Search for lepton-flavour-violating decays of the Z boson into a τ-lepton and a light lepton with the ATLAS detector

Lepton flavour violation in the charged lepton sector is an unambiguous signal of physics beyond the Standard Model. Searches for lepton flavour violation in decays of the Z boson with the ATLAS detector is reported, focusing on decays into an electron or muon and a hadronically decaying τ-lepton, using pp collisions data with a centre-of-mass energy of 13 TeV. Upper limits on the branching ratios of lepton-flavor-violating decays are set at the 95% confidence level: B(Z → eτ)< 5.8×10−5 and B(Z → μτ)< 2.4×10−5. When combined with a previous ATLAS result based on pp collisions data with a centreof-mass energy of 8 TeV, an upper limit of B(Z → μτ)< 1.3× 10−5 is obtained. Copyright W. S. Chan et al. This work is licensed under the Creative Commons Attribution 4.0 International License. Published by the SciPost Foundation. Received 07-12-2018 Accepted 17-01-2019 Published 22-02-2019 Check for updates doi:10.21468/SciPostPhysProc.1.048


Introduction
In the Standard Model (SM), flavour is not a conserved global symmetry in general. It is well known that flavour-changing processes exist in the quark and neutrino sectors. These processes can be described by the CKM quark-mixing matrix and the PMNS neutrinomixing matrix. However, the mixing of charged leptons have not yet been observed so far. In the SM, lepton-flavour-violating (LFV) processes such as Z → µτ are possible beyond tree level with neutrino oscillations considered (Fig. 1), but with vanishingly small branching ratios (∼ 10 −54 ) [1]. Therefore, searches for such processes are free from irreducible SM backgrounds, and any observation would be an unambiguous signal of Beyond-the-Standard-Model (BSM) phenomena.
The Z boson is a SM particle with well-measured properties and has a high production rate at the LHC. This makes LFV Z boson decays an interesting signal to probe BSM theories with LFV predictions, including models with heavy neutrinos [2], extended gauge [3] or supersymmetry [4].
Copyright 2018 CERN for the benefit of the ATLAS Collaboration. Reproduction of this article or parts of it is allowed as specified in the CC-BY-4.0 license. This article presents the searches for the LFV decays of the Z boson into an electron or a muon, hereafter referred to as a light lepton or , and a hadronically decaying τ -lepton [9] with the ATLAS detector, using pp collisions data with a centre-of-mass energy of 13 TeV.

The ATLAS detector
The ATLAS detector 1 [10] at the LHC is a multipurpose particle detector with a forwardbackward symmetric cylindrical geometry and a nearly 4π coverage in solid angle. It consists of three major parts: The inner detector provides precision tracking with silicon pixel and micro strip detectors and additional tracking with a transition-radiation tracker. The inner detector is placed at the centre of the ATLAS detector, surrounded by a superconducting solenoid that provides a 2 T magnetic field.
The electromagnetic and hadronic calorimeters are placed surrounding the solenoid. The electromagnetic calorimeter uses liquid argon and the hadronic calorimeter uses scintillator tiles in the barrel section and liquid argon in the endcaps.
The muon spectrometer is the outermost part of the ATLAS detector. Precise momentum measurements for muons are provided by three layers of tracking chambers and three surrounding large superconducting toroid magnets each containing eight coils.
A two-level trigger system [11] was used during the √ s = 13 TeV data-taking period, which reduced the recorded event rate to approximately 1 kHz on average.

Preselection
Events selected in this analysis are required to have exactly one reconstructed light lepton that passed trigger-matching, isolation and identification criteria [12,13]. The events must also have at least one reconstructed candidate of visible hadronic τ -lepton decay products 1 ATLAS uses a right-handed coordinate system with its origin at the nominal interaction point (IP) in the center of the detector and the z-axis along the beam pipe. The x-axis points from the IP to the center of the LHC ring, and the y-axis points upward. Cylindrical coordinates (r, φ) are used in the transverse plane, with φ as the azimuthal angle around the beam pipe. The pseudorapidity is defined in terms of the polar angle θ as η = − ln tan(θ/2). The transverse momentum and the transverse energy are defined as pT = p sin θ and ET = E sin θ, respectively.  Figure 2: Expected distributions of m T (τ had-vis , E miss T ) in Z → τ τ , W +jets and signal events in the eτ (left) and µτ (right) channels after preselection requirements. The Z → τ τ and W +jets distributions also include the contributions to fakes from the corresponding processes as predicted by MC simulations. All distributions are normalised to unity.
(τ had-vis ) that passed the "tight" identification criteria [14,15]. The light lepton and the τ had-vis candidate with leading p T must carry opposite charge. To reduce backgrounds with top quarks, events with b-tagged jets [16] are vetoed. Due to the high → τ misreconstruction rates, events with |η(τ had-vis )| > 2.2 (< 0.1) are rejected for the eτ (µτ ) channel. The selection described is hereafter referred to as the preselection.

Signal region
In order to obtain a high signal sensitivity and accurate background estimation, signal region (SR) and calibration regions (CRs) are defined. In the SR, accepted events must satisfy the preselection and two additional selections.
The first selection requires the transverse mass of the τ had-vis candidate and the missing transverse energy E miss T , to be smaller than 35 (30) GeV for the eτ (µτ ) channel. The selection can be justified by the fact that the signal events are expected to have E miss T from the τ -neutrino in a direction close to the τ had-vis candidate. This results in small m T (τ had-vis , E miss T ) values. The major backgrounds, W +jets (where jets are misidentified as τ had-vis candidates) and Z → τ τ events, are expected to have higher m T (τ had-vis , E miss T ) values. The selection is illustrated in Figure 2.
The second selection requires events in which the τ had-vis candidate has one associated track (1-prong τ had-vis ) to pass cuts on the measured visible invariant mass, m(τ track, ) or m(τ had-vis , ), to reject Z → events with a light lepton misidentified as a τ had-vis candidate. The visible invariant mass m(τ track, ) is reconstructed using the momentum of the track associated to the τ had-vis candidate as measured by the inner detector, While m(τ had-vis , ) is reconstructed using energy deposit of the τ had-vis candidate in the calorimeters. The requirements are m(τ track, ) > 105 GeV and m(τ track, ) < 84 GeV (80 GeV) if |η(τ had-vis )| < 2.0 (> 2.0). Furthermore, events that satisfies 80 GeV < m(τ had-vis , ) < 100 GeV must have m(τ track, ) > 40 GeV. The selection is illustrated in Figure 3.

Event classification
Events in the SR are classified using neural network (NN) classifiers. Two binary classifiers, the "Z classifier" and the "W classifier", are trained to discriminate signal events from the two major backgrounds, Z → τ τ and W +jets, respectively. Additionally, for events with 1-prong τ had-vis candidates, a "Zll classifier" is trained to discriminate signal events from Z → events. The classifiers are trained separately for the eτ and µτ channels. The NNs are trained using simulated events passing the preselection but with the τ had-vis identification criteria loosen to increase the training sample size. Moreover, for the signal-Z → classifier, only simulated events with a true light lepton misreconstructed as a τ had-vis candidate are used. The 4-momenta of the reconstructed light lepton, τ had-vis candidate and E miss T are used as input variables to the NNs. In addition, two high-level kinematic variables are also directly inputted to the NNs, including the collinear mass and ∆α [17]: where p(τ had-vis ) and p( ) are the 4-momenta of the τ had-vis and light-lepton candidates respectively, and m Z and m τ are the known rest masses of the Z boson and the τ -lepton. For the signal-Z → classifier, it is found that the visible invariant mass m(τ had-vis , ) is also an effective input variable and is also used. The inputs are preprocessed by boosting and rotating the -τ had-vis -E miss T system to remove degeneracy from known symmetries. The outputs of the different NN classifiers are combined into a final discriminant that is effective in discriminating the signal events from all the major backgrounds. For events with τ had-vis candidates that have three associated tracks (3-prong τ had-vis ), the outputs of the Z and W classifiers, X Z and X W , are combined as one subtracted by the normalised distance in the X Z -X W plane from the most signal-like point (X Z = 1, X W = 1): Similarly, for events with 1-prong τ had-vis candidates, where X Zll is the output of the Zll classifier.

Background estimation
The backgrounds are estimated using a combination of Monte Carlo (MC) simulations and data-driven techniques. MC simulations are used to estimate background events in which the τ had-vis candidate originates from a true lepton, such as Z → τ τ , tt and diboson events. For events in which a jet is misidentified as a τ had-vis candidate ("fakes"), such as W +jets and QCD multijet events, a data-driven method known as the fake factor (FF) method is used.

The fake factor method
In order to estimate backgrounds with fakes, the fake factor method is used. Four fakesenriched CRs are defined as described in Table 1, from which four fake factors, F W +jets , F top , F Z→ and F QCD , are measured, each corresponds to a physical process as indicated in the subscripts.
In each CR, the corresponding fake factor is measured in data as the ratio of the number of events where the τ had-vis candidate passes the tight identification criteria to that fails the criteria. The fake factor is measured in bins of p T (τ had-vis ) and p T (τ track). Contributions from background processes that are not the corresponding target process of the CR or from events where the τ had-vis candidate does not originate from a jet are estimated by MC simulations and are subtracted from data for the calculation of the fake factors. The fake factors are then combined into a weighted average F , where the individual fake factors are weighted by the fraction of expected contribution from the corresponding process to the total fakes in the SR as predicted by MC simulations. The total yield of fakes in the SR is then estimated by multiplying F to the observed number of events in the SR where the τ had-vis candidate fails the tight identification criteria.

Normalisation of major backgrounds
To reduce theoretical uncertainties, the Z → τ τ , Z → and fakes backgrounds are all normalised to data. The Z → background is normalised to data in a control region with over 99% purity. The normalisation of the Z → τ τ and fakes backgrounds are fit to data simultaneously in a binned maximum-likelihood fit as described in Section 5.

Results and interpretations
In order to extract evidence of signal events or set upper limit to the LFV branching ratios, binned maximum-likelihood fits to the combined NN output distribution of data are performed. Free parameters of the fit include the LFV decay branching ratio B(Z → τ ) and the normalisations of the Z → τ τ and fakes backgrounds. Systematic uncertainties, including uncertainties in reconstruction, identification and isolation efficiencies, as well as statistical and theoretical uncertainties in the predicted number of events are incorporated in the fit as nuisance parameters with Gaussian or Poisson constraints. The fits are performed separately for the eτ and µτ channels, since the corresponding branching ratios are not necessarily correlated. Due to the difference in background compositions, events with 1-prong and 3-prong τ had-vis candidates are fit separately but simultaneously.
The probability of compatibility between data and the background-plus-signal hypothesis is assessed using the CL S method [18]. By analysing 36.1 fb −1 of pp collision data at a centre-of-mass energy of 13 TeV, no significant excess (> 3σ) of events above the expected background is found. A slight excess in the eτ channel is observed with significance 2.3σ. The resulting observed (expected) exclusion upper limits at 95% confidence level are B(Z → eτ ) < 5.8 × 10 −5 (2.8 × 10 −5 ) and B(Z → µτ ) < 2.4 × 10 −5 (2.4 × 10 −5 ). The observed and best-fit expected distributions of the combined NN output distributions are shown in Figure 4.
The result of the µτ channel is combined with previous result published by ATLAS with pp collision data at a centre-of-mass energy of 8 TeV [19]. With a combined fit, the observed (expected) exclusion upper limit at 95% confidence level are set at B(Z → µτ ) < 1.3×10 −5 (1.8 × 10 −5 ).

Conclusion
Direct searches for LFV decays of the Z boson into a light lepton and a hadronically decaying τ -lepton are presented. Events that exhibits the expected characteristics of the signal events are selected and are discriminated from backgrounds using NN classifiers. The expected NN output distributions are fit to data to quantify the probability of compatibility between data and the background-plus-signal hypothesis, and set exclusion upper limit on the LFV branching ratios. No significant excess of events above the expected backgorund is observed and the upper limits at 95% confidence level are set: B(Z → eτ ) < 5.8 × 10 −5 and B(Z → µτ ) < 2.4 × 10 −5 . When combined with previous published ATLAS results, the upper limit B(Z → µτ ) < 1.3 × 10 −5 is set. The obtained limit is close to the current most stringent limit from LEP experiment: B(Z → µτ ) < 1.2 × 10 −5 .