Cross-section measurements of the Higgs boson decaying into a pair of τ -leptons in proton-proton collisions at ﬃﬃ s p = 13 TeV with the ATLAS detector

A measurement of production cross sections of the Higgs boson in proton-proton collisions is presented in the H → ττ decay channel. The analysis is performed using 36 . 1 fb − 1 of data recorded by the ATLAS experiment at the Large Hadron Collider at a center-of-mass energy of ﬃﬃﬃ s p ¼ 13 TeV. All combinations of leptonic ( τ → l v ¯ v with l ¼ e; μ ) and hadronic ( τ → hadrons v ) τ decays are considered. The H → ττ signal over the expected background from other Standard Model processes is established with an observed (expected) significance of 4.4 (4.1) standard deviations. Combined with results obtained using data taken at 7 and 8 TeV center-of-mass energies, the observed (expected) significance amounts to 6.4 (5.4) standard deviations and constitutes an observation of H → ττ decays. Using the data taken at ﬃﬃﬃ s p ¼ 13 TeV, the total cross section in the H → ττ decay channel is measured to be 3 . 77 þ 0 . 60 − 0 . 59 ð stat Þ þ 0 . 87 − 0 . 74 ð syst Þ pb, for a Higgs boson of mass 125 GeV assuming the relative contributions of its production modes as predicted by the Standard Model. Total cross sections in the H → ττ decay channel are determined separately for vector-boson-fusion production and gluon-gluon-fusion production to be σ VBF H → ττ ¼ 0 . 28 (cid:2) 0 . 09 ð stat Þ þ 0 . 11 − 0 . 09 ð syst Þ pb and σ gg F H → ττ ¼ 3 . 1 (cid:2) 1 . 0 ð stat Þ þ 1 . 6 − 1 . 3 ð syst Þ pb, respectively. Similarly, results of a fit are reported in the framework of simplified template cross sections. All measurements are in agreement with Standard Model expectations.

The coupling of the Higgs boson to the fermionic sector has been established with the observation of the H → ττ decay mode with a signal significance of 5.5σ from a combination of ATLAS and CMS results [15][16][17] using LHC Run-1 data. A measurement performed by the CMS Collaboration with Run-2 data at ffiffi ffi s p ¼ 13 TeV reached a significance of 4.9σ using 35.9 fb −1 of integrated luminosity and 5.9σ combined with data from Run 1 [18]. While the Higgs-boson coupling to other fermions such as top quarks [19,20] and bottom quarks [21,22] have been observed, only upper limits exist on its coupling to muons [23,24] and the H → ττ decay mode has been the only accessible leptonic decay mode. It was also used to constrain CP violation in the production via vector-boson fusion (VBF) [25] and is unique in that it provides sensitivity to CP violation in the Higgs-boson coupling to leptons [26]. This paper presents cross-section times branchingfraction measurements of Higgs bosons that decay into a pair of τ-leptons in proton-proton (pp) collisions at ffiffi ffi s p ¼ 13 TeV using data collected by the ATLAS experiment in 2015 and 2016, corresponding to an integrated luminosity of 36.1 fb −1 . All combinations of leptonic (τ → lvv with l ¼ e; μ) and hadronic (τ → hadrons v) τ decays are considered. 1 The corresponding three analysis channels are denoted by τ lep τ lep , τ lep τ had and τ had τ had and are composed of different dominant backgrounds. While Z → ττ is a dominant background in all channels, the relative contributions from other backgrounds from top-quark and other vectorboson decays, as well as from misidentified leptonic or hadronic τ decays, vary considerably between the channels. Two analysis categories are defined that are predominantly sensitive to Higgs bosons produced via VBF and gluongluon fusion (ggF). A maximum-likelihood fit is performed on data using distributions of the reconstructed di-τ mass in signal regions (SRs), simultaneously with event yields from control regions (CRs) that are included to constrain normalizations of major backgrounds estimated from simulation. The dominant and irreducible Z → ττ background is estimated from simulation. This is different from the search for H → ττ decays in Run 1 [15], which used the embedding technique [27]. A reliable modeling of this background is therefore of crucial importance for this analysis. Validation regions (VRs) based on Z → ll events are studied, but not included in the fit, to verify as precisely as possible the modeling of the Z → ττ background. The paper is organized as follows. Section II describes the ATLAS detector. This is followed in Sec. III by a description of the data set and Monte Carlo (MC) simulated samples employed by this measurement. Section IV details the reconstruction of particles and jets. The event selection for each channel and event category as well as signal, control and validation regions are discussed in Sec. V. Background estimation techniques and the systematic uncertainties of the analysis are described in Secs. VI and VII, respectively. The signal extraction procedure and the results of the Higgs cross-section measurements in the H → ττ decay mode are presented in Sec. VIII. Section IX gives the conclusions.

II. THE ATLAS DETECTOR
The ATLAS experiment [28] at the LHC is a multipurpose particle detector with a forward-backward symmetric cylindrical geometry and a near-4π coverage in solid angle. 2 It consists of an inner tracking detector surrounded by a thin superconducting solenoid, electromagnetic and hadron calorimeters, and a muon spectrometer. The inner tracking detector covers the pseudorapidity range jηj < 2.5. It consists of a silicon pixel detector, which has an additional innermost layer (positioned at a radial distance of 3.3 cm from the beam line) that was installed after Run 1 [29,30], and a silicon microstrip detector surrounding the pixel detector, both covering jηj < 2.5, followed by a transition radiation straw-tube tracker covering jηj < 2. The inner tracking detector is immersed in a 2 T axial magnetic field provided by the solenoid. Lead/liquid-argon (LAr) sampling calorimeters provide electromagnetic (EM) energy measurements with high granularity. A hadron (steel/scintillator-tile) calorimeter covers the central pseudorapidity range (jηj < 1.7). The end-cap and forward regions are instrumented with LAr calorimeters for both the EM and hadronic energy measurements up to jηj ¼ 4.9. The muon spectrometer surrounds the calorimeters and is based on three large air-core toroidal superconducting magnets with eight coils each. The field integral of the toroids ranges between 2.0 and 6.0 T m across most of the detector. The muon spectrometer includes a system of precision tracking chambers and fast detectors for triggering.
Events are selected using a two-level trigger system. The first-level trigger is implemented in hardware and uses a subset of the detector information to filter events that are then processed by a software-based high-level trigger. This further reduces the average recorded collision rate to approximately 1 kHz.

III. DATA AND SIMULATION SAMPLES
The data used in this analysis were taken from pp collisions at the LHC where proton bunches are collided every 25 ns at ffiffi ffi s p ¼ 13 TeV. A combination of several triggers for single light leptons, two light leptons and two hadronically decaying τ-leptons were used to record the data for the analysis, depending on the analysis channel (see Sec. VA). After data quality requirements, the samples used for this measurement consist of 3.2 fb −1 of data recorded in 2015, with an average of 14 interactions per bunch crossing, and 32.9 fb −1 recorded in 2016, with an average of 25 interactions per bunch crossing.
Samples of signal and background processes were simulated using various MC generators as summarized in Table I. The signal contributions considered include the following four processes for Higgs-boson production at the LHC: ggF, VBF and associated production of a Higgs boson with a vector boson (VH) or with a top-antitop quark pair (ttH) where all decay modes for the H → ττ process are included. Other Higgs production processes such as associated production with a bottom-antibottom quark pair and with a single top quark are found to be negligible. Higgs decays into WW are considered background and simulated similarly for these production processes. The mass of the Higgs boson was assumed to be 125 GeV [31].
Higgs production by ggF was simulated with the POWHEG-BOX v2 [32][33][34][35] NNLOPS program [36] at next-to-leading-order (NLO) accuracy in quantum chromodynamics (QCD) using the MiNLO approach [37], and reweighted to next-to-next-to-leading order (NNLO) in QCD in the Higgs rapidity. The VBF and VH production 2 The ATLAS Collaboration 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 upwards. Cylindrical coordinates ðr; ϕÞ are used in the transverse plane, ϕ being the azimuthal angle around the z axis. The pseudorapidity is defined in terms of the polar angle θ as η ¼ − ln tanðθ=2Þ. Angular distance is measured in units of ΔR ≡ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi ðΔηÞ 2 þ ðΔϕÞ 2 p .
processes were simulated at NLO accuracy in QCD using POWHEG-BOX with the MiNLO approach. The ttH production process was simulated with MADGRAPH5_aMC@NLO v2.2.2 [38] at NLO accuracy in QCD. For these signal samples, the simulation was interfaced to the PYTHIA 8.212 [39] model of parton showering, hadronization and underlying event (UEPS). To estimate the impact of UEPS uncertainties, the ggF, VBF and VH samples were also simulated with the HERWIG 7.0.3 [40,41] UEPS model. The PDF4LHC15 [42] parametrization of the parton distribution functions (PDFs) was used for these production processes.
The AZNLO [43] set of tuned parameters was used, with the CTEQ6L1 [44] PDF set, for the modeling of nonperturbative effects. For the ttH production process the NNPDF30LO [45] PDF parametrization was used in the matrix element and the NNPDF23LO [46] PDF parametrization for the UEPS model with the A14 [47] set of tuned parameters for the modeling of nonperturbative effects. PHOTOS++ version 3.52 [48] was used for QED emissions from electroweak (EW) vertices and charged leptons. The overall normalization of the ggF process is taken from a next-to-next-to-next-to-leading-order (N 3 LO) QCD calculation with NLO EW corrections included [49][50][51][52]. Production by VBF is normalized to an approximate-NNLO QCD cross section with NLO EW corrections included [53][54][55]. The VH samples are normalized to cross sections calculated at NNLO in QCD, with NLO EW corrections included [56][57][58]. The ttH process is normalized to a cross section calculated at NLO in QCD with NLO EW corrections applied [59][60][61][62][63][64].
Background samples of EW production of W=Z bosons from VBF, W=Z-boson production with associated jets and diboson production processes were simulated with the SHERPA 2.2.1 [65] generator. Matrix elements were calculated using the Comix [66] and OpenLoops [67] matrixelement generators and merged with the SHERPA UEPS model [68] using the ME+PS@NLO prescription [69]. For W and Z production with associated jets the matrix elements were calculated for up to two partons at NLO and four partons at LO precision. Their inclusive cross sections are normalized to NNLO calculations from FEWZ [70,71].
In particular, the dominant Z → ττ background is estimated using these simulations of Z-boson production. For diboson production, the matrix elements were calculated for up to one additional parton at NLO and up to three additional partons at LO precision. For all samples the NNPDF30NNLO [45] PDF set was used together with the SHERPA UEPS model.
The impact of UEPS uncertainties, and other modeling uncertainties such as LO/NLO precision comparison for leading jets, on the main background from Z → ττ is studied in an alternative sample which was simulated using MADGRAPH5_aMC@NLO 2.2.2 [38] at leading order interfaced to the PYTHIA 8.186 UEPS model. The A14 set of tuned parameters [47] was used together with the NNPDF23LO PDF set [46].
For the generation of tt production, the POWHEG-BOX v2 [32][33][34]72] generator with the CT10 PDF sets in the matrix element calculations was used. The predicted tt cross section was calculated with the TOP++2.0 program to NNLO in perturbative QCD, including soft-gluon resummation to next-to-next-to-leading-log order [73]. Single topquark production of Wt was simulated using the POWHEG-BOX v1 [74,75] generator. This generator uses the fourflavor scheme for the NLO matrix-element calculations together with the fixed four-flavor PDF set CT10F4. For all top-quark production processes, top-quark spin correlations were preserved, using MadSpin [76] for the t-channel. The parton shower, hadronization, and the underlying event were simulated using PYTHIA 6.428 [77] with the CTEQ6L1 PDF set and the corresponding Perugia 2012 set of tuned parameters [78]. The top mass was assumed to be 172.5 GeV. The EvtGen v.1.2.0 program [79] was used for the properties of b-and c-hadron decays.
For all samples, a full simulation of the ATLAS detector response [80] using the GEANT4 program [81] was performed. The effect of multiple pp interactions in the same and neighboring bunch crossings (pileup) was included by overlaying minimum-bias events simulated with PYTHIA 8.186 using the MSTW2008LO PDF [82] and the A2 [83] set of tuned parameters on each generated signal and background event. The number of overlaid events was TABLE I. Monte Carlo generators used to describe all signal and background processes together with the corresponding PDF set and the model of parton showering, hadronization and underlying event (UEPS). In addition, the order of the total cross-section calculation is given. The total cross section for VBF production is calculated at approximate-NNLO QCD. More details are given in the text. chosen such that the distribution of the average number of interactions per pp bunch crossing in the simulation matches that observed in data.

IV. OBJECT RECONSTRUCTION
Electron candidates are reconstructed from energy deposits in the electromagnetic calorimeter associated with a charged-particle track measured in the inner detector. The electron candidates are required to pass the "loose" likelihood-based identification selection of Refs. [84,85], to have transverse momentum p T > 15 GeV and to be in the fiducial volume of the inner detector, jηj < 2.47. The transition region between the barrel and end-cap calorimeters (1.37 < jηj < 1.52) is excluded. The trigger efficiency for single electrons selected in the analysis ranges between 90% and 95% [86]. Electron candidates are ignored if they share their reconstructed track with a muon candidate defined below or if their angular distance from a jet is within 0.2 < ΔR < 0.4.
Muon candidates are constructed by matching an inner detector track with a track reconstructed in the muon spectrometer [87]. The muon candidates are required to have p T > 10 GeV and jηj < 2.5 and to pass the "loose" muon identification requirements of Ref. [87]. The trigger efficiency for single muons selected in the analysis is close to 80% (70%) in the barrel in the 2016 (2015) data set and 90% in the end caps [86]. Muon candidates are ignored if their angular distance from a jet is ΔR < 0.4 with the following exceptions: If ΔR < 0.2 or the muon track is associated with the jet, and if the jet has either less than three tracks or less than twice the transverse momentum of the muon candidate, the jet is removed instead. This recovers efficiency for muons that radiate a hard bremsstrahlung photon in the calorimeter.
In the τ lep τ lep and τ lep τ had signal regions, events are selected only if the selected electron and muon candidates satisfy their respective "medium" identification criteria. The reconstruction and identification efficiency for muons with the "medium" identification requirement has been measured in Z → μμ events [87]. It is well above 98% over the full phase space, except for jηj < 0.1 where the reconstruction efficiency is about 70%. The combined identification and reconstruction efficiency for "medium" electrons ranges from 80% to 90% in the p T range of 10 GeV to 80 GeV as measured in Z → ee events [85]. In addition, the electrons and muons must satisfy the "gradient" isolation criterion, which requires that there are no additional high-p T tracks in a cone around the track and no significant energy deposits in a cone around the calorimeter clusters of the object after correcting for pileup. The size of the respective cones depends on the p T of the light lepton. This isolation requirement rejects about 10% of light leptons for low p T and less than 1% for p T > 60 GeV [85,87].
Jets are reconstructed from topological clusters in the calorimeter using the anti-k t algorithm [88,89], with a radius parameter value R ¼ 0.4, and have p T > 20 GeV and jηj < 4.9. To reject jets from pileup, a "Jet Vertex Tagger" (JVT) [90] algorithm is used for jets with p T < 50 GeV and jηj < 2.4. It employs a multivariate technique that relies on jet-tracking and calorimeter-cluster-shape variables to determine the likelihood that the jet originates from pileup. Similarly, pileup jets in the forward region are suppressed with a forward JVT [91] algorithm, relying in this case only on calorimeter-cluster-shape variables, which is applied to all jets with p T < 50 GeV and jηj > 2.5. In the pseudorapidity range jηj < 2.5, b-jets are selected using a multivariate algorithm [92,93]. A working point is chosen that corresponds to an efficiency of approximately 85% for b-jets and rejection factors of 2.8 and 28 for c-jets and lightflavor jets, respectively, in simulated tt events. A jet is ignored if it is within ΔR ¼ 0.2 of an electron or hadronically decaying τ candidate.
Leptonic τ decays are reconstructed as electrons and muons. The reconstruction of the visible decay products of hadronic τ decays (τ had-vis ) [94] starts with a reconstructed jet that has p T > 10 GeV and jηj < 2.5. As in the case of electron reconstruction the transition region between the barrel and end-cap calorimeters is excluded. To discriminate τ had-vis from jets initiated by light-quarks or gluons, an identification algorithm using multivariate techniques is applied to τ had-vis candidates. They have to pass the "loose" identification requirement of Ref. [94]. In addition, the τ had-vis candidates are required to have p T > 20 GeV, to have one or three associated tracks and an absolute electric charge of one. Their energy is reconstructed by multivariate regression techniques using information about the associated tracks and calorimeter clusters, as well as the average number of collisions recorded. The trigger efficiency per τ had-vis selected in the analysis is 95% and 85% for 1-prong and 3-prong τ-leptons, respectively [95]. The τ had-vis candidates are ignored if they are within ΔR ¼ 0.2 of a muon or electron candidate or if they have a high likelihood score of being an electron [85]. The requirement on the likelihood score corresponds to a τ had-vis efficiency measured in Z → ττ decays of 95% [94].
In the τ lep τ had signal regions, events are selected only if the τ had-vis candidate passes the "medium" identification requirement, corresponding to an efficiency of 55% and 40% for real 1-prong and 3-prong τ had-vis , respectively [94]. In addition, if a 1-prong τ had-vis candidate and an electron candidate are selected, a dedicated multivariate algorithm to reject electrons misidentified as τ had-vis is applied to suppress Z → ee events. In the τ had τ had signal regions, both selected τ had-vis candidates have to fulfill the "tight" identification requirement, which corresponds to a selection efficiency of 45% for real 1-prong τ had-vis and 30% for real 3-prong τ had-vis [94].
The missing transverse momentum vector is calculated as the negative vectorial sum of the p T of the fully calibrated and reconstructed physics objects [96]. This procedure includes a soft term, which is calculated from the inner detector tracks that originate from the vertex associated with the hard-scattering process and that are not associated with any of the reconstructed objects. The missing transverse momentum (E miss T ) is defined as the magnitude of this vector.
The Higgs-boson candidate is reconstructed from the visible decay products of the τ-leptons and from the E miss T , which is assumed to originate from the final-state neutrinos. The di-τ invariant mass (m MMC ττ ) is determined using the missing-mass calculator (MMC) [97]. The standard deviation of the reconstructed di-τ mass is 17.0, 15.3 and 14.7 GeV for signal events selected in the τ lep τ lep , τ lep τ had and τ had τ had channels, respectively. The p T of the Higgs-boson candidate (p ττ T ) is computed as the vector sum of the transverse momenta of the visible decay products of the τ-leptons and the missing transverse momentum vector.

V. EVENT SELECTION AND CATEGORIZATION
In addition to data quality criteria that ensure that the detector was functioning properly, events are rejected if they contain reconstructed jets associated with energy deposits that can arise from hardware problems, beamhalo events or cosmic-ray showers. Furthermore, events are required to have at least one reconstructed primary vertex with at least two associated tracks with p T > 0.5 GeV, which rejects noncollision events originating from cosmic rays or beam-halo events. The primary vertex is chosen as the pp vertex candidate with the highest sum of the squared transverse momenta of all associated tracks.
The triggers and event selection for the three analysis channels are described in Sec. VA. Selected events are categorized into exclusive signal regions, with enhanced signal-to-background ratios. In addition, control regions are defined where a specific background is dominant, and thus a CR facilitates the adjustment of the simulated prediction of a background contribution to match the observed data. The signal and control regions are included in the fit described in Sec. VIII. They are described in Sec. V B together with validation regions (VRs) used to validate the simulation of the dominant Z þ jets background.

A. Event selection
Depending on the trigger, transverse momentum requirements are applied to selected electron, muon, and τ had-vis candidates. They are summarized in Table II and their perobject efficiencies are given in Sec. IV. Due to the increasing luminosity and the different pileup conditions, the p T thresholds of the triggers were increased during data-taking in 2016, which is taken into account in the p T requirements of the event selection. In the τ lep τ lep channel, the triggers for multiple light leptons are used only if the highest-p T light lepton does not pass the corresponding single-light-lepton trigger p T requirement. This ensures that each trigger selects an exclusive set of events.
All channels require the exact number of identified "loose" leptons, i.e., electrons, muons and τ had-vis , as defined in Sec. IV, corresponding to their respective final state. Events with additional "loose" leptons are rejected. The two leptons are required to be of opposite charge and they have to fulfill the p T requirements of the respective trigger shown in Table II. The selected τ had-vis in the τ lep τ had channel is required to have p T > 30 GeV.
The event selection for the three analysis channels is summarized in Table III. Only events with E miss T > 20 GeV are selected to reject events without neutrinos. In the τ lep τ lep channel with two same-flavor (SF) light leptons this requirement is further tightened to suppress the large Z → ll background. For the same reason, requirements are tightened on the invariant mass of two light leptons (m ll ) and a requirement is introduced on the E miss T calculated only from the physics objects without the soft track term (E miss;hard T ). Requirements on the angular distance between the visible decay products of the two selected τ-lepton decays (ΔR ττ ) and their pseudorapidity difference (jΔη ττ j) are applied in all channels to reject nonresonant background events. Requirements are applied to the fractions of the τ-lepton momenta carried by each visible decay product where p vis i and p miss i are the visible and missing momenta of the ith τ lepton, ordered in descending p T , calculated in the collinear approximation [98], to suppress events with E miss T that is incompatible with a di-τ decay. Low transverse mass (m T ), calculated from E miss T and the momentum of the selected light lepton, is required in the τ lep τ had channel to reject events with leptonic W decays. A requirement on the di-τ mass calculated in the collinear approximation (m coll ττ ) of m coll ττ > m Z − 25 GeV is introduced in the τ lep τ lep channel to suppress events from Z → ll and to ensure orthogonality between this TABLE II. Summary of the triggers used to select events for the three analysis channels during 2015 and 2016 data-taking and the corresponding p T requirements applied in the analysis. For the electron þ muon trigger the first number corresponds to the electron p T requirement, the second to the muon p T requirement. For the τ had τ had channel, at least one high-p T jet in addition to the two τ had-vis candidates is required for the 2016 data set (see Sec. VA). measurement and the measurement of H → WW Ã → lνlν [99], which has a similar final state. All channels require at least one jet (j 1 ) with p j 1 T > 40 GeV to select Higgs bosons produced by VBF and to suppress background from Z → ττ events when selecting Higgs bosons produced through ggF. Since 2016 the diτ had-vis first-level trigger requires a jet with p T > 25 GeV calibrated at trigger level with jηj < 3.2 in addition to the two τ had-vis candidates. In the τ had τ had channel the jet p T requirement is thus raised to p j 1 T > 70 GeV to achieve uniform trigger selection efficiency as a function of p j 1 T . The trigger efficiency for the additional jet ranges from 95% to 100% for these requirements. In the τ lep τ lep and τ lep τ had channels, the top-quark background is suppressed by requiring that no jet with p T > 25 GeV is tagged as a b-jet.

B. Signal, control and validation regions
To exploit signal-sensitive event topologies, a "VBF" and a "boosted" analysis category are defined without any overlap in phase space. The VBF category targets events with a Higgs boson produced by VBF and is characterized by the presence of a second high-p T jet (p j 2 T > 30 GeV). In addition, the two jets are required to be in opposite hemispheres of the detector with a large pseudorapidity separation of jΔη jj j > 3 and their invariant mass (m jj ) is required to be larger than 400 GeV. The selected leptons are required to have η-values that lie between those of the two jets ("central leptons"). Although this category is dominated by VBF production, it also includes significant contributions from ggF production, amounting to up to 30% of the total expected Higgs-boson signal.
The boosted category targets events with Higgs bosons produced through ggF with additional recoiling jets, which is motivated by the harder p T -spectrum of the H → ττ signal compared to the dominant background from Z → ττ. It contains all events with p ττ T > 100 GeV that do not pass the VBF selection. In addition to events from ggF, the boosted categories contain sizable contributions from VBF and VH production of 10-20% of the expected signal. Events that pass the event selection, detailed in Table III, but do not fall into the VBF or boosted categories, are not used in the analysis.
Using p ττ T , ΔR ττ and m jj , the VBF and boosted categories, referred to as "inclusive" categories, are split further into 13 exclusive signal regions with different signal-to-background ratios to improve the sensitivity. Table IV summarizes the analysis categories and signal region definitions. Figure 1 illustrates the expected signal and background composition in the signal and control regions of all analysis channels. Figure 2 compares for each analysis channel the observed distributions with predictions, as resulting from the fit described in Sec. VIII, for p ττ T in the boosted inclusive categories, and for m jj in the VBF inclusive categories. The observed data agree within the given uncertainties with the background expectation described in Sec. VI for all distributions.
Six control regions are defined to constrain the normalization of the dominant backgrounds in regions of phase III. Summary of the event selection requirements for the three analysis channels that are applied in addition to the respective lepton p T requirements listed in Table II. E miss;hard T is an alternative E miss T calculated only from the physics objects without the soft-track term. The transverse mass (m T ) is calculated from E miss T and the momentum of the selected light lepton. The visible momentum fractions x 1 and x 2 of the respective τ-lepton and the collinear di-τ mass (m coll ττ ) are calculated in the collinear approximation [98].
space where their purity is high. Their definitions are summarized in Table V. Two Z → ll CRs, which are both more than 90% pure in Z → ll events, are defined by applying the same selection as for the SF τ lep τ lep VBF and boosted inclusive regions, respectively, but with the m ll requirement modified to 80 < m ll < 100 GeV. The   TABLE IV. Definition of the VBF and boosted analysis categories and of their respective signal regions (SRs). The selection criteria, which are applied in addition to those described in Table III, are listed for each channel. The VBF high-p ττ T SR is only defined for the τ had τ had channel, resulting in a total of seven VBF SRs and six boosted SRs. All SRs are exclusive and their yields add up to those of the corresponding VBF and boosted inclusive regions.

Signal region
Inclusive Comparisons between data and predictions as computed by the fit of (top) the p T of the Higgs-boson candidate (p ττ T ) in the boosted inclusive category and (bottom) the invariant mass of the two highest-p T jets (m jj ) in the VBF inclusive category for (left) the τ lep τ lep channel, (center) the τ lep τ had channel and (right) the τ had τ had channel. The ratios of the data to the background model are shown in the lower panels. The observed Higgs-boson signal (μ ¼ 1.09) is shown with the solid red line. Entries with values that would exceed the x-axis range are shown in the last bin of each distribution. The size of the combined statistical, experimental and theoretical uncertainties in the background is indicated by the hatched bands. TABLE V. Definitions of the six control regions (CRs) used to constrain the Z → ll and top backgrounds to the event yield in data in the τ lep τ lep and τ lep τ had channels. "SF" denotes a selection of same-flavor light leptons.

Region
Selection and about 60% in the boosted top CR. No such control regions are defined for the τ had τ had channel since the top and Z → ll backgrounds are negligible in this case. One validation region is defined for each signal region ("Z → ττ VRs") to validate the event yields and kinematic distributions of simulated Z → ττ events. The Z → ττ VRs are composed of Z → ll events with kinematics similar to the Z → ττ background in the respective signal regions. This is achieved by starting with an event selection that is based on the SF τ lep τ lep channel preselection with the following differences that account for the selection of light leptons instead of decay products from τ-leptons: The m coll ττ , E miss T and E miss;hard T requirements are dropped and the m ll requirement is inverted to m ll > 80 GeV. The other requirements on τ-lepton decays are replaced with requirements on the two light leptons. In particular, the requirements on p ττ T are substituted by the p T of the Z boson computed from the p T of the light leptons (p ll T ). Requirements on jets are unchanged since they define the shape of most kinematic distributions for Z-boson production similarly in the SRs and the Z → ττ VRs. More than 99% of the selected events are from Z → ll in all Z → ττ VRs.

VI. BACKGROUND ESTIMATION
The final-state topologies of the three analysis channels have different background compositions, which necessitates different strategies for the background estimation. In each SR, the expected number of background events and the associated kinematic distributions are derived from a mixture of data-driven methods and simulation.
Background contributions with τ had-vis , with prompt light leptons and with light leptons from τ-lepton decays are estimated from simulation. If their contribution is significant, their normalization is constrained by the observed event yields in CRs. For smaller contributions of this type, their normalization is entirely taken from the theoretical cross sections with the precision in QCD listed in Table I. This includes di-boson processes and a small contribution from EW production of W=Z bosons from VBF. Contributions from light-and heavy-flavor jets that are misidentified as prompt, light leptons or τ had-vis are estimated using data-driven methods. They are labeled as "fake-l" and "fake-τ had-vis " backgrounds, respectively, and collectively as "misidentified τ", throughout this paper. The contamination from H → WW Ã decays is treated as a background in the τ lep τ lep channel, while it is negligible in other channels.
For the background sources that have their normalization constrained using data, Table VI shows the normalization factors and their uncertainties obtained from the fit (see Sec. VIII). For simulated backgrounds, the factors compare the background normalizations with values determined from their theoretical cross sections. The normalization factor for the data-driven fake-τ had-vis background scales the event yield of the template of events that fail the oppositecharge requirement (see Sec. VI D). The Z → ττ normalization is constrained by data in the m MMC ττ distributions of the signal regions. Systematic uncertainties are the dominant contribution to the normalization factor uncertainties.

A. Z → ττ background validation
The Drell-Yan process pp → Z=γ Ã → ττ is a dominant irreducible background in all analysis categories and contributes between 50% and 90% of the total background depending on the signal region. The separation between the Drell-Yan and the H → ττ signal processes is limited by the m MMC ττ resolution. The modeling of this important background is validated using Z → ττ VRs that consist of Z → ll events. In Fig. 3, the observed distributions of several variables are compared with simulation normalized to the event yield in data. The selected observables correspond to either variables correlated with m MMC ττ (p l 1 T and p l 2 T ), or to major variables used for categorization (p ll T , ΔR ll , Δη jj and m jj ), or to variables to which different requirements are applied in each decay channel (p j 1 T ). Generally, the SHERPA simulation describes the shape of data distributions within the experimental and theoretical uncertainties (see Sec. VII), with the exception of a slight trend in the ratio of data to simulation as a function of Δη jj and m jj shown in Fig. 3. These trends have no impact on the modeling of m MMC ττ . Reweighting the simulation with the observed m jj distribution, which is an important variable for VBF categorization, has a negligible impact on the measurement. In the fit, the normalization of the Z → ττ background is correlated across the decay channels and constrained by data in the m MMC ττ distributions of the signal regions associated with the boosted and VBF  T ); (f) the angular distance between the light leptons (ΔR ll ); (h) the p T of the highest-p T light lepton (p l 1 T ); and (i) the p T of the second-highest-p T light lepton (p l 2 T ). The predictions in these validation regions are not computed by the fit, but are simply normalized to the event yield in data. The size of the combined statistical, experimental and theoretical uncertainties is indicated by the hatched bands. The ratios of the data to the background model are shown in the lower panels together with the theoretical uncertainties in the SHERPA simulation of Z → ll, which are indicated by the blue lines. categories, independently. As shown in Table VI, it is constrained to AE5% in the boosted category and to AE9% in the VBF category. The relative acceptance of events among the signal regions within a category is validated by applying the corresponding event-selection criteria to the Z → ττ VRs. The expected relative acceptance from simulation agrees with data within uncertainties for all regions. Figures 8 and 9 show the good modeling of the Z → ττ m MMC ττ distribution in all signal regions. Additional uncertainties in the relative acceptances and in the shape of the m MMC ττ distributions in the signal regions are evaluated from theoretical and experimental uncertainties described in Sec. VII.

B. Z → ll background
Decays of Z bosons into light leptons are a significant background for the τ lep τ lep and τ lep τ had channels, where mismeasured E miss T can bias the reconstructed m MMC ττ of light-lepton pairs towards values similar to those expected for the signal. The observed event yields in the Z → llCRs constrain the normalization of simulated Z → ll events in the τ lep τ lep channel to AE40% in the VBF category and to AE25% in the boosted category, as shown in Table VI. The good modeling of the m MMC ττ distribution in the τ lep τ lep VBF Z → ll CR is shown in Fig. 4(a). In other channels, the contribution from Z → ll events is normalized to its theoretical cross section. In the τ lep τ had channel, Z → ll background contributes primarily through Z → ee decays where an electron is misidentified as a τ had-vis candidate. Due to the dedicated electron veto algorithm applied to selected 1-prong τ had-vis candidates (see Sec. VA), this background is small. This and other backgrounds from light leptons misidentified as τ had-vis in this channel are estimated from simulation, with the probability for electrons misidentified as τ had-vis candidates scaled to match that observed in data [94].

C. Top-quark background
The production of tt pairs or single top quarks is a significant background ("top background") for the τ lep τ lep and τ lep τ had channels, due to the production of prompt light leptons with associated E miss T in the top-quark decay chain t → Wb, W → lν; τν. Events where a selected τ-lepton decay product is misidentified, are estimated using datadriven methods that are discussed in Sec. VI D. The remaining top background is estimated from simulation. In the τ lep τ lep and τ lep τ had channels the normalization of simulated top background is additionally constrained by the absolute event yields in their respective top CRs to AE30% in the τ lep τ had VBF top CR and less than AE10% in the other top CRs, as shown in Table VI

D. Backgrounds from misidentified τ
Apart from the small contribution from light leptons misidentified as τ had-vis described in Sec. VI B, hadronic jets can be misidentified as τ had-vis , electrons and muons. These sources of background contribute up to half of the total background, depending on the signal region, and are estimated with data-driven techniques. Since the background sources depend on the event topology, specific methods are applied to each individual channel.
In the τ lep τ lep channel, the main sources of the fake-l background are multijets, W bosons in association with jets, and semileptonically decaying tt events. All these background sources are treated together. Fake-l regions are defined in data by requiring that the light lepton with the  second-highest p T does not satisfy the "gradient" isolation criterion. This is referred to as "inverted" isolation. In addition, if the light lepton is an electron, its identification criteria are relaxed to "loose." Fake-l templates are created from these samples by subtracting top and Z → ll backgrounds that produce real light leptons, estimated from simulation. The normalization of each template is then scaled by a factor that corrects for the inverted-isolation requirement. These correction factors are computed for each combination of lepton flavor from events that pass the τ lep τ lep selection but have same-charge light leptons, subtracting simulated top and Z → ll backgrounds. Fake-l background in the top-quark CRs is estimated following the same procedure.
Systematic uncertainties in the shape and normalization of the fake-l background in the τ lep τ lep channel depend on the p T of the second-highest-p T lepton and are estimated as follows. A closure test of the background estimate is performed using events where the leptons are required to have the same charge and yields an uncertainty ranging between 20% and 65%. An uncertainty in the heavy-flavor content is estimated by using isolation correction factors that are computed from samples selected with inverted b-jet requirements. This uncertainty is as large as 50%. Minor contributions come from the uncertainty in the fractional composition of the fake-l background in top-quark decays, multijet events and W-boson production.
In the τ lep τ had channel, a "fake-factor" method is used to derive estimates for fake-τ had-vis events, composed mainly of multijet events and W-boson production in association with jets. A fake-factor is defined as the ratio of the number of events where the highest-p T jet is identified as a "medium" τ had-vis candidate to the number of events with a highest-p T jet that passes a very loose τ had-vis identification but fails the "medium" one. Fake-factors depend on the p T and track multiplicity of the τ had-vis candidate and on the type of parton initiating the jet. Therefore, they are computed depending on the p T and the track multiplicity, in both quark-jet-dominated "W-enhanced" and gluon-jetdominated "multijet-enhanced" regions. The W-enhanced regions are defined by inverting the m T < 70 GeV requirement and the multijet-enhanced regions are defined by inverting the light-lepton isolation, relative to the inclusive boosted and VBF selections. Backgrounds from Z-boson production with associated jets and semileptonically decaying tt have fake-factors similar to those found in backgrounds from W bosons, and their contributions are negligible. The fake-factors are in the range 0.15-0.25 for 1-prong and 0.01-0.04 for 3-prong τ had-vis . To obtain the fake-τ had-vis background estimate for the signal regions, these fake-factors are first weighted by the multijets-to-W fraction. The weighted fake-factors are then applied to events in regions defined by the selections of the corresponding signal regions, except that the highest-p T τ had-vis candidate passes a very loose τ had-vis identification and fails the "medium" one ("anti-ID" regions). The relative multijet contribution in each anti-ID region is estimated from the yield of events that fail the light-lepton isolation requirement, multiplied by a factor that corrects for this requirement. The multijet contribution varies by more than 50% and depends on the lepton p T and on the Δϕ between τ had-vis and E miss T . The good agreement between data and background estimates is shown in Fig. 5(a) for the main discriminant of the analysis, m MMC ττ , in the boosted W-enhanced region.
The dominant contribution to the uncertainties in the fake-τ had-vis background in the τ lep τ had channel originates from the statistical uncertainty in the individual fake-factors of up to 10% in the boosted signal regions and up to 35% in the VBF signal regions. Minor contributions originate from 50   the statistical uncertainty in the anti-ID regions and uncertainties in the fractional size of the multijet contribution to the fake-τ had-vis background.
In the τ had τ had channel, the multijet background is modeled using a template extracted from data that pass the signal-region selections, but where the τ had-vis candidates are allowed to have two tracks and required to fail the opposite-charge requirement (nOC region). The contribution of events with true τ-leptons from other SM processes is subtracted from this template using simulation. The template is then reweighted using scale factors dependent on the difference in ϕ between the τ had-vis candidates (Δϕ ττ ). These scale factors are derived by comparing the template from an nOC selection with a region obtained by requiring the τ had-vis pair to have opposite charge and the second-highest-p T τ had-vis to fail the "tight" but pass the "medium" identification requirements. As the yield of events that pass these identification requirements is small, the scale factors are derived from events that pass the τ had τ had selection with looser Δη ττ and ΔR ττ requirements to gain statistical power. The normalization of the multijet background is constrained in the fit by data in the m MMC ττ distribution in the signal regions. For this, a normalization factor is defined and it is correlated across all τ had τ had signal regions. Figure 5(b) shows good agreement between data and background predictions in the distribution of Δη between the two τ had-vis , which has a quite different shape for the multijets than for the Z → ττ process. In this figure, events are selected that pass the τ had τ had boosted low-p ττ T selection. Contributions from other backgrounds, such as W with associated jets, range from 2% to 5% in the τ had τ had SRs.
The event yield of the multijet background in the τ had τ had channel is constrained by data to AE15% in the signal regions as shown in Table VI. The dominant contribution to the uncertainties that affect the m MMC ττ shape originates from the statistical uncertainties in the Δϕ ττ scale factors and amounts to 8%. The systematic uncertainty in these scale factors is estimated by comparing them with scale factors computed from the nOC region and a CR defined by requiring opposite-charge τ had-vis to pass "loose" but not "medium" identification. Minor contributions arise from the uncertainty in the extrapolation from the nOC requirement and the uncertainty from the subtraction of simulated backgrounds. The combination of these uncertainties leads to a total variation in the m MMC ττ template shape by at most 10% between bins.

VII. SYSTEMATIC UNCERTAINTIES
The expected signal and background yields in the various signal and control regions as well as the shape of the m MMC ττ distributions in the signal regions are affected by systematic uncertainties. These are discussed below, grouped into three categories: theoretical uncertainties in signal, theoretical uncertainties in background, and experimental uncertainties. The uncertainties in backgrounds from misidentified τ-leptons, which are estimated using data-driven techniques, are discussed in Sec. VI D. The effects of all uncertainties are included in the fit model described in Sec. VIII.

A. Theoretical uncertainties in signal
The procedures to estimate the uncertainty in the Higgs production cross sections follow the recommendations by the LHC Higgs Cross Section Working Group [100]. They are briefly summarized below. Uncertainties are evaluated separately for their impact on the total cross section, their impact on the acceptance in different SRs, and on the shape of the m MMC ττ distribution in each SR. The cross section of ggF production in association with an exclusive number of additional jets has large uncertainties from higher-order QCD corrections [101]. In this analysis, the boosted and VBF categories almost exclusively select ggF events with one and two additional jets, respectively. To take this effect into account, nine uncertainty sources are included. Four sources account for uncertainties in the jet multiplicities due to missing higher-order corrections: Two sources account for yield uncertainties and two sources account for migration uncertainties of zero to one jets and one to at least two jets in the event, respectively, using the STWZ [102] and BLPTW [102][103][104] predictions as an input. Three uncertainty sources parametrize modeling uncertainties in the Higgsboson p T , two of which encapsulate the migration uncertainty between the intermediate and high-p T regions of events with at least one jet, and one which encapsulates the treatment of the top-quark mass in the loop corrections, where the difference between the LO and NLO predictions is taken as an uncertainty due to missing higher-order corrections. Two sources account for the acceptance uncertainties of ggF production in the VBF phase space from selecting exactly two and at least three jets, respectively. Their size is estimated using an extension of the Stewart-Tackmann method [105,106]. The resulting acceptance uncertainties from these nine sources range from 1% to 10%, with the dominant uncertainties due to the modeling of the Higgs p T distribution in all SRs, to the scale variations in the boosted SRs, and to the acceptance uncertainties in the VBF signal regions.
For VBF and VH production cross sections, the uncertainties due to missing higher-order QCD corrections are estimated by varying the factorization and renormalization scales by factors of two around the nominal scale. The resulting uncertainties in the total cross section are below 1% for VBF and WH production and below 5% for ZH production. The uncertainties in the acceptance in the different SRs are about 1% for VBF production in all categories. For VH production the relative acceptance uncertainty ranges between −10% and þ20% in VBF SRs. It is below 10% in boosted SRs.
Uncertainties related to the simulation of the underlying event, hadronization and parton shower for all signal samples are estimated by comparing the acceptance when using the default UEPS model from PYTHIA 8.212 with an alternative UEPS model from HERWIG 7.0.3. The resulting acceptance uncertainties range from 2% to 26% for ggF production and from 2% to 18% for VBF production, depending on the signal region. The PDF uncertainties are estimated using 30 eigenvector variations and two α S variations that are evaluated independently relative to the default PDF set PDF4LHC15 [42]. The total uncertainty due to these variations is 5% or less depending on the SR and the Higgs production mode. Finally, an uncertainty in the H → ττ decay branching ratio of 1% [100] affects the signal rates. All sources of theoretical uncertainties in the signal expectation are correlated across SRs.

B. Theoretical uncertainties in backgrounds
Uncertainties from missing higher-order corrections, the PDF parametrization and the UEPS modelling are also considered for the dominant Z → ττ background. The UEPS modelling uncertainties are estimated by comparing with an alternative Z → ττ sample as described in Sec. III. Since its overall normalization is constrained separately in the VBF and boosted SRs, variations due to these uncertainties are considered in the event migration within an analysis channel, in the m MMC ττ shape and in the relative change in acceptance between the three analysis channels. These variations are treated as uncorrelated between the VBF and boosted SRs. In addition, the first two types of variations are treated as uncorrelated between the three analysis channels. This treatment accounts for the differences in the corresponding event selections. The largest uncertainties are due to the CKKW matching [107] and are evaluated as a function of the number of true jets and the Z-boson p T . They vary between 1% and 5% depending on the SR. The uncertainty in the measured cross section for electroweak Z production with two associated jets [108] is found to be small compared to the other uncertainties in Z-boson production.
The top-quark background normalization in the τ lep τ lep and τ lep τ had channels as well as the Z → ll background normalization in the τ lep τ lep channel are constrained by data in dedicated CRs. All other simulated background contributions are normalized to their Monte Carlo prediction. For all simulated background contributions, other than Z → ττ, no theoretical uncertainties are considered, as their impact is small compared to the uncertainties in the dominant backgrounds from Z → ττ and misidentified leptons.

C. Experimental uncertainties
Experimental systematic uncertainties result from uncertainties in efficiencies for triggering, object reconstruction and identification, as well as from uncertainties in the energy scale and resolution of jets, τ had-vis , light leptons and E miss T . These uncertainties affect both the event yields and the shape of the m MMC ττ . The dominant experimental uncertainties in the final result are related to jet and τ had-vis reconstruction. The impact of the electron-and muon-related uncertainties [86,87,109] on the measurement are small. Uncertainties in the integrated luminosity affect the number of predicted signal and background events, with the exception of processes that are normalized to data, see Table VI. This uncertainty is 2.1% for the combined 2015 þ 2016 data set. It is derived using a methodology similar to that detailed in Ref. [110], and using the LUCID-2 detector for the baseline luminosity measurements [111], from a calibration of the luminosity scale using x-y beam-separation scans.
The uncertainties of the τ had-vis identification efficiency are in the range of 2-4.5% for the reconstruction efficiency [112], 3-14% for the trigger efficiency (depending on the τ had-vis p T ), 5-6% for the identification efficiency and 3-14% for the rate at which an electron is misidentified as τ had-vis (depending on the τ had-vis η) [94]. The uncertainties of the b-tagging efficiencies are measured in dedicated calibration analyses [92] and are decomposed into uncorrelated components. Uncertainties in the efficiency to pass the JVT and forward JVT requirements are also considered [91,113]. Simulated events are corrected for differences in these efficiencies between data and simulation and the associated uncertainties are propagated through the analysis.
The uncertainties of the τ had-vis energy scale [94] are determined by fitting the Z-boson mass in Z → ττ events, reconstructed using the visible τ decay products. The precision amounts to 2-3%, which is dominated by the uncertainty of background modeling. Additional uncertainties based on the modeling of the calorimeter response to single particles are added for τ had-vis with p T > 50 GeV [114]. The jet energy scale and its uncertainty are derived by combining information from test-beam data, LHC collision data and simulation [115]. The uncertainties from these measurements are factorized into eight principal components. Additional uncertainties that are considered are related to jet flavor, pileup corrections, η-dependence, and high-p T jets, yielding a total of 20 independent sources. The uncertainties amount to 1-6% per jet, depending on the jet p T . The jet energy resolution uncertainties [116] are divided into 11 independent components and amount to 1-6%.
Since systematic uncertainties of the energy scales of all objects affect the reconstructed E miss T , this is recalculated after each variation is applied. The scale uncertainty of E miss T due to the energy in the calorimeter cells not associated with physics objects is also taken into account [96]. The uncertainty of the resolution of E miss T arises from the energy resolution uncertainties of each of the E miss T terms and the modeling of pileup and its effects on the soft term (see Sec. IV).

VIII. RESULTS
Maximum-likelihood fits are performed on data to extract parameters of interest that probe H → ττ production with increasing granularity. Firstly, a single parameter is fitted to measure the total cross section of the H → ττ production processes. Then, a two-parameter cross-section fit is presented separating the ggF and VBF production processes. Finally, a three-parameter fit is performed to measure ggF production cross sections in two exclusive regions of phase space. For the small contribution from H → WW Ã decays, the measurements assume the SM predictions for production cross section and branching ratio.
A probability model is constructed that describes the m MMC ττ distributions in the 13 signal regions and the event yields in 6 control regions. The latter are included to constrain the normalizations of the dominant backgrounds. Each signal region is modeled by a product of Poisson distributions, where each such distribution describes the expected event count in intervals of m MMC ττ . Each control region is modeled by a single Poisson distribution that describes the total expected event count in that region. Signal and background predictions depend on systematic uncertainties, which are parametrized as nuisance parameters and are constrained using Gaussian or log-normal probability distributions. The latter are used for normalization factors (see Table VI) to ensure that they are always positive. The dependence of the predictions on nuisance parameters related to systematic uncertainties is modeled with an interpolation approach between yields obtained at different fixed systematic uncertainty settings. A smoothing procedure is applied to remove occasional large local fluctuations in the m MMC ττ distribution templates, which encode systematic uncertainties of some background processes in certain regions. For the measurements, all theoretical uncertainties are included, except those related to the respective measured signal cross sections, and are correlated as described in Sec. VII A. The experimental uncertainties are fully correlated across categories and the background modeling uncertainties are generally uncorrelated, with the exception of the normalization factors as described in Sec. VI. Estimates of the parameters of interest and the confidence intervals are calculated with the profile likelihood ratio [117] test statistic, whereas the test statistic q 0 [117] is used to compute the significances of the deviations from the background-only hypothesis.
The observed (expected) significance of the signal excess relative to the background-only hypothesis computed from the likelihood fit is 4.4 (4.1) standard deviations, compatible with a SM Higgs boson with a mass m H ¼ 125 GeV. This result is combined with the result of the search for H → ττ using data at 7 and 8 TeV center-of-mass energies [15]. The combined observed (expected) significance amounts to 6.4 (5.4) standard deviations. In this combination, all nuisance parameters are treated as uncorrelated between the two analyses. In particular, the dominant Z → ττ background is estimated differently, as mentioned in Sec. I.
The parameter σ H→ττ ≡ σ H · BðH → ττÞ is fitted, where σ H is the total cross section of the considered Higgs-boson production processes ggF, VBF, VH and ttH, and where BðH → ττÞ is the H → ττ branching fraction. For this measurement, the relative contributions from the various Higgs production processes are assumed as predicted by the SM and the uncertainties related to the predicted total signal cross section are excluded. The measured value of σ H→ττ is 3.77 þ0.60 −0.59 ðstatÞ þ0.87 −0.74 ðsystÞ pb, consistent with the SM prediction, σ SM H→ττ ¼ 3.46 AE 0.13 pb [100]. The signal strength μ H→ττ is defined as the ratio of the measured signal yield to the Standard Model expectation. It is computed by the fit described above, including uncertainties in the predicted signal cross section, and is evaluated to be 1.09 þ0.18 −0.17 ðstatÞ þ0.26 −0.22 ðsystÞ þ0.16 −0.11 ðtheory systÞ. Tables VII-IX summarize the expected signal and background yields computed by the fit in each signal region for the σ H→ττ measurement. The signal event yields are given separately for each production process of relevance. Within the uncertainties, good agreement is observed between the data and the predicted sum of signal and background contributions, for a SM Higgs boson of mass m H ¼ 125 GeV with the measured value of σ H→ττ reported above. Table X shows a summary of the dominant uncertainties in σ H→ττ , grouped by their respective sources. Figure 6 shows the systematic uncertainties with the largest impact, together with a comparison with their nominal values used as input to the fit. In both the table and the figure the shown uncertainties are ranked by their fractional impact on the measurement of σ H→ττ . To compute the impact for each nuisance parameter, a separate fit is performed again with the parameter fixed to its fitted value, and the resulting uncertainty in σ H→ττ is subtracted from the uncertainty obtained in the original fit via variance subtraction. The dominant uncertainties are related to the limited number of events in the simulated samples, the missing higher-order QCD corrections to the signal process cross sections, the jet energy resolution, the τ had-vis identification and the normalizations of the Z → ττ and Z → ll backgrounds. Figure 6 also shows that in most cases the fitted parameters are in agreement with the nominal values, except for the uncertainties related to jet energy resolution and scale. In the case of real di-τ events, the distribution of m MMC ττ is sensitive to the jet-related uncertainties because selected diτ events in the VBF and boosted categories are characterized by one or more high-p T jets that recoil against the two τ-leptons. The main contributions to E miss T are thus the neutrinos in the τ-lepton decays and the impact of the jet energy resolution when projected onto the E miss T direction. Applying both the jet energy resolution and scale uncertainties causes a shift in the mean jet p T , which therefore translates directly into a shift of the reconstructed E miss T . This, in turn, translates into a shift of the reconstructed m MMC ττ that is constrained by data in the region of the Z → ττ mass peak.
Results of the fit when only the data of an individual channel or of an individual category are used, are shown in  Fig. 8, separately for the combined signal regions of τ had τ had , τ lep τ had and τ lep τ lep analysis channels, and in Fig. 9, separately for the combined VBF and the combined boosted signal regions. A weighted combination of the m MMC ττ distributions in all signal regions is shown in Fig. 10. The events are weighted by a factor of lnð1 þ S=BÞ which enhances the events compatible with the signal hypothesis. Here, S=B is the expected signal-to-background ratio in the corresponding signal region. TABLE X. Summary of different sources of uncertainty in decreasing order of their impact on σ H→ττ . Their observed and expected fractional (%) impacts, both computed by the fit, are given, relative to the σ H→ττ value. Experimental uncertainties in reconstructed objects combine efficiency and energy/momentum scale and resolution uncertainties. Background statistics includes the bin-by-bin statistical uncertainties in the simulated backgrounds as well as statistical uncertainties in misidentified τ backgrounds, which are estimated using data. Background normalization describes the combined impact of all background normalization uncertainties.   Table VI. Their uncertainties do not include uncertainties in total simulated cross sections extrapolated to the selected phase space. Figure 7 illustrates that the VBF and boosted categories provide good sensitivity, respectively, to VBF and ggF Higgs-boson production. A two-parameter fit is therefore performed to determine the cross sections of these production processes by exploiting the sensitivity offered by the use of the event categories in the analysis of the three channels. Two cross-section parameters σ VBF H→ττ and σ ggF H→ττ are introduced and the data are fitted to these parameters, separating the vector-boson-mediated VBF process from the fermion-mediated ggF process, while the contributions from other Higgs production processes are set to their predicted SM values. The two-dimensional 68% and 95% confidence level (C.L.) contours in the plane of σ VBF H→ττ and σ ggF H→ττ are shown in Fig. 11 [100]. The two results are strongly anti-correlated (correlation coefficient of −52%), as can be seen in Fig. 11.
The ggF signal provides enough events to measure ggF cross sections in mutually exclusive regions of the ggF phase space. Two ggF regions are defined by particle-level events with at least one jet where a jet is required to have p T > 30 GeV: events with a Higgs-boson p T of 60 < p H T < 120 GeV and events with p H T > 120 GeV. A crosssection parameter for each of the two ggF regions is introduced, along with a parameter for VBF production in an inclusive region, and a combined three-parameter fit is performed using the event categories in the analysis of the     three channels. The particle-level definitions of all three phase-space regions closely follow the framework of simplified template cross sections [101] where the Higgs-boson rapidity y H is required to satisfy jy H j < 2.5. The ggF and VBF production cross sections outside the respective particle-level region requirements are set to the measured values reported above. Cross sections of other Higgs-boson production processes are set to their SM values.      FIG. 11. Likelihood contours for the combination of all channels in the (σ ggF H→ττ , σ VBF H→ττ ) plane. The 68% and 95% C.L. contours are shown as dashed and solid lines, respectively, for m H ¼ 125 GeV. The SM expectation is indicated by a plus symbol and the best fit to the data is shown as a star. predictions in the respective particle-level region. The measurements in all regions have a precision similar to that of the inclusive ggF and VBF measurements reported above.

IX. CONCLUSIONS
A measurement of total production cross sections of the Higgs boson in proton-proton collisions is presented in the H → ττ decay channel. The analysis was performed using 36.1 fb −1 of data recorded by the ATLAS experiment at the LHC at a center-of-mass energy of ffiffi ffi s p ¼ 13 TeV. All combinations of leptonic and hadronic τ decays were considered. An excess of events over the expected background from other Standard Model processes was found with an observed (expected) significance of 4.4 (4.1) standard deviations. Combined with results using data taken at ffiffi ffi s p of 7 and 8 TeV, the observed (expected) significance amounts to 6.4 (5.4) standard deviations and constitutes an observation of H → ττ decays by the ATLAS experiment. Using the data taken at ffiffi ffi s p ¼ 13 TeV, the pp → H → ττ total cross section is measured to be 3.77 þ0.60 −0.59 ðstatÞ þ0.87 −0.74 ðsystÞ pb, for a Higgs boson of mass 125 GeV. A two-dimensional fit was performed to separate the vector-boson-mediated VBF process from the fermion-mediated ggF process. The cross sections of the Higgs boson decaying into two τ leptons are measured to be σ VBF H→ττ ¼0.28AE0.09ðstatÞ þ0.11 −0.09 ðsystÞpb and σ ggF H→ττ ¼ 3.1 AE 1.0ðstatÞ þ1.6 −1.3 ðsystÞ pb, respectively, for the two production processes. Similarly, a three-dimensional fit was performed in the framework of simplified template cross sections. Results are reported for the VBF cross section in an inclusive phase space and ggF cross sections in two exclusive regions of phase space defined by particle-level requirements on the Higgs-boson p T . All measurements are consistent with SM predictions.

ACKNOWLEDGMENTS
We thank CERN for the very successful operation of the LHC, as well as the support staff from our institutions without whom ATLAS could not be operated efficiently. We acknowledge the support of ANPCyT, Argentina; YerPhI, Armenia; ARC, Australia; BMWFW and FWF,   XI. Measurement of the VBF and ggF production cross sections in three mutually exclusive regions of phase space of particle-level events. The number of jets N jets in ggF events comprises all jets with p T > 30 GeV. The cross section of ggF events that fail the particle-level requirements of the two ggF regions is set to the measured σ ggF H→ττ value. Results are shown along with the SM predictions in the respective particle-level regions. The definitions of the regions closely follow the framework of simplified template cross sections [101].

Process
Particle distributions as used in the fit in all signal regions (SRs) in the VBF category for the τ lep τ lep (left), τ lep τ had (middle) and τ had τ had (right) analysis channels. The bottom panels show the ratio of observed data events to expected background events (black points). The observed Higgs-boson signal (μ ¼ 1.09) is shown with the solid red line. Entries with values that would exceed the x-axis range are shown in the last bin of each distribution. The signal and background predictions are determined in the likelihood fit. The size of the combined statistical, experimental and theoretical uncertainties in the background is indicated by the hatched bands.