Physics Letters B 779 (2018) 283–316 Contents lists available at ScienceDirect Physics Letters B www.elsevier.com/locate/physletb Observation of the Higgs boson decay to a pair of τ leptons with the CMS detector .The CMS Collaboration � CERN, Switzerland a r t i c l e i n f o a b s t r a c t Article history: Received 1 August 2017 Received in revised form 1 February 2018 Accepted 2 February 2018 Available online 7 February 2018 Editor: M. Doser Keywords: CMS Physics Tau Higgs Observation LHC A measurement of the H → ττ signal strength is performed using events recorded in proton–proton collisions by the CMS experiment at the LHC in 2016 at a center-of-mass energy of 13 TeV. The data set corresponds to an integrated luminosity of 35.9 fb−1. The H → ττ signal is established with a significance of 4.9 standard deviations, to be compared to an expected significance of 4.7 standard deviations. The best fit of the product of the observed H → ττ signal production cross section and branching fraction is 1.09+0.27 −0.26 times the standard model expectation. The combination with the corresponding measurement performed with data collected by the CMS experiment at center-of-mass energies of 7 and 8 TeV leads to an observed significance of 5.9 standard deviations, equal to the expected significance. This is the first observation of Higgs boson decays to τ leptons by a single experiment. © 2018 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP3. 1. Introduction In the standard model (SM) of particle physics [1–3], elec- troweak symmetry breaking is achieved via the Brout–Englert– Higgs mechanism [4–9], leading, in its minimal version, to the prediction of the existence of one physical neutral scalar particle, commonly known as the Higgs boson (H). A particle compatible with such a boson was observed by the ATLAS and CMS experi- ments at the CERN LHC in the ZZ, γ γ , and W+W− decay chan- nels [10–12], during the proton–proton (pp) data taking period in 2011 and 2012 at center-of-mass energies of √ s = 7 and 8 TeV, re- spectively. Subsequent results from both experiments, described in Refs. [13–18], established that the measured properties of the new particle, including its spin, CP properties, and coupling strengths to SM particles, are consistent with those expected for the Higgs bo- son predicted by the SM. The mass of the Higgs boson has been determined to be 125.09 ± 0.21 (stat) ± 0.11 (syst) GeV, from a combination of ATLAS and CMS measurements [19]. To establish the mass generation mechanism for fermions, it is necessary to probe the direct coupling of the Higgs boson to such particles. The most promising decay channel is τ+τ− , because of the large event rate expected in the SM compared to the μ+μ− decay channel (B(H → τ+τ−) = 6.3% for a mass of 125.09 GeV), � E-mail address: cms-publication-committee-chair@cern.ch. and of the smaller contribution from background events with re- spect to the bb decay channel. Searches for a Higgs boson decaying to a τ lepton pair were performed at the LEP [20–23], Tevatron [24,25], and LHC colliders. Using pp collision data at √ s = 7 and 8 TeV, the CMS Collabora- tion showed evidence for this process with an observed (expected) significance of 3.2 (3.7) standard deviations (s.d.) [26]. The ATLAS experiment reported evidence for Higgs bosons decaying into pairs of τ leptons with an observed (expected) significance of 4.5 (3.4) s.d. for a Higgs boson mass of 125 GeV [27]. The combination of the results from both experiments yields an observed (expected) significance of 5.5 (5.0) s.d. [28]. This Letter reports on a measurement of the H → ττ signal strength. The analysis targets both the gluon fusion and the vector boson fusion production mechanisms. The analyzed data set corre- sponds to an integrated luminosity of 35.9 fb−1, and was collected in 2016 in pp collisions at a center-of-mass energy of 13 TeV. In the following, the symbol � refers to electrons or muons, the sym- bol τh refers to τ leptons reconstructed in their hadronic decays, and H → τ+τ− and H → W+W− are simply denoted as H → ττ and H → WW, respectively. All possible ττ final states are stud- ied, except for those with two muons or two electrons because of the low branching fraction and large background contribution. The analysis covers about 94% of all possible ττ final states. https://doi.org/10.1016/j.physletb.2018.02.004 0370-2693/© 2018 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP3. https://doi.org/10.1016/j.physletb.2018.02.004 http://www.ScienceDirect.com/ http://www.elsevier.com/locate/physletb http://creativecommons.org/licenses/by/4.0/ mailto:cms-publication-committee-chair@cern.ch https://doi.org/10.1016/j.physletb.2018.02.004 http://creativecommons.org/licenses/by/4.0/ http://crossmark.crossref.org/dialog/?doi=10.1016/j.physletb.2018.02.004&domain=pdf 284 The CMS Collaboration / Physics Letters B 779 (2018) 283–316 2. The CMS detector The central feature of the CMS apparatus is a superconducting solenoid of 6 m internal diameter, providing a magnetic field of 3.8 T. Within the solenoid volume, there are a silicon pixel and strip tracker, a lead tungstate crystal electromagnetic calorimeter (ECAL), and a brass and scintillator hadron calorimeter (HCAL), each composed of a barrel and two endcap sections. Forward calorimeters extend the pseudorapidity coverage provided by the barrel and endcap detectors. Muons are detected in gas-ionization chambers embedded in the steel flux-return yoke outside the solenoid. Events of interest are selected using a two-tiered trigger sys- tem [29]. The first level (L1), composed of custom hardware pro- cessors, uses information from the calorimeters and muon detec- tors to select events at a rate of around 100 kHz within a time interval of less than 4 μs. The second level, known as the high-level trigger (HLT), consists of a farm of processors running a version of the full event reconstruction software optimized for fast process- ing, and reduces the event rate to about 1 kHz before data storage. Significant upgrades of the L1 trigger during the first long shut- down of the LHC have benefited this analysis, especially in the τhτh channel. These upgrades improved the τh identification at L1 by giving more flexibility to object isolation, allowing new tech- niques to suppress the contribution from additional pp interactions per bunch crossing, and to reconstruct the L1 τh object in a fidu- cial region that matches more closely that of a true hadronic τ decay. The flexibility is achieved by employing high bandwidth op- tical links for data communication and large field-programmable gate arrays (FPGAs) for data processing. A more detailed description of the CMS detector, together with a definition of the coordinate system used and the relevant kine- matic variables, can be found in Ref. [30]. 3. Simulated samples Signal and background processes are modeled with samples of simulated events. The signal samples with a Higgs boson produced through gluon fusion (ggH), vector boson fusion (VBF), or in as- sociation with a W or Z boson (WH or ZH), are generated at next-to-leading order (NLO) in perturbative quantum chromody- namics (pQCD) with the powheg 2.0 [31–35] generator. The minlo hvJ [36] extension of powheg 2.0 is used for the WH and ZH sim- ulated samples. The set of parton distribution functions (PDFs) is NNPDF30_nlo_as_0118 [37]. The ttH process is negligible. The var- ious production cross sections and branching fractions for the SM Higgs boson production, and their corresponding uncertainties are taken from Refs. [38–40] and references therein. The MG5_amc@nlo [41] generator is used for Z + jets and W + jets processes. They are simulated at leading order (LO) with the MLM jet matching and merging [42]. The MG5_amc@nlo gen- erator is also used for diboson production simulated at next-to- LO (NLO) with the FxFx jet matching and merging [43], whereas powheg 2.0 and 1.0 are used for tt and single top quark pro- duction, respectively. The generators are interfaced with pythia 8.212 [44] to model the parton showering and fragmentation, as well as the decay of the τ leptons. The pythia parameters affecting the description of the underlying event are set to the CUETP8M1 tune [45]. Generated events are processed through a simulation of the CMS detector based on Geant4 [46], and are reconstructed with the same algorithms used for data. The simulated samples include additional pp interactions per bunch crossing, referred to as “pile- up”. The effect of pileup is taken into account by generating con- current minimum bias collision events generated with pythia. The simulated events are weighted such that the distribution of the number of additional pileup interactions, estimated from the mea- sured instantaneous luminosity for each bunch crossing, matches that in data, with an average of approximately 27 interactions per bunch crossing. 4. Event reconstruction The reconstruction of observed and simulated events relies on the particle-flow (PF) algorithm [47], which combines the infor- mation from the CMS subdetectors to identify and reconstruct the particles emerging from pp collisions: charged hadrons, neutral hadrons, photons, muons, and electrons. Combinations of these PF objects are used to reconstruct higher-level objects such as jets, τh candidates, or missing transverse momentum. The reconstructed vertex with the largest value of summed physics-object p2 T is taken to be the primary pp interaction vertex. The physics objects are the objects constructed by a jet finding algorithm [48,49] applied to all charged tracks associated with the vertex, including tracks from lepton candidates, and the corresponding associated missing transverse momentum. Muons are identified with requirements on the quality of the track reconstruction and on the number of measurements in the tracker and the muon systems [50]. Electrons are identified with a multivariate discriminant combining several quantities describing the track quality, the shape of the energy deposits in the ECAL, and the compatibility of the measurements from the tracker and the ECAL [51]. To reject non-prompt or misidentified leptons, a relative lepton isolation is defined as: I� ≡ ∑ charged pT + max ( 0, ∑ neutral pT − 1 2 ∑ charged, PU pT ) p� T . (1) In this expression, ∑ charged pT is the scalar sum of the transverse momenta of the charged particles originating from the primary vertex and located in a cone of size �R = √ (�η)2 + (�φ)2 = 0.4 (0.3) centered on the muon (electron) direction. The sum ∑ neutral pT represents a similar quantity for neutral particles. The contribution of photons and neutral hadrons originating from pileup vertices is estimated from the scalar sum of the transverse momenta of charged hadrons in the cone originating from pileup vertices, ∑ charged, PU pT. This sum is multiplied by a factor of 1/2, which corresponds approximately to the ratio of neutral to charged hadron production in the hadronization process of inelastic pp col- lisions, as estimated from simulation. The expression p� T stands for the pT of the lepton. Isolation requirements used in this analysis, based on I� , are listed in Table 1. Jets are reconstructed with an anti-kT clustering algorithm im- plemented in the FastJet library [49,52]. It is based on the cluster- ing of neutral and charged PF candidates within a distance param- eter of 0.4. Charged PF candidates not associated with the primary vertex of the interaction are not considered when building jets. An offset correction is applied to jet energies to take into account the contribution from additional pp interactions within the same or nearby bunch crossings. The energy of a jet is calibrated based on simulation and data through correction factors [53]. In this anal- ysis, jets are required to have pT greater than 30 GeV and |η| less than 4.7, and are separated from the selected leptons by a �R of at least 0.5. The combined secondary vertex (CSV) algo- rithm is used to identify jets that are likely to originate from a b quark (“b jets”). The algorithm exploits the track-based lifetime in- formation together with the secondary vertices associated with the jet to provide a likelihood ratio discriminator for the b jet identi- fication. A set of pT-dependent correction factors are applied to The CMS Collaboration / Physics Letters B 779 (2018) 283–316 285 Table 1 Kinematic selection requirements for the four di-τ decay channels. The trigger requirement is defined by a combination of trigger candidates with pT over a given threshold (in GeV), indicated inside parentheses. The pseudorapidity thresholds come from trigger and object reconstruction constraints. The pT thresholds for the lepton selection are driven by the trigger requirements, except for the leading τh candidate in the τhτh channel, the τh candidate in the μτh and eτh channels, and the muon in the eμ channel, where they have been optimized to increase the significance of the analysis. Channel Trigger requirement Lepton selection pT (GeV) η Isolation τhτh τh(35)&τh(35) pτh T > 50 & 40 |ητh | < 2.1 MVA τh ID μτh μ(22) pμ T > 23 |ημ| < 2.1 Iμ < 0.15 pτh T > 30 |ητh | < 2.3 MVA τh ID μ(19)&τh(21) 20 < pμ T < 23 |ημ| < 2.1 Iμ < 0.15 pτh T > 30 |ητh | < 2.3 MVA τh ID eτh e(25) pe T > 26 |ηe| < 2.1 Ie < 0.1 pτh T > 30 |ητh | < 2.3 MVA τh ID eμ e(12)&μ(23) pe T > 13 |ηe| < 2.5 Ie < 0.15 pμ T > 24 |ημ| < 2.4 Iμ < 0.2 e(23)&μ(8) pe T > 24 |ηe| < 2.5 Ie < 0.15 pμ T > 15 |ημ| < 2.4 Iμ < 0.2 simulated events to account for differences in the b tagging effi- ciency between data and simulation. The working point chosen in this analysis gives an efficiency for real b jets of about 70%, and for about 1% of light flavor or quark jets being misidentified. Hadronically decaying τ leptons are reconstructed with the hadron-plus-strips (HPS) algorithm [54,55], which is seeded with anti-kT jets. The HPS algorithm reconstructs τh candidates on the basis of the number of tracks and of the number of ECAL strips in the η–φ plane with energy deposits, in the 1-prong, 1-prong + π0(s), and 3-prong decay modes. A multivariate (MVA) discriminator [56], including isolation and lifetime information, is used to reduce the rate for quark- and gluon-initiated jets to be identified as τh candidates. The working point used in this anal- ysis has an efficiency of about 60% for genuine τh, with about 1% misidentification rate for quark- and gluon-initiated jets, for a pT range typical of τh originating from a Z boson. Electrons and muons misidentified as τh candidates are suppressed using dedi- cated criteria based on the consistency between the measurements in the tracker, the calorimeters, and the muon detectors [54,55]. The working points of these discriminators depend on the decay channel studied. The τh energy scale in simulation is corrected per decay mode, on the basis of a measurement in Z → ττ events. The rate and the energy scale of electrons and muons misidentified as τh candidates are also corrected in simulation, on the basis of a tag-and-probe measurement [57] in Z → �� events. All particles reconstructed in the event are used to determine the missing transverse momentum, �pmiss T . The missing transverse momentum is defined as the negative vectorial sum of the trans- verse momenta of all PF candidates [58]. It is adjusted for the effect of jet energy corrections. Corrections to the �pmiss T are applied to reduce the mismodeling of the simulated Z + jets, W + jets and Higgs boson samples. The corrections are applied to the simulated events on the basis of the vectorial difference of the measured missing transverse momentum and total transverse momentum of neutrinos originating from the decay of the Z, W, or Higgs boson. Their average effect is the reduction of the pmiss T obtained from simulation by a few GeV. The visible mass of the ττ system, mvis, can be used to sep- arate the H → ττ signal events from the large contribution of irreducible Z → ττ events. However, the neutrinos from the τ lepton decays carry a large fraction of the τ lepton energy and re- duce the discriminating power of this variable. The svfit algorithm combines the �pmiss T with the four-vectors of both τ candidates to calculate a more accurate estimate of the mass of the parent bo- son, denoted as mττ . The resolution of mττ is between 15 and 20% depending on the ττ final state. A detailed description of the al- gorithm can be found in Ref. [59]. Both variables are used in the analysis, as detailed in Section 6, and mvis is preferred over mττ when the background from Z → �� events is large. 5. Event selection Selected events are classified into the various decay channels according to the number of selected electrons, muons, and τh candidates. The resulting event samples are made mutually exclu- sive by discarding events that have additional loosely identified and isolated muons or electrons. Leptons must meet the mini- mum requirement that the distance of closest approach to the primary vertex satisfies |dz| < 0.2 cm along the beam direction, and |dxy | < 0.045 cm in the transverse plane. The two leptons as- signed to the Higgs boson decay are required to have opposite-sign electric charges. In the μτh channel, events are selected with a combination of online criteria that require at least one isolated muon trigger candidate, or at least one isolated muon and one τh trigger candidate, depending on the offline muon pT. In the eτh channel, the trigger system requires at least one isolated electron object, whereas in the eμ channel, the triggers rely on the pres- ence of both an electron and a muon, allowing lower online pT thresholds. In the τhτh channel, the trigger selects events with two loosely isolated τh objects. The selection criteria are summarized in Table 1. In the �τh channels, the large W + jets background is reduced by requiring the transverse mass, mT, to satisfy mT ≡ √ 2p� T pmiss T [1 − cos(�φ)] < 50 GeV, (2) where p� T is the transverse momentum of the lepton �, and �φ is the azimuthal angle between its direction and the �pmiss T . In the eμ channel, the tt background is reduced by requir- ing pζ − 0.85 pvis ζ > −35 or −10 GeV depending on the category, where pζ is the component of the �pmiss T along the bisector of the transverse momenta of the two leptons and pvis ζ is the sum of the components of the lepton transverse momenta along the same di- rection [60]. This selection criterion has a high signal efficiency because the �pmiss T is typically oriented in the same direction as the visible di-τ system in signal events. In addition, events with a b- tagged jet are discarded to further suppress the tt background in the eμ channel. 286 The CMS Collaboration / Physics Letters B 779 (2018) 283–316 Table 2 Category selection and observables used to build the 2D kinematic distributions. The events neither selected in the 0-jet nor in the VBF category are included in the boosted category, as denoted by “Others”. 0-jet VBF Boosted Selection τhτh No jet ≥2 jets, pττ T > 100 GeV, �ηjj > 2.5 Others μτh No jet ≥2 jets, mjj > 300 GeV, pττ T > 50 GeV, pτh T > 40 GeV Others eτh No jet ≥2 jets, mjj > 300 GeV, pττ T > 50 GeV Others eμ No jet 2 jets, mjj > 300 GeV Others Observables τhτh mττ mjj , mττ pττ T , mττ μτh τh decay mode, mvis mjj , mττ pττ T , mττ eτh τh decay mode, mvis mjj , mττ pττ T , mττ eμ pμ T , mvis mjj , mττ pττ T , mττ 6. Categorization The event sample is split into three mutually exclusive cat- egories per decay channel. In each category the two variables that maximize the H → ττ sensitivity are chosen to build two- dimensional (2D) distributions. The three categories are defined as: • 0-jet: This category targets Higgs boson events produced via gluon fusion. The two variables chosen to extract the results are mvis and the reconstructed τh candidate decay mode (in the μτh and eτh decay channels) or the pT of the muon (in the eμ channel). The Z → �� background is large in the 1-prong and 1-prong + π0(s) τh decay modes in the μτh and eτh channels. The mvis variable is used as a final discrimi- nant in the fit instead of mττ because it separates the signal from the Z → �� background, which peaks around the Z boson mass. The reconstructed τh candidate decay mode is used as the other discriminant in the μτh and eτh decay channels be- cause the Z → �� background is negligible for τh reconstructed in the 3-prong decay mode, leading to an increased signal-to- background ratio for this particular decay mode, and several systematic uncertainties related to the τh decay mode can be constrained with more precision. The 2D distributions for the signal and Z → �� background in the 0-jet category of the μτh decay channel are shown in Fig. 1 (top). In the τhτh decay channel, only one observable, mττ , is considered because of the low event yields due to the relatively high pT thresholds on the τh at trigger level, and because of the sharply falling τh pT distribution. Simulations indicate that about 98% of sig- nal events in the 0-jet category correspond to the gluon fusion production mechanism. • VBF: This category targets Higgs boson events produced via VBF. Events are selected with at least two (exactly two) jets with pT > 30 GeV in the τhτh, μτh, and eτh (eμ) channels. In the μτh, eτh, and eμ channels, the two leading jets are re- quired to have an invariant mass, mjj , larger than 300 GeV. The variable pττ T , defined as the magnitude of the vectorial sum of the �pT of the visible decay products of the τ lep- tons and �pmiss T , is required to be greater than 50 (100) GeV in the μτh and eτh (τhτh) channels to reduce the contribution from W + jets backgrounds. This selection criterion also sup- presses the background from SM events composed uniquely of jets produced through the strong interaction, referred to as quantum chromodynamics (QCD) multijet events. In addition, the pT threshold on the τh candidate is raised to 40 GeV in the μτh channel, and the two leading jets in the τhτh channel should be separated in pseudorapidity by �η > 2.5. The two observables in the VBF category are mττ and mjj . The 2D dis- tributions for the signal and Z → ττ background in the VBF category of the μτh decay channel are shown in Fig. 1 (cen- ter). Integrating over the whole mjj phase space, up to 57% of the signal events in the VBF category are produced in the VBF production mode, but this proportion increases with mjj . • Boosted: This category contains all the events that do not en- ter one of the previous categories, namely events with one jet and events with several jets that fail the specific requirements of the VBF category. It contains gluon fusion events produced in association with one or more jets (78–80% of signal events), VBF events where one of the jets has escaped detection or has low mjj (11–13%), as well as Higgs bosons produced in asso- ciation with a W or a Z boson decaying hadronically (4–8%). While mττ is chosen as one of the dimensions of the distri- butions, pττ T is taken as the second dimension to specifically target Higgs boson events produced in gluon fusion, with a Lorentz-boosted boson recoiling against jets. Most background processes, including W + jets and QCD multijet events, typi- cally have low pττ T . The 2D distributions for the signal and W + jets background in the boosted category of the μτh decay channel are shown in Fig. 1 (bottom). The categories and the variables used to build the 2D distribu- tions are summarized in Table 2. The results of the analysis are extracted with a global maximum likelihood fit based on the 2D distributions in the various signal regions, and on some control re- gions, detailed in Section 7, that constrain the normalizations of the main backgrounds. 7. Background estimation The largest irreducible source of background is the Drell–Yan production of Z/γ ∗ → ττ , ��. In order to correct the yield and distributions of the Z/γ ∗ → ττ , �� simulations to better repro- duce the Drell–Yan process in data, a dedicated control sample of Z/γ ∗ → μμ events is collected in data with a single-muon trigger, and compared to simulation. The control sample is composed of events with two well-identified and well-isolated opposite-charge muons with pT greater than 25 GeV and an invariant mass be- tween 70 and 110 GeV. More than 99% of events in this region come from Z/γ ∗ → μμ decays. Differences in the distributions of m��/ττ and pT(��/ττ ) in data and in simulations are observed in this control region, and 2D weights based on these variables are derived and applied to simulated Z/γ ∗ → ττ , �� events in the sig- nal region of the analysis. In addition, corrections depending on mjj are derived from the Z/γ ∗ → μμ region and applied to the Z/γ ∗ → ττ , �� simulation for events with at least two jets pass- ing the VBF category selection criteria. After this reweighting, good agreement between data in the Z/γ ∗ → μμ region and simula- tion is found for all other variables. The simulated sample is split, on the basis of the matching between objects at the generator and The CMS Collaboration / Physics Letters B 779 (2018) 283–316 287 Fig. 1. Distributions for the signal (left) and for some dominant background processes (right) of the two observables chosen in the 0-jet (top), VBF (center), and boosted (bottom) categories in the μτh decay channel. The background processes are chosen for illustrative purpose for their separation from the signal. The Z → μμ background in the 0-jet category is concentrated in the regions where the visible mass is close to 90 GeV and is negligible when the τh candidate is reconstructed in the 3-prong decay mode. The Z → ττ background in the VBF category mostly lies at low mjj values whereas the distribution of VBF signal events extends to high mjj values. In the boosted category, the W+jets background, which behaves similarly to the QCD multijet background, is rather flat with respect to mττ , and is concentrated at low pττ T values. These distributions are not used as such to extract the results. 288 The CMS Collaboration / Physics Letters B 779 (2018) 283–316 Fig. 2. Control regions enriched in the W + jets background used in the maximum likelihood fit, together with the signal regions, to extract the results. The normalization of the predicted background distributions corresponds to the result of the global fit. These regions, defined with mT > 80 GeV, control the yields of the W + jets background in the μτh and eτh channels. The constraints obtained in the boosted categories are propagated to the VBF categories of the corresponding channels. at the detector levels, into events with prompt leptons (muons or electrons), hadronic decays of the τ leptons, and jets or misiden- tified objects at the detector level that do not have corresponding objects at generator level within �R < 0.2. The electroweak pro- duction of Z bosons in association with two jets is also taken into account in the analysis; it contributes up to 8% of the Z boson pro- duction in the VBF category. The background from W + jets production contributes signifi- cantly to the μτh and eτh channels, when the W boson decays lep- tonically and a jet is misidentified as a τh candidate. The W + jets distributions are modeled using simulation, while their yields are estimated using data, as detailed below. In the boosted and VBF categories, statistical fluctuations in the distributions from simula- tions are reduced by relaxing the isolation of the τh and � candi- dates, which has been checked not to bias the distributions. The simulated sample is normalized in such a way as to obtain agree- ment between the yields in data and the predicted backgrounds in a control region enriched in the W + jets background, which is ob- tained by applying all selection criteria, with the exception that mT is required to be greater than 80 GeV instead of less than 50 GeV. The W + jets event purity in this region varies from about 50% in the boosted category to 85% in the 0-jet category. The high-mT sidebands described above, for each category, are considered as control regions in this fit. The constraints obtained in the boosted category are extrapolated to the VBF category of the corresponding decay channel because the topology of the boosted and VBF events is similar, and few data events would pass the high-mT sideband selection in the VBF category. Fig. 2 shows the control regions with mT > 80 GeV in the 0-jet and boosted categories of the μτh and eτh channels. These control regions are composed of only one bin because they are used solely to constrain the normalization of the W + jets process. In the eμ and τhτh decay channels, the W + jets background is small compared to other backgrounds, and its con- tribution is estimated from simulations. The QCD multijet events constitute another important source of reducible background in the �τh channels, and it is entirely estimated from data. Various control samples are constituted to estimate the shape and the yield of the QCD multijet background in these channels, as explained below: 1. The raw yield is extracted using a sample where the � and the τh candidates have the same sign. Using this sample, the QCD multijet process is estimated from data by subtracting the con- tribution of the Drell–Yan, tt, diboson, and W + jets processes. 2. The yield obtained above is corrected to account for differ- ences between the background composition in the same-sign and opposite-sign regions. The extrapolation factor between the same-sign and opposite-sign regions is determined by comparing the yield of the QCD multijet background for events with � candidates passing inverted isolation criteria, in the same-sign and opposite-sign regions. It is constrained and measured by adding to the global fit the opposite-sign region where the � candidates pass inverted isolation criteria, using the QCD multijet background estimate from the same-sign re- gion with � candidates passing inverted isolation criteria. For the same reasons as in the case of the W + jets background, the constraints are also extrapolated to the VBF signal region. Fig. 3 shows these control regions for the 0-jet and boosted categories of the μτh and eτh channels; the observable is mvis or mττ to provide discrimination between the QCD multijet and the Z → ττ processes. 3. The 2D distributions of the QCD multijet background are esti- mated from a region with same-sign leptons, as for the yield estimate, but the isolation of the � and τh candidates is ad- ditionally relaxed to reduce the statistical fluctuations in the distributions. Again the contribution of the Drell–Yan, tt, dibo- son, and W + jets processes are subtracted from data to extract the QCD multijet contribution in this region. The same technique is used in the eμ decay channel, but no con- trol region is included in the fit because QCD multijet events con- tribute little to the total background in this decay channel. In the τhτh channel, the large QCD multijet background is esti- mated with a slightly different method, from a sample composed of events with opposite-sign τh satisfying a relaxed isolation re- quirement, disjoint from the signal region. In this region, the QCD multijet background shape and yield are obtained by subtracting the contribution of the Drell–Yan, tt, and W + jets processes, esti- mated as explained above, from the data. The QCD multijet back- ground yield in the signal region is obtained by multiplying the yield previously obtained in the control region by an extrapola- tion factor. The extrapolation factor is measured in events passing identical selection criteria as those in the signal region, and in the relaxed isolation region, except that the τh candidates are required to have the same sign. The events selected with opposite-sign τh candidates passing relaxed isolation requirements form control re- gions, shown in Fig. 4, and are used in the fit to extract the results. The tt production process is one of the main backgrounds in the eμ channel. The 2D distributions in all decay channels are predicted by simulation. The normalization is adjusted to the one observed in a tt-enriched sample orthogonal to the signal region. This control region, shown in Fig. 5, is added to the global fit to ex- tract the results, and is defined similarly as the eμ signal region, except that the pζ requirement is inverted and the events should contain at least one jet. The CMS Collaboration / Physics Letters B 779 (2018) 283–316 289 Fig. 3. Control regions enriched in the QCD multijet background used in the maximum likelihood fit, together with the signal regions, to extract the results. The normalization of the predicted background distributions corresponds to the result of the global fit. These regions, defined by selecting events with opposite-sign � and τh candidates with � passing inverted isolation conditions, control the yields of the QCD multijet background in the μτh and eτh channels. The constraints obtained in the boosted categories are propagated to the VBF categories of the corresponding channels. Fig. 4. Control regions enriched in the QCD multijet background used in the maximum likelihood fit, together with the signal regions, to extract the results. The normalization of the predicted background distributions corresponds to the result of the global fit. These regions, formed by selecting events with opposite-sign τh candidates passing relaxed isolation requirements, control the yields of the QCD multijet background in the τhτh channel. 290 The CMS Collaboration / Physics Letters B 779 (2018) 283–316 Fig. 5. Control region enriched in the tt background, used in the maximum likeli- hood fit, together with the signal regions, to extract the results. The normalization of the predicted background distributions corresponds to the result of the global fit. This region, defined by inverting the pζ requirement and rejecting events with no jet in the eμ final state, is used to estimate the yields of the tt background in all channels. The contributions from diboson and single top quark production are estimated from simulation, as is the H → WW background. 8. Systematic uncertainties 8.1. Uncertainties related to object reconstruction and identification The overall uncertainty in the τh identification efficiency for genuine τh leptons is 5%, which has been measured with a tag- and-probe method in Z → ττ events. This number is not fully correlated among the di-τ channels because the τh candidates are required to pass different working points of the discrimina- tors that reduce the misidentification rate of electrons and muons as τh candidates. The trigger efficiency uncertainty per τh candi- date amounts to an additional 5%, which leads to a total trigger uncertainty of 10% for processes estimated from simulation in the τhτh decay channel. This uncertainty has also been measured with a tag-and-probe method in Z → ττ events. An uncertainty of 1.2% in the visible energy scale of genuine τh leptons affects both the distributions and the signal and back- ground yields. It is uncorrelated among the 1-prong, 1-prong +π0, and 3-prong decay modes. The magnitude of the uncertainty was determined in Z → ττ events with one τ lepton decaying hadroni- cally and the other one to a muon, by performing maximum likeli- hood fits for different values of the visible energy scale of genuine τh leptons. Among these events, less than half overlap with the events selected in the μτh channel of this analysis. The fit con- strains the visible τh energy scale uncertainty to about 0.3% for all decay modes. The constraint mostly comes from highly populated regions with a high τh purity, namely the 0-jet and boosted cate- gories of the μτh and τhτh channels. The decrease in the size of the uncertainty is explained by the addition of two other decay channels with τh candidates (τhτh and eτh), by the higher number of events in the MC simulations, and by the finer categorization that leads to regions with a high Z → ττ event purity. Even in the most boosted categories, reconstructed τh candidates typically have moderate pT (pT less than 100 GeV) and are found in the barrel region of the detector. As tracks are well measured in the CMS detector for this range of pT, the visible energy scale of gen- uine τh leptons is fully correlated for all τh leptons reconstructed in the same decay mode, irrespective of their pT and η. The uncer- tainties in the visible energy scale for genuine τh leptons together contribute an uncertainty of 5% to the measurement of the signal strength. In the 0-jet category of the μτh and eτh channels, the relative contribution of τh in a given reconstructed decay mode is allowed to fluctuate by 3% to account for the possibility that the recon- struction and identification efficiencies are different for each decay mode. This uncertainty has been measured in a region enriched in Z → ττ events with one τ lepton decaying hadronically and the other one decaying to a muon, by comparing the level of agree- ment in exclusive bins of the reconstructed τh decay mode, after adjusting the inclusive normalization of the Z → ττ simulation to its best-fit value. The effect of migration between the recon- structed τh decay modes is negligible in other categories, where all decay modes are treated together. For events where muons or electrons are misidentified as τh candidates, essentially Z → μμ events in the μτh decay channel and Z → ee events in the eτh decay channel, the τh identification leads to rate uncertainties of 25 and 12%, respectively, per recon- structed τh decay mode. Using mvis and the reconstructed τh decay mode as the observables in the 0-jet category of the μτh and eτh channels helps reduce the uncertainty after the signal extraction fit: the uncertainty in the rate of muons or electrons misidentified as τh becomes of the order of 5%. The energy scale uncertainty for muons or electrons misidentified as τh candidates is 1.5 or 3%, respectively, and is uncorrelated between reconstructed τh decay modes. The fit constrains these uncertainties to about one third of their initial values. For events where quark- or gluon-initiated jets are misidentified as τh candidates, a linear uncertainty that increases by 20% per 100 GeV in τh pT accounts for a potential mismodeling of the jet → τh misidentification rate as a function of the τh pT in simulations. The uncertainty has been determined from a region enriched in W + jets events, using events with a muon and a τh candidate in the final state, characterized by a large transverse mass between the pmiss T and the muon [54,55]. In the decay channels with muons or electrons, the uncertain- ties in the muon and electron identification, isolation, and trig- ger efficiencies lead to the rate uncertainty of 2% for both muons and electrons. The uncertainty in the electron energy scale, which amounts to 2.5% in the endcaps and 1% in the barrel of the detec- tor, is relevant only in the eμ decay channel, where it affects the final distributions. In all channels, the effect of the uncertainty in the muon energy scale is negligible. The uncertainties in the jet energy scale depend on the pT and η of the jet [53]. They are propagated to the computation of the number of jets, which affects the repartition of events between the 0-jet, VBF, and boosted categories, and to the computation of mjj , which is one of the observables in the VBF category. The rate uncertainty related to discarding events with a b- tagged jet in the eμ decay channel is up to 5% for the tt back- ground. The uncertainty in the mistagging rate of gluon and light- flavor jets is negligible. The �pmiss T scale uncertainties [61], which are computed event- by-event, affect the normalization of various processes through the event selection, as well as their distributions through the prop- agation of these uncertainties to the di-τ mass mττ . The �pmiss T scale uncertainties arising from unclustered energy deposits in the detector come from four independent sources related to the tracker, ECAL, HCAL, and forward calorimeters subdetectors. Addi- tionally, �pmiss T scale uncertainties related to the uncertainties in the jet energy scale measurement, which lead to uncertainties in the �pmiss T calculation, are taken into account. The combination of both sources of uncertainties in the �pmiss T scale leads to an uncertainty of about 10% in the measured signal strength. The CMS Collaboration / Physics Letters B 779 (2018) 283–316 291 8.2. Background estimation uncertainties The Z → ττ background yield and distribution are corrected based on the agreement between data and the background pre- diction in a control region enriched in the Z → μμ events, as explained in Section 7. The extrapolation uncertainty related to kinematic differences in the selections in the signal and control regions ranges between 3 and 10%, depending on the category. In addition, shape uncertainties related to the uncertainties in the ap- plied corrections are considered; they reach 20% for some ranges of mjj in the VBF category. These uncertainties arise from the different level of agreement between data and simulation in the Z → μμ control region obtained when varying the threshold on the muon pT. The uncertainties in the W + jets event yield determined from the control regions in the μτh and eτh channels account for the statistical uncertainty of the observed data, the statistical uncer- tainty of the W + jets simulated sample, and the systematic un- certainties associated with background processes in these control regions. Additionally, an uncertainty in the extrapolation of the constraints from the high-mT (mT > 80 GeV) control regions to the low-mT (mT < 50 GeV) signal regions is additionally taken into account. The latter ranges from 5 to 10%, and is obtained by com- paring the mT distributions of simulated and observed Z → μμ events where one of the muons is removed and the �pmiss T adjusted accordingly, to mimic W + jets events. The reconstructed invariant mass of the parent boson in the rest frame is multiplied by the ra- tio of the W and Z boson masses before removing the muon. In the τhτh and eμ channels, where the W + jets background is es- timated from simulation, the uncertainty in the yield of this small background is equal to 4 and 20%, respectively. The larger value for the eμ channel includes uncertainties in the misidentification rates of jets as electrons and muons, whereas the uncertainty in the misidentification rate of jets as τh candidates in the τhτh chan- nel is accounted for by the linear uncertainty as a function of the τh pT described earlier. The uncertainty in the QCD multijet background yield in the eμ decay channel ranges from 10 to 20%, depending on the cate- gory. It corresponds to the uncertainty in the extrapolation factor from the same-sign to opposite-sign region, measured in events with anti-isolated leptons. In the μτh and eτh decay channels, un- certainties from the fit of the control regions with leptons passing relaxed isolation conditions are considered, together with an ad- ditional 20% uncertainty that accounts for the extrapolation from the relaxed-isolation control region to the isolated signal region. In the τhτh decay channel, the uncertainty in the QCD mutlijet back- ground yield is a combination of the uncertainties obtained from fitting the dedicated control regions with τh candidates passing relaxed isolation criteria, and of extrapolation uncertainties to the signal region ranging from 3 to 15% and accounting for limited dis- agreement between prediction and data in signal-free regions with various loose isolation criteria. The yield of events in a tt-enriched region is added to the max- imum likelihood fit to control the normalization of this process in the signal region, as explained in Section 7. The uncertainty from the fit in the control region is automatically propagated to the sig- nal regions, resulting in an uncertainty of about 5% on the tt cross section. Per-channel uncertainties related to the object reconstruc- tion and identification are considered when extrapolating from the eμ final state to the others. The tt simulation is corrected for dif- ferences in the top quark pT distributions observed between data and simulation, and an uncertainty in the correction is taken into account. The combined systematic uncertainty in the background yield arising from diboson and single top quark production processes is estimated to be 5% on the basis of recent CMS measurements [62, 63]. 8.3. Signal prediction uncertainties The rate and acceptance uncertainties for the signal processes related to the theoretical calculations are due to uncertainties in the PDFs, variations of the QCD renormalization and factorization scales, and uncertainties in the modeling of parton showers. The magnitude of the rate uncertainty depends on the production pro- cess and on the event category. The inclusive uncertainty related to the PDFs amounts to 3.2, 2.1, 1.9, and 1.6%, respectively, for the ggH, VBF, WH, and ZH pro- duction modes [38]. The corresponding uncertainty for the varia- tion of the renormalization and factorization scales is 3.9, 0.4, 0.7, and 3.8%, respectively [38]. The acceptance uncertainties related to the particular selection criteria used in this analysis are less than 1% for the ggH and VBF productions for the PDF uncertainties. The acceptance uncertainties for the VBF production in the renor- malization and factorization scale uncertainties are also less than 1%, while the corresponding uncertainties for the ggH process are treated as shape uncertainties as the uncertainty increases linearly with pττ T and mjj . The pT distribution of the Higgs boson in the powheg 2.0 sim- ulations is tuned to match more closely the next-to-NLO (NNLO) plus next-to-next-to-leading-logarithmic (NNLL) prediction in the HRes2.1 generator [64,65]. The acceptance changes with the varia- tion of the parton shower tune in herwig++ 2.6 samples [66] are considered as additional uncertainties, and amount to up to 7% in the boosted category. The theoretical uncertainty in the branching fraction of the Higgs boson to τ leptons is equal to 2.1% [38]. The theoretical uncertainties in the signal production depend on the jet multiplicity; this effect is included by following the pre- scriptions in Ref. [67]. This effect needs to be taken into account because the definitions of the three categories used in the analysis are based partially on the number of reconstructed jets. Additional uncertainties for boosted Higgs bosons, related to the treatment of the top quark mass in the calculations, are considered for signal events with pττ T > 150 GeV. Theory uncertainties in the signal prediction contribute an un- certainty of 10% to the measurement of the signal strength. 8.4. Other uncertainties The uncertainty in the integrated luminosity amounts to 2.5% [68]. Uncertainties related to the finite number of simulated events, or to the limited number of events in data control regions, are taken into account. They are considered for all bins of the distri- butions used to extract the results if the uncertainty is larger than 5%. They are uncorrelated across different samples, and across bins of a single distribution. Taken together, they contribute an uncer- tainty of about 12% to the signal strength measurement, coming essentially from the VBF category, where the background templates are less populated than in the other categories. The systematic uncertainties considered in the analysis are summarized in Table 3. 9. Results The extraction of the results involves a global maximum like- lihood fit based on 2D distributions in all channels, shown in Figs. 6–17, together with the control regions for the tt, QCD multi- jet, and W + jets backgrounds. The choice of the binning is driven by the statistical precision of the background and data templates, 292 The CMS Collaboration / Physics Letters B 779 (2018) 283–316 Table 3 Sources of systematic uncertainty. If the global fit to the signal and control regions, described in the next section, signifi- cantly constrains these uncertainties, the values of the uncertainties after the global fit are indicated in the third column. The acronyms CR and ID stand for control region and identification, respectively. Source of uncertainty Prefit Postfit (%) τh energy scale 1.2% in energy scale 0.2–0.3 e energy scale 1–2.5% in energy scale 0.2–0.5 e misidentified as τh energy scale 3% in energy scale 0.6–0.8 μ misidentified as τh energy scale 1.5% in energy scale 0.3–1.0 Jet energy scale Dependent upon pT and η – �pmiss T energy scale Dependent upon pT and η – τh ID & isolation 5% per τh 3.5 τh trigger 5% per τh 3 τh reconstruction per decay mode 3% migration between decay modes 2 e ID & isolation & trigger 2% – μ ID & isolation & trigger 2% – e misidentified as τh rate 12% 5 μ misidentified as τh rate 25% 3–8 Jet misidentified as τh rate 20% per 100 GeV τh pT 15 Z → ττ/�� estimation Normalization: 7–15% 3–15 Uncertainty in m��/ττ , pT(��/ττ ), – and mjj corrections W + jets estimation Normalization (eμ, τhτh): 4–20% – Unc. from CR (eτh, μτh): �5–15 – Extrap. from high-mT CR (eτh, μτh): 5–10% – QCD multijet estimation Normalization (eμ): 10–20% 5–20% Unc. from CR (eτh, τhτh, μτh): �5–15% – Extrap. from anti-iso. CR (eτh, μτh): 20% 7–10 Extrap. from anti-iso. CR (τhτh): 3–15% 3–10 Diboson normalization 5% – Single top quark normalization 5% – tt estimation Normalization from CR: �5% – Uncertainty on top quark pT reweighting – Integrated luminosity 2.5% – b-tagged jet rejection (eμ) 3.5–5.0% – Limited number of events Statistical uncertainty in individual bins – Signal theoretical uncertainty Up to 20% – Fig. 6. Observed and predicted 2D distributions in the VBF category of the τhτh decay channel. The normalization of the predicted background distributions corresponds to the result of the global fit. The signal distribution is normalized to its best fit signal strength. The background histograms are stacked. The “Others” background contribution includes events from diboson and single top quark production, as well as Higgs boson decays to a pair of W bosons. The background uncertainty band accounts for all sources of background uncertainty, systematic as well as statistical, after the global fit. The signal is shown both as a stacked filled histogram and an open overlaid histogram. The CMS Collaboration / Physics Letters B 779 (2018) 283–316 293 Fig. 7. Observed and predicted 2D distributions in the VBF category of the μτh decay channel. The description of the histograms is the same as in Fig. 6. Fig. 8. Observed and predicted 2D distributions in the VBF category of the eτh decay channel. The description of the histograms is the same as in Fig. 6. Fig. 9. Observed and predicted 2D distributions in the VBF category of the eμ decay channel. The description of the histograms is the same as in Fig. 6. 294 The CMS Collaboration / Physics Letters B 779 (2018) 283–316 Fig. 10. Observed and predicted 2D distributions in the boosted category of the τhτh decay channel. The description of the histograms is the same as in Fig. 6. Fig. 11. Observed and predicted 2D distributions in the boosted category of the μτh decay channel. The description of the histograms is the same as in Fig. 6. Fig. 12. Observed and predicted 2D distributions in the boosted category of the eτh decay channel. The description of the histograms is the same as in Fig. 6. The CMS Collaboration / Physics Letters B 779 (2018) 283–316 295 Fig. 13. Observed and predicted 2D distributions in the boosted category of the eμ decay channel. The description of the histograms is the same as in Fig. 6. Fig. 14. Observed and predicted distributions in the 0-jet category of the τhτh decay channel. The description of the histograms is the same as in Fig. 6. Fig. 15. Observed and predicted 2D distributions in the 0-jet category of the μτh decay channel. The description of the histograms is the same as in Fig. 6. 296 The CMS Collaboration / Physics Letters B 779 (2018) 283–316 Fig. 16. Observed and predicted 2D distributions in the 0-jet category of the eτh decay channel. The description of the histograms is the same as in Fig. 6. Fig. 17. Observed and predicted 2D distributions in the 0-jet category of the eμ decay channel. The description of the histograms is the same as in Fig. 6. Table 4 Background and signal expectations, together with the number of observed events, for bins in the signal region for which log10(S/(S + B)) > −0.9, where S and B are, respectively, the number of expected signal events for a Higgs boson with a mass mH = 125.09 GeV and of expected background events, in those bins. The background uncertainty accounts for all sources of background uncertainty, systematic as well as statistical, after the global fit. The contribution from “other backgrounds” includes events from diboson and single top quark production. The contribution from Higgs boson decays to a pair of W bosons is zero in these bins. Process eμ eτh μτh τhτh Z → ττ 5.8 ± 2.2 21.2 ± 3.3 34.6 ± 4.9 89.1 ± 6.9 Z → ee/μμ 0.0 ± 0.0 2.9 ± 0.2 3.7 ± 0.2 5.0 ± 0.2 tt + jets 1.9 ± 0.1 10.4 ± 0.3 22.2 ± 1.8 13.9 ± 0.5 W + jets 0.8 ± 0.02 4.0 ± 0.3 6.6 ± 1.3 7.6 ± 0.8 QCD multijet 2.1 ± 0.3 3.3 ± 2.5 5.0 ± 1.3 35.5 ± 2.1 Other backgrounds 1.4 ± 0.1 5.2 ± 0.2 6.1 ± 0.2 7.3 ± 0.2 ggH,H → ττ 0.6 ± 0.1 5.0 ± 0.6 6.0 ± 0.6 27.4 ± 2.1 VBF H → ττ 2.8 ± 0.3 5.1 ± 0.5 12.55 ± 1.0 17.5 ± 1.0 VH,H → ττ 0.0 ± 0.0 0.3 ± 0.0 0.2 ± 0.0 1.3 ± 0.1 Total backgrounds 12.1 ± 2.2 46.5 ± 4.1 77.7 ± 5.5 156.2 ± 7.3 Total signal 3.4 ± 0.4 10.9 ± 0.8 19.2 ± 1.4 48.3 ± 2.6 Observed 11 54 91 207 The CMS Collaboration / Physics Letters B 779 (2018) 283–316 297 Fig. 18. Distribution of the decimal logarithm of the ratio between the expected signal and the sum of expected signal and expected background in each bin of the mass distributions used to extract the results, in all signal regions. The background contributions are separated by decay channel. The inset shows the corresponding difference between the observed data and expected background distributions di- vided by the background expectation, as well as the signal expectation divided by the background expectation. leading to wider bins in the poorly-populated VBF category. The most sensitive category, VBF, is shown first and is followed by the boosted and 0-jet categories. The signal prediction for a Higgs boson with mH = 125.09 GeV is normalized to its best fit cross section times branching fraction. The background distributions are adjusted to the results of the global maximum likelihood fit. The 2D distributions of the final discriminating variables ob- tained for each category and each channel in the signal regions, along with the control regions, are combined in a binned likeli- hood involving the expected and observed numbers of events in each bin. The expected number of signal events is the one pre- dicted for the production of a SM Higgs boson of mass mH = 125.09 GeV decaying into a pair of τ leptons, multiplied by a sig- nal strength modifier μ treated as a free parameter in the fit. The systematic uncertainties are represented by nuisance pa- rameters that are varied in the fit according to their probability density functions. A log-normal probability density function is as- sumed for the nuisance parameters affecting the event yields of the various background contributions, whereas systematic uncer- tainties that affect the shape of the distributions are represented by nuisance parameters whose variation results in a continuous perturbation of the spectrum [69] and which are assumed to have a Gaussian probability density function. Overall, the statistical un- certainty in the observed event yields is the dominant source of uncertainty for all combined results. Grouping events in the signal region by their decimal logarithm of the ratio of the signal (S) to signal-plus-background (S + B) in each bin (Fig. 18), an excess of observed events with respect to the SM background expectation is clearly visible in the most sensitive bins of the analysis. The expected background and sig- nal contributions, as well as the observed number of events, are indicated per process and category in Table 4 for the bins with log10(S/(S + B)) > −0.9. The channel that contributes the most to these bins is τhτh. An excess of observed events relative to the background expec- tation is also visible in Fig. 19, where every mass distribution for a constant range of the second dimension of the signal distributions Fig. 19. Combined observed and predicted mττ distributions. The top panel includes the VBF category of the μτh, eτh and eμ channels, and the bottom panel includes all other channels that make use of mττ instead of mvis for the signal strength fit. The binning reflects the one used in the 2D distributions, and does not allow merg- ing of the two figures. The normalization of the predicted background distributions corresponds to the result of the global fit, while the signal is normalized to its best fit signal strength. The mass distributions for a constant range of the second di- mension of the signal distributions are weighted according to S/(S + B), where S and B are computed, respectively, as the signal or background contribution in the mass distribution excluding the first and last bins. The “Others” background contri- bution includes events from diboson, tt, and single top quark production, as well as Higgs boson decay to a pair of W bosons and Z bosons decaying to a pair of light leptons. The background uncertainty band accounts for all sources of background uncertainty, systematic as well as statistical, after the global fit. The inset shows the corresponding difference between the observed data and expected background dis- tributions, together with the signal expectation. The signal yield is not affected by the reweighting. has been summed with a weight of S/(S + B) to increase the con- tribution of the most sensitive distributions. In this case, S and B are computed, respectively, as the signal or background contribu- tion in the mass distribution excluding the first and last bins, in which the amount of signal is negligible. The signal regions that use mvis instead of mττ , namely the 0-jet category of the μτh, eτh 298 The CMS Collaboration / Physics Letters B 779 (2018) 283–316 Fig. 20. Local p-value and significance as a function of the SM Higgs boson mass hy- pothesis. The observation (red, solid) is compared to the expectation (blue, dashed) for a Higgs boson with a mass mH = 125.09 GeV. The background includes Higgs boson decays to pairs of W bosons, with mH = 125.09 GeV. and eμ channels, are not included. The two panes of Fig. 19 group the compatible bins of Figs. 6–17. The excess in data is quantified by calculating the corre- sponding local p-value using a profile likelihood ratio test statis- tic [70–73]. As shown in Fig. 20, the observed significance for a SM Higgs boson with mH = 125.09 GeV is 4.9 standard deviations, for an expected significance of 4.7 standard deviations. The corresponding best fit value for the signal strength μ is 1.09+0.27 −0.26 at mH = 125.09 GeV. The uncertainty in the best fit signal strength can be decomposed into four components: the- oretical uncertainties, bin-by-bin statistical uncertainties on the backgrounds, other systematic uncertainties, and the statistical uncertainty. In this format, the best fit signal strength is μ = 1.09+0.15 −0.15 (stat)+0.16 −0.15 (syst)+0.10 −0.08 (theo)+0.13 −0.12 (bin-by-bin). The indi- vidual best fit signal strengths per channel and per category, using the constraints obtained on the systematic uncertainties through the global fit, are given in Fig. 21; they demonstrate the channel- and category-wise consistency of the observation with the SM Higgs boson hypothesis. A likelihood scan is performed for mH = 125.09 GeV in the (κV, κf) parameter space, where κV and κf quantify, respectively, the ratio between the measured and the SM value for the cou- plings of the Higgs boson to vector bosons and fermions, with the methods described in Ref. [26]. For this scan only, Higgs boson de- cays to pairs of W bosons are considered as part of the signal. All nuisance parameters are profiled for each point of the scan. As shown in Fig. 22, the observed likelihood contour is consistent with the SM expectation of κV and κf equal to unity. The results are combined with the results of the search for H → ττ performed with the data collected with the CMS detec- tor at center-of-mass energies of 7 and 8 TeV [14], using a com- mon signal strength for all data taking periods. All uncertainties are considered as fully uncorrelated between the different center- of-mass energies. The combination leads to an observed and an expected significance of 5.9 standard deviations. The correspond- ing best fit value for the signal strength μ is 0.98 ± 0.18 at mH = 125.09 GeV. This constitutes the most significant direct mea- surement of the coupling of the Higgs boson to fermions by a single experiment. Fig. 21. Best fit signal strength per category (top) and channel (bottom), for mH = 125.09 GeV. The constraints from the global fit are used to extract each of the individual best fit signal strengths. The combined best fit signal strength is μ = 1.09+0.27 −0.26. 10. Summary A measurement of the H → ττ signal strength, using events recorded in proton–proton collisions by the CMS experiment at the LHC in 2016 at a center-of-mass energy of 13 TeV, has been pre- sented. Event categories are designed to target Higgs boson signal events produced by gluon or vector boson fusion. The results are extracted via maximum likelihood fits in two-dimensional planes, and give an observed significance for Higgs boson decays to τ lepton pairs of 4.9 standard deviations, to be compared with an expected significance of 4.7 standard deviations. The combination with the corresponding measurement performed at center-of-mass energies of 7 and 8 TeV with the CMS detector leads to the first observation by a single experiment of decays of the Higgs boson to pairs of τ leptons, with a significance of 5.9 standard deviations. The CMS Collaboration / Physics Letters B 779 (2018) 283–316 299 Fig. 22. Scan of the negative log-likelihood difference as a function of κV and κ f , for mH = 125.09 GeV. All nuisance parameters are profiled for each point. For this scan, the pp → H → WW contribution is treated as a signal process. Acknowledgements We congratulate our colleagues in the CERN accelerator depart- ments for the excellent performance of the LHC and thank the technical and administrative staffs at CERN and at other CMS in- stitutes for their contributions to the success of the CMS effort. In addition, we gratefully acknowledge the computing centers and personnel of the Worldwide LHC Computing Grid for delivering so effectively the computing infrastructure essential to our analyses. Finally, we acknowledge the enduring support for the construc- tion and operation of the LHC and the CMS detector provided by the following funding agencies: BMWFW and FWF (Austria); FNRS and FWO (Belgium); CNPq, CAPES, FAPERJ, and FAPESP (Brazil); MES (Bulgaria); CERN; CAS, MOST, and NSFC (China); COLCIEN- CIAS (Colombia); MSES and CSF (Croatia); RPF (Cyprus); SENESCYT (Ecuador); MoER, ERC IUT, and ERDF (Estonia); Academy of Fin- land, MEC, and HIP (Finland); CEA and CNRS/IN2P3 (France); BMBF, DFG, and HGF (Germany); GSRT (Greece); OTKA and NIH (Hun- gary); DAE and DST (India); IPM (Iran); SFI (Ireland); INFN (Italy); MSIP and NRF (Republic of Korea); LAS (Lithuania); MOE and UM (Malaysia); BUAP, CINVESTAV, CONACYT, LNS, SEP, and UASLP-FAI (Mexico); MBIE (New Zealand); PAEC (Pakistan); MSHE and NSC (Poland); FCT (Portugal); JINR (Dubna); MON, ROSATOM, RAS, RFBR and RAEP (Russia); MESTD (Serbia); SEIDI, CPAN, PCTI and FEDER (Spain); Swiss Funding Agencies (Switzerland); MST (Taipei); ThEP- Center, IPST, STAR, and NSTDA (Thailand); TUBITAK and TAEK (Turkey); NASU and SFFR (Ukraine); STFC (United Kingdom); DOE and NSF (USA). Individuals have received support from the Marie-Curie pro- gram and the European Research Council and Horizon 2020 Grant, contract No. 675440 (European Union); the Leventis Foundation; the Alfred P. Sloan Foundation; the Alexander von Humboldt Foun- dation; the Belgian Federal Science Policy Office; the Fonds pour la Formation à la Recherche dans l’Industrie et dans l’Agriculture (FRIA-Belgium); the Agentschap voor Innovatie door Wetenschap en Technologie (IWT-Belgium); the Ministry of Education, Youth and Sports (MEYS) of the Czech Republic; the Council of Sci- ence and Industrial Research, India; the HOMING PLUS program of the Foundation for Polish Science, cofinanced from European Union, Regional Development Fund, the Mobility Plus program of the Ministry of Science and Higher Education, the National Science Center (Poland), contracts Harmonia 2014/14/M/ST2/00428, Opus 2014/13/B/ST2/02543, 2014/15/B/ST2/03998, and 2015/19/B/ST2/ 02861, Sonata-bis 2012/07/E/ST2/01406; the National Priorities Re- search Program by Qatar National Research Fund; the Programa Clarín-COFUND del Principado de Asturias; the Thalis and Aris- teia programs cofinanced by EU-ESF and the Greek NSRF; the Rachadapisek Sompot Fund for Postdoctoral Fellowship, Chula- longkorn University and the Chulalongkorn Academic into Its 2nd Century Project Advancement Project (Thailand); and the Welch Foundation, contract C-1845. 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