Search for the Standard Model Higgs boson in the H to tau+ tau- decay mode in sqrt(s) = 7 TeV pp collisions with ATLAS

A search for the Standard Model Higgs boson decaying into a pair of tau leptons is reported. The analysis is based on a data sample of proton-proton collisions collected by the ATLAS experiment at the LHC and corresponding to an integrated luminosity of 4.7 fb^-1. No significant excess over the expected background is observed in the Higgs boson mass range of 100-150 GeV. The observed (expected) upper limits on the cross section times the branching ratio for H to tau+ tau- are found to be between 2.9 (3.4) and 11.7 (8.2) times the Standard Model prediction for this mass range.


Introduction
The Higgs boson is the only fundamental particle in the Standard Model (SM) of particle physics that has not yet been observed. It is predicted by the Higgs mechanism [1][2][3][4][5][6], which in the SM gives mass to particles. The search for the Higgs boson is a centrepiece of the Large Hadron Collider (LHC) physics programme.
An indirect constraint on the Higgs boson mass of m H < 185 GeV at the 95% confidence level (CL) has been set using global fits to electroweak precision data [7]. Direct searches at LEP and the Tevatron have placed exclusion limits at 95% CL for m H < 114. 4 GeV and in the region 147 GeV < m H < 179 GeV [8,9], respectively. The results of searches in various channels using data corresponding to an integrated luminosity of up to 5 fb −1 have recently been reported by both the ATLAS and CMS Collaborations [10,11] excluding the mass range between 112.9 GeV and 115.5 GeV and the region between 127 GeV and 600 GeV, again at the 95% CL.
In the Higgs boson mass range 100-150 GeV, the H → τ + τ − decay mode is a promising channel for the search at the LHC with branching ratios between 8% and 1.8%. The H → τ + τ − search is complementary to searches with other decays in the same mass range and enhances the overall sensitivity. Also, if the Higgs boson is discovered, the measurement of the H → τ + τ − decay rate provides a test of the SM prediction for the τ Yukawa coupling.
The process with the largest cross section to produce a SM Higgs boson at the LHC is gluon fusion gg → H. However, Higgs boson production via vector boson (W W , ZZ) fusion qq → qqH (VBF) and via Higgs-strahlung qq → V H, in association with a hadronically decaying vector boson (V = W or Z), are highly relevant as well because they lead to additional jets in the final state, which provide distinct experimental signatures. In particular the VBF topology of two high-energy jets with a large rapidity separation offers a good discrimination against background processes. For all production processes above, the Higgs boson is typically more boosted in the transverse plane if there are additional high-p T jets in the event, which increases the transverse momentum of the τ decay products and thus facilitates the measurement of the τ + τ − invariant mass and the discrimination of the signal from background processes. This paper presents SM Higgs boson searches in the the H → τ + lep τ − lep , H → τ + lep τ − had , and H → τ + had τ − had channels, 1 where τ lep and τ had denote leptonically and hadronically decaying τ leptons, respectively. The data analyses use proton-proton (pp) collisions at √ s = 7 TeV collected by the ATLAS experiment in 2011, which correspond to an integrated luminosity of 4.7 fb −1 . In order to enhance the sensitivity of the search, the selected events are analysed in several separate categories according to the number and topology of reconstructed jets.

Data and Monte Carlo simulated samples
The ATLAS detector is a multipurpose apparatus with a forward-backward symmetric cylindrical geometry and nearly 4π coverage in solid angle [12]. It consists of an inner tracking detector surrounded by a thin superconducting solenoid, electromagnetic and hadronic calorimeters, and an external muon spectrometer incorporating three large superconducting air-core toroid magnets. Electrons, muons, τ leptons and jets can be reconstructed and identified in the ATLAS detector. 2 Only data taken with all sub-systems relevant to this analysis the barrel and end-cap calorimeters (1.37 < |η| < 1. 52), and meet quality requirements based on the expected shower shape [50]. Muon candidates are formed from a track measured in the inner detector and linked to a track in the muon spectrometer [51]. They are required to have a transverse momentum p T > 10 GeV and to lie within |η| < 2.5. Additionally, the difference between the z-position of the point of closest approach of the muon inner detector track to the beam-line and the z-coordinate of the primary vertex is required to be less than 1 cm. 3 This requirement reduces the contamination due to cosmic ray muons and beam-induced backgrounds. Muon quality criteria based on, e.g., inner detector hit requirements are applied in order to achieve a precise measurement of the muon momentum and reduce the misidentification rate.
Identified electrons and muons are required to be isolated: the additional transverse energy in the electromagnetic and hadronic calorimeters must be less than 8% (4%) of the electron transverse energy (muon transverse momentum) in a cone of radius ∆R = (∆η) 2 + (∆φ) 2 = 0.2 around the electron (muon) direction. The sum of the transverse momenta of all tracks with p T above 1 GeV located within a cone of radius ∆R = 0.4 around the electron (muon) direction and originating from the same primary vertex must be less than 6% of the electron transverse energy (muon transverse momentum).
Jets are reconstructed using the anti-k t algorithm [52] with a distance parameter value of R = 0.4, taking as input three-dimensional noise-suppressed clusters in the calorimeters. Reconstructed jets with p T > 20 GeV and within |η| < 4.5 are selected. Events are discarded if a jet is associated with out-of-time activity or calorimeter noise. After having associated tracks to jets by requiring ∆R < 0.4 between tracks and the jet direction, a jet-vertex fraction (JVF) is computed for each jet as the scalar p T sum of all associated tracks from the primary vertex divided by the scalar p T sum of all tracks associated with the jet. Conventionally, JVF = −1 is assigned to jets with no associated tracks. Jets with |η| < 2.4 are required to have |JVF| > 0.75 in order to suppress pileup contributions. In the pseudorapidity range |η| < 2.5, b-jets are identified using a tagging algorithm based on the discrimination power of the impact parameter information and of the reconstruction of the displaced vertices of the hadron decays inside the jets [53]. The b-tagging algorithm has an average efficiency of 58% for b-jets in tt events [54]. The corresponding light-quark jet misidentification probability is 0.1-0.5%, depending on the jet p T and η [55].
Hadronic decays of τ leptons are characterised by the presence of one or three charged hadrons accompanied by a neutrino and possibly neutral hadrons, which results in a collimated shower profile in the calorimeters and only a few nearby tracks. The visible decay products are combined into τ had candidates. These candidates are reconstructed as jets, which are recalibrated to account for the different calorimeter response to hadronic decays as compared to hadronic jets. The four-momentum of the τ had candidates are reconstructed from the energy deposits in the calorimeters and the rejection of jets misidentified as hadronic τ decays is performed by a multivariate discriminator based on a boosted decision tree [56] that uses 3 The primary vertex is defined as the vertex with the largest p 2 T of the associated tracks.
both tracking and calorimeter information. The identification is optimised to be 50% efficient while the jet misidentification probability is kept below 1%. A τ had candidate must lie within |η| < 2.5, have a transverse momentum greater than 20 GeV, one or three associated tracks (with p T > 1 GeV) and a total charge of ±1 computed from the associated tracks. Dedicated electron and muon veto algorithms are used. When different objects selected according to the above criteria overlap with each other geometrically (within ∆R < 0.2), only one of them is considered for further analysis. The overlap is resolved by selecting muon, electron, τ had and jet candidates in this order of priority.
The magnitude of the missing transverse momentum [57] (E miss T ) is reconstructed including contributions from muon tracks and energy deposits in the calorimeters. Calorimeter cells belonging to three-dimensional noise-suppressed clusters are used and they are calibrated taking into account the reconstructed physics object to which they belong.

Preselection
An initial selection of events is performed by requiring a vertex from the primary pp collisions that is consistent with the beam spot position, with at least three associated tracks, each with p T > 500 MeV. Overall quality criteria are applied to suppress events with fake E miss T , produced by non-collision activity such as cosmic ray muons, beam-related backgrounds, or noise in the calorimeters.
The ℓℓ, ℓτ had and τ had τ had final states. 4 considered in this search are defined in a mutually exclusive way: a requirement of exactly two, one, or zero electrons or muons is imposed, respectively.

H → τ lep τ lep
Signal events in this channel are selected by requiring exactly two isolated and oppositelycharged light leptons (electrons and/or muons). Single lepton and di-lepton triggers are used to preselect the data. The trigger object quality requirements were tightened during the data-taking period to cope with increasing instantaneous luminosity. The single muon trigger requires p T > 18 GeV; for the single electron trigger the E T threshold changes from 20 GeV to 22 GeV depending on the LHC instantaneous luminosity; the di-muon trigger requires p T > 15 GeV for the leading muon and p T > 10 GeV for the sub-leading muon; the dielectron trigger requires E T > 12 GeV for each of the two electrons; the eµ trigger requires E T > 10 GeV for the electron and p T > 6 GeV for the muon. In addition to the trigger requirements, the preselection requires E T > 22 GeV if the electron satisfies only the single electron trigger. The E T requirement is increased to 24 GeV when the trigger threshold is 22 GeV. If a muon is associated only with the single muon trigger object, it is required to have p T > 20 GeV. For the eµ channel the di-lepton invariant mass is required to be in the range of 30 GeV < m ℓℓ < 100 GeV, whereas for the ee and µµ channels 30 GeV < m ℓℓ < 75 GeV is required, reducing the contamination from Z/γ * → ℓℓ .

H → τ lep τ had
Signal events in this channel are characterised by exactly one isolated light lepton ℓ, a τ had candidate, and large E miss T due to the undetected neutrinos. For the eτ had (µτ had ) final states, events are preselected using the single electron (muon) trigger described in Section 4.1. Exactly one electron with E T > 25 GeV or one muon with p T > 20 GeV, and one oppositelycharged τ had candidate with p T > 20 GeV are required in the event. Events with more than one electron or muon candidate are rejected to suppress events from Z/γ * → ℓ + ℓ − decays and from tt or single top-quark production. 5 The transverse mass of the lepton and E miss T is calculated as where p ℓ T denotes the magnitude of the transverse momentum of the lepton and ∆φ is the angle between the lepton and E miss T directions in the plane perpendicular to the beam direction. In order to reduce contributions from the W +jets and tt background processes, only events with m T < 30 GeV are considered for further analysis. In addition, E miss T is used for further event selection and categorisation, as described in Section 5.

H → τ had τ had
Signal events in this channel are characterised by two identified hadronic τ decays and large E miss T from the undetected neutrinos. The corresponding event selection starts with a double hadronic τ trigger, where the p T thresholds are 29 GeV and 20 GeV for the leading and sub-leading hadronic τ objects, respectively. A requirement of exactly zero charged light leptons, as defined in Section 3, is imposed. Two identified opposite charge τ had candidates with p T > 35 GeV and p T > 25 GeV are required, each matching a τ trigger object [58].

Analysis categories
For further analysis, the selected event samples are split into several categories according to the number and topology of reconstructed jets. The sensitivity of the search is usually higher for categories where the presence of one or more jets is required, as discussed in Section 1, but events without any reconstructed high-p T jets are also considered in order to maximise the sensitivity.

H → τ lep τ lep
Four categories defined by their jet multiplicity and kinematics are used for this channel: H +2-jet VBF, H +2-jet V H, H +1-jet and H +0-jet. The first two categories require the presence of at least two jets and the cuts are optimised in one case for the VBF process [59][60][61], and in the other for the V H and gg → H processes [62].
The H +0-jet category uses an inclusive selection to collect part of the signal not selected by the categories with jets. In the H + 0-jet category, only the eµ final state is considered because of the overwhelming Z/γ * → ℓℓ background in the ee and µµ final states. In order to suppress the tt background, it is required that the di-lepton azimuthal opening angle be ∆φ ℓℓ > 2.5 rad and that the leptonic transverse energy be H lep T = p ℓ1 T +p ℓ2 T +E miss T < 120 GeV, where p ℓ1 T and p ℓ2 T are the magnitudes of the transverse momenta of the leading and sub-leading leptons, respectively.
In categories with jets (H +2-jet VBF, H +2-jet V H and H +1-jet), the presence of a hadronic jet with a transverse momentum p T > 40 GeV is required and, to suppress the tt background, the event is rejected if any jet with p T > 25 GeV is identified as a b-jet. In addition, E miss T > 40 GeV (E miss T > 20 GeV) for the ee, µµ (eµ) channels is also required. The collinear approximation technique [63] is used to reconstruct the kinematics of the τ τ system. The approximation is based on two assumptions: that the neutrinos from each τ decay are nearly collinear with the corresponding visible τ decay products and that the E miss T in the event is due only to neutrinos. In this case, the total invisible momentum carried away by neutrinos in each τ decay can be estimated from the polar and azimuthal angles of the visible products of each τ decay. Then, the invariant mass of the τ τ system can be calculated as m τ τ = m ℓℓ / √ x 1 · x 2 , where x 1 and x 2 are the momentum fractions of the two τ candidates carried away by their visible decay products. Events that do not satisfy 0.1 < x 1 , x 2 < 1.0 are rejected. In categories with jets, there is an additional requirement that 0.5 rad < ∆φ ℓℓ < 2.5 rad to suppress the Z/γ * → ℓℓ background.
For the H +2-jet categories, a subleading jet with p T > 25 GeV is required in addition. For the H +2-jet VBF category, a pseudorapidity difference between the two selected jets of ∆η jj > 3 and a di-jet invariant mass of m jj > 350 GeV are required. Finally, the event is rejected in the H +2-jet VBF category if any additional jet with p T > 25 GeV and |η| < 2.4 is found in the pseudorapidity range between the two leading jets.
For the H +2-jet V H category, the requirement on the pseudorapidity separation of the jets and on the di-jet invariant mass are instead: ∆η jj < 2 and 50 GeV < m jj < 120 GeV.
Only events failing the cuts for the H +2-jet categories are considered in the H +1-jet category. For the H +1-jet category, the invariant mass of the two τ leptons and the leading jet is required to fulfil m τ τ j > 225 GeV, where the τ momenta are taken from the collinear approximation. The main Higgs production mechanism in this category is the gg → H process plus a high-p T parton.
The m τ τ calculated with the collinear approximation ("collinear mass") is used in categories with jets. Because this variable displays poor resolution in the H +0-jet category due to the back-to-back configuration of the two leptons, the effective mass (m eff τ τ ), defined as the invariant mass of the two leptons and the E miss T , is used instead.

H → τ lep τ had
The selected data are split into seven categories based on jet properties and E miss T .
The H +2-jet VBF category includes all selected events with E miss T > 20 GeV and at least two jets with p T > 25 GeV, where the two leading jets are found in opposite hemispheres of the detector (η jet1 · η jet2 < 0), with ∆η jj > 3 and m jj > 300 GeV. Both the lepton and the τ had candidate are required to be found in the pseudorapidity range between the two leading jets. Due to the limited size of the selected event samples, the VBF category combines the eτ had and µτ had final states.
Two H +1-jet categories include all selected events with E miss T > 20 GeV and at least one jet with p T > 25 GeV, that fail the VBF selection. The eτ had and µτ had final states are considered separately.
Four H +0-jet categories include all selected events without any jet with p T > 25 GeV. The eτ had and µτ had final states are considered separately. In addition, the analysis is separated into events with E miss T > 20 GeV and E miss T < 20 GeV. The low-E miss T region is included here because, in the absence of high-p T jets, the Higgs decay products, including the neutrinos, are typically less boosted than for events with additional jet activity.
For each category, the mass of the τ τ system is reconstructed using the Missing Mass Calculator (MMC) [64]. This technique provides a full reconstruction of event kinematics in the τ τ final state with 99% efficiency and 13-20% resolution in m τ τ , depending on the event topology (better resolution is obtained for events with high-p T jets). Conceptually, the MMC is a more sophisticated version of the collinear approximation. The main improvement comes from requiring that relative orientations of the neutrinos and other decay products are consistent with the mass and kinematics of a τ lepton decay. This is achieved by maximising a probability defined in the kinematically allowed phase space region.

H → τ had τ had
In the H → τ had τ had channel, only a single H + 1-jet category is defined. After selecting two hadronic τ candidates, the collinear mass approximation cuts 0 < x 1 , x 2 < 1 are applied. Events at this stage are used as a control sample to derive the normalisation of the Z/γ * → τ τ background. Then, events are selected if E miss T > 20 GeV and if the leading jet has a transverse momentum p T > 40 GeV. The two τ candidates are required to be separated by ∆R(τ, τ ) < 2.2. Also, only events with an invariant mass of the τ τ pair and the leading jet m τ τ j > 225 GeV are considered for further analysis. The event selection criteria described here are effective against the multi-jet and Z/γ * → τ τ backgrounds. The collinear mass approximation is used for the Higgs mass reconstruction.

Background estimation and modelling
The background composition and normalisation are determined using data-driven methods and the simulated event samples described in Section 2.
The main background to the Higgs boson signal in all selected final states is the largely irreducible Z/γ * → τ τ process. While it is not possible to select a Higgs signal-free Z/γ * → τ τ sample directly from the data, this background is still modelled in a data-driven way, by  choosing a control sample where the expected signal contamination is negligible. In a sample of selected Z/γ * → µµ data events, the muon tracks and associated calorimeter cells are replaced by τ leptons from a simulated Z/γ * → τ τ decay with the same kinematics, where the τ polarisation and spin correlations are modelled with the TAUOLA program and the τ -µ mass difference is taken into account as well. Thus, only the τ decays and the corresponding detector response are taken from the simulation, whereas the underlying event kinematics and all other properties-including pileup effects-are obtained from the data. These embedded data are used to model the shape of the relevant Z/γ * → τ τ background distributions as well as the efficiency for selecting Z/γ * → τ τ events from the preselected sample. The overall normalisation at the preselection level is obtained from simulation.
The procedure is extensively validated: example results for the H → τ lep τ had channel are shown in Figure 1. Systematic effects intrinsic to the method are studied by replacing the muons selected in data by simulated muons instead of τ decays. Figure 1(a) shows a comparison of the E miss T distributions from the selected Z/γ * → µµ events in data before and after this muon embedding, demonstrating that the embedding procedure does not introduce any significant bias to the reconstruction of the event properties. Figure 1(b) compares the MMC mass distributions reconstructed from the τ -embedded Z/γ * → µµ data and simulated Z/γ * → τ τ events after the preselection described in Section 4; good agreement is found and similar studies for the other channels yield the same conclusions.

H → τ lep τ lep
The Z/γ * → τ τ background is modelled using the embedding procedure described above. The contribution from Z/γ * → ℓ + ℓ − is determined by scaling the yields in the Monte Carlo simulation using correction factors obtained by comparing data to simulation in low-and high-E miss T control regions enriched in these backgrounds. The correction factors are obtained separately for Z/γ * → ee and Z/γ * → µµ and for the different analysis categories and are on the order of 10%.
The fake lepton background consists of events that have a reconstructed lepton that did not originate from the decay of a τ lepton or the leptonic decay of a W or Z boson. The normalisation and shape of relevant distributions are obtained from data with a template method using a control region in which the lepton isolation requirement is reversed. The chosen template shape is the p T distribution of the sub-leading lepton. For this method to be applied, it is first verified that the template shapes of the fake lepton distribution in the control and signal regions agree within uncertainties. This is performed at intermediate steps of the event selection where the data sample is dominated by background events and where the number of expected signal events is negligible.
After subtracting the simulated backgrounds, the template shape in a given distribution is obtained from the control region, while the normalisation is obtained from a fit of the distribution of the events in the signal region with the template shape. The uncertainty related to the estimation of backgrounds with fake leptons is calculated from the uncertainty on the subtraction of other processes from Monte Carlo simulation and from the difference in the p T shape of the events in the control region and signal regions. Such systematic uncertainties lie in the range of 30-40%.
The contributions of the tt , single top-quark and electroweak di-boson backgrounds are estimated from simulation. The Monte Carlo description of the top-quark backgrounds has been validated using data by selecting control regions enriched in top-quark background processes. The control regions are defined by inverting the b-jet selection for the H + 2-jet VBF, H +2-jet V H, H +1-jet categories and by inverting the H lep T selection for the H +0-jet category. Table 1 displays the number of events expected and observed in the four categories after all selection criteria including all systematic uncertainties described in Section 7. The estimated combined background contributions are found to give a good description of all quantities relevant to the analysis. As examples, the distributions of the jet multiplicity, E miss T , the invariant mass of the two leading jets and their pseudorapidity difference are shown in Figure 2. Figure 3 displays the invariant mass spectra of the selected events for the four categories.    Data

H → τ lep τ had
In order to estimate the background contributions to the selected H → τ lep τ had candidate events, a control sample in data is obtained by applying the signal selection described in Section 5.2 but now requiring that the light lepton and the τ had candidate have the same charge. This control sample is referred to as the same-sign (SS) sample here, in contrast to the opposite-sign (OS) signal sample. The number of OS background events in the signal region (n bkg OS ) can be expressed as where n all SS is the sum of all SS backgrounds in the signal region and the remaining terms are the differences between the number of OS and SS events for W + jets , Z/γ * → τ τ and other backgrounds, respectively. Due to their large production cross sections, multi-jet processes provide a significant background if quark/gluon jets are misidentified as hadronic τ decays. The ratio of OS to SS events for the multi-jet background (r QCD OS/SS ) is expected to be close to unity and therefore n QCD OS−SS = 0 is assumed. This assumption is validated with a control sample that is dominated by low-p T jets from multi-jet processes. This sample is selected by replacing the requirement E miss T > 20 GeV with E miss T < 15 GeV and removing the isolation criteria of the electron or muon candidate. After subtraction of the other backgrounds using simulation, a value of r QCD OS/SS = 1.10 ± 0.01(stat.) ± 0.09(syst.) is obtained. The observed deviation of r QCD OS/SS from unity is taken into account as a systematic uncertainty for the final result.
The Z/γ * → τ τ contribution is estimated from the τ -embedded Z/γ * → µµ sample in the data, as described previously. For the W +jets background, a significant deviation of the ratio of OS and SS events (r W OS/SS ) from unity is expected since W + jets production is dominated by gu/gd-processes that often give rise to a jet originating from a quark, the charge of which is anti-correlated with the W boson charge. The predicted number of W +jets background events is obtained from the simulation after applying a normalisation correction factor determined from W -dominated data control samples. 6 The remaining contributions n other OS−SS are taken from the simulation. Table 2 displays the number of events expected and observed in the seven categories after the full signal selection, including all systematic uncertainties as described in Section 7. The estimated combined background contributions are found to give a good description of all quantities relevant to the analysis. As examples, the distributions of E miss T , the transverse mass of the lepton-E miss T system as well as the invariant mass of the two leading jets and their pseudorapidity difference are shown in Figure 4. Figure 5 shows the corresponding τ τ invariant mass spectra, where the electron and muon categories have been combined for illustration purposes. The data are found to be consistent with the estimated combined background contributions in both normalisation and shape within the uncertainties. Table 2. Predicted number of signal events (for m H = 120 GeV) and predicted backgrounds obtained as described in the text, together with the observed number of events in data for the H → τ lep τ had categories. The total background yield predicted by the alternative estimation method is given as well for comparison. The listed uncertainties are statistical and systematic, in that order.
Further studies of specific background contributions are performed by estimating the probability to misidentify jets as τ had candidates in the signal region and using data control regions for the background from tt production processes. Results are consistent with the background estimates in Table 2 in both cases.

H → τ had τ had
The dominant backgrounds in the H → τ had τ had channel are Z/γ * → τ τ and multi-jet production. For both, the normalisation and shape of the mass distribution are estimated using data-driven methods.
The normalisation of the Z/γ * → τ τ background is obtained by using collision data events at an early stage of the event selection. This data-driven control sample is defined by requiring that events contain two τ had candidates that pass the hadronic selections including the collinear approximation cuts (0 < x 1,2 < 1 and ∆R(τ τ ) < 2.8). To avoid signal contamination in this control sample, a requirement that m τ τ < 100 GeV is applied; this results in a SM Higgs signal contamination of less than 0.2%. The Z/γ * → τ τ contribution is obtained by fitting the track multiplicity of the two τ candidates simultaneously. The tracks associated to the τ had candidates are counted in the cone defined by ∆R < 0.6, as motivated by the momentum correlation between tracks in τ had candidates [56]. A two-dimensional distribution of the track multiplicities for these two τ candidates is formed, and a track multiplicity fit is performed. The multi-jet template is modelled from the same-sign (SS) candidates in the data while the Z/γ * → τ τ contribution is modelled by the simulation. The less significant backgrounds are estimated from the simulation and subtracted before the fit is performed. The result of the fit is used to normalise the τ -embedded Z/γ * → µµ sample described above, and then this sample is used to model the acceptance of the later cuts and the mass shape in the signal region.
The multi-jet contribution is estimated by the same two-dimensional track multiplicity fitting technique, where the fit is now performed in the signal region. The contribution from di-τ events is allowed to float in the fit, where the shape comes from the simulation. It is assumed that the shape of the two-dimensional track multiplicity in the Z/γ * → τ τ and Higgs boson signal processes are the same.
The systematic uncertainties considered for the background prediction arise from the jet template statistics, alternative multi-jet track multiplicity templates, the presence of non-di-τ background, signal contamination, charge misidentification probability and variations in the pileup conditions. Instead of using the SS events for the multi-jet track template, the alternative multi-jet track multiplicity template is built from events with one additional electron or muon which enhances the contribution of W +jets events, where two jets are misidentified as the hadronic taus. This provides a different mix of quark-and gluon-initiated jets from the inclusive multijet sample, addressing a possible flavour dependence of the track multiplicity distribution.
The mass shape from the multi-jet events is modelled by dropping the opposite-sign and τ had track multiplicity requirements. In order to obtain a data sample that is enriched with the multi-jet background, events are accepted if they are same-sign events or if the sum of the charges of the products of a single τ decay is 0 or ±2. This mass shape model is tested against several other hypothesis obtained, e.g., from pure SS samples or events selected with looser τ identification criteria. Figure 6 shows the kinematic distributions of (a) the ∆R of the two τ candidates, (b) the missing transverse momentum, (c) the collinear mass and (d) the invariant mass of the reconstructed Higgs boson and the leading jet in the H → τ had τ had control region. Table 3 presents the event yields after the full event selection, where the yields are normalised to 4.7 fb −1 . The collinear mass distribution after full selection is presented in Figure 7.  Figure 7. Reconstructed m τ τ of the selected events in the H → τ had τ had channel. Expectations from the Higgs boson signal (m H = 120 GeV) and from backgrounds are given. Results are shown after all selection criteria (see text). For illustration only, the signal contribution has been scaled by a factor given in the legend.

Systematic uncertainties
Systematic uncertainties on the normalisation and shape of the signal and background mass distributions are taken into account. These are treated either as fully correlated or uncorrelated across categories. In the case of partial correlations, the source is separated into correlated and uncorrelated components. The dominant correlated systematic uncertainties are those on the measurement of the integrated luminosity and on the theoretical predictions of the signal production cross sections and decay branching ratios, as well as those related to detector response that impact the analyses through the reconstruction of electrons, muons, hadronic τ decays, jets, E miss T and b-tagging.
Theoretical uncertainties: The Higgs boson cross section, branching ratios and their uncertainties are compiled in Refs. [65,66]. The QCD scale uncertainties on the signal cross sections depend on m H and are of the order of 1% for the VBF and V H production modes and in the range of 8-25% for gg → H depending on jet multiplicity [67,68]. An uncertainty of 4-5% is assumed for the inclusive cross section of the single vector boson and di-boson production mechanisms and a relative uncertainty of 24% is added in quadrature per additional jet. For both tt production and single top-quark production, the QCD scale uncertainties are in the range of 3-6% [69][70][71]. The uncertainties related to the PDF amount to 8% for the predominantly gluon-initiated processes, gg → H and tt , and 4% for the predominantly quark-initiated processes, VBF, V H, single vector boson and di-boson production [72][73][74][75]. The systematic uncertainty arising from the choice of different sets of PDF is included. In addition to the theoretical errors considered in Ref. [66], other effects are taken into account. Uncertainties related to hadronisation effects are estimated by replacing PYTHIA with HER-WIG. Effects due to initial and final state radiation are assessed with PYTHIA samples where the gluon emission is changed according to Ref. [76]. The effect of a different choice of parton shower and underlying event parametrisation yields a total uncertainty of about 10% on the acceptance of the Higgs boson produced via the VBF mechanism in the H+2jet VBF channel.
Detector-related uncertainties: The uncertainty on the integrated luminosity is considered as fully correlated across all analysis categories and amounts to 3.9% [77,78]. The effect of pileup on the signal and background expectations is modelled in the Monte Carlo simulations and the corresponding uncertainty is taken into account.
Appropriate scale factors for the trigger efficiencies of electron, muon and hadronic τ triggers are obtained from data and applied to the Monte Carlo simulations. The associated systematic uncertainties are typically 1-2%. Differences between data and Monte Carlo simulations in the reconstruction and identification efficiencies of τ leptons, electrons and muons are taken into account, as well as the differences in the momentum scales and resolutions.
The systematic uncertainties on the hadronic τ decay identification efficiency are estimated from data samples enriched in W → τ ν and Z/γ * → τ τ events and they are less than 4%. The energy scale uncertainties on the hadronic τ and jets are evaluated based on the single hadron response in the calorimeters [79]. In addition, the τ had energy scale is validated in data samples enriched in Z/γ * → τ τ events. The systematic uncertainties related to the τ and jet energy scale, resolution and b-veto are modelled as functions of η and p T . The jet and τ energy scale and resolution uncertainties are treated as correlated and propagated to the E miss T calculation. Uncertainties associated with the remaining pileup noise and cluster activity in the calorimeters are also considered as independent E miss T uncertainties. The detector-related uncertainties depend on the event topology and are typically small compared to the theoretical uncertainties. The main exceptions are the jet energy scale uncertainty, which reaches up to 12%, and the τ energy scale uncertainty, which is in the range 2-5%.
Background modelling uncertainties: The modelling of the Z/γ * → τ τ background is performed with the data, as described in Section 2. Corresponding uncertainties are obtained by propagating variations of the Z/γ * → µµ event selection and the muon energy subtraction procedure through the τ -embedding procedure. Backgrounds with misreconstructed leptons and τ had candidates are estimated with data and the uncertainty in the estimation lies in the range of 6-40%. The uncertainty takes into account the dependence on the number of jets. The treatment of the other background processes varies across channels and the uncertainties related to the modelling are taken into account as described in Section 6.

Statistical analysis
The statistical analysis of the data employs a binned likelihood function constructed as the product of the likelihood terms for each category. A total of twelve categories are considered from the H → τ lep τ lep , H → τ lep τ had and H → τ had τ had channels. The likelihood in each category is a product over bins in the distributions of the MMC mass, collinear mass or effective mass shown in Figs. 3, 5 and 7.
The expected signal and background, as well as the observed number of events, in each bin of the mass distributions enter in the definition of the likelihood function L(µ, θ). A "signal strength" parameter (µ) multiplies the expected signal in each bin. The signal strength is a free parameter in the fit procedure. The value µ = 0 (µ = 1) corresponds to the absence (presence) of a Higgs boson signal with the SM production cross-section. Signal and background predictions (s and b) depend on systematic uncertainties that are parametrised by nuisance parameters θ, which in turn are constrained using Gaussian functions. The correlation of the systematic uncertainties across categories are taken into account: Gaussian(θ|0, 1). (8.1) The expected signal and background event counts in each bin are functions of θ. The parametrisation is chosen such that the rates in each channel are log-normally distributed for a normally distributed θ. The test statistic q µ is defined as: q µ = −2 ln L(µ,θ µ )/L(μ,θ) , whereμ andθ refer to the global maximum of the likelihood (with the constraint 0 ≤μ ≤ µ) andθ µ corresponds to the conditional maximum likelihood of θ for a given µ. This test statistic is used to compute exclusion limits following the modified frequentist method known as CL s [80]. The asymptotic approximation [81] is used to evaluate the Gaussian probability density functions rather than performing pseudo-experiments and the procedure has been validated using ensemble tests. The profile likelihood formalism used in this statistical analysis incorporates the information on the observed and expected number of events, nuisance parameters, probability density functions and parameters of interest. The statistical significance of an excess is evaluated in terms of the same profile likelihood test statistic. The expected sensitivity and the ±1, 2 σ bands are obtained for the background expectation in the absence of a Standard Model Higgs boson signal. The consistency with the background-only hypothesis is quantified using the p-value, the probability that the test statistic of a background-only experiment fluctuates to at least the observed one.

Results
No significant excess is observed in the data compared to the SM expectation in any of the channels studied here. Exclusion limits at the 95% confidence level, normalised to the Standard Model cross section times the branching ratio of H → τ + τ − (σ SM ), are set as a function of the Higgs boson mass. Figure 8 shows expected and observed limits for the individual channels and for the combined result. The combined expected limits vary between 3.4 and 8.2 times the predicted Standard Model cross section times branching ratio for the mass range 100-150 GeV. The most sensitive categories are the H + 1-jet category in the τ had τ had channel, the H +2-jet VBF category in the τ lep τ had channel and the H +2-jet VBF category in the τ lep τ lep channel. The observed limits are in the range between 2.9 and 11.7 times the predicted Standard Model cross section times branching ratio for the same mass range. The most significant deviation from the background-only hypothesis is observed in the combined limit for m H = 150 GeV with a local p-value of 10%, corresponding to a significance of 1.3 σ.

Conclusions
A search for a Higgs boson decaying in the H → τ τ channel has been performed with the ATLAS detector at the Large Hadron Collider. It uses the full 2011 data sample of 4.7 fb −1 collected at a centre-of-mass energy of 7 TeV. The H → τ lep τ lep , H → τ lep τ had and H → τ had τ had decays are considered in this search. No significant excess is observed in the mass range of 100-150 GeV. The observed (expected) upper limits on the cross section times the branching ratio of H → τ τ are between 2.9 (3.4) and 11.7 (8.2) times the SM prediction. These limits are similar to results recently reported by the CMS experiment [82].  The ATLAS Collaboration