Search for lepton flavour violating decays of the Higgs boson to e tau and e mu in proton-proton collisions at sqrt(s) = 8 TeV

A direct search for lepton flavour violating decays of the Higgs boson (H) in the H to e tau and H to e mu channels is described. The data sample used in the search was collected in proton-proton collisions at sqrt(s) = 8 TeV with the CMS detector at the LHC and corresponds to an integrated luminosity of 19.7 inverse femtobarns. No evidence is found for lepton flavour violating decays in either final state. Upper limits on the branching fractions, B(H to e tau )<0.69% and B(H to e mu)<0.035%, are set at the 95% confidence level. The constraint set on B(H to e tau) is an order of magnitude more stringent than the existing indirect limits. The limits are used to constrain the corresponding flavour violating Yukawa couplings, absent in the standard model.


Introduction
The discovery of the Higgs boson [1][2][3] has generated great interest in exploring its properties.In the standard model (SM), lepton flavour violating (LFV) decays of the Higgs boson are forbidden.Such decays can occur naturally in models with more than one Higgs boson doublet [4].They also arise in supersymmetric models [5][6][7][8][9][10][11], composite Higgs models [12,13], models with flavour symmetries [14], Randall-Sundrum models [15][16][17], and others [18][19][20][21][22][23][24][25][26].The CMS Collaboration has recently published a search in the H → µτ channel [27] showing an excess of data with respect to the SM background-only hypothesis at M H = 125 GeV with a significance of 2.4 standard deviations (σ).A constraint is set on the branching fraction B(H → µτ) < 1.51% at 95% confidence level (CL), while the best fit branching fraction is B(H → µτ) = (0.84 +0.39  −0.37 )%.The ATLAS Collaboration finds a deviation from the background expectation of 1.3σ significance in the H → µτ channel and sets an upper limit of B(H → µτ) < 1.85% at 95% CL with a best fit branching fraction of B(H → µτ) = (0.77 ± 0.62)% [28].To date, no dedicated searches have been published for the H → eµ channel.The ATLAS collaboration recently reported searches for H → eτ and H → µτ, finding no significant excess of events over the background expectation.The searches in channels with leptonic tau decays are sensitive only to a difference between B(H → eτ) and B(H → µτ).These are combined with the searches in channels with hadronic tau decays to set limits of B(H → eτ) < 1.04%, B(H → µτ) < 1.43% at 95% CL [29].There are also indirect constraints.The presence of LFV Higgs boson couplings allows, µ → e, τ → µ, and τ → e to proceed via a virtual Higgs boson [30,31].The experimental limits on these decays have been translated into constraints on B(H → eµ), B(H → µτ) and B(H → eτ) [32,33].The null result for µ → eγ [34] strongly constrains B(H → eµ) < O(10 −8 ).However, the constraint B(H → eτ) < O(10%) is much less stringent.This comes from searches for rare τ decays [35] such as τ → eγ, and the measurement of the electron magnetic moment.Exclusion limits on the electric dipole moment of the electron [36] also provide complementary constraints.This letter describes a search for LFV decays of the Higgs boson with M H = 125 GeV, based on proton-proton collision data recorded at √ s = 8 TeV with the CMS detector at the CERN LHC, corresponding to an integrated luminosity of 19.7 fb −1 .The search is performed in three decay channels, H → eτ µ , H → eτ h , and H → eµ, where τ µ and τ h correspond to muonic and hadronic decay channels of tau leptons, respectively.The decay channel, H → eτ e , is not considered due to the large background contribution from Z → ee decays.The expected final state signatures are very similar to the SM H → τ e τ h and H → τ e τ µ decays, studied by CMS [37,38] and ATLAS [39], but with some significant kinematic differences.The electron in the LFV H → eτ decay is produced promptly, and tends to have a larger momentum than in the SM H → τ e τ h decay.In the H → eµ channel, M H can be measured with good resolution due to the absence of neutrinos.This letter is organized as follows.After a description of the CMS detector (Section 2) and of the collision data and simulated samples used in the analysis (Section 3), the event reconstruction is described in Section 4. The event selection and the estimation of the background and its components are described separately for the two Higgs decay modes H → eτ and H → eµ in Sections 5 and 6.The results are then presented in Section 7.

The CMS detector
A detailed description of the CMS detector, together with a definition of the coordinate system used and the relevant kinematic variables, can be found in Ref. [40].The momenta of charged particles are measured with a silicon pixel and strip tracker that covers the pseudorapidity range |η| < 2.5, in a 3.8 T axial magnetic field.A lead tungstate crystal electromagnetic calorimeter (ECAL) and a brass and scintillator hadron calorimeter, both consisting of a barrel section and two endcaps, cover the pseudorapidity range |η| < 3.0.A steel and quartz-fibre Cherenkov forward detector extends the calorimetric coverage to |η| < 5.0.The outermost component of the CMS detector is the muon system, consisting of gas-ionization detectors placed in the steel flux-return yoke of the magnet to identify the muons traversing the detector.The two-level CMS trigger system selects events of interest for permanent storage.The first trigger level, composed of custom hardware processors, uses information from the calorimeters and muon detectors to select events in less than 3.2 µs.The software algorithms of the high-level trigger, executed on a farm of commercial processors, reduce the event rate to less than 1 kHz using information from all detector subsystems.

Collision data and simulated events
The triggers for the H → eτ µ and H → eµ analyses require an electron and a muon candidate.The trigger for H → eτ h requires a single electron.More details on the trigger selection are given in Sections 5.1 and 6.1, for the H → eτ and H → eµ channels respectively.Simulated samples of signal and background events are produced with several event generators.The CMS detector response is modelled using GEANT4 [41].The Higgs bosons are produced in proton-proton collisions predominantly by gluon fusion (GF) [42], but also by vector boson fusion (VBF) [43] and in association with a W or Z boson [44].The H → eτ decay sample is produced with PYTHIA 8.176 [45] using the CTEQ6L parton distribution functions (PDF).The H → eµ decay sample is produced with PYTHIA 6.426 [46] using the CT10 parton distribution functions [47].The SM Higgs boson samples are generated using POWHEG 1.0 [48][49][50][51][52], with CT10 parton distribution functions, interfaced to PYTHIA 6.426.The MADGRAPH 5.1.3.30[53] generator is used for Z+jets, W+jets, top anti-top quark pair production tt, and diboson production, and POWHEG for single top quark production.The POWHEG and MADGRAPH generators are interfaced to PYTHIA 6.426 for parton shower and hadronization.The PYTHIA parameters for the underlying event description are set to the Z2* tune.The Z2* tune is derived from the Z1 tune [54], which uses the CTEQ5L parton distribution set, whereas Z2* adopts CTEQ6L.Due to the high luminosities attained during data-taking, many events have multiple proton-proton interactions per bunch crossing (pileup).All simulated samples are reweighted to match the pileup distribution observed in data.

Event reconstruction
Data were collected at an average pileup of 21 interactions per bunch crossing.The tracking system is able to separate collision vertices as close as 0.5 mm to each other along the beam direction [55].The primary vertex, assumed to correspond to the hard-scattering process, is the vertex for which the sum of the squared transverse momentum p 2 T of all the associated tracks is the largest.The pileup interactions also affect the identification of most of the physics objects, such as jets, and variables such as lepton isolation.
A particle-flow (PF) algorithm [56][57][58] combines the information from all CMS subdetectors to identify and reconstruct the individual particles emerging from all interactions in the event: charged and neutral hadrons, photons, muons, and electrons.These particles are then required to be consistent with the primary vertex and used to reconstruct jets, hadronic τ decays, quantify the isolation of leptons and photons and reconstruct E miss T .The missing transverse energy vector, E miss T , is defined as the negative of the vector sum of the p T of all identified PF objects in the event [59].Its magnitude is referred to as E miss T .The variable ∆R = √ (∆η) 2 + (∆φ) 2 , where φ is the azimuthal co-ordinate, is used to measure the separation between reconstructed objects in the detector.
Electron reconstruction requires the matching of an energy cluster in the ECAL with a track in the silicon tracker [60].Electron candidates are accepted in the range |η| < 2.5, with the exception of the region 1.44 < |η| < 1.56 where service infrastructure for the detector is located.Electron identification uses a multivariate discriminant that combines observables sensitive to the amount of bremsstrahlung along the electron trajectory, the geometrical and momentum matching between the electron trajectory and associated clusters, and shower-shape observables.Additional requirements are imposed to remove electrons produced by photon conversions.The electron energy is corrected for imperfection of the reconstruction using a regression based on a boosted decision tree [61].
Muon candidates are obtained from combined fits of tracks in the tracker and muon detector seeded by track segments in the muon detector alone, including compatibility with small energy depositions in the calorimeters.Identification is based on track quality and isolation.The muon momentum is estimated with the combined fit.Any possible bias in the measured muon momentum is determined from the position of the Z → µµ mass peak as a function of muon kinematic variables, and a small correction is obtained using the procedure described in Ref. [62].
Hadronically decaying τ leptons are reconstructed and identified using an algorithm [63] that selects the decay modes with one charged hadron and up to two neutral pions, or three charged hadrons.A photon from a neutral-pion decay can convert in the tracker material into an electron-positron pair, which can then radiate photons.These particles give rise to several ECAL energy deposits at the same η value but separated in φ.They are reconstructed as several photons by the PF algorithm.To increase the acceptance for these converted photons, the neutral pions are identified by clustering the reconstructed photons in narrow strips along the φ direction.The charge of τ h candidates is reconstructed by summing the charges of all particles included in the construction of the candidate, except for the electrons contained in strips.Dedicated discriminators veto against electrons and muons.
Jets misidentified as electrons, muons or taus are suppressed by imposing isolation requirements, summing the neutral and charged particle contributions in cones of ∆R about the lepton.The energy deposited within the isolation cone is contaminated by energy from pileup and the underlying event.The effect of pileup is reduced by requiring the tracks considered in the isolation sum to be compatible with originating from the production vertex of the lepton.The contribution to the isolation from pileup and the underlying event is subtracted on an event-by-event basis.In the case of electrons, this contribution is estimated from the product of the measured energy density ρ for the event, determined using the ρ median estimator implemented in FASTJET [64], and an effective area corresponding to the isolation cone.In the case of muons and hadronically decaying τ leptons, it is estimated on a statistical basis through the modified ∆β correction described in Ref. [63].
Jets are reconstructed from all the particles using the anti-k T jet clustering algorithm [65] implemented in FASTJET, with a distance parameter of ∆R = 0.5.The jet energies are corrected by subtracting the contribution of particles created in pileup interactions and in the underlying event [66].Particles from different pileup vertices can be clustered into a pileup jet, or significantly overlap a jet from the primary vertex below the selected jet p T threshold.These jets are identified and removed [67].The events are then divided into categories within each channel according to the number of jets in the event.Jets are required to pass identification criteria, have p T > 30 GeV, and lie in the region |η| < 4.7.The 0-jet and 1-jet categories contain events primarily produced by GF.The 2-jet category is defined to enrich the contribution from events produced via the VBF process.
The main observable used to discriminate between the signal and the background is the collinear mass, M col , which provides an estimate of M H using the observed decay products.It is constructed using the collinear approximation based on the observation that, since M H M τ , the τ decay products are highly Lorentz boosted in the direction of the τ [68].The neutrino momenta can be approximated to have the same direction as the other visible decay products of the τ (τ vis ) and the component of the E miss T in the direction of the visible τ decay products is used to estimate the transverse component of the neutrino momentum (p ν, est T ).The collinear mass can then be derived from the visible mass of the τ-e system (M vis ) as M col = M vis / x vis τ , where x vis τ is the fraction of energy carried by the visible decay products of the τ (x vis τ = p τ vis T /(p τ vis T + p ν, est T )).
Figure 1 shows the observed M col distribution and estimated backgrounds for each category and channel, after the loose selection.The simulated signal for B(H → eτ) = 100% is shown.
The principal backgrounds are estimated with collision data using techniques described in Section 5.2.There is good agreement between the observed distributions and the corresponding background estimations.The agreement is similar in all of the kinematic variables that are subsequently used to suppress backgrounds.The analysis is subsequently performed blinded by using a fixed selection and checking the agreement between relevant observed and simulated distributions outside the sensitive region 100 GeV < M col < 150 GeV.
Next, a set of kinematic variables is defined, and the event selection criteria are set to maximise the significance S/ √ S + B, where S and B are the expected signal and background event yields in the mass window 100 GeV < M col < 150 GeV.The signal event yield corresponds to the SM Higgs boson production cross section at M H = 125 GeV with B(H → eτ) = 1%.The selection criteria for each category and channel are given in Table 1.The variables used are: the lepton transverse momenta p T with = e, µ, τ h ; azimuthal angles between the leptons ∆φ Events in which at least one of the jets is identified as arising from a b quark decay are vetoed using the combined secondary vertex (CSV) b-tagging algorithm [69].To enhance the VBF contribution in the 2-jet category further requirements are applied.In the H → eτ h channel, events in this category are additionally required to have two jets separated by |∆η| > 2.3 and a dijet invariant mass M jj > 400 GeV.In the H → eτ µ channel, the requirements are |∆η| > 3 and M jj > 200 GeV.
After the full selection, a binned likelihood is used to fit the distributions of M col for the signal and the background contributions.The modified-frequentist CL s method [70,71] is used to set upper bounds on the signal strength µ, or determine a signal significance.

Background processes
The contributions from the dominant background processes are estimated using collision data while the less significant backgrounds are estimated using simulation.The largest backgrounds are from Z → ττ decays and from W+jets and QCD multijet production.In the latter, PF objects (predominantly jets), are misidentified as leptons.

Z → ττ background
The Z → ττ background contribution is estimated using an embedding technique [38,72].First, a sample of Z → µµ events is selected from collision data using the loose muon selection.
The muons are then replaced with simulated τ decays reconstructed with the PF algorithm.Thus, the key features of the event topology such as jet multiplicity, instrumental sources of E miss T , and the underlying event are taken directly from collision data.Only the τ lepton decays are simulated.The normalization of the sample is obtained from simulation.The technique is validated by comparing the collinear mass distributions obtained from the Z → ττ simulation and the embedding technique applied to a simulated sample of Z → µµ events.A shift of 2% in the mass peak of the embedded sample relative to simulation is observed.This shift reflects a bias in the embedding technique, which does not take the differences between muons and taus in final-state radiation of photons into account, and is corrected for.Identification and isolation corrections obtained from the comparison are applied to the embedded sample.

Misidentified lepton background
The misidentified lepton background is estimated from collision data by defining a sample with the same selection as the signal sample, but inverting the isolation requirements on one of the leptons, to enrich the contribution from W+jets and QCD multijets.The probability for PF objects to be misidentified as leptons is measured using an independent collision data set, defined below, and this probability is applied to the background enriched sample to compute the misidentified lepton background in the signal sample.The technique is shown schematically in Table 2 in which four regions are defined including the signal (I) and background (III) enriched regions and two control Regions (II & IV), defined with the same selections as Regions I & III respectively, except with leptons of the same charge.
Table 2: Definition of the samples used to estimate the misidentified lepton ( ) background.They are defined by the charge of the two leptons and by the isolation requirements on each.The definition of not-isolated differs between the two channels.

Region I
Region II The misidentified electron background is negligible in the H → eτ µ channel due to the high p T electron threshold.The misidentified muon background is estimated with Region I defined as the signal selection with an isolated electron and an isolated muon of opposite charge.Region III is defined as the signal selection except the muon is required not to be isolated.Small background sources of prompt leptons are subtracted using simulation.The misidenti-Events / 10 GeV fied muon background in Region I is then estimated by multiplying the event yield in Region III by a factor f µ , where f µ is the ratio of isolated to nonisolated muons.It is computed on an independent collision data sample of Z → µµ + X events, where X is an object identified as a muon, in bins of muon p T and η.In the estimation of f µ , background sources of three prompt leptons, predominantly WZ and ZZ, are subtracted from the Z → µµ + X sample using simulation.The technique is validated using like-sign lepton collision data in Regions II and IV.In Fig. 2 (left) the event yield in Region II is compared to the estimate from scaling the Region IV sample by the measured misidentification rate.The Region II sample is dominated by misidentified leptons but also includes small contributions of true leptons arising from vector boson decays, estimated with simulated samples.
In the H → eτ h channel either lepton candidate can arise from a misidentified PF object, predominantly in W+jets and QCD multijet events, but also from Z → ee+jets and tt production.The misidentification rates f τ and f e are defined as the fraction of loosely isolated τ h or electron candidates that also pass a tight isolation requirement.This is measured in Z → ee + X collision data events, where X is an object identified as a τ h or e.The misidentified τ h contribution is estimated with Region I defined as the signal selection.Region III is the signal selection except the τ h is required to have loose and not tight isolation.The misidentified τ h lepton background in Region I is then estimated by multiplying the event yield in Region III by a factor f τ /(1 − f τ ).The same procedure is used to estimate the misidentified electron background by defining Region I as the signal selection and Region III as the signal selection but with a loose and not tight isolated electron, and scaling by f e /(1 − f e ).To avoid double counting, the event yield in Region III, multiplied by a factor f e /(1 − f e ) × f τ /(1 − f τ ), is subtracted from the sum of misidentified electrons and taus.The procedure is validated with the like-sign eτ samples.Figure 2 (right) shows the collision data in Region II compared to the estimate derived from Region IV.The method assumes that the misidentification rate in Z → ee + X events is the same as in the W+jets and QCD processes.To check this assumption, the misidentification rates are also measured in a collision data control sample of jets coming from QCD processes and found to be consistent.This sample is the same Z → ee + X sample as above but with one of the electron candidates required to be not isolated and the p T threshold lowered.

Other backgrounds
The leptonic decay of W bosons from tt pairs produces opposite sign dileptons and E miss T .This background is estimated using simulated tt events to compute the M col distribution and a collision data control region for normalization.The control region is the 2-jet selection described in Section 5.1, including the VBF requirements, with the additional requirement that at least one of the jets is b-tagged in order to enhance the tt contribution.Other smaller backgrounds enter from SM Higgs boson production (H → ττ), WW, WZ, ZZ + jets, Wγ ( * ) + jets processes, and single top quark production.Each of these is estimated using simulation [38].

Systematic uncertainties
Systematic uncertainties are implemented as nuisance parameters in the signal and background fit to determine the scale of their effect.Some of these nuisance parameters affect only the background and signal normalizations, while others also affect the shape of the M col distributions.

Normalization uncertainties
The values of the systematic uncertainties implemented as nuisance parameters in the signal and background fit are summarized in Tables 3 and 4. The uncertainties in the muon, electron and τ h selection efficiencies (trigger, identification, and isolation) are estimated using collision data samples of Z → µµ, ee, τ µ τ h events [63,72].The uncertainty in the Z → ττ background yield comes from the cross section uncertainty measurement (3% [73]) and from the uncertainty in the τ identification efficiency when applying to the embedded technique (5-10% uncorrelated between categories).The uncertainties in the estimation of the misidentified lepton rate come from the difference in rates measured in different collision data samples (QCD multijet and W+jets).The systematic uncertainty in the pileup modelling is evaluated by varying the total inelastic cross section by ±5% [74].The uncertainties in the production cross sections estimated from simulation are also included [38].
Uncertainties on diboson and single top production correspond to the uncertainties of the respective cross section measurements [75,76].A 10% uncertainty from the cross section measurement [77] is applied to the yield of the tt background.In the 2-jet categories an additional uncertainty (10% for H → eτ µ and 33% for H → eτ h ) is considered corresponding to the statistical uncertainty of the tt background yield.
Table 4: Theoretical uncertainties in percentage for the Higgs boson production cross section for each production process and category.All uncertainties are treated as fully correlated between categories except those denoted by a negative superscript which are fully anticorrelated due to the migration of events.

Systematic uncertainty Gluon fusion
Vector boson fusion 0-jet 1-jet 2-jet 0-jet 1 There are several theoretical uncertainties on the Higgs boson production cross section that depend on the production mechanism and the analysis category, as reported in Table 4.These uncertainties affect both the LFV Higgs boson and the SM Higgs boson background and are fully correlated.The uncertainty in the parton distribution function is evaluated by comparing the yields in each category, that span the parameter range of three different PDF sets, CT10 [47], MSTW [78], NNPDF [79] following the PDF4LHC [80] recommendation.The uncertainty due to the renormalization and factorization scales, µ R and µ F , is estimated by scaling up and down by a factor of two relative to their nominal values (µ R = µ F = M H /2). The uncertainty in the simulation of the underlying event and parton showers is estimated by using two different PYTHIA tunes, AUET2 and Z2*.All uncertainties are treated as fully correlated between cate-gories except those denoted by a negative superscript which are fully anticorrelated due to the migration of events.The systematic uncertainties that lead to a change in the shape of the M col distribution are summarized in Table 5.A 2% shift in the M col distribution of the embedded Z → ττ sample used to estimate the background is observed relative to simulation.It occurs only in the H → eτ µ channel as the effects of bremsstrahlung from the muon are neglected in the simulation.The M col distribution is corrected by 2 ± 2% for this effect.There is a systematic uncertainty of 5% in Z → ee background in the H → eτ h channel, due to the mismeasured energy of the electron reconstructed as a τ h .It causes a shift in the M col distribution, estimated by comparing collision data with simulation in a control region of Z → ee events in which one of the two electrons that form the Z peak is also identified as a τ h [63].Corrections are applied for the jet energy scale and resolution [66].They are determined with dijet and γ/Z+jets collision data and the most significant uncertainty arises from the photon energy scale.Other uncertainties such as jet fragmentation modelling, single pion response, and uncertainties in the pileup corrections are also included.The jet energy scale uncertainties (3-7%) are applied as a function of p T and η, including all correlations, to all jets in the event, propagated to the E miss T , and the resultant M col distribution is used in the fit.There is also an additional uncertainty to account for the unclustered energy scale uncertainty.The unclustered energy comes from jets below 10 GeV and PF candidates not within jets.It is also propagated to E miss T .These effects cause a shift of the M col distribution.The uncertainty in the jet energy resolution is used to smear the jets as a function of p T and η and the recomputed M col distribution is used in the fit.A 3% uncertainty in the τ h energy scale is estimated by comparing Z → ττ events in collision data and simulation.Potential uncertainties in the shape of the misidentified lepton backgrounds are also considered.In the H → eτ µ channel the misidentified lepton rates are applied in bins of p T and η.In the H → eτ h channel, the τ h misidentification rate is found to be approximately independent of p T but to depend on η.These rates are all varied by one standard deviation and the differences in the shapes are used as nuisance parameters in the fit.Finally, the distributions used in the fit have statistical uncertainties in each mass bin which is included as an uncertainty that is uncorrelated between the bins.

H → eµ analysis 6.1 Event selection
To select H → eµ events, the trigger requirement is an electron and a muon with p T greater than 17 and 8 GeV respectively.To enhance the signal sensitivity the event sample is divided into nine different categories according to the region of detection of the leptons and the number of jets, and a further two categories enriched in vector boson fusion production.The resolution of the reconstructed mass of the electron muon system, M eµ , depends on whether the leptons are detected in the barrel (|η e | < 1.48, |η µ | < 0.80) or endcap (1.57< |η e | < 2.50, 0.8 < |η µ | < 2.4), while the composition and rate of backgrounds varies with the number of jets.The definition of the categories is shown in Table 6.The two leptons are required to be isolated in all categories.Categories 0-8, which are selected according to the region of detection of the lepton and number of jets, are mutually exclusive with jets required to have p T > 20 GeV.To suppress backgrounds with significant E miss T , such as WW+jets, E miss T is required to be less than 20, 25 or 30 GeV, depending on the category.Jets arising from b quark decays are vetoed using the CSV discriminant to significantly reduce the tt background.In the VBF categories, the two highest p T jets are required to have |η| < 4.7 and to be separated by |η j 1 − η j 2 | > 3.0.In addition the jets are required to have | < 2.5, where = e or µ, η 1 2 denotes the pseudorapidity of the dilepton system and j 1 , j 2 are the two jets.The ∆φ between the dijet system and the dilepton system is required to be greater than 2.6 rad.The VBF tight category selection further requires that both jets have p T > 30 GeV and the dijet invariant mass be M j 1 j 2 > 500 GeV, while the VBF loose category relaxes the second jet requirement to p T > 20 GeV with M j 1 j 2 > 250 GeV and is exclusive to the VBF tight category.The leptons in both VBF categories can be in either the barrel or endcap.To avoid an event appearing in more than one category the VBF assignment is made first.Events with more than two jets are not considered.The selection efficiency, summed over all categories, is 24% (22%) for the GF (VBF) production mechanism.
Table 6: The H → eµ event selection criteria and background model for each event category.The categories are primarily defined according to whether the leptons are detected in the barrel ( B ) or endcap ( EC ), and the number of jets (N-jets).Requirements are also made on p T , E miss T and a veto on jets arising from a b-quark decay.The background model function and order of that function are also given.

Signal and background modelling
The signal model is the sum of two Gaussian functions, determined from simulation for each category.The reconstructed mass resolutions depend on whether the leptons are in the barrel (B) or endcap (EC) calorimeter and are: 2.0-2.1 GeV for e B µ B , 2.4-2.5 GeV for e B µ EC , 3.2-3.6 GeV for e EC µ B or EC categories and 2.4 (4.0) GeV for the VBF tight (loose) categories.The background, modelled as either a polynomial function, a sum of exponential functions, or a sum of power law functions is given in Table 6 for each category.The procedure to determine the background function follows the method described in [3].It is designed to choose a model with sufficient parameters to accurately describe the background while ensuring that the signal shape is not absorbed into the background function.The background model for each category is chosen independently using this procedure.
In a first step, reference functions are selected for each type of function (polynomial, sum of exponentials, sum of power laws).The order of the function is chosen such that the next higher order does not give a significantly better fit result when fit to the observed M eµ distribution in the range 110 GeV < M eµ < 160 GeV.
In a second step, an ensemble of distributions is drawn from each of the three reference background models combined with a signal contribution corresponding to B(H → eµ) = 0.1%, and fitted for signal and background with each of the three classes of functions of different orders.
On average, the signal yield extracted from the distributions using a signal plus background fit will differ from the injected signal due to the imperfect modelling of the background.The bias is defined as the median deviation of the fit signal event yield from the generated number of signal events.The possible combinations of generated distributions with the fit signal plus background models are then reduced by requiring the bias to be less than a threshold which results in less than 1% uncertainty in the fit signal event yield.The combination in which the fit model has the least parameters is then selected and the fit function is used as the background model for the collision data.If there is more than one model with the same minimal number of parameters then the one with the least bias is selected.

Systematic uncertainties
The systematic uncertainties are summarized in Table 7.The background is fit to the observed mass distribution with a negligible systematic uncertainty of <1% in the signal yield arising from the choice of background model as described above.Correction factors are applied to the lepton trigger, isolation, and identification efficiencies for each simulated signal sample to adjust for discrepancies with the collision data.The uncertainty in the signal yield from the lepton isolation and identification corrections is 2.0% and is estimated with the "tag-and-probe" method [72] applied to a collision data sample of Z bosons decaying to lepton pairs [60,62].The uncertainties in the lepton energy scale and the dilepton mass resolution are taken from the H → ZZ analysis [61].The systematic uncertainty in the pileup modelling is evaluated by varying the total inelastic cross section by ±5% [74].It varies according to the production process and category between 0.7% and 2.3%.There are systematic uncertainties in the efficiency of the b quark jet veto that also vary with production process and category from 0.05% to 0.7%.The uncertainty on the integrated luminosity is 2.6% [81].The effects of systematic uncertainties in the jet energy scale and resolution, and the uncertainties in PDF's on the selection efficiency are estimated as described in Section 5.3.2 for the H → eτ channel.The largest values of these systematic uncertainties occur due to the migration of events to, or from, a category with low statistics.
The theoretical uncertainties on the Higgs boson production cross section are also described in Section 5.3.2.

H → eτ
The distributions of the fitted signal and background contributions, after the full selection, are shown in Fig. 3 and the corresponding event yields in the mass range 100 GeV < M col < 150 GeV are given in Table 8.There is no evidence of a signal.Table 9 shows the expected and observed 95% CL mean upper limits on B(H → eτ) which are summarized in Fig. 4 for the individual categories in the eτ µ and eτ h channels and for the combination.The combined observed (expected) upper limit on B(H → eτ) is 0.69 (0.75)% at 95% CL. [70,71,82].

H → eµ
The M eµ distribution of the collision data sample, after all selection criteria, for all categories combined is shown in Fig. 5. Also shown are the combinations of the inclusive jet-tagged categories (0-8) and the VBF categories (9-10).The expected yields of signal (B(H → eµ) = 0.1%) and background events for 124 GeV < M eµ < 126 GeV, after all the selection criteria, are given in background are taken from simulation and given for information only, they are not used in the analysis.The dominant background contributions are from Drell-Yan production of τ lepton pairs and electroweak diboson production.There is no signal observed.An exclusion limit on Table 10: Event yields in the mass window 124 GeV < M eµ < 126 GeV for the H → eµ channel.The expected contributions, estimated from simulation, are normalized to an integrated luminosity of 19.7 fb −1 .The LFV Higgs boson signal is the expectation for B(H → eµ) = 0.1% assuming the SM production cross section.Values for background processes are given for information only and are not used for the analysis.The expected number of background events in the VBF categories obtained from simulation are associated with large uncertainties and are therefore not quoted here; we expect 1.5 ± 1.2 events from signal and observe 2 events.the branching fraction B(H → eµ) with M H = 125 GeV is derived using the CL s asymptotic model [83].It is shown in Fig. 4 for the inclusive categories grouped by number of jets, the VBF categories, and all categories combined.The expected limit is B(H → eµ) < 0.048% at 95% CL and the observed limit is B(H → eµ) < 0.035% at 95% CL.

Limits on lepton flavour violating couplings
The constraints on B(H → eτ) and B(H → eµ) can be interpreted in terms of the LFV Yukawa couplings |Y eτ |, |Y τe | and |Y eµ |, |Y µe | respectively [33].The LFV decays H → eτ, eµ arise at tree level in the Lagrangian, L V , from the flavour-violating Yukawa interactions, Y α β , where α , β denote the leptons e, µ, τ, and α = β .The subscripts L and R refer to the left and right handed components of the leptons, respectively.
The decay width Γ(H → α β ) in terms of the Yukawa couplings is given by: and the branching fraction by: The SM Higgs boson decay width is Γ SM = 4.1 MeV for a 125 GeV Higgs boson [84].The 95% CL constraints on the Yukawa couplings, derived from B(H → eτ) < 0.69% and B(H → eµ) < 0.035% using the expression for the branching fraction above are:  The expected (red solid line) and observed (black solid line) limits are derived from the limits on B(H → eτ) and B(H → eµ) from the present analysis.The flavour diagonal Yukawa couplings are approximated by their SM values.The green (yellow) band indicates the range that is expected to contain 68% (95%) of all observed limit excursions.The shaded regions in the left plot are derived constraints from null searches for τ → 3e (grey), τ → eγ (dark green) and the present analysis (light blue).The shaded regions in the right plot are derived constraints from null searches for µ → eγ (dark green), µ → 3e (light blue) and µ → e conversions (grey).The purple diagonal line is the theoretical naturalness limit Y ij Y ji ≤ m i m j /v 2 [33].

p 1 T − p 2 T;Figure 1 :
Figure 1: Comparison of the observed collinear mass distributions with the background expectations after the loose selection requirements.The shaded grey bands indicate the total background uncertainty.The open histograms correspond to the expected signal distributions for B(H → eτ) = 100%.The left column is H → eτ µ and the right column is H → eτ h ; the upper, middle and lower rows are the 0-jet, 1-jet and 2-jet categories, respectively.

Figure 3 :
Figure 3: Comparison of the observed collinear mass distributions with the background expectations after the fit.The simulated distributions for the signal are shown for the branching fraction B(H → eτ) = 0.69%.The left column is H → eτ µ and the right column is H → eτ h ; the upper, middle and lower rows are the 0-jet, 1-jet and 2-jet categories, respectively.

Figure 6 :
Figure 6: Constraints on the flavour violating Yukawa couplings |Y eτ |, |Y τe | (left) and |Y eµ |, |Y µe | (right).The expected (red solid line) and observed (black solid line) limits are derived from the limits on B(H → eτ) and B(H → eµ) from the present analysis.The flavour diagonal Yukawa couplings are approximated by their SM values.The green (yellow) band indicates the range that is expected to contain 68% (95%) of all observed limit excursions.The shaded regions in the left plot are derived constraints from null searches for τ → 3e (grey), τ → eγ (dark green) and the present analysis (light blue).The shaded regions in the right plot are derived constraints from null searches for µ → eγ (dark green), µ → 3e (light blue) and µ → e conversions (grey).The purple diagonal line is the theoretical naturalness limit Y ij Y ji ≤ m i m j /v 2[33].

A
search for lepton flavour violating decays of the Higgs boson to eτ or eµ, based on the full √ s = 8 TeV collision data set collected by the CMS experiment in 2012, is presented.No evidence is found for such decays.Observed upper limits of B(H → eτ) < 0.69% and B(H → eµ) < 0.035% at 95% CL are set for M H = 125 GeV.These limits are used to constrain the Y eτ and Y eµ Yukawa couplings as follows: |Y eτ | 2 + |Y τe | 2 < 2.4 × 10 −3 and |Y eµ | 2 + |Y µe | 2 < 5.4 × 10 −4 at 95% CL.

5 H → eτ analysis 5.1 Event selection
44ose selection is then made for both channels.Electron, muon and hadronic tau lepton candidates are required to be isolated and to lie in the pseudorapidity ranges where they can be well reconstructed; |η e | < 1.44or 1.57 < |η e | < 2.30, |η µ | < 2.1 and |η τ h | < 2.3, respectively.Leptons are also required to be compatible with the primary vertex and to be separated by ∆R > 0.4 from any jet in the event with p T > 30 GeV.The H → eτ µ channel then requires an electron (p e T > 40 GeV) and an oppositely charged muon (p > 10 GeV), or hadronic tau leptons (p T > 20 GeV) are rejected. A

Table 1 :
Event selection criteria for the kinematic variables after applying loose selection requirements.

Table 3 :
The systematic uncertainties in the expected event yields in percentage for the eτ h and eτ µ channels.All uncertainties are treated as correlated between the categories, except when two values are quoted, in which case the number denoted by an asterisk is treated as uncorrelated between categories. 3 ⊕ 5 * 3 ⊕ 10 * 3 ⊕ 5 * 3 ⊕ 5 * 3 ⊕ 10 * *

Table 5 :
Systematic uncertainties in the shape of the signal and background distributions, expressed in percentage.The systematic uncertainty and its implementation are described in the text.

Table 7 :
Systematic uncertainties in percentage on the expected yield for H → eµ.Ranges are given where the uncertainty varies with production process and category.All uncertainties are treated as correlated between categories.

Table 8 :
Event yields in the signal region, 100 GeV < M col < 150 GeV, after fitting for signal and background for the H → eτ channel, normalized to an integrated luminosity of 19.7 fb −1 .The LFV Higgs boson signal is the expected yield for B(H → eτ) = 0.69% assuming the SM Higgs boson production cross section.

Table 9 :
The expected and observed upper limits at 95% CL, and best fit values for the branching fractions B(H → eτ) for different jet categories and analysis channels.The asymmetric one standard-deviation uncertainties around the expected limits are shown in parentheses.
Table 10 and compared to the collision data event yield.The contributions to the 95% CL upper limits by category for the LFV decays for M H = 125 GeV.Left: H → eτ.Right: H → eµ for categories combined by number of jets, the VBF categories combined, and all categories combined.
CMSFigure 4: [33]e | 2 < 2.4 × 10 −3 , |Y eµ | 2 + |Y µe | 2 < 5.4 × 10 −4 .Figures 6 compare these results to the constraints from previous indirect measurements.The absence of µ → eγ decays implies a limit of |Y eµ | 2 + |Y µe | 2 < 3.6 × 10 −6[33]assuming that flavour changing neutral currents are dominated by the Higgs boson contributions.However, this limit can be degraded by the cancellation of lepton flavour violating effects from other new physics. Te direct search for H → eµ decays presented here is therefore complementary to indirect limits obtained from searches for rare decays at lower energies.