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Search for lepton-flavour-violating H µ decays of the Higgs boson with the ATLAS detector

A direct search for lepton–ﬂavour–violating (LFV) H → µτ decays of the recently discovered Higgs boson with the ATLAS detector at the LHC is presented. The analysis is performed in the H → µτ had channel, where τ had is a hadronically decaying τ –lepton. The search is based on the data sample of proton–proton collisions collected by the ATLAS experiment corresponding to an integrated luminosity of 20.3 fb − 1 at a centre–of–mass energy of √ s = 8 TeV. No statistically signiﬁcant excess of data over the predicted background is observed. The observed (expected) 95% conﬁdence–level upper limit on the branching fraction, Br( H → µτ ), is 1.85% (1.24%).


Introduction
The observation of the Higgs boson [1,2] with a mass of about 125 GeV [3] by the ATLAS and CMS experiments is a great success of the Large Hadron Collider (LHC) physics program at CERN. The next important step in this program are searches for signs of new physics beyond the Standard Model (SM) and detailed studies of the Higgs boson properties. Direct evidence for physics beyond the SM could be indicated via lepton-flavour-violating (LFV) Higgs boson decays. If the SM is replaced with an effective field theory, which has a single Higgs boson and is required to be renormalizable only to a finite mass scale, then LFV couplings may be introduced [4]. LFV decays can also occur naturally in models with more than one Higgs doublet [5][6][7][8], composite Higgs models [9,10], models with flavour symmetries [11], Randall-Sundrum models [12] and many others [13][14][15][16][17][18].
There are three possibilities for LFV effects mediated via virtual Higgs bosons: µ-e, τ-µ, and τ-e transitions. Indirect experimental constraints are reviewed and translated into constraints on Br(H → eµ, µτ, eτ) in recent papers [4,19]. Searches for µ → eγ [20] place a very stringent constraint on H → eµ decays: Br(H → eµ) < O(10 −8 ) [4,19]. The indirect constraints on H → µτ, eτ decays mostly come from searches for τ → µγ, eγ [21][22][23] or other rare τ-lepton decays [24], as well as from measurements of the anomalous magnetic moment of the muon and the electron [25] and are much less stringent: Br(H → µτ, eτ) < O(10%) [4,19]. A relatively large Br(H → µτ) can be achieved without any particular tuning of the effective couplings, while a large Br(H → eτ) is possible only at the cost of some finetuning of the corresponding couplings [19]. It is also important to note that the presence of a H → µτ signal would essentially exclude the presence of a H → eτ signal, and vice versa, at an experimentally observable level at the LHC due to strong experimental bounds on µ → eγ decays [19]. The CMS Collaboration has recently performed the first direct search for LFV H → µτ decays [26] and reported a slight excess (2.4 standard deviations) of data over the predicted background. Their results give a 1.57% upper limit on Br(H → µτ) at the 95% confidence level (CL). This paper presents a search for lepton-flavour-violating H → µτ decays of the recently discovered Higgs boson with one muon and one hadronically decaying τ-lepton (τ had ) in the final state. The analysis is based on the data sample of pp collisions which was collected at a centre-of-mass energy of √ s = 8 TeV and corresponds to an integrated luminosity of 20.3 fb −1 .
The signature of LFV H → µτ decays used in this search is characterised by the presence of an energetic muon, originating directly from a Higgs boson decay and carrying roughly half of its energy, and the hadronic decay products of a τ-lepton. The data were collected with a single-muon trigger with a transverse 1 ATLAS uses a right-handed coordinate system with its origin at the nominal interaction point (IP) in the centre of the detector and the z-axis along the beam pipe. The x-axis points from the IP to the centre of the LHC ring, and the y-axis points upward. Cylindrical coordinates (r, φ) are used in the transverse plane, φ being the azimuthal angle around the beam pipe. The pseudorapidity is defined in terms of the polar angle θ as η = − ln tan(θ/2). momentum, p T = p sin θ, threshold of p T = 24 GeV. The H → ττ and the LFV H → µτ signatures with a muon and τ had in the final state share many common features. Therefore, the object definitions and data quality cuts used in this analysis are the same as those in the recently published ATLAS search for H → ττ decays [28]. A brief description of the object definitions is provided below.
Muon candidates are reconstructed using an algorithm [29] that combines information from the ID and the MS. Muon quality criteria such as inner detector hit requirements are applied to achieve a precise measurement of the muon momentum and to reduce the misidentification rate. Muons are required to have p T >10 GeV and to be within |η| < 2.5. Typical reconstruction and identification efficiencies for muons satisfying these selection criteria are above 95% [29]. Exactly one identified muon is required in this analysis.
Electron candidates are reconstructed from energy clusters in the electromagnetic calorimeters matched to tracks in the ID. They are required to have a transverse energy, E T = E sin θ, greater than 15 GeV, to be within the pseudorapidity range |η| < 2.47, and to satisfy the medium shower shape and track selection criteria defined in ref. [30]. Candidates found in the transition region between the end-cap and barrel calorimeters (1.37 < |η| < 1.52) are not considered. Typical reconstruction and identification efficiencies for electrons satisfying these selection criteria range between 80% and 90% depending on E T and η. Since electrons do not appear in the H → µ + τ had decay mode, events with identified electrons are rejected.
Jets are reconstructed using the anti-k t jet clustering algorithm [31] with a radius parameter R = 0.4, taking clusters of calorimeter cells with deposited energy as inputs. Fully calibrated jets [32] are required to be reconstructed in the range |η| < 4.5 and to have p T > 30 GeV. To reduce the contamination of jets by additional interactions in the same or neighbouring bunch crossings (pile-up), tracks originating from the primary vertex must contribute a large fraction of the jet p T when summing the scalar p T of all tracks in the jet. The primary vertex is chosen as the proton-proton collision vertex candidate with the highest sum of the squared transverse momenta of all associated tracks. This jet vertex fraction is required to be at least 50% for jets with |η| <2.4 and p T <50 GeV (no cut is applied to jets with p T > 50 GeV). Jets with no associated tracks are retained. In the pseudorapidity range |η| < 2.5, jets containing b-hadrons (b-jets) are selected using a tagging algorithm [33], which has an efficiency of ∼70% for b-jets in tt events. The corresponding light-flavour jet misidentification probability is 0.1-1%, depending on the p T and η of the jet. Only a very small fraction of signal events have b-jets, therefore events with identified b-jets are vetoed in the selection of signal events.
Hadronically decaying τ-leptons are identified by means of a multivariate analysis technique [34] based on boosted decision trees, which exploits information about ID tracks and clusters in the electromagnetic and hadronic calorimeters. The τ had candidates are required to have charge q τ = ±1 in units of electron charge, and must be 1-or 3-track (1-or 3-prong) candidates. Events with exactly one τ had candidate satisfying the medium identification criteria [34] with p T >20 GeV and |η| <2.47 are considered in this analysis. The identification efficiency for τ had candidates satisfying these requirements is 55-60%. Dedicated criteria [34] to separate τ had candidates from misidentified electrons are also applied, with a selection efficiency for true τ had decays of 95%. To reduce the contamination due to backgrounds where a muon fakes a τ had signature, events where an identified muon with p T (µ) > 4 GeV overlaps with an identified τ had are rejected [28]. The probability to misidentify a jet with p T > 20 GeV as a τ had candidate is typically 1-2%.
The missing transverse momentum (with magnitude E miss T ) is reconstructed using the energy deposits in calorimeter cells calibrated according to the reconstructed physics objects (e, γ, τ had , jets and µ) with which they are associated [35]. The energy from calorimeter cells not associated with any physics object is included in the E miss T calculation. It is scaled by the ratio of the scalar sum of p T of tracks which originate from the primary vertex but are not matched to any objects and the scalar sum of p T of all tracks in the event which are not matched to objects. The scaling procedure achieves a more accurate reconstruction of E miss T in high pile-up conditions. In this search, E miss T is a signature of neutrinos, and it is used to select and reconstruct signal events, as described below.

Event selection and categorization
Signal H → µτ events in the µτ had final state are characterised by the presence of an energetic muon and a τ had of opposite charge as well as moderate E miss T , which tends to be aligned with the τ had direction. Backgrounds for this signature can be broadly classified into two major categories: • Events with true muon and τ had signatures, dominated by irreducible Z/γ * → ττ production with some contributions from the VV → µτ + X (where V = W, Z), tt, single-top and SM H → ττ production processes; these events exhibit a very strong charge correlation between the muon and the τ had ; therefore, the expected number of events with opposite-sign (OS) charges (N OS ) is much larger than the number of events with same-sign (SS) charges (N SS ).
• Events with a fake τ had signature, dominated by W+jets events with some contribution from multijet (many multi-jet background events have genuine muons from semileptonic decays of heavyflavour hadrons), diboson (VV), tt and single-top events with some charge asymmetry N OS > N SS ; Z → µµ+jets events, where a τ had signature can be faked by either a jet (no charge correlation) or a muon (strong charge correlation), also contribute to this category.
Events with a fake τ had tend to have a much softer p T (τ had ) spectrum and a larger angular separation between the τ had and E miss T directions. These properties are exploited to suppress such backgrounds and define signal and control regions. Events with exactly one muon and exactly one τ had with p T (µ) > 26 GeV, p T (τ had ) > 45 GeV and |η(µ) − η(τ had )| < 2 form a baseline sample. The |η(µ) − η(τ had )| cut has ∼99% efficiency for signal and rejects a considerable fraction of multi-jet and W+jets events. At this stage of the event selection, the identified muon is also required to be isolated [28] in the calorimeters and in the tracking detector in order to reduce contamination from the multi-jet background. Two signal regions are defined using the transverse mass, m T , 2 of the µ-E miss T and τ had -E miss T systems: OS events with m T (µ, E miss T ) > 40 GeV and m T (τ had , E miss T ) < 30 GeV form the signal region-1 (SR1), while OS events with m T (µ, E miss T ) < 40 GeV and m T (τ had , E miss T ) < 60 GeV form the signal region-2 (SR2). The dominant backgrounds in SR1 and SR2 are W+jets and Z/γ * → ττ events, respectively. The modelling of the W+jets background is checked in a dedicated control region (WCR) formed by events with m T (µ, E miss T ) > 60 GeV and m T (τ had , E miss T ) > 40 GeV. The choice of the m T cuts to define SR1, SR2 and WCR is motivated by correlations between m T (µ, E miss T ) and m T (τ had , E miss T ) in H → µτ signal and major background (W+jets and Z/γ * → ττ) events, as illustrated in figure 1. No events with identified b-jets are allowed in SR1, SR2 and WCR. The modelling of the tt and single-top backgrounds is checked in a dedicated control region (TCR), formed by events that satisfy the baseline selection and have at least two jets, with at least one being b-tagged. Table 1 provides a summary of the event selection cuts used to define the signal and control regions.  The LFV signal is searched for by performing a fit to the mass distribution in data, m MMC µτ , reconstructed from the observed muon, τ had and E miss T objects by means of the Missing Mass Calculator [36] (MMC). Conceptually, the MMC is a more sophisticated version of the collinear approximation [37]. The main improvement comes from requiring that the relative orientations of the neutrinos and other τ-lepton decay products are consistent with the mass and kinematics of a τ-lepton decay. This is achieved by maximising a probability defined in the kinematically allowed phase space region. The MMC used in the H → ττ analysis [28] is modified to take into account that there is only one neutrino from a hadronic τlepton decay in LFV H → µτ events. For a Higgs boson with m H = 125 GeV, the reconstructed m MMC µτ distribution has a roughly Gaussian shape with a full width at half maximum of ∼19 GeV. The analysis is performed "blinded" in the 110 GeV< m MMC µτ <150 GeV regions of SR1 and SR2, which contains ∼94% of the expected signal events.

Background estimation
The background estimation method takes into account the background properties and composition discussed in section 3. It also relies on the assumption that the shape of the m MMC µτ distribution for the multi-jet background is the same for OS and SS events. This assumption was verified in the published H → ττ search [38]. In addition, it was confirmed using a dedicated control region, MJCR, with an enhanced contribution from the multi-jet background. Events in this control region are required to pass all criteria for SR1 and SR2 with the exception of the requirement on |η(µ) − η(τ had )|, which is reversed: |η(µ) − η(τ had )| > 2. Therefore, the number of the total OS background events, N bkg OS in each bin of the m MMC µτ (or any other) distribution in SR1 and SR2 can be obtained according to the following formula: where the individual terms are described below. N data SS is the number of SS data events, which are dominated by W+jets events but also contain contributions from multi-jet and other backgrounds. The fractions of multi-jet background in SS data events inside the 110 GeV< m MMC µτ <150 GeV mass window are ∼17% and ∼44% in SR1 and SR2, respectively. The contributions N bkg−i are add-on terms for the different backgrounds components (where bkg-i indicates the i th background source: Z → ττ, Z → µµ, W+jets, VV, H → ττ and events with t-quarks), which also account for components of these backgrounds already included in SS data events. 3 The factor r QCD = N multi−jet OS /N multi−jet SS accounts for potential differences in flavour composition (and, as a consequence, in jet → τ had fake rates) of final-state jets introduced by the same-sign or opposite-sign charge requirements. The value of r QCD = 1.10 ± 0.14 is obtained from a multi-jet-enriched control region in data, as discussed in detail in ref. [38]. It was verified in the MJCR in this search.
The largely irreducible Z/γ * → ττ background is modelled by Z/γ * → µµ data events, where the muon tracks and associated energy deposits in the calorimeters are replaced by the corresponding simulated signatures of the final-state particles of the τ-lepton decay. In this approach, essential features such as the modelling of the kinematics of the produced boson, the modelling of the hadronic activity of the event (jets and underlying event) as well as contributions from pile-up are taken from data. Therefore, the dependence on the simulation is minimized and only the τ-lepton decays and the detector response to the τ-lepton decay products are based on simulation. This hybrid sample is referred to as embedded data in the following. A detailed description of the embedding procedure can be found in ref. [39]. The Z/γ * → ττ normalization is a free-floating parameter in the final fit to data and it is mainly constrained by events with 60 GeV<m MMC µτ <110 GeV in SR2. The W+jets and Z → µµ backgrounds are modelled by the ALPGEN [40] event generator interfaced with PYTHIA8 [41] to provide the parton showering, hadronization and the modelling of the underlying event. 3 The r QCD · N bkg−i SS correction in the add-on term is needed because same-sign data events include multi-jet as well as electroweak events (Z → ττ, Z → µµ, W+jets, VV, H → ττ and events with t-quarks) and their contributions cannot be separated.
In all W+jets events, the τ had signature is faked by jets. The WCR region is used to check the modelling of the W+jets kinematics and to obtain normalizations for OS and SS W+jets events. An additional overall normalization factor for the N W+jets OS−SS term in eq. (1) is introduced as a free-floating parameter in the final fit in SR1. By studying WCR events and SR1 events with m MMC µτ > 150 GeV (dominated by W+jets background), it is also found that a m MMC µτ shape correction, which depends on the number of jets, p T (τ had ) and |η(µ) − η(τ had )|, needs to be applied in SR1. This correction is derived from SR1 events with m MMC µτ > 150 GeV and it is applied to events with all values of m MMC µτ . A 50% difference between the SR1-based correction and that obtained in WCR is taken as a corresponding modelling uncertainty on the m MMC µτ shape for the W+jets background in SR1. The size of this uncertainty depends on m MMC µτ and it is as large as ±10% for W+jets events with m MMC µτ < 150 GeV. In the case of SR2, a good modelling of the N jet , p T (τ had ) and |η(µ) − η(τ had )| distributions suggests that such a correction is not needed. However, a modelling uncertainty on the m MMC µτ shape of the W+jets background in SR2 is assigned based on the 50% difference between the default m MMC µτ shape and the one obtained after applying the correction derived for SR1 events. The size of this uncertainty is below 5% in the 110 GeV< m MMC µτ <150 GeV region, that contains most of the signal events. It was also checked that applying the same correction in SR2 as in SR1 had a negligible effect on the final result and the extracted branching ratio Br(H → µτ) (see Section 6) would only be affected at a level below 3%. The modelling of jet fragmentation and the underlying event has a significant effect on the estimate of the jet → τ had fake rate in different regions of the phase space and has to be accounted for with a corresponding systematic uncertainty. To estimate this effect, the analysis was repeated using a sample of W+jets events modelled by ALPGEN interfaced with the HERWIG [42] event generator. Differences in the W+jets predictions in SR1 and SR2 are found to be ±9% and ±2%, respectively, and are taken as corresponding systematic uncertainties.
In the case of the Z → µµ background, there are two components: events where a muon fakes a τ had and events where a jet fakes a τ had . Predictions for the shape and normalization of the Z → µµ (where µ → τ fake had ) background are obtained from simulation. For the Z → µµ background where a jet is misidentified as a τ had candidate, the normalization factor and shape corrections, which depend on the number of jets, p T (τ had ) and |η(µ) − η(τ had )|, are derived by using events with two identified OS muons with an invariant mass, m µµ , in the range of 80-100 GeV. Since this background does not have an OS-SS charge asymmetry, a single correction factor is derived for OS and SS events. A 50% difference between the m MMC µτ shape with and without this correction is taken as a corresponding systematic uncertainty.
The backgrounds with top quarks are modelled by the POWHEG [43][44][45] (for tt, Wt and s-channel single-top production) and AcerMC [46] (t-channel single-top production) event generators interfaced with PYTHIA8 to provide the parton showering, hadronization and the modelling of the underlying event. The TCR is used to check the modelling and to obtain normalizations for OS and SS events with top quarks. The normalization factors obtained in the TCR are extrapolated into SR1 and SR2, where tt and single-top events may have different properties. To estimate the uncertainty associated with such an extrapolation, the analysis is repeated using the MC@NLO [47] event generator instead of POWHEG for tt production. 4 This uncertainty is found to be ±7.2% (±3.7%) for backgrounds with top quarks in SR1 (SR2).
The background due to diboson (WW, ZZ and WZ) production is estimated from simulation, normalized to the cross sections calculated at next-to-leading order (NLO) in QCD [48]. The ALPGEN event generator interfaced with HERWIG is used to model the WW process, and HERWIG is used for the ZZ and WZ processes. Finally, events with Higgs bosons produced via gluon fusion or vector-boson fusion (VBF) processes are generated at NLO accuracy with POWHEG [49] event generator interfaced with PYTHIA8 to provide the parton showering, hadronization and the modelling of the underlying event. The associated production (ZH and WH) samples are simulated using PYTHIA8. All events with Higgs bosons are produced with a mass of m H = 125 GeV and normalized to cross sections calculated at next-to-next-to-leading order in QCD [50][51][52]. The SM H → ττ decays are simulated by PYTHIA8. The LFV Higgs boson decays are modelled by the EvtGen [53] event generator according to the phase-space model. In the H → µτ decays, the τ-lepton decays are treated as unpolarised because the left-and right-handed τ-lepton polarisation states are produced at equal rates.
All simulated samples are passed through the GEANT4-based ATLAS detector simulation [54,55]. The simulated events are overlaid with additional minimum-bias events to account for the effect of multiple pp interactions (pile-up) occurring in the same and neighbouring bunch crossings. Figure 2 shows the m MMC µτ distributions for data and the predicted backgrounds in each of the signal regions. The backgrounds are estimated using the method described above. The signal efficiencies for passing the SR1 or SR2 selection requirements are 2.1% and 1.5%, respectively, and the combined efficiency is 3.6%. The numbers of observed events in the data as well as the signal and background predictions in the mass region 110 GeV< m MMC µτ <150 GeV can be found in table 2.

Systematic uncertainties
The largest systematic uncertainties arise from the normalization (±10% uncertainty) and modelling 5 of the W+jets background. The uncertainties on r QCD (±12.7%) and on the normalization (±6% uncertainty) and modelling of Z → ττ also play an important role. The other major sources of experimental uncertainty, affecting both the shape and normalization of signal and backgrounds, are the uncertainty on the τ had energy scale [34] (measured with ±(2-4)% precision) and uncertainties on the embedding method used to model the Z → ττ background [28]. Less significant sources of experimental uncertainty, affecting the shape and normalization of signal and backgrounds, are the uncertainty on the jet energy scale [32, 56] and resolution [57]. The uncertainties in the τ had energy resolution, the momentum scale and resolution of muons, and the scale uncertainty on E miss T due to the energy in calorimeter cells not associated with physics objects are taken into account, however, they are found to be relatively small. The following experimental uncertainties primarily affect the normalization of signal and backgrounds: the ±2.8% uncertainty on the integrated luminosity [58], the uncertainty on the τ had identification efficiency [34], which is measured to be ±(2-3)% for 1-prong and ±(3-5)% for 3-prong decays, the ±2.1% uncertainty for triggering, reconstructing and identifying muons [29,59], and the ±2% uncertainty on the b-jet tagging efficiency [33].
Theoretical uncertainties are estimated for the signal and for the H → ττ, VV and Z → µµ (with µ → τ fake had ) backgrounds, which are modelled with the simulation and are not normalized to data in dedicated control regions. Uncertainties due to missing higher-order QCD corrections on the production cross sections are found to be [60] ±10.1% (±7.8%) for the Higgs boson production via gluon fusion in SR1 (SR2), ±1% for the Z → µµ background and for VBF and V H Higgs boson production, and ±5% for the VV background. The systematic uncertainties due to the choice of parton distribution functions used in the simulation are evaluated based on the prescription described in ref.
[60] and the following values are used in this analysis: ±7.5% for the Higgs boson production via gluon fusion, ±2.8% for the VBF 5 Some of these uncertainties (e.g., uncertainties due to m MMC µτ shape corrections and extrapolation uncertainties) are discussed in the text above. and V H Higgs boson production, and ±4% for the Z → µµ and VV backgrounds. Finally, an additional ±5.7% systematic uncertainty on Br(H → ττ) is applied to the SM H → ττ background.

Results
A simultaneous binned maximum-likelihood fit is performed on the m MMC µτ distributions in SR1 and SR2 and on event yields in WCR and TCR to extract the LFV branching ratio Br(H → µτ). The fit exploits the control regions and the distinct shapes of the W+jets and Z → ττ backgrounds in the signal regions to constrain some of the systematic uncertainties. This leads to an improved sensitivity of the analysis. The post-fit m MMC µτ distributions in SR1 and SR2 are shown in figure 2, and the combined m MMC µτ distribution for both signal regions is presented in figure 3. Figure 2 illustrates good agreement between data and background expectations in SR1. A small excess of the data over the predicted background is observed in the 120 GeV< m MMC µτ <140 GeV region in SR2. This small excess in SR2 has a local significance of 2.2 standard deviations and a combined significance for both signal regions of 1.3 standard deviations. This corresponds to a best fit value for the branching fraction of Br(H → µτ)=(0.77 ± 0.62)%. Due to the low significance of the observed excess, an upper limit on the LFV branching ratio Br(H → µτ) for a Higgs boson with m H = 125 GeV is set using the CL s modified frequentist formalism [61] with the profile likelihood-ratio test statistics [62]. The observed and the median expected 95% CL upper limits are 1.85% and 1.24 +0. 50 −0.35 %, respectively. Table 3 provides a summary of all results.

Summary
A direct search for lepton-flavour-violating H → µτ decays of the recently discovered Higgs boson is performed in the τ had decay mode of τ-leptons using a data sample of proton-proton collisions recorded by the ATLAS detector at the LHC corresponding to an integrated luminosity of 20.3 fb −1 at a centreof-mass energy of √ s = 8 TeV. The observed and the median expected upper limits at 95% CL on the branching fraction, Br(H → µτ), are 1.85% and 1.24 +0. 50 −0.35 %, respectively. This search places significantly more stringent constraints on Br(H → µτ) compared to earlier indirect estimates. The result of this analysis is found to be consistent with the one published by the CMS Collaboration [26].  [58] ATLAS Collaboration, Improved luminosity determination in pp collisions at sqrt(s) = 7 TeV using the ATLAS detector at the LHC, Eur. Phys. J. C73 no. The ATLAS Collaboration