipe. The x-axis points from the IP to the center of the LHC ring, and the y axis points

upward. Cylindrical coordinates (R, φ ) are used in the transverse plane, φ being the azimuthal angle around the beam pipe.The pseudorapidity is defined in terms of the polar angle θ as η = −ln tan(θ/2).

2

in the innermost pixel layer is one of the ≈ 3.5% which are inactive, to reduce the contamination frommisidentified electrons

The angle between the two selected photons is determined from the interaction vertex position and the

photon impact points in the calorimeter. For converted photons with tracks having a precise measurement

in the z direction, the vertex position is estimated from the intercept of the line joining the reconstructed

conversion position and the calorimeter impact point with the beam line. For all other photons, the

vertex position is estimated from the shower position measurements in the first and second layers of the

calorimeter which can be used to calculate the photon direction. Finally, the independent vertex position

measurements from both photons are combined also taking into account the average beam spot position

in z. For photons reconstructed in the endcap region, a correction is applied to the z coordinate of the

vertex position estimated from the photon in order to compensate for a difference between data and MC

simulation. This correction is determined as a function of η from electrons in Z→ ee decays.The diphoton invariant mass distribution (mγγ ) is shown in Figure 1 (top) for the 22489 events passing

the selection in the mass region 100 GeV< mγγ <160 GeV. The sum of the background-only fits indifferent categories described in Sections 3 and 4, as well as the signal expectation for a SM Higgs boson

with mass equal to 120 GeV, are also shown. Details of the background and signal models are given in

Section 4. Figure 1 (bottom) shows the residual of the data with respect to the sum of the background-

only fits as a function of mγγ .

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Figure 1: Invariant mass distribution for the inclusive data sample, overlaid with the sum of the

background-only fits in different categories described in Sections 3 and 4 and the signal expectation

for a mass hypothesis of 120 GeV corresponding to the SM cross section. The figure below displays the

residual of the data with respect to the background-only fit sum.

3

2.2 Sample Composition

The composition of the inclusive sample, after the selection described above, is studied using different

data-driven techniques. The estimates obtained with these methods, however, are not used in the limit

calculation described in Section 6.

The background to a potential Higgs boson signal is expected to be mainly composed of the dipho-

ton processes (γγ) together with events where either of the photon candidates come from misidentifiedjets (fake photons), mainly through fragmentation into π0 (γ j and j j). A very small fraction of thebackground is due to misidentified electrons.

A double two-dimensional sideband method is used to extrapolate the jet backgrounds from control

regions into the signal region by classifying the leading and subleading photon candidates into those

passing or failing the isolation and tight identification cuts [7]. Events with diphotons from possible

Higgs boson decays and misidentified Drell-Yan (DY) events (see discussion below), as well as prompt

diphoton production events, are classified as γγ events. The estimation of each composition is performedin each bin of the mγγ distribution. By construction, the sum of the components in each bin of the mγγ

distribution amounts exactly to the number of events in that bin. Systematic uncertainties arise mainly

from variations of the control samples and a MC-based estimation of the diphoton event fraction in the

regions dominated by jets.

The Drell-Yan background is studied separately by selecting Z→ ee decays in data where either oneor both electrons pass the photon selection. In this way an e→ γ misidentification rate is obtained andthe number of Z→ ee events where both electrons are misidentified as photons is estimated.The sample composition in bins of mγγ is shown in Figure 2. The composition of the entire sample

is summarized in Table 1. The diphoton purity is estimated to be (71±5)% in the full data sample, andconsistent values are found in subsamples with different amounts of pileup. The event fractions of each

component estimated with MC simulations are consistent with these data-driven results.

The sample composition is also studied with other two data-driven methods. The first one is a two-

dimensional fit method fitting simultaneously the isolation distributions of leading and subleading photon

candidates with templates obtained from control samples [12]. The second method measures the rate of

jets which are misidentified as photons inW (→ eν)+jets events and extrapolates the fake photon back-grounds into the signal region using a two-dimensional sideband technique. All methods give compatible

results.

Table 1: Composition of the selected inclusive sample obtained from the measurement using the data

as described in Section 2.2. The first uncertainty is statistical and the second systematic. Only the total

uncertainty is quoted for the relative fractions.

Composition γγ γ j j j Drell-Yan

Events 16000±200±1100 5230±130±880 1130±50±600 165±2±8Relative fraction (71±5)% (23±4)% (5±3)% (0.7±0.1)%

3 Event Categorization

In the previous analysis [7] events were divided according to the photon reconstruction topologies (con-

verted, unconverted) and η direction in five categories with different signal-to-background ratios andinvariant mass resolutions:

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Figure 2: Composition of the inclusive data sample as a function of mγγ , extracted from the double two-

dimensional sideband method after the inclusive event selection. The various components are stacked on

top of each other. The error bars correspond to the statistical uncertainties on each component separately.

The gray bands show the overall uncertainty on each component.

• Unconverted central: both photons are unconverted and located in the central part of the barrelcalorimeter (|η | <0.75). This is the category with the best invariant mass resolution;

• Unconverted rest: both photons are unconverted and at least one photon does not lie in the centralpart of the barrel calorimeter;

• Converted central: at least one photon is converted and both photons are found in the central partof the barrel calorimeter;

• Converted transition: at least one photon is converted and at least one photon is located near thetransition between barrel and endcap calorimeter (1.3< |η | <1.75). Given the larger amount ofmaterial in this region, the energy resolution, in particular for converted photons, can be signifi-

cantly degraded;

• Converted rest: all other events with at least one converted photon.

With the increased data set corresponding to 4.9 fb−1 it is possible to further split some of the cate-gories to optimize the sensitivity to a potential Higgs boson signal. This analysis therefore introduces a

new diphoton observable, pTt, which is defined as the component of ~pγγT transverse to the diphoton thrust

axis [13, 14], as shown in Figure 3.

thrust axis

pT

ggp

Tt

pTl

pT

g1pT

g2

Figure 3: Sketch of the pTt definition.

5

The diphoton thrust axis, t̂, is defined as:

t̂ =~p

γ1T −~p

γ2T

|~pγ1T −~p

γ2T |

,

where the ~pγ1T and ~p

γ2T are the transverse momenta of the two selected photons. The transverse momentum

of the diphoton system, pγγT , is given by:

~pγγT = ~p

γ1T +~p

γ2T .

The pTt is then calculated as follows:

~pTt = ~pγγT − (~p

γγT · t̂) · t̂,

pTt = |~pγγT × t̂|.

Four of the aforementioned five categories are split into a low pTt category and a high pTt category,

separated at pTt = 40 GeV. The categorization based on the pTt variable leads to a better sensitivityfor the Higgs boson signal than one based on p

γγT due to the resolution of pTt being better than that of

pγγT . Moreover, the shape of the mγγ distribution based on the pTt categorization can be better described

with an exponential shape, which is not the case for the pγγT categorization. By introducing these pTt

categories, the expected sensitivity of the analysis is improved by 5 – 10% depending on the hypothesized

Higgs boson mass. The number of data events in each of the nine categories are shown in Table 2.

Table 2: The number of events found in 4.9 fb−1 of data for the nine categories.

Category Conversion and η pTt cut Number of data events

CP1 Unconverted central pTt≤ 40 GeV 1763

CP2 Unconverted central pTt> 40 GeV 235

CP3 Unconverted rest pTt≤ 40 GeV 6234

CP4 Unconverted rest pTt> 40 GeV 1006

CP5 Converted central pTt≤ 40 GeV 1318

CP6 Converted central pTt> 40 GeV 184

CP7 Converted rest pTt≤ 40 GeV 7311

CP8 Converted rest pTt> 40 GeV 1072

CP9 Converted transition No cut 3366

Total 22489

4 Signal and Background Modelling

4.1 Signal Model

The Higgs boson signal is studied using MC samples which are then passed through a full detector

simulation [15] using Geant 4 [16]. POWHEG [17] is used for gluon fusion and vector boson fusion

(VBF) production, interfaced with PYTHIA [18] for showering and hadronization. PYTHIA is used to

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generate the associated Higgs boson production modes (WH, ZH and tt̄H). Pileup effects are simulated

by overlaying each MC event with a variable number of MC inelastic proton-proton collisions [19],

taking into account both in-time and out-of-time pileup and the LHC bunch train structure. The predicted

signal is normalised using NNLO cross section predictions for the gluon fusion [20–23], VBF [24] and

W/Z associated production [25]. The cross section of the tt̄H process is known at NLO [26]. The

branching ratio of a Higgs boson decaying to two photons is taken from Refs. [27, 28].

Signal samples are produced in 5 GeV steps of Higgs boson mass between 110 GeV and 150 GeV,

and the following corrections are applied to these samples to match, as closely as possible, the conditions

found in the data:

• The shower shape variables used in the photon identification are shifted to better resemble the cor-responding distributions in the data [10]. The photon identification efficiency was cross-checked

in data measurements using electrons in Z→ ee and photons in Z→ ℓℓγ (ℓ = e,µ). Where simpleshifts of the shower shape variables are insufficient to reproduce the data results, additional MC

reweighing is used.

• The photon energy is smeared to account for small differences in resolution between data andsimulation observed in studies of data Z→ ee events [7];

• The MC samples are reweighted to reproduce the average number of interactions per bunch cross-ing observed in the data. The average number is approximately 6 until the end of August and then

approximately 12 until the end of the proton-proton collision data-taking in 2011;

• The signal samples were produced with a longitudinal beam spot distribution corresponding to aGaussian with width σz ∼ 7.5 cm, which is larger than that observed in the data (σz ∼ 6 cm). TheMC samples are therefore reweighted to correct for this difference;

• The MC signal yields are rescaled by the data-to-MC ratio for the isolation cut efficiency, asdetermined from Z → ee events. The shift evaluated from the isolation distribution of electronsbetween data and MC simulation is applied to the isolation variable of photons in the Higgs boson

signal MC samples. This gives a 4.4% reduction in the expected signal yield;

• The MC samples for the gluon fusion process are reweighted to take into account the expecteddestructive interference between the gg→ γγ continuum background and the gg→ H→ γγ pro-cess [29]. The correction depends on the Higgs mass and the η of the photons and is in the range2−5%;

• Events from the gluon fusion process are reweighted so that the distribution of the Higgs boson pTmatches that obtained from the HqT calculation [30].

The expected number of signal events for any given value ofmH is obtained by a 3rd order polynomial

fit to the signal yields extracted from the simulated samples. The number of expected signal events in

each category is given in Table 3. The signal shapes as a function of mγγ in each category are obtained

from a simultaneous fit to the mγγ distributions for all the generated Higgs boson mass points using the

sum of a Crystal Ball (CB) function [31] and a wide but small amplitude Gaussian component describing

the tails. The CB function is defined as:

N ·{e−t

2/2 if t > −αCB,( nCBαCB

)nCB · e−α2CB/2 · ( nCBαCB−αCB− t)−nCB otherwise

where t = (mγγ −mH − δmH)/σCB, N is a normalization parameter, δmH is a category dependent offset,σCB represents the diphoton invariant mass resolution, and nCB and αCB parametrize the non-Gaussian

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Table 3: Expected Higgs boson signal yields after full event selection in 4.9 fb−1 integrated over a massrange of 100-160 GeV for various values of mH in each category and the sum.

mH [GeV] 110 115 120 125 130 135 140 145 150

CP1: Unconverted central, low pTt 8.9 8.9 8.7 8.2 7.5 6.7 5.7 4.6 3.5

CP2: Unconverted central, high pTt 2.5 2.6 2.6 2.5 2.3 2.1 1.8 1.5 1.2

CP3: Unconverted rest, low pTt 16.3 16.7 16.6 16.0 15.0 13.6 11.9 9.8 7.4

CP4: Unconverted rest, high pTt 4.4 4.6 4.6 4.5 4.3 4.0 3.5 2.9 2.2

CP5: Converted central, low pTt 5.9 5.9 5.8 5.5 5.1 4.6 4.0 3.3 2.4

CP6: Converted central, high pTt 1.6 1.7 1.6 1.6 1.6 1.4 1.3 1.1 0.8

CP7: Converted rest, low pTt 17.5 18.1 17.9 17.1 15.8 14.1 12.0 9.7 7.2

CP8: Converted rest, high pTt 4.6 4.7 4.7 4.6 4.4 4.1 3.6 2.9 2.2

CP9: Converted transition 8.2 8.4 8.4 8.1 7.6 6.9 6.0 4.9 3.7

Total 69.9 71.5 70.9 68.3 63.7 57.5 49.8 40.8 30.6

tail. The variables δmH , σCB and αCB of the CB function depend linearly on the Higgs boson mass. Themean and σ of the additional Gaussian function are constrained to the value of mH + δmH and κ ·σCB.The variables δmH , σCB, αCB and κ and a fraction of the component of the CB function are determinedwith the simultaneous fit fixing nCB to be 10. The core component of the mass resolution, σCB, rangesfrom 1.4 GeV in the “Unconverted Central” categories to 2.3 GeV in the “Converted Transition” category

over the full mass range that is studied. The effect of the pileup on the mass resolution is negligible.

The result of the simultaneous fit for events selected with the inclusive analysis (i.e. without cate-

gorization) for a mass hypothesis of 120 GeV is displayed in Figure 4. Table 4 summarizes the mass

resolution, σCB and full width half-maximum (FWHM), the expected number of signal events, the es-timated number of background events in each category as determined from the data (Section 4.2), and

their ratio in the mass window of ±1.4σCB, for a Higgs signal of mH=120 GeV.

4.2 Background Model

The background is estimated from the data by fitting the diphoton mass spectrum in the whole range

of 100 – 160 GeV with a single exponential function. Such a function was found to describe all the

categories very well, as obtained from studies using large samples of diphoton events produced by the

RESBOS [32] and DIPHOX [33] MC generators. Figures 5 and 6 show the invariant mass spectra

reconstructed in data and the results of the unbinned maximum likelihood fit under the background-only

hypothesis for the nine categories.

The systematic uncertainty on the background modelling is assigned by estimating, for each category,

the potential difference between the true background shape and the single exponential function which

could fake a signal-like signature. This is obtained from MC by calculating the difference between the

mass distributions of the events generated with RESBOS and DIPHOX and the result of the exponential

fit to these distributions. The maximum difference integrated over a window of 4 GeV normalised to the

total event count in each category is assigned as uncertainty (Table 5). Other functional forms, including

2nd order Bernstein polynomials and double exponential functions, were fitted to the data and compared

to the exponential fit. The uncertainties arising from these comparisons were found to be of similar size

to the MC-based estimate.

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Figure 4: Reconstructed inclusive invariant mass distribution for a simulated signal of mH = 120 GeV.The result of the simultaneous fit to all Higgs boson mass points is superimposed. The core component

of the mass resolution, σCB, is 1.7 GeV and the FWHM of the distribution is 4.0 GeV.

Table 4: The mass resolution of Higgs signal events (σCB and FWHM), the expected number of signalevents (Nsig), the estimated number of background events (NBG) from data, and their ratio (Nsig/NBG) in

the mass window of ±1.4σCB for mH = 120 GeV corresponding to an integrated luminosity of 4.9 fb−1.

Category σCB [GeV] FWHM [GeV] Nsig NBG Nsig/NBG

CP1: Unconverted central, low pTt 1.4 3.4 7.3 142 0.051

CP2: Unconverted central, high pTt 1.4 3.3 2.2 18 0.117

CP3: Unconverted rest, low pTt 1.7 4.1 13.5 589 0.023

CP4: Unconverted rest, high pTt 1.6 3.9 3.8 87 0.043

CP5: Converted central, low pTt 1.7 3.9 4.7 125 0.038

CP6: Converted central, high pTt 1.6 3.7 1.4 16 0.085

CP7: Converted rest, low pTt 2.0 4.7 14.0 805 0.017

CP8: Converted rest, high pTt 1.9 4.5 3.7 110 0.034

CP9: Converted transition 2.3 5.8 5.9 429 0.014

Table 5: Systematic uncertainty (the number of events for data of 4.9 fb−1) on the background modellingin different categories.

Category CP1 CP2 CP3 CP4 CP5 CP6 CP7 CP8 CP9

Events ±4.3 ±0.2 ±3.7 ±0.5 ±3.2 ±0.1 ±5.6 ±0.6 ±2.3

5 Systematic Uncertainties

Systematic uncertainties affecting the extraction of a possible signal from the diphoton invariant mass

distribution related to the modelling of the signal itself can be classified into three types: uncertainties9

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Figure 5: Diphoton invariant mass distributions for the data (points with error bars) for the four “uncon-

verted” categories (CP1-CP4). For each plot the line shows the result of the exponential fit.

on the predicted yield, uncertainties on the signal invariant mass resolution and uncertainties on event

migration between categories.

The uncertainties on the predicted signal yield are the following:

• A ±11% uncertainty from the photon reconstruction and identification. This is estimated by com-paring the MC-based efficiencies with those extrapolated from measurement of electrons from

W /Z-boson decays, and with the direct measurements of photons in Z → ℓℓγ (ℓ = e,µ) decayswhich only cover the ET range 25 – 60 GeV. The impact of possible additional material in front of

the calorimeter, as estimated with MC simulations, is also included;

• A ±4% uncertainty from the effect of the pileup on the photon reconstruction and identificationefficiency. This is estimated by looking at the variation of the tight photon identification efficiency

as a function of the average number of interactions per bunch crossing;

• The effect of the photon energy scale uncertainty (≈ 0.5%) was found be to small (0.3%), and istherefore neglected;

• A ±5% uncertainty on the isolation cut efficiency. This is estimated from the difference betweenthe isolation cut efficiency in data and MC simulation using Z→ ee events;

• A ±1% uncertainty on the trigger efficiency. This comes from the uncertainty in the measurementof the trigger efficiency for diphoton candidates using control triggers, and from possible differ-

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Figure 6: Diphoton invariant mass distributions for the data (points with error bars) for the five “con-

verted” categories (CP5-CP9). For each plot the line shows the result of the exponential fit.

ences, evaluated with MC samples, between the trigger efficiency for photons from Higgs boson

decays and for photons from all diphoton candidates;

• A +15%/− 11% uncertainty on the signal cross section [27]. This is evaluated by varying therenormalization and factorization scales and using different parton distributions (PDF) [34] in the

gluon fusion process, which has the largest uncertainty compared to other processes and dominates

in all the categories (95% for low pTt and 80% for low pTt). The same uncertainty is applied to

signal samples produced with other processes;

11

• A ±1% uncertainty on the signal acceptance from the modelling of the Higgs boson pT, which isestimated by comparing the predictions of the HqT [30] and RESBOS [35] programs;

• A ±3.9% overall uncertainty on the total integrated luminosity in the full 2011 data set, as extrap-olated from Ref. [36].

The uncertainties on the mass resolution arise from the following:

• A ±12% uncertainty from the calorimeter energy resolution. This results from the uncertainty onthe sampling term, which is estimated to be ±10%, and from the uncertainty on the constant term,which is estimated to be

(1.2+0.5−0.6

)% for the barrel and (1.8±0.6)% for the endcap calorimeter

using Z→ ee events [9];

• A ±6% uncertainty arising from the extrapolation of the electron energy calibration to that forphotons. This extrapolation, obtained from MC studies, is affected by the imperfect knowledge of

the material in front of the active part of the calorimeter. The effect of this imperfect knowledge

on the mass resolution is evaluated using simulations with a different amount of material in front

of the calorimeter.

• A ±3% uncertainty from the effect of the pileup on the energy resolution. Pileup fluctuations con-tributing to the cluster energy measurement were checked using reconstructed clusters in randomly-

triggered bunch crossings, selected in proportion to the instantaneous luminosity in the data [7];

• A ±1% uncertainty from the photon angle measurement on the mass resolution. This was studiedin Z→ ee events comparing track-based with calorimeter-based direction measurements [7].

The uncertainties on the event migration between categories arise from the following:

• A±8%migration of events from the high pTt categories to the low pTt categories. This is estimatedfrom gluon fusion Higgs boson signal MC events by varying the renormalization, factorization and

resummation scales and PDF choices for the modelling of the pγγT spectrum in the HqT program.

The same uncertainty is applied to signal samples produced with other processes. The effect of

photon energy scale uncertainty on this migration is small (0.5%) and is neglected;

• A ±4.5% migration of events from the unconverted categories to the converted categories. Theimpact of pileup and additional material in front of the calorimeter is estimated from MC samples

with different pileup and material configurations.

The systematic uncertainties on the expected signal are summarized in Table 6. Systematic uncertain-

ties on the event yield and the mass resolution are taken as fully correlated between different categories,

while those on the event migration are anti-correlated between the high and low pTt categories and be-

tween the unconverted and converted categories. Systematic uncertainties on the background modelling

yield between±0.1 and±5.6 events depending on the category (Table 5). These uncertainties are treatedas uncorrelated between categories except for those that share the same η and pTt classification but dif-ferent conversion status.

6 Results

The statistical interpretation of the data follows the procedure described in Ref. [5] which adopts a

modified frequentist approach (CLS) [37] for setting the limit and a frequentist approach to calculate

the p0-value. The combined likelihood function is constructed from the likelihood functions of the nine

categories, and the systematic uncertainties are incorporated by introducing 31 nuisance parameters with

12

Table 6: Summary of systematic uncertainties on the expected signal.

Type and source Uncertainty

Event yield

Photon reconstruction and identification ±11%Effect of pileup on photon identification ±4%Isolation cut efficiency ±5%Trigger efficiency ±1%Higgs boson cross section +15%/−11%Higgs boson pT modeling ±1%Luminosity ±3.9%

Mass resolution

Calorimeter energy resolution ±12%Photon energy calibration ±6%Effect of pileup on energy resolution ±3%Photon angular resolution ±1%

Migration

Higgs boson pT modeling ±8%Conversion reconstruction ±4.5%

Gaussian constraints. Asymptotic formulae [38] were used to derive the limit and p0-values, and pseudo-

experiments were generated to confirm the validity of this procedure.

The p0-value, used to quantify the probability of seeing an excess at least as large as this in the

background-only hypothesis, is evaluated for Higgs boson mass hypotheses between 110 GeV and

150 GeV in steps of 1 GeV. The expected and observed p0-values are shown in Figure 7. The expected

p0-value is evaluated assuming a SM Higgs boson signal plus background for a given hypothesized

Higgs boson mass. The minimal observed p0-value is 0.27% and is found for a mass hypothesis of

mH = 126 GeV. This p0-value corresponds to 2.8 standard deviations. The probability of such an excessappearing anywhere in the mass range investigated due to a background fluctuation, accounting for the

look-elsewhere effect, is estimated to be approximately 7% and it reduces the observed significance to

1.5 standard deviations. This was determined using the prescription described in Ref. [39]. As cross

checks, the observed p0-values were reevaluated using alternate background models, including the 2nd

order Bernstein polynomials. Also, the uncertainties on the background modelling due to the use of a

single exponential (Table 5) were set to zero or doubled. Furthermore, a photon energy scale uncertainty

of≈ 0.5% was introduced into the likelihood fits. All of these checks gave observed p0-values which aresimilar to the quoted result. The largest change in the observed significance at mH = 126 GeV was 0.16standard deviations.

The 95% confidence level (CL) limits on the ratio of the inclusive production cross section of a SM-

like Higgs boson relative to the SM cross section are also derived as shown in Figure 8. The expected

limits vary between 1.6 and 1.8 times the predicted SM cross section in the mass range 115 – 130 GeV,

and between 1.6 and 2.9 times the SM cross section over the full mass range that is studied. The observed

limits are set between 0.9 and 4.0 times the SM cross section over the full mass range. A SMHiggs boson

in the mass ranges 114 – 115 GeV and 135 – 136 GeV is excluded. The numerical values of the limits

and p0-values in steps of 1 GeV are listed in Table 7.

13

[GeV]Hm

110 115 120 125 130 135 140 145 150

0p

­410

­310

­210

­110

1

10 0Observed p

0 expected pγγ →SM H

= 7 TeVsData 2011,

­1Ldt = 4.9 fb∫

ATLAS Preliminary

σ1

σ2

σ3

Figure 7: The observed and expected p0-value as a function of the hypothesized Higgs boson mass

without taking the look-elsewhere effect into account. The dotted-dashed lines indicate the corresponding

significance.

7 Conclusions

A search for the SM Higgs boson in the diphoton decay channel has been performed using data corre-

sponding to an integrated luminosity of 4.9 fb−1 recorded by the ATLAS experiment in 2011. Over thediphoton mass range 110 – 150 GeV the maximum deviation from the background-only expectation is

observed at 126 GeV with a local significance of 2.8 standard deviations. Taking the look-elsewhere ef-

fect into account, the significance is 1.5 standard deviations. The expected cross section exclusion at 95%

confidence level varies between 1.6 and 1.8 times the SM cross section in the mass range 115 – 130 GeV,

and between 1.6 and 2.9 over the full mass range that is studied. The observed exclusions are set between

0.9 and 4.0 times the SM cross section over the full mass range. A SM Higgs boson is excluded at 95%

CL in the mass ranges of 114 – 115 GeV and 135 – 136 GeV.

14

[GeV]Hm

110 115 120 125 130 135 140 145 150

S

Mσ/

σ9

5%

CL lim

it o

n

1

2

3

4

5

6

7

8 limitsObserved CL

limits

Expected CL

σ 1±σ 2±

ATLAS Preliminary

γγ →H

= 7 TeVsData 2011,

­1Ldt = 4.9 fb∫

Figure 8: The observed and expected 95% confidence level limits, normalised to the SM Higgs boson

cross sections, as a function of the hypothesized Higgs boson mass.

15

Table 7: The expected and observed limits, normalised to the Higgs boson cross section as predicted by

the SM, and the observed and expected (for a SM Higgs boson) p0-values.

mH [GeV] Expected limit Observed limit Expected p0 Observed p0

110 2.01 1.94 0.15 0.50

111 1.95 1.67 0.15 0.50

112 1.90 1.32 0.14 0.50

113 1.85 1.01 0.13 0.50

114 1.82 0.86 0.13 0.50

115 1.78 0.93 0.12 0.50

116 1.74 1.28 0.12 0.50

117 1.72 1.83 0.11 0.46

118 1.70 2.12 0.11 0.29

119 1.67 1.85 0.10 0.42

120 1.66 1.41 0.10 0.50

121 1.65 1.15 0.097 0.50

122 1.64 1.23 0.094 0.50

123 1.63 1.73 0.093 0.48

124 1.63 2.62 0.092 0.11

125 1.61 3.55 0.092 0.013

126 1.61 4.04 0.089 0.0027

127 1.63 3.82 0.089 0.0055

128 1.63 3.06 0.089 0.053

129 1.64 2.19 0.091 0.27

130 1.65 1.65 0.093 0.50

131 1.66 1.43 0.095 0.50

132 1.67 1.34 0.096 0.50

133 1.69 1.28 0.096 0.50

134 1.71 1.14 0.10 0.50

135 1.73 0.98 0.10 0.50

136 1.77 0.95 0.10 0.50

137 1.79 1.21 0.11 0.50

138 1.83 1.68 0.11 0.50

139 1.88 1.96 0.11 0.41

140 1.91 1.76 0.12 0.50

141 1.97 1.46 0.12 0.50

142 2.03 1.46 0.13 0.50

143 2.09 1.87 0.14 0.50

144 2.16 2.47 0.15 0.33

145 2.25 2.88 0.16 0.24

146 2.34 2.85 0.16 0.31

147 2.44 2.54 0.17 0.49

148 2.56 2.25 0.18 0.50

149 2.70 2.02 0.19 0.50

150 2.87 1.92 0.20 0.50

16

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19

Appendix: Auxiliary public plots

[GeV]γγm110 112 114 116 118 120 122 124 126 128 130

/ 0

.5 G

eV

γγ1

/N d

N/d

m

0

0.02

0.04

0.06

0.08

0.1

0.12ATLAS Preliminary

(Simulation)

=120 GeVH

, mγγ→ H→gg

Fit

6≤ µ

9≤ µ6 <

12≤ µ9 <

> 12µ

[GeV]γγm110 112 114 116 118 120 122 124 126 128 130

/ 0

.5 G

eV

γγ1

/N d

N/d

m

0

0.02

0.04

0.06

0.08

0.1

0.12ATLAS Preliminary

(Simulation)

*=1 mβ=120 GeV

H, mγγ→ H→gg

Fit

truth vertex

2

T pΣ

Calo/Conv pointing

Figure 9: The reconstructed diphoton mass in simulated H → γγ events using the fit with the sum ofa Crystal Ball function plus a Gaussian for the inclusive event selection. In the left plot, the method

explained in Section 2.1 (“Calo/Conv pointing”) is used to determine the vertex position. Four different

results are shown corresponding to four different pile-up conditions. The number of average interac-

tions per bunch crossing is denoted by µ . On the right, the fit results using the vertex determined with“Calo/Conv pointing” method is compared to two other methods to deduce the angle between the pho-

tons. The truth vertex gives the best possible result by using MC truth information to deduce the correct

primary vertex. In the Σp2T method the primary vertex is chosen as the one with the largest sum of the p2T

of the tracks associated to it. The improvement of the mass resolution by using the “Calo/Conv pointing”

method instead of the Σp2T method amounts to 5 – 20%, depending on the pile-up conditions.

20

Period

*=1.5 mβ *=1.0 mβ All

­1E

ve

nts

/pb

0

1

2

3

4

5

6

+DY dataγγj dataγ

jj data

Stat.+syst. error

ATLAS Preliminary

­1 Ldt = 4.9 fb∫ = 7 TeV, s

Data 2011

Figure 10: Background components in the inclusive analysis extracted by the double two-dimensional

sideband method for two data taking periods. The first period taken with LHC beam optics parame-

ter β ∗ = 1.5 m corresponds to an integrated luminosity of 2.1 fb−1 and on average 6 interactions perbunch crossing. The later period taken with β ∗ = 1.0 m corresponds to 2.8 fb−1 and 12 interactions perbunch crossing on average. The statistical uncertainty is negligible small comparing to the systematic

uncertainty.

γγ jγ jj DYγγ jγ jj DY

Num

ber

of E

vents

0

2000

4000

6000

8000

10000

12000

14000

16000

18000

20000

Data-driven estimations

expectedγγ

j expectedγ

jj expected

DY expected

ATLAS Preliminary

-1 Ldt=4.9 fb∫

γγ jγ jj DYγγ jγ jj DY

Num

ber

of E

vents

0

2000

4000

6000

8000

10000

12000

14000

16000

18000

20000

Figure 11: Comparison of the number of background events for each component predicted using theory

andMC simulation to the results of the data-driven data decomposition using the double two-dimensional

sideband method. This is an update of the results in Ref. [1] using the full 2011 data sample.

[1] The ATLAS Collaboration, Search for the Higgs boson in the Diphoton Channel with the ATLAS

Detector using 209 pb−1 of 7 TeV Data taken in 2011, ATLAS-CONF-2011-085 (2011).

21

[GeV]Hm

110 115 120 125 130 135 140 145 150

0p

­410

­310

­210

­110

1

10 0Observed p

0 expected pγγ →SM H

(Hybrid) 0

Observed p (Bernstein)

0Observed p

= 7 TeVsData 2011,

­1Ldt = 4.9 fb∫

ATLAS Preliminary

σ1

σ2

σ3

Figure 12: The observed and expected local p0-value as a function of mH for three different background

models without taking the look-elsewhere effect into account. The black solid line is the result described

in detail in this note, using single exponential functions in all categories. In the Hybrid model the high

pTt categories are fitted with the 2nd order Bernstein polynomials, the other categories with the single

exponential. In the model Bernstein all categories are fitted with the Bernstein function. The p0-values

near the minima at 126 GeV are very similar in all cases: p0=0.38% using the Hybrid model, and

p0=0.25% using the Bernestein function.

22

Figure 13: Event display of a candidate diphoton event where both photon candidates are uncon-

verted. The event number is 86694500 and it was recorded during run 191426. The leading photon

has ET=64.2 GeV and η=-0.34. The subleading photon has ET=61.4 GeV and η=-0.61. The measureddiphoton mass is 126.6 GeV. The pT and pTt of the diphoton are 6.1 GeV and 5.4 GeV, respectively.

Only reconstructed tracks with pT > 1 GeV, hits in the pixel and SCT layers and TRT hits with a highthreshold are shown.

23

Figure 14: Event display of a candidate diphoton event where the leading (subleading) photon candidate

is unconverted (converted). The event number is 19448322 and it was recorded during run 191190.

The leading photon has ET=66.8 GeV and η=-0.27. The subleading photon has ET=56.9 GeV and η=-0.67. The measured diphoton mass is 125.8 GeV. The pT and pTt of the diphoton are 10.4 GeV and

3.1 GeV, respectively. The conversion radius of the subleading photon is measured to be 8.1 cm. Only

reconstructed tracks with pT> 1 GeV, hits in the pixel and SCT layers and TRT hits with a high thresholdare shown.

24

Figure 15: Close-up view in the transverse plane of the converted photon candidate shown in Fig-

ure 14 (run number = 191190, event number = 19448322). Only reconstructed tracks with pT > 2 GeVand |η | < 1.4 are shown, and only the hits in the pixel, SCT and TRT layers with −1 < |η | < 0 areshown. Starting from the primary vertex (shown as a large magenta dot on the left), the photon conver-

sion vertex (brown dot) can be seen at a radius of 8.1 cm, followed by the pixel hits (magenta dots), SCT

clusters (green segments) and TRT hits (blue dots for normal dE/dx hits and red dots for hits above thehigh threshold required for transition radiation). The electron track (blue line) has pT = 56.1 GeV andmatches well with the electromagnetic cluster (shown in yellow at the outer radius). The positron track

has pT = 4.0 GeV and a fraction of its energy actually lies outside the main cluster.

25

Figure 16: Close-up view in the transverse plane of the longitudinal shower profile in the barrel electro-

magnetic calorimeter of the converted photon candidate shown in Figure 14 (run number = 191190, event

number = 19448322). The layers of the EM calorimeter are shown as green boxes with sizes represent-

ing their real dimensions and with heights proportional to the energy deposited (normalised differently

for each layer for viewing purposes). The two electrons from the photon conversions encounter first

the presampler layer (which provides an estimate of the energy lost by bremsstrahlung in front of the

active calorimeter), then the strip layer, which is fine-grained in η and provides good γ/π0 rejection, andfinally the second layer where most of the energy is deposited. The conversion is quite asymmetric and

the showers initiated by the two electrons appear in different strip-layer modules (in φ ) but line up verywell with each other in η , as expected for such an electron pair.

26