Measurements of Higgs boson production cross-sections in the $H\to\tau^{+}\tau^{-}$ decay channel in $pp$ collisions at $\sqrt{s}=13\,\text{TeV}$ with the ATLAS detector

Measurements of the production cross-sections of the Standard Model (SM) Higgs boson ($H$) decaying into a pair of $\tau$-leptons are presented. The measurements use data collected with the ATLAS detector from $pp$ collisions produced at the Large Hadron Collider at a centre-of-mass energy of $\sqrt{s}=13\,\text{TeV}$, corresponding to an integrated luminosity of $139\,\text{fb}^{-1}$. Leptonic ($\tau\to\ell\nu_{\ell}\nu_{\tau}$) and hadronic ($\tau\to\text{hadrons}~\nu_{\tau}$) decays of the $\tau$-lepton are considered. All measurements account for the branching ratio of $H\to\tau\tau$ and are performed with a requirement $|y_H|<2.5$, where $y_H$ is the true Higgs boson rapidity. The cross-section of the $pp\to H\to\tau\tau$ process is measured to be $2.94 \pm 0.21 \text{(stat)} ^{+\,0.37}_{-\,0.32} \text{(syst)}$ pb, in agreement with the SM prediction of $3.17\pm0.09~ \mbox{pb}$. Inclusive cross-sections are determined separately for the four dominant production modes: $2.65 \pm 0.41 \text{(stat)} ^{+\,0.91}_{-\,0.67} \text{(syst)}$ pb for gluon$-$gluon fusion, $0.197 \pm 0.028 \text{(stat)} ^{+\,0.032}_{-\,0.026} \text{(syst)}$ pb for vector-boson fusion, $0.115 \pm 0.058 \text{(stat)} ^{+\,0.042}_{-\,0.040} \text{(syst)}$ pb for vector-boson associated production, and $0.033 \pm 0.031 \text{(stat)} ^{+\,0.022}_{-\,0.017} \text{(syst)}$ pb for top-quark pair associated production. Measurements in exclusive regions of the phase space, using the simplified template cross-section framework, are also performed. All results are in agreement with the SM predictions.


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This work uses 139 fb −1 of pp collision data collected at a centre-of-mass energy of 13 TeV, to be compared with 36 fb −1 for the previous H → τ τ cross-section measurements [22]. It introduces a new reconstructed-event categorisation designed for the improved stage 1.2 binning [33] of the simplified template cross-section (STXS) framework [27]. The treatment of ggF events with Higgs boson produced with a large transverse momentum is refined with three times more categories. Selected events are categorised with requirements on the transverse momentum of the reconstructed Higgs boson candidate (p T (H)) and on the potential additional hadronic jets. Two new categories targeting production modes where the Higgs boson is created in association with other objects are added, based on requirements on the kinematics and tagged flavour of the jets in the event. The first targets the production of a Higgs boson in association with a pair of top quarks (ttH), where both top quarks and both τ -leptons decay hadronically, complementing the explorations in ref. [34], and is denoted by tt(0 )H → τ had τ had in the rest of this paper. The second targets the production of a Higgs boson in association with a vector boson V (W , Z). This new category, referred to as V(had)H, focuses on events with a hadronic decay of the V boson while the production of Z(→ )H and W (→ ν)H events is studied separately [35]. Finally, the selection of VBF events was also improved by multivariate techniques.
In addition to the new extended categorisation, several improvements to the analysis methodology have been implemented: the object selection has been improved, multivariate discriminants have been optimised to enhance the purity of the SRs in the targeted Higgs boson production modes, the number of simulated background events has been increased significantly and the usage of the Z → control region has been refined. The latter relies on a new simplified implementation of the embedding technique [36,37] which, instead of replacing the reconstructed electrons and muons from Z → events by equivalent simulated τ -lepton decay products, simply rescales their transverse momentum to that of an equivalent τ -lepton.
This document is organised as follows. Section 2 describes the ATLAS detector. This is followed in section 3 by a description of the dataset and Monte Carlo (MC) simulated samples employed in the measurement. Section 4.1 details the reconstruction of the physics objects. The event selection and categorisation is described in section 4.2. In section 5, the estimation of the background processes is discussed with an emphasis on the simplified embedding technique to model Z → τ τ processes in section 5.1 and the data-driven estimates of the processes with at least one jet misidentified as an electron, a muon or a τ had in section 5.2. Section 6 presents the systematic uncertainties affecting the measurement and their estimation. The details of the signal extraction fit are discussed in section 7, and section 8 presents the results of the measurement. Section 9 summarises the conclusions of this work. periods. Events are selected for analysis only if they are of good quality and if all the relevant detector components are known to have been in good operating condition [47], which corresponds to a total integrated luminosity of 139.0 fb −1 . MC simulated events are used to model most of the backgrounds from SM processes and the H → τ τ signal processes. A summary of all the generators used for the simulation of the signal and background processes is shown in table 1. The same event generators as in ref. [22] were used, but the number of simulated events in each sample was at least quadrupled, which is the factor by which the integrated luminosity grew since the previous publication. In addition, the total number of simulated Z → τ τ events was increased by a further factor of approximately four. This computationally expensive task helps to densely populate the phase space where Z → τ τ events are produced in association with several jets.

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All samples of simulated events were processed through the ATLAS detector simulation [48] based on Geant4 [49]. The effects of multiple interactions in the same and nearby bunch crossings (pile-up) were modelled by overlaying minimum-bias events, simulated using the soft QCD processes of Pythia 8.186 [50] with the A3 [51] set of tuned parameters and NNPDF2.3lo [52] parton distribution functions (PDF).
The decays and spin correlations for τ -leptons are handled by Sherpa for the samples it generated, and by Pythia for the other MC event generators. The decays and spin correlations have been included in Pythia version 8.150 [53], and have been thoroughly validated by comparisons with Tauola [54].

Object reconstruction
Tracks measured in the ID are used to reconstruct interaction vertices [126], of which the one with the highest sum of squared transverse momenta of the associated tracks is selected as the primary vertex of the hard interaction.
Electrons are reconstructed from topological clusters of energy deposits in the electromagnetic calorimeter which are matched to a track reconstructed in the ID [127]. They are required to satisfy the 'Loose' identification criteria, to have p T > 15 GeV, and to be in the fiducial volume of the ID and the high-granularity electromagnetic calorimeters, |η cluster | < 2.47. The transition region between the barrel and endcap calorimeters (1.37 < |η cluster | < 1.52) is excluded except for the Z → control region where it is kept to facilitate the embedding procedure (see section 5.1). In the τ e τ µ and τ e τ had channels, the selected electron is further required to satisfy the 'Medium' identification, which has an associated efficiency of 80% to 90%, and the 'Loose' isolation criterion [127] in the signal regions and most control regions, which has an efficiency of 90% for 15 GeV candidates, increasing to more than 98% for 30 GeV candidates. In the τ e τ had channel, the requirement on the electron transverse momentum is further tightened by 1 GeV above the nominal trigger p T threshold for electrons matched to the single-electron trigger to ensure operation at the trigger's plateau efficiency. Similarly, in the τ e τ µ channel, the requirement is tightened if the event is accepted by the single-electron trigger or the electron-muon trigger. Table 2 summarises the exact requirements used depending on the data-taking period.
Muons are reconstructed from signals in the MS matched with tracks inside the ID. They are required to satisfy the 'Loose' identification criteria [132], corresponding to an efficiency above 97% for all muon candidates considered in this analysis, and to have p T > 10 GeV and |η| < 2.5. In the τ e τ µ and τ µ τ had channels, the selected muon in the signal regions is further required to satisfy a 'Tight' isolation criterion [132] based on track information. This requirement has an efficiency increasing from 85% to 99% for muons with transverse momentum increasing from 10 GeV to 50 GeV and above. In the τ µ τ had channel, the requirement on the muon transverse momentum is further tightened to select events in which the single-muon trigger operates with very high efficiency. Similarly, in the τ e τ µ channel, the requirement is further tightened if the event is accepted by the single-muon trigger or the electron-muon trigger. Table 2 summarises the requirements used depending on the data-taking period.
Jets are reconstructed using a particle-flow algorithm [133] from noise-suppressed positive-energy topological clusters in the calorimeter using the anti-k t algorithm with a p T (sub-leading τ had-vis ) > 30 Table 2. Transverse momentum thresholds applied to the selected electrons, muons and τ had-vis depending on the trigger signature and the data-taking period. The p T thresholds of the ATLAS lowest unprescaled triggers during the Run 2 data-taking are reported in refs. [128][129][130][131]. The electron and muon trigger menu evolution throughout the Run 2 data-taking is discussed in refs. [43,44].
radius parameter R = 0.4. Cleaning criteria are used to identify jets arising from noncollision backgrounds or noise in the calorimeters [134], and events containing such jets are removed. A jet vertex tagger (JVT) [135] is used to remove jets with p T < 60 GeV and |η| < 2.5 that are identified as not being associated with the primary vertex of the hard interaction. Similarly, pile-up jets in the forward region are suppressed with a "forward JVT" [136] algorithm, exploiting jet shapes and topological jet correlations in pile-up interactions, which is applied to all jets with p T < 60 GeV and |η| > 2. 5. Only jets with p T > 20 GeV are considered.
Jets with p T > 20 GeV and |η| < 2.5 containing b-hadrons are identified using the DL1r b-tagging algorithm [137,138]. In the τ e τ µ and τ lep τ had channels, the fixed 85% efficiency working point is used, while the 70% efficiency working point is used in the τ had τ had channel (the target efficiencies being measured in simulated tt events). Since the algorithm is used to veto b-tagged jets, the 70% efficiency working point offers a looser veto criterion which improves the sensitivity in the τ had τ had channel where the backgrounds from tt events are less significant. The rejection factors for b-tagged jets initiated by c-quarks and light partons are 9.4 (2.6) and 390 (29) respectively for the 70% (85%) efficiency working point.
Decays of τ had are composed of a neutrino and a set of visible decay products, most frequently one or three charged pions and up to two neutral pions and denoted by τ had-vis . The reconstruction of the τ had-vis is seeded by jets reconstructed using the anti-k t algorithm [139], using calibrated topological clusters [140] as inputs, with a radius parameter of R = 0.4 [141]. The jets form τ had-vis candidates and are additionally required to have p T > 10 GeV and |η| < 2.5. Reconstructed tracks are matched to τ had-vis candidates. A multivariate discriminant is used to assess whether these tracks are likely to have been produced by the charged τ had decay products, and is used to reject tracks originating from other interactions, nearby jets, photon conversions or misreconstructed tracks. The τ had-vis objects are required to have one or three associated tracks selected by this discriminant. Their charge (q) is defined as the sum of the measured charges of these associated tracks and -9 -JHEP08(2022)175 must have |q| = 1. The τ had-vis objects must also satisfy the requirements p T > 20 GeV and |η| < 2.47, excluding the region 1.37 < |η| < 1.52. These requirements have an efficiency of about 85% (70%) for the majority of hadronic τ decays with one (three) associated tracks measured in simulated Z → τ τ events. The τ had-vis energy scale is determined by combining information from the associated tracks, calorimeter clusters and reconstructed neutral pions [142] using a multivariate regression technique [141] trained in MC samples.
To separate the τ had-vis candidates produced by hadronic τ decays from those due to jets initiated by quarks or gluons, a recurrent neural network (RNN) identification algorithm [143] is constructed employing information from reconstructed charged-particle tracks and calorimeter energy clusters associated with τ had-vis candidates, as well as high-level discriminating variables. A separate boosted decision tree discriminant ('eBDT') is also constructed to reject backgrounds arising from electrons misidentified as τ had-vis (mainly from Z → ee events in the τ e τ had channel in this analysis). This discriminant is built using information from the calorimeter and the tracking detector, most notably transition radiation information from the TRT system and variables sensitive to the ratio of the energy deposited in the calorimeter and the visible momentum measured from the reconstructed tracks. In addition, a very loose requirement on the RNN score (corresponding to a percent level efficiency loss for signal τ had-vis ) is applied, as well as a dedicated muon veto criterion, designed to reject muons misreconstructed as τ had-vis (typically due to large calorimeter energy deposits).
In the τ had τ had channel, the reconstructed τ had-vis objects are required to match the two τ had-vis candidates of the τ τ trigger, thus defining the two selected τ had-vis of the event.
In the τ lep τ had channel, the τ had-vis candidate with the highest transverse momentum is the only one kept, and other ones are considered as jets. This minimum requirement is much looser than the final RNN selection, and leads to a small loss of signal events where a quark-or gluon-initiated jet is taken as the τ had-vis candidate, quantified to be at the level of 2.5% (4%) for the ggF (VBF) production process. However, this strategy simplifies the treatment of the background processes with jets misidentified as τ had-vis . The estimation of this background relies on a control region defined by inverting the final RNN selection. Picking a minimum requirement aimed at recovering the majority of this signal efficiency loss would sacrifice 30% to 40% of the statistical power in the control region, and would consequently degrade the estimate of this background (see section 5.2).
The τ had-vis objects are further required to fulfil the 'Medium' identification criteria in the signal regions of the τ lep τ had and τ had τ had channels, which corresponds to an efficiency of 75% (60%) for candidates with 1 (3) associated track(s). In the τ e τ had channel, for events where the τ had-vis object has only one associated charged track, the τ had-vis object is required to pass the 'Medium' working point of the eBDT algorithm, which corresponds to an 85% efficiency for candidates which already satisfy the identification requirement. The transverse momentum requirement for the τ had-vis objects in the τ had τ had final state is tightened to select events recorded with the τ had-vis trigger operating at its plateau efficiency, as shown in table 2. In the τ lep τ had final state, the τ had-vis transverse momentum requirement is also tightened to p T > 30 GeV to improve background rejection.  The reconstructed objects used in this analysis are not built from disjoint sets of tracks or calorimetric clusters. It is therefore possible that two different objects share most of their constituents. An overlap removal procedure is applied to resolve this ambiguity. This procedure is summarised in table 3. It uses a definition of angular distance, ∆R y = (∆y) 2 + (∆φ) 2 , that is based on the rapidities y of the objects.
The missing transverse momentum vector, E miss T , is reconstructed as the negative vector sum of the transverse momenta of leptons, τ had-vis and jets, and a "soft-term". The soft-term is calculated as the vectorial sum of the p T of tracks matched to the primary vertex but not associated with a reconstructed lepton, τ had-vis or jet [144]. The magnitude of E miss T is referred to as the missing transverse momentum, E miss T .

Event selection
Events are selected if they contain a H → τ τ candidate in one of the final states under study (τ e τ µ , τ lep τ had , τ had τ had ). The Higgs boson candidate is formed by the vector momentum sum of the visible τ -lepton decay products and E miss T . Its invariant mass (m MMC τ τ ) is calculated using an advanced likelihood-based technique, the Missing Mass Calculator (MMC) [145], which relies on information about the τ -lepton candidate momenta, the presence of additional jets, E miss T and the type of τ -lepton decay. The addition of information about the number of reconstructed charged and neutral pions [142] in hadronic decays of the τ -leptons in new parameterisations for the likelihood function derived using Z → τ τ MC events are improvements with respect to ref.
[22] and lead to a 1% absolute improvement on the width of the reconstructed mass distribution.
For each channel a series of selection criteria are applied to enhance the sensitivity to the SM Higgs boson signal and ensure a robust estimate of the invariant mass of the reconstructed τ + τ − system. These are summarised in table 4.
In the τ e τ µ channel, events must have a single reconstructed electron and a single reconstructed muon satisfying the criteria discussed in section 4.1. In order to reject events coming from W +jets, Z+jets and top processes, 8 the charges of the two reconstructed leptons must be of opposite sign, the invariant mass of the eµ system (m eµ ) must be between 30 GeV and 100 GeV, and the collinear mass 9 (m coll τ τ ) must be greater than (m Z − 25 ) GeV. This last criterion ensures the selected dataset does not include any event considered in the signal regions of the ATLAS measurements of the H → W W * process discussed in ref. [147]. To further reduce backgrounds from top processes, events with a b-tagged jet are rejected. In addition, angular requirements are placed on ∆R eµ and |∆η eµ |. Finally, a p T > 40 GeV requirement is applied to the leading jet in the event to suppress backgrounds, as the signal final states considered include at least one high-p T jet.
In the τ lep τ had channel, events must have a single reconstructed light lepton and a single reconstructed τ had-vis satisfying the criteria discussed in section 4.1. In order to reject events coming from W +jets and top processes, the charges of the reconstructed light lepton and the reconstructed τ had-vis must be of opposite sign. The transverse mass of the lepton+E miss T system (m T ) is required to be smaller than 70 GeV in order to efficiently suppress W +jets processes. To further reduce backgrounds from top processes, an explicit requirement is imposed to reject events with a b-tagged jet. In addition, angular requirements are placed on ∆R τ had-vis and |∆η τ had-vis |. The requirement on the leading jet transverse momentum in the event is the same as for the τ e τ µ channel.
In the τ had τ had channel, events must have exactly two reconstructed τ had-vis objects satisfying the criteria discussed in section 4.1. In order to maintain low thresholds for the p T of the τ had-vis , additional criteria for the angular separation of the two τ had-vis 8 In the following, 'top processes' in the text ('Top' in tables and figures) collectively refer to single and pair production of top quarks. 9 The τ τ mass reconstructed in the collinear approximation assumes that the neutrinos from the τ -lepton decays propagate in the same direction as the visible decay products and that the missing transverse momentum is caused solely by those neutrinos [146].

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Criteria |∆η eµ | < 1.5 |∆η τ had-vis | < 1.5 |∆η τ had-vis τ had-vis | < 1.5 Coll. app. Table 4. Summary of the event selection for all sub-channels. The electron and muon p T thresholds correspond to the 2016-2018 dataset. In the τ e τ µ channel, events recorded with the electron trigger must satisfy p T (e) > 27 GeV and p T (µ) > 10 GeV, events recorded with the muon trigger must satisfy p T (e) > 15 GeV and p T (µ) > 27.3 GeV, and events recorded with the electron-muon trigger must satisfy p T (e) > 18 GeV and p T (µ) > 14.7 GeV. Thresholds for the 2015 dataset are given in table 2. The b-veto requirement in the τ had τ had channel is not applied in the tt(0 )H → τ had τ had category. The quantities x 1 and x 2 are the momentum fractions carried by the visible decay products of the two τ -leptons in the collinear approximation, as described in the text.

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and the presence of an additional jet in the event were added to the lowest unprescaled τ τ trigger during the Run 2 data-taking. The additional criteria were imposed on the regions-of-interest (ROI) defining the τ had-vis candidates at the L1 trigger. In order to ensure that the ROIs of the two reconstructed τ had-vis do not have overlapping cores, the criterion ∆R τ had-vis τ had-vis > 0.6 is applied. The extra-jet trigger criterion mentioned above translates into a requirement on the presence of at least one jet with |η| < 3.2 and p T greater than 70 GeV. Similarly to the τ e τ µ and τ lep τ had channels, the charges of the two reconstructed τ had-vis must be of opposite sign in order to reject events coming from W +jets and top processes. Events with b-tagged jets are rejected, except for the tt(0 )H → τ had τ had signal region (see next section 4.3). Finally, criteria concerning E miss T and the fraction of the τ -lepton's momentum carried by its visible decay products, computed with the E miss T components decomposed into the collinear approximation (defined as x 1 and x 2 for leading and sub-leading reconstructed visible τ -lepton candidates respectively) are applied to improve the invariant mass estimation in the three channels.
Assuming SM predictions, about 2920 H → τ τ events (330, 1410, and 1180 events in the τ e τ µ , τ lep τ had , and τ had τ had channels respectively) are expected to be reconstructed and satisfy the event selection from the ≈ 440 · 10 3 H → τ τ events that were produced with |y H | < 2.5 during the LHC Run 2. In data, 204 442 events are selected.

Event categorisation
The categorisation of selected events targets the four dominant Higgs boson production modes (see section 1), uses their unique and characteristic signatures and is designed to closely match the production bins within the stage 1.2 of the STXS framework. Bins of the full stage 1.2 scheme are merged to match the available sensitivity of the selected H → τ τ events. Both the STXS bins and the event categories are illustrated in figure 1.
Requirements on the reconstructed Higgs boson transverse momentum, p T (H), and on properties of additional jets are described in the following. Events in the VBF, V(had)H and tt(0 )H → τ had τ had categories are further split with BDT taggers into two subcategories, the first (suffixed _1) with enhanced signal fractions and the second (suffixed _0) containing the remaining events. All taggers are designed inclusively for all τ τ decay modes and the variables are chosen to avoid any potential bias in the m MMC τ τ distribution. For each tagger, this is verified by comparing templates of the m MMC τ τ distribution for signal and background processes between the relevant subcategories. The taggers are described in the following and their input variables are listed in table 5. tt(0 )H → τ had τ had categorisation. The final state targeted in the tt(0 )H → τ had τ had category includes six jets and two of these jets are initiated by the hadronisation of a b-quark. However, to enhance the signal acceptance, the selection allows exactly one of these two numbers to be off by one unit. Therefore, the event selection in the tt(0 )H → τ had τ had category requires the presence of either six jets with p T greater than 20 GeV including at least one b-tagged jet or five jets including at least two b-tagged jets. The events satisfying these criteria are not considered by the analysis reported in ref. [ Table 5. Variables used in the four multivariate taggers employed in the analysis. For each tagger, the presence or absence of a • indicates whether the variable is used or not. The symbol τ stands for any reconstructed τ -lepton candidate (electron, muon or τ had-vis ) as appropriate in each channel. The symbols τ τ and jj indicate the vectorial sums of the momenta of two visible τ -lepton candidates and of the two leading jets, respectively. The Higgs boson candidate H is formed by the vector sum of the two τ -lepton candidates' momenta and E

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The signal-enhancing separation in this category uses two BDTs: one BDT is optimised to enhance ttH signal events over Z → τ τ background events, while the second BDT is optimised to enhance ttH signal events over tt background events. A variety of twodimensional combinations of requirements on the two BDT scores were studied, using the expected counting-experiment statistical significance, 10 including an estimate of the systematic uncertainties in the background normalisations, as an estimator for their performance; none was found to outperform a simple rectangular requirement in the plane formed by the two BDT scores, and this was the requirement ultimately selected. Of all Higgs boson events selected in the ttH_0 (ttH_1) categories 74% (92%) are due to the ttH process.
All other event categories in the τ had τ had channel require that no b-tagged jets with p T > 20 GeV and |η| < 2.5 are present.
VBF categorisation. The VBF categories are designed to select Higgs bosons produced from the fusion of two vector bosons emitted by two quarks of the colliding protons. The scattered quarks give rise to two high-p T jets with a large rapidity gap and therefore large invariant mass m jj . This signature allows VBF events to be experimentally distinguished from the other Higgs production modes and Z → τ τ events.
To match the STXS qq → H particle-level p jet T requirement and m jj binning, events selected in the VBF categories must have m jj > 350 GeV and p T of the sub-leading jet greater than 30 GeV. Additional selection criteria are applied to enhance the VBF Higgs production mode relative to the Z → τ τ background. The product of the pseudorapidities of the two leading jets (η(j 0 ) × η(j 1 )) is required to be negative (i.e. jets must be in opposite hemispheres of the detector). The absolute difference in pseudorapidity (|∆η jj |) is required to be greater than 3. Finally, the visible decay products of the τ -leptons are required to be reconstructed in the rapidity gap between the VBF jets.
The VBF tagger is optimised by treating both the ggF H → τ τ and Z → τ τ events as backgrounds and relies solely on observables based on the kinematics of the two leading jets (see table 5). While the expected contribution from ggF H → τ τ events is small, the considerably larger theoretical uncertainty associated with its cross-section prediction in this kinematic phase space can significantly enlarge the systematic uncertainty of the VBF production cross-section measurement.
The BDT score requirement used to define the categories was optimised to give the smallest uncertainty in the VBF cross-section, and provides a selection where the fraction of VBF events among all Higgs boson events is about 94% (63%) in the VBF_1 (VBF_0) region.

V(had)H categorisation.
To match the STXS qq → V (→ qq)H particle-level p jet T requirement and m jj binning, events selected in the V(had) categories must satisfy 60 GeV < m jj < 120 GeV and p T of the sub-leading jet greater than 30 GeV.
The V(had)H tagger was trained by treating all Higgs events produced by processes other than V H as background. The BDT score requirement used to define the two categories was optimised to give the smallest uncertainty for the V(had)H cross-section, and provides   To match the STXS gg → H particle-level requirements, events are further categorised by p T (H) value and by the total number of jets with p T greater than 30 GeV (N jets (p T > 30 GeV)). Events with p T (H) < 200 GeV are separated into 1-jet and ≥2-jet categories, while for p T (H) > 200 GeV events with at least one jet are considered without further jet-multiplicity separation of the events. Table 6 describes the boost phase-space categorisation.
The three analysis channels are therefore split into six kinematic categories in the boost phase space for a total of eighteen categories in the fit performed for the cross-section measurement.
Summary. Nine bins of the STXS framework are targeted in the measurement presented in this paper and are illustrated in figure 1. The expected signal yields for each of these bins is presented in figure 2(a), while figure 2(b) illustrates the relative population of these nine bins in each reconstruction category described in this section. Events selected in each reconstruction category are used to build templates of the m MMC τ τ variable for each of the nine bins. As illustrated in figure 2, ggF events produced with p T (H) < 200 GeV and two additional jets forming a system with m jj > 350 GeV are mainly reconstructed in the VBF_0 category (61%) and the boost_1_ge2J category (36%). It is difficult to select these events in only a single category but through the simultaneous usage of all the categories, their production rate can be measured. In contrast, the reconstructed ggF event candidates satisfying 60 GeV < p T (H) < 120 GeV are further separated into those produced with a single jet (boost_0_1J) and those produced with two jets forming a system with m jj < 350 GeV (boost_0_ge2J). However, the categorisation does not provide enough sensitivity to measure these two contributions individually and they are therefore combined. [GeV]: [GeV]: Relative contribution of each of the nine measured STXS bins to the total H → τ τ signal expectation in each reconstructed-event category. The spades symbol (♠) indicates that the criteria for m jj only apply to events with at least two reconstructed jets. Yields are summed over the three τ τ decay channels (τ e τ µ , τ lep τ had , τ had τ had ).

Background modelling
The expectations from SM processes other than the H → τ τ signal in the phase space of the analysis are evaluated using a mixture of simulations and data-driven techniques. Processes with τ had-vis , prompt light leptons or light leptons from τ -lepton decays are estimated through simulations. Among these, Z(→ τ τ ) + jets and top processes are dominant, and dedicated control regions are employed to validate the simulations of both processes and to constrain their normalisation in the signal regions. For the Z(→ τ τ ) + jets background, a control region enriched in Z(→ ) + jets events is defined as described in section 5.1. In the τ e τ µ and τ lep τ had channels, control regions enriched in top-induced processes are defined by replacing the b-jet veto from the event selection (see table 4) with a requirement of at least one b-tagged jet. Using these control regions, the templates of the m MMC τ τ observable from the simulations are checked in each event category (see section 4.3). Very good agreement with the data is observed.
Smaller background contributions are due to diboson, Z(→ ) + jets and H → W W * processes. They are normalised to their theoretical expectations. Contributions from lightand heavy-flavour jets misidentified as electrons, muons or τ had-vis , as well as non-prompt electrons or muons, collectively referred to as misidentified τ background, are estimated using data-driven techniques. Their estimation is detailed in section 5.2. Figure 3 illustrates the measured composition of the selected events in each category of the analysis.   -21 -JHEP08(2022)175

Z → τ τ background modelling using Z → events
Events from the Z(→ τ τ ) + jets process form the dominant source of background in this measurement. They account for 79% of the background across all signal regions, and up to 90% of the background in the most boosted regime investigated in the analysis. They are estimated using MC simulations validated with data. The predictions from these MC simulations are corrected using dedicated control regions based on the Z(→ ) + jets process with kinematic properties of the events similar to those of the corresponding signal regions as explained in the following. In order to mimic as well as possible the boson kinematics and the associated production of jets in Z(→ τ τ ) + jets events selected in the signal regions, the selected Z(→ ) + jets events are modified through a simplified implementation of the embedding procedure. The kinematic properties of the boson are reconstructed with a much better resolution in the Z → decay channel than in the Z → τ τ one due to the absence of neutrinos and the excellent momentum resolution of the ATLAS detector for electrons and muons. While the original method presented in refs. [36,37] relied on substituting the detector signatures of the objects before re-reconstructing the event, the simplified embedding consists of a rescaling of the transverse momentum of each reconstructed lepton through parameterisations, followed by a recomputation of all the relevant kinematic quantities in the analysis. The method used entails a significant reduction of complexity.
Embedding techniques are of particular interest in this analysis, where no statistically significant study of the Z(→ τ τ ) + jets background can be performed in data without looking at the signal regions. In this context, the simplified embedding can be applied to data events passing the Z(→ ) + jets selection, thus obtaining a Z → τ τ control region that is orthogonal to the signal region. This control region can also be used to measure the Z → τ τ normalisation in a phase space relevant to this measurement.
The Z(→ ) + jets events are selected using the single-lepton triggers and are required to have exactly two electrons or two muons with opposite charge. The selected electrons and muons must satisfy the identification and isolation criteria defined in table 4. Additionally, the invariant mass of the dilepton system must be above 80 GeV. The selected sample contains about 9.3·10 6 data events and 99% of them are expected to come from Z(→ )+jets processes. A small contribution from diboson and top processes with two electrons or two muons in the final state is also expected and the embedding procedure is also applied to them. Contributions from processes with jets misidentified as leptons were found to be negligible. Selected events in data and simulation are then randomly separated into three subsets to provide a statistically independent control region for each of the τ e τ µ , τ lep τ had and τ had τ had signal regions.
Weights derived in simulations are applied to each event to remove the kinematic biases and normalisation effects introduced by the electron and muon trigger, reconstruction, identification, and isolation algorithms. The four-vectors of the reconstructed electrons and muons are used to pair each lepton in the Z(→ ) + jets event with a scaling term, which parameterises the effects of τ -lepton decay kinematics and of the energy calibration algorithms for τ -leptons with similar four-vectors. The scaling term is derived as a function JHEP08(2022)175 of the transverse momentum and the pseudorapidity of the τ -lepton before it decays. The original four-vectors of the electrons and muons are scaled using this term so that they match those of the visible reconstructed decay products of either leptonically or hadronically decaying τ -leptons. The Z(→ ) + jets event yields are then reweighted to account for the expected efficiencies of the reconstruction, identification and calibration steps for the visible τ decay products.
The per-lepton weights assume collinearity of the τ -lepton and its visible decay products and cannot take into account any correlation between the boson decay products. All event variables used in the signal region definitions are recalculated using the kinematics of the new final-state physics objects, and a weight is applied to each event to account for the expected trigger efficiency associated with these objects. The implementation of the new embedding procedure is validated by comparing Z → simulated events, after applying this procedure, with Z → τ τ simulations, where both the kinematic and spin-correlation effects are modelled correctly. Figure 4 shows good agreement between the distributions of the two samples for two illustrative cases and indicates that the assumptions made in calculating the weights have negligible impact on the relevant observables.
All uncertainties affecting the reconstructed physics objects used in embedding are propagated through the full procedure, including those associated with the parameterisations. Dedicated uncertainties affecting each control region are assigned to account for the differences in modelling observed between the Z → τ τ and embedded Z → MC predictions, which are expected to come from approximations associated with the simplified embedding procedure. These uncertainties are derived by studying the change in the data-to-simulation normalisation factors as events are moved between different control regions to cover the observed acceptance mismodeling. They are found to be at the 1% level and cover for the residual non-closure observed in figure 4.
Distributions for this control region, and a comparison with the embedding of all the simulated background processes, are shown in figure 5. The observed discrepancies are consistent with the results reported in dedicated measurements of the Z+jets processes [149,150]. The impact of this mismodelling on the analysis is alleviated by the use of control regions mimicking the event selection criteria after the embedding procedure is applied to data and simulated events.      Only the acceptance uncertainties in each category are considered. The shape variations, translating to potential bin-by-bin changes, were estimated to be minor and are not displayed.

Data-driven estimate of misidentified τ processes
Processes with at least one jet misidentified as an electron, muon or τ had are collectively referred to as misidentified τ background. They account for a fraction of the total background ranging from 5% to 25%, with less importance in the more boosted categories. They are evaluated in a similar fashion in the three channels of the analysis. First, data events are selected using the same criteria as for the SRs with the exception of the criteria for electron or muon identification and isolation and the criteria for τ had-vis identification. These criteria are loosened or inverted depending on the specific methodology used in each channel. Then, transfer factors are computed in dedicated control regions. These factors are used to correct for the kinematic and normalisation differences between the events with altered isolation or identification criteria and the SRs.
In the τ e τ µ channel, the misidentified τ background is estimated using the matrixmethod technique [151]. Data events are selected by removing the lepton isolation criteria from the nominal selection, and loosening the identification criteria for electrons. The expected number of fake leptons in the SR is computed from a system of equations relating the efficiencies for real ( r ) and fake leptons ( f ) to the observed event yields. The efficiencies are estimated separately for electrons and muons and are parameterised as a function of the p T and η of the leptons. The real-lepton efficiencies r are estimated using simulations, while the fake-lepton efficiencies f are measured using data events selected to have two leptons of the same charge. For the latter, the contribution from events with real leptons is subtracted using MC simulations; they account for approximately 35% of the 1333 selected events.
Dedicated uncertainties estimated for these predictions account for: statistical uncertainties in the derived efficiencies (∼10%), dependencies of f on the numbers of jets and b-tagged jets in the final state (∼35%), the dependency of r on whether they are measured in tt, Z(→ ) + jets or Z(→ τ τ ) + jets events (∼15%), and the uncertainty associated with the normalisation of the contribution from real leptons during the measurement of f (∼15%).
In the τ lep τ had channel, the misidentified τ background refers to events with a jet misidentified as a τ had-vis . Contributions with a real τ had and a jet misidentified as an electron or a muon are estimated from simulations to be negligible. The misidentified τ background is evaluated using the fake-factor technique [152]. Data events are selected if they satisfy a very loose requirement on the τ had-vis identification score but do not satisfy the 'Medium' working point criteria (such events are 'reverse-identified'). All other criteria of the nominal selection of the τ lep τ had channel are applied. Residual contributions from processes with real τ had-vis satisfying this requirement are evaluated using simulations and subtracted accordingly. They account for approximately 18% of the 136 500 selected events.
The distribution of the misidentified τ background component in the SR is obtained by multiplying the contribution of the data events selected by the reverse-identified criterion with a fake factor defined as the ratio of misidentified τ had-vis that respectively pass or fail the 'Medium' working point of the τ had-vis identification algorithm. These fake factors are parameterised as a function of the p T and track multiplicity of the τ had-vis . Two sets of fake factors are derived in separate regions and then combined for the final estimate. The first set is derived in a region enriched in W +jets processes obtained by inverting the SR criterion -26 -

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for m T (see table 4). The second set is derived in a control region enriched in QCD multijet processes obtained by inverting the isolation criteria for the selected electron or muon. An estimate of the fraction of events expected to originate from QCD multijets is used to determine the relative weighting of both sets of fake factors; it is parameterised as a function of the p T and η of the τ had-vis candidate. This estimate is obtained by scaling the number of events in the second control region by the ratio of events where the light lepton respectively fails or passes the isolation requirements, measured in another QCD-multijet-enriched region where the τ lep and τ had have the same charge.
Uncertainties in the fake factors are estimated, and account for statistical uncertainties in the fake factors and their relative weighting (∼15%), for uncertainties associated with the subtraction of the residual contributions from processes with real τ had (∼10%), and for uncertainties in the flavour composition (∼10%), taken from comparisons between the predicted and observed backgrounds in a dedicated validation region.
In the τ had τ had channel, the misidentified τ background is also determined using a fake-factor approach. The method differs slightly from the one used in the τ lep τ had channel: the fake factors are parameterised to simultaneously account for processes with one or two jets misidentified as τ had-vis . Additionally, the reconstructed τ had-vis candidates are matched to their high-level-trigger counterparts. The fake factors are estimated in the W +jets-enriched region defined for the τ lep τ had channel, but with the addition of the trigger-matching requirement in the τ had-vis definition.
Two alternative sets of fake factors are computed in control regions defined with two τ had-vis . The first alternative set is derived by inverting the requirement on the ∆η(τ had-vis , τ had-vis ) variable with respect to the signal region. The second is derived by requiring the charges of the two τ had-vis to have the same sign. The difference between these two alternative sets and the nominal fake factors derived in the W +jets-enriched control region is used to estimate the uncertainty in the composition of the misidentified τ background (∼15%). Two additional uncertainties in the misidentified τ background estimate in the τ had τ had channel are considered: the statistical uncertainty of the fake-factor calculation (∼15%), and uncertainties related to the parameterisation choice for the fake factors (∼5%).
In the τ e τ µ and τ lep τ had channels, the analysis employs control regions enriched in top processes. In these control regions, heavy-flavour jets misidentified as electrons or muons represent 70% to 80% of the expected contributions for the τ e τ µ channel, while for the τ lep τ had channel about 25% of misidentified τ had-vis originate from heavy-flavour jets. To estimate these contributions, the data-driven estimate described above is repeated with the b-jet veto replaced by a b-tagged jet requirement to mimic the control region selection.
The modelling of the misidentified τ background was validated in dedicated regions for each channel. In the τ had τ had channel, the validation region selects events with ∆η(τ had-vis , τ had-vis ) > 2.0. In the τ lep τ had channel, the validation region contains events with a light lepton and τ had-vis of the same charge. Finally, events with same-charge leptons are used as the validation region for the τ e τ µ channel. Figure 6 illustrates the modelling of the misidentified τ background in the validation region for each channel. Good agreement between the observed data and the prediction is seen in all cases.   Table 7. Summary of the different sources of uncertainty in decreasing order of their impact on σ(pp → H → τ τ ). Their observed and expected fractional impacts, both computed by the fit, are given, relative to the σ(pp → H → τ τ ) value. Experimental uncertainties for reconstructed objects combine efficiency and energy/momentum scale and resolution uncertainties. Background sample size 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.

Systematic uncertainties
Systematic uncertainties affect the yields in the various signal and control regions as well as the distribution shape of the main fit observable (m MMC τ τ ). They can be assigned to three main groups: the experimental uncertainties, the theoretical uncertainties for the backgrounds and the theoretical uncertainties for the signal. They are detailed in the following sections. Their impact on the measured pp → H → τ τ cross-section is summarised in table 7. Systematic uncertainty sources are parameterised in the statistical analysis using nuisance parameters with Gaussian priors (see section 7).

Experimental uncertainties
In addition to the object misidentification rate already discussed in section 5.2, experimental systematic uncertainties include those on the trigger, reconstruction, identification and isolation efficiencies for the final-state particle candidates, and their energy scale and resolution. These uncertainties affect the shape of the m MMC τ τ distribution, the background yields and the signal cross-section through their effects on the acceptance and the migration between different event categories.

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The dominant experimental uncertainties in the measurement of the pp → H → τ τ cross-section are related to the jet energy scale and resolution, to the τ had-vis candidate identification and energy scale, and to the object misidentification rates, as shown in table 7. The uncertainties related to the reconstruction and identification of electrons and muons and the jet b-tagging efficiency have only a minor impact on the measurement.
The jet energy scale uncertainty consists of components related to the in situ calibration of jets as well as pile-up, the extrapolation to higher transverse momentum, and uncertainties related to the different responses to quark-and gluon-initiated jets. The latter is of particular importance and covers both the uncertainties in the response of the detector to particular jet flavours and the uncertainty in the response due to the unknown fractions of quarkand gluon-initiated jets within the sample. The jet energy scale uncertainty for central jets (|η| < 1.2) varies from 1% for a wide range of jet p T (250 GeV < p T < 2000 GeV), to 5% for very low p T jets (20 GeV) and 3.5% for very high p T jets (> 2.5 TeV). The relative jet energy resolution is measured in a dedicated analysis [153] and ranges from (24 ± 5)% at 20 GeV to (6 ± 0.5)% at 300 GeV.
The uncertainties in the τ had-vis identification efficiency are in the range of 2% to 6%, while the trigger efficiency and the eBDT efficiency uncertainties are of the order of 1% to 1.5% and 1% to 2%, respectively. All these uncertainties are parameterised as a function of the τ had-vis p T and number of associated tracks (identification and trigger efficiency) or τ decay mode (eBDT efficiency). As this analysis is highly sensitive to the τ had-vis reconstruction efficiency uncertainty due to the introduction of the Z → control regions, this efficiency is left as a free parameter in the fit and measured in situ; the associated uncertainty is found to be at the 2% level. For the τ had-vis energy scale, the total uncertainty is in the range of 1% to 4%, arising from a combination of measurements: a direct measurement with Z → τ τ → µτ had-vis + 3 ν events, measurements of the calorimeter response to single particles, and comparisons between simulations using different detector geometries or Geant4 physics lists. This uncertainty is also parameterised as a function of the τ had-vis p T and number of associated tracks [141].
All of the above uncertainties affecting the different hard objects are propagated through the E miss T calculation. Additional uncertainties associated with the scale and resolution of the soft-term of the E miss T [144] are also considered. The luminosity uncertainty is considered only for the background samples whose normalisations are not determined in data (diboson, Z → , non-(H → τ τ ) Higgs) and to derive the signal cross-sections from the measured yields. The uncertainty in the combined 2015-2018 integrated luminosity is 1.7% [154], obtained using the LUCID-2 detector [155] for the primary luminosity measurements.

Background theoretical uncertainties
Theoretical uncertainties are considered for the two main background contributions in this analysis: Z+jets and tt. The normalisation of these backgrounds is determined in the fit to the data in the signal and control regions (see section 7). The theoretical uncertainties of Z+jets and tt are therefore parameterised to account for the migration across the analysis regions and to account for their impact on the m MMC τ τ templates in each region.

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For Z+jets, uncertainties were considered for renormalisation (µ r ), factorisation (µ f ) and resummation scale (µ q ) variations, for the jet-to-parton matching scheme (CKKW), for variations in the choice of α s value, and for the choice of PDFs. Uncertainties from missing higher orders were evaluated [156] using six variations of the QCD µ r and µ f scales in the matrix elements by factors of 0.5 and 2, avoiding the extreme variations in opposite directions. Uncertainties in the nominal PDF set were evaluated using 100 replica variations; an uncertainty is derived in each bin of the m MMC τ τ templates by evaluating the ±1σ spread of the 100 replica variations. The effect of the uncertainty in the strong coupling constant α s was assessed by variations of ±0.001. The resummation scale uncertainties were estimated using generator-level parameterisations derived from samples with µ q varied by factors of 2 and 0.5 from its nominal value. Similarly, the jet-to-parton matching uncertainties were estimated using generator-level parameterisations derived from samples with the CKKW parameter set to 15 GeV and 30 GeV, compared to the nominal value of 20 GeV.
For tt, uncertainties were considered for the choice of matrix element and parton shower generators, the choice of model for initial-and final-state radiation (ISR and FSR respectively), and the choice of PDFs. The uncertainty due to ISR was estimated by simultaneously varying the h damp parameter and the µ r and µ f scales, and propagating the α s uncertainties through the Var3c parameter of the A14 tune as described in ref. [157]. The impact of FSR was evaluated by varying the µ r scale for emissions from the parton shower by factors of 2 and 0.5. The impact of using a different matrix element was evaluated by comparing the nominal tt sample with an event sample produced using MadGraph5_aMC@NLO 2.6.0 instead of Powheg Box v2 but keeping the same parton shower model. The impact of using a different parton shower and hadronisation model was evaluated by comparing the nominal tt sample with an event sample which was interfaced with Herwig 7.04 [158,159] instead of Pythia 8 and used the H7UE set of tuned parameters [159] and the MMHT2014lo PDF set [160].
The NNPDF3.0lo replicas were used to evaluate the PDF uncertainties for the nominal PDF. For both Z+jets and tt, the central value of the PDF was additionally compared with the central values of the CT14nnlo [161] and MMHT2014nnlo [160] PDF sets.
Theory uncertainties in Z+jets and tt predictions represent a sub-leading contribution, compared to signal theoretical uncertainties and experimental uncertainties (see table 7).
For renormalisation and factorisation scale variations and PDF uncertainties, their impact on the extrapolation factor between each SR and its corresponding Z → control region, and on the shape of the m MMC τ τ distribution, is treated as uncorrelated across the different categories. This choice is driven by the structure of the statistical analysis, which employs a dedicated control region to constrain the Z+jets prediction in each signal region.

Signal theoretical uncertainties
Signal theoretical uncertainties are the dominant source of uncertainty for this analysis. For each signal process, several sources of uncertainty are considered, including the uncertainty in the total inclusive cross-section (evaluated only for the pp → H → τ τ cross-section measurement), the parton-shower and hadronisation model effect and the migration uncertainties among the STXS bins. The migration uncertainties stem from the -31 -JHEP08(2022)175 determination of the kinematic quantities used in the STXS framework as well the expected relative contribution of each process in the signal regions. These uncertainties can affect signal acceptance in the various SRs as well as the m MMC τ τ shape. For all production modes, uncertainties are estimated for the PDF and α s , the parton shower and hadronisation model, and missing higher orders in the matrix element calculation. PDF and α s uncertainties were estimated using the PDF4LHC15nlo set of eigenvectors. The impact of using a different parton shower and hadronisation model is evaluated by comparing the nominal sample with an event sample which was interfaced with Herwig 7 instead of Pythia 8. The effects on the signal expectations are treated as uncorrelated between the production modes, and the comparison leads to the largest uncertainty in the pp → H → τ τ cross-section measurement. Uncertainties from missing higher orders are calculated following the methodology outlined in refs. [27,162] and are determined as follows.
For the ggF process, 15 main sources of uncertainty were considered. Four of these are jet-multiplicity-related uncertainties due to missing high-order corrections, and are estimated using the approach described in refs. [27,163]. Three uncertainties parameterise the uncertainties in modelling the Higgs boson p T and the 0-jet bin, one of which encapsulates the treatment of the top-quark mass in the loop corrections. Three uncertainties take into account dijet mass migrations across the STXS bin boundaries. Finally, three uncertainties are considered for the modelling of the ggF process in the VBF phase space. Two of them are derived using the method described in ref. [164], from the study of the selection of exactly two or at least three jets. The third one is derived from the comparison of the Powheg prediction with MadGraph5_aMC@NLO samples using the FxFx prescriptions [165] to merge the jet multiplicities and it also applies to the V H phase space. As the ggF process in the VBF phase space is difficult to model, the impact of increasing its contribution in the VBF_1 category was estimated. Doubling its contribution induced a 7% shift in the apparent VBF production cross-section.
For the VBF and V H processes, ten uncertainties related to the STXS categorisation were considered: one related to the inclusive cross-section of the process, one related to the two-jet requirement, one related to the Higgs boson p T selection at 200 GeV, one related to the p T balance between the Higgs boson and the dijet system in events with two or three jets, and six uncertainties taking into account dijet mass migrations across the STXS bin boundaries.
For the ttH process, six other uncertainties are included: one related to the inclusive cross-section of the process, and five migration uncertainties related to Higgs boson p T boundaries in the STXS scheme.

Statistical analysis
A statistical analysis of the collected data is performed to measure the pp → H → τ τ crosssections. The procedure relies on a likelihood function constructed as the product of Poisson probability terms over the bins of the input distributions. The uncertainties affecting the model (see section 6) are included in the likelihood function through nuisance parameters that are constrained by Gaussian probability terms that multiply the Poisson probability -32 -

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terms. The parameters of interest (POIs) of the model are estimated by maximising the likelihood. The likelihood function comprises 32 signal regions and 36 control regions. In each signal region, Poisson terms describe the expected event counts in each bin of the m MMC τ τ distribution, while in each control region a single Poisson term describes the total expected event yield in that region. Figure 7 illustrates the usage of the signal and control regions in the construction of the likelihood function. The test statistic is constructed from the profile likelihood ratio and the confidence intervals on the parameters of interest are derived unsing the asymptotic approximation [166].
The normalisation of the Z → τ τ background is left as a freely floating parameter in the fit in several regions. Each signal region in the boost, VBF and V(had)H categories is paired with an associated embedded Z → control region and both share a common Z → τ τ normalisation factor. Additionally, a common Z → τ τ normalisation factor is shared between the ttH_0 and ttH_1 signal regions. In total, 31 floating normalisation factors are defined in order to constrain the yields of the Z → τ τ background in the signal regions. The normalisation of the top processes is also allowed to float freely with six normalisation factors defined for boost, VBF, and V(had)H signal regions in the τ e τ µ and τ lep τ had channels separately and one for the ttH categories in the τ had τ had channel. The other backgrounds are normalised to their expected cross-section and the integrated luminosity of the recorded data.
In the signal regions, a smoothing procedure is applied to remove potentially large local fluctuations in the m MMC The m MMC τ τ discriminant distributions in each SR are binned in a way that maximises the significance of each targeted signal production mode, taking into account the full uncertainties. Effectively, this leads to a fine binning near the resonant Z → τ τ peak with coarser binning further away from it.
Three different measurements are performed. They include the branching ratio of H → τ τ and are performed with true Higgs boson rapidity |y H | < 2.5. They differ in the definition of the POIs (see also figure 1): 1. pp → H → τ τ cross-section: a single POI, corresponding to the pp → H → τ τ cross-section, is estimated by the fit. In the likelihood function, the signal yields in each category are parameterised as the product of the pp → H → τ τ cross-section, the integrated luminosity and the efficiency (including the acceptance of the ATLAS detector) of the selection for a SM Higgs boson with a mass of 125.09 GeV. In this measurement, the relative contributions to the pp → H → τ τ cross-section from the various production modes are fixed to the SM predictions.

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Signal Regions  The VBF production cross-section measurement is the most precise of the four dominant production mechanisms. The theoretical uncertainties in VBF production are smaller than in the other channels, and the VBF_1 categories represent the best combination of high signal yields and purity in this measurement. The measured VBF cross-section is 0.197 ± 0.028(stat) + 0.032 − 0.026 (syst) pb. The second most precisely measured cross-section is that of ggF, 2.7 ± 0.4(stat) + 0.9 − 0.6 (syst) pb, corresponding to an observed (expected) significance of 3.9σ (4.6σ). The V H and ttH production modes are determined with lower precision. The measured V H cross-section is 0.12 ± 0.06(stat) ± 0.04(syst) pb, while the ttH cross-section is 0.033 + 0.033 − 0.029 (stat) + 0.022 − 0.017 (syst) pb. Figure 13 (b) illustrates the observed correlation between the measured cross-section parameters in the fit. The ggF cross-section exhibits an anticorrelation of 24% and 29% with the VBF and V H cross-sections respectively. This is caused by a significant contribution of ggF events to the VBF_0, VH_0 and VH_1 categories as illustrated by figure 2. The simultaneous measurement of the cross-sections of the four dominant production modes is compatible with the SM expectations, with a p-value of 0.88. The EW production mode includes the VBF and qq → V (→ qq)H processes and is measured in m jj intervals. In the interval with m jj between 60 GeV and 120 GeV, the measurement has an uncertainty of 63%. The EW production mode for events with m jj greater than 120 GeV is measured with an uncertainty of 26% and is the most precise crosssection determined within the simplified template cross-section framework in this paper. It exhibits an anti-correlation of approximately 40% with the cross-section for gluon-gluon fusion events produced in the same interval (m jj > 350 GeV) as illustrated on figure 14(b).        Table 13. Observed event yields and predictions as computed by the fit in the boost signal regions of the τ e τ µ channel. Uncertainties include statistical and systematic components. The prediction for each sample is determined from the likelihood fit performed to measure the pp → H → τ τ cross-section.      ) for all events in the boost categories of the τ had τ had channel. The bottom panel shows the differences between the numbers of observed data events and expected background events (black points). The observed Higgs boson signal, corresponding to (σ × B)/(σ × B) SM = 0.93, is shown with a filled red histogram. Entries with values above the x-axis range are shown in the last bin of each distributions. The dashed band indicates the total uncertainty on the total predicted yields. The prediction for each sample is determined from the likelihood fit performed to measure the pp → H → τ τ cross-section.

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