Search for excited electrons singly produced in proton–proton collisions at √ s = 13 TeV with the ATLAS experiment at the LHC

A search for excited electrons produced in pp collisions at √ s = 13 TeV via a contact interaction q ¯ q → ee ∗ is presented. The search uses 36.1 fb − 1 of data collected in 2015 and 2016 by the ATLAS experiment at the Large Hadron Collider. Decays of the excited electron into an electron and a pair of quarks ( eq ¯ q ) are targeted in ﬁnal states with two electrons and two hadronic jets, and decays via a gauge interaction into a neutrino and a W boson ( ν W ) are probed in ﬁnal states with an electron, missing transverse momentum, and a large-radius jet consistent with a hadronically decaying W boson. No signiﬁcant excess is observed over the expected backgrounds. Upper limits are calculated for the pp → ee ∗ → eeq ¯ q and pp → ee ∗ → e ν W production cross sections as a function of the excited electron mass m e ∗ at 95% conﬁdence level. The limits are translated into lower bounds on the compositeness scale parameter Λ of the model as a function of m e ∗ . For m e ∗ < 0 . 5 TeV, the lower bound for Λ is 11 TeV. In the special case of m e ∗ = Λ , the values of m e ∗ < 4 . 8 TeV are excluded. The presented limits on Λ are more stringent than those obtained in previous searches.


Introduction
Excited leptons appear in a number of composite models [1][2][3][4][5][6] seeking to explain the existence of the three generations of quarks and leptons in the Standard Model (SM). This analysis uses the model presented in Ref. [6] as a benchmark. The composite models introduce new constituent particles called preons that bind at a high scale Λ to form SM fermions and their excited states. The preon bound states are mapped into representations of the SU(2) × U(1) SM gauge group. The SM fermions are identified as a set of left-and right-handed chiral states protected by the SU(2) symmetry from obtaining masses of the order of Λ [6]. The remaining vector-like states, SU(2) doublets and singlets, acquire masses of the order of Λ and are thus interpreted as excited fermions. The effective Lagrangian introduces four-fermion contact-interaction (CI) terms (Eqs. (1) and (2)) and gauge-mediated (GM) currents (Eq. (3)): Here, f = , q and f * = * , q * denote SM and excited leptons and quarks, and the subscripts L and R stand for left-and right-handed components of the fermion field f , respectively. The j µ term is the fermion current of f and f * . The W µν and B µν are the field-strength tensors of the SU(2) and U(1) gauge fields, and g and g are the corresponding coupling constants of the electroweak theory. The left-and right-handed excited fermions are both SU(2) doublets, with the weak hypercharge Y such that f * electric charges coincide with the ones of their ground states f . The weak hypercharge Y of the * L,R doublet is −1, so that its isospin T 3 = −1/2 component represents an excited lepton with electric charge Q = −1.
Therefore, the excited lepton model introduces two unknown parameters relevant for this analysis, the excited lepton mass m e * and the compositeness scale Λ, which define the preferred search channels and kinematic properties of the final states. The four-fermion CI terms are suppressed by 1/Λ 2 implying the parton-level e * production cross section growing proportionally toŝ. The considered models allow only left-handed currents in the contact-interaction terms, and all dimensionless couplings defining the relative strength of the residual interactions are set to unity [6]. The restriction m e * < Λ follows from unitarity constraints on the contact interactions [6,7]. Branching ratios (B) for excited electrons as functions of m e * for the case of Λ = 10 TeVare presented in Figure 1. Gauge-mediated decays dominate at m e * Λ while the decay via a contact interaction becomes dominant for m e * Λ/3. This article presents a search for excited electrons singly produced in pp collisions at √ s = 13 TeV via a contact interaction qq → ee * and decaying either to an electron and a pair of quarks (eqq) via a contact interaction or to a neutrino and a W boson (νW) via a gauge interaction, depicted in Figures 2(a) and 2(b), respectively. Given the sensitivity of the search, the contribution of gauge-mediated production of the excited electrons is non-negligible relative to the contact-interaction production only for m e * < 200 GeV The present search uses two experimental channels. The first channel targets the production of excited electrons via a contact interaction qq → ee * and their decay via a contact interaction e * → eqq, resulting in two energetic electrons and at least two hadronic jets j. In the second channel, the excited electrons are produced via a contact interaction as well, but their decay is via a gauge-mediated interaction into a W and a ν, where the W boson decays hadronically, yielding an ee * → eνqq final state. Experimentally, this gives final states with exactly one energetic electron, a large-radius (large-R) jet J produced by two collimated quarks, and missing transverse momentum. The large-R jet approach is sufficient for the current analysis, as the analysis selection with two resolved jets has minor efficiency. In the following, the final states resulting from contact-and gauge-mediated decays of singly produced e * are denoted by ee j j and eνJ, respectively. The combination of the two channels maximizes the sensitivity of the search for all m e * /Λ values. For possible reinterpretations, the results are also presented in terms of model-independent upper limits on the number of signal events and on the visible signal cross section.
final state are used for background studies in the ee j j channel and are selected using a combination of the two single-muon triggers with the transverse momentum p T thresholds of 26 and 50 GeV.
Selected events contain proton-proton collisions in the same or neighboring bunch crossing (pile-up). The events used in the analysis contain 24 pile-up interactions on average, resulting in multiple interaction vertices in an event. The primary vertex (PV) is defined as the vertex with the highest Σp 2 T of charged-particle tracks. This PV must have at least two tracks with the transverse momentum p T > 400 MeV.
The signal samples were simulated by P 8.210 [30], using a leading-order (LO) matrix element (ME), the NNPDF23LO [31] set of parton distribution functions (PDFs) and the A14 [32] set of tuned parameters. The e * widths for the simulated signal samples were derived from C HEP 3.6.25 [33], which takes into account phase-space effects due to quark masses. The samples were generated for a compositeness scale Λ = 5 TeV and masses of excited electrons ranging from 100 GeV to 4 TeV. The effect of a finite Λ-dependent e * width on the analysis is negligible for m e * < Λ.
As shown in Section 5, the dominant backgrounds in the ee j j and eνJ channels are from Z/γ * + jets and W + jets production, respectively. The sub-leading background in both channels is from tt production, followed by single-top and diboson production. The estimation of background processes involving prompt leptons from W and Z/γ * decays relies on simulated event samples.
The Z/γ * + jets and W + jets processes were simulated using S 2.2.1 [34]. Parton-level final states with up to two partons produced along with the Z and W bosons were generated at next-to-leading order (NLO), and those with three or four partons were generated at LO, using the O L [35] and C [36] for the NLO and LO cases, respectively. Double counting of events with the same partonic final state generated by various combinations of the ME and parton shower (PS) was eliminated according to the ME+PS@NLO prescription [37]. The NNPDF 3.0 [38] set of PDFs was used. The Z/γ * + jets and W + jets simulated event samples were normalized to the next-to-next-to-leading-order (NNLO) inclusive cross sections computed with the FEWZ program [39].
The tt simulated event samples were generated at NLO accuracy in the strong coupling constant using P -B v2 [40][41][42][43], with the top-quark spin correlations preserved, and the CT10 [44] PDF set. Electroweak sand t-channel single-top-quark events as well as events with a single top-quark produced in association with a W boson were generated using P -B v1 [45,46]. Parton showering, hadronization and the underlying event were handled by P 8.210 for tt production and by P 6.428 [47] for single-top production. P 8.210 and P 6.428 used the A14 and Perugia 2012 [48] sets of tuned parameters, respectively. The tt simulated event sample was normalized to the inclusive cross section calculated using the Top++ v2.0 [49] at NNLO accuracy in the strong coupling constant, with soft gluon emission accounted for in the next-to-next-to-leading logarithmic order (NNLL). The single-top simulated event samples were normalized to the cross sections computed at NLO+NNLL accuracy [50].
The Z Z, ZW and WW simulated event samples were generated using S 2.2.1. Events containing zero or one final-state parton were generated using an NLO ME. Events with two or three recoiling quarks or gluons were generated with a LO ME. The NNPDF 3.0 PDF set was used. The event generator cross sections are used in this case.
Decays of band c-hadrons in the simulated event samples of tt, single-top, and signal processes were handled by EvtGen v1.2.0 [51].
The pile-up interactions are described by overlaying minimum-bias events on each simulated signal or background event. The minimum-bias events were generated with P 8.186 [52] with the A2 [53] set of tuned parameters and the MSTW2008LO [54] PDFs. The distribution of the average number of interactions per bunch crossing in simulated event samples is reweighted to match the observed data.
All the simulated event samples were passed through a simulation of the ATLAS detector [55]. The detector response was obtained from a detector model that uses G 4 [56]. For the simulation of the ee * → eeqq signal samples, G 4 based inner detector simulation was combined with a parameterized calorimeter simulation [55]. The simulated event samples were processed with the same reconstruction software as used for data.

Object and event selection
Events satisfying basic quality, trigger and vertex requirements are selected for the analysis using the criteria applied to electrons, muons, hadronic jets, and their kinematic quantities. The looser baseline selections are applied at stages which aim to eliminate double counting of detected objects (electrons, muons, jets, tracks, vertices, etc.) in an event and double-counting of events in the two analysis channels. The tighter final selection defines objects used in the analysis. In the following, both the baseline and final object selections are specified in Table 1, and the order of the event criteria applied in the analysis is given in Table 2. These selections form the preselection stage.
An electron candidate is reconstructed as a clustered energy deposition in the calorimeter matched to a track from the ID [57]. The direction of an electron is taken from its track and the energy is measured from the EM cluster. The energy is corrected for losses in the material before the calorimeter and for leakage outside of the cluster [58]. The coverage of the ID limits the pseudorapidity of electrons to |η| < 2.47. Electrons with 1.37 < |η| < 1.52 are excluded because they point to the barrel-to-endcap transition regions. To reject electron candidates originating from hadronic jets and photon conversions, electrons are required to satisfy a set of likelihood-based identification criteria determined by variables characterizing longitudinal and lateral calorimeter shower shapes, ID track properties, and track-cluster matching. These criteria are referred to, in order of increasing background rejection, as loose, medium and tight and are defined so that an electron satisfying a tighter criterion always satisfies looser ones. The loose identification is approximately 95% efficient for prompt electrons with p T > 30 GeV. In the same p T range, signal efficiency for medium identification is greater than 90%. The efficiency of tight identification is greater than 85% for prompt electrons with p T > 65 GeV [57]. Further rejection of background is achieved by applying EM calorimeter and ID isolation requirements [57]. The loose isolation requirement applied in this analysis is designed to achieve 99% selection efficiency for prompt electrons. Electrons originating from the primary interaction vertex are selected by requiring the reconstructed electron track to have a transverse impact parameter significance |d 0 |/σ d 0 < 5, where σ d 0 is the uncertainty in the transverse impact parameter, and a longitudinal impact parameter |z 0 sin θ| < 0.5 mm.
Muons are reconstructed using a combined fit of tracks measured with the ID and MS. Muons from in-flight decays of charged hadrons are suppressed with the medium set of identification requirements [59]. The muon identification efficiency exceeds 96% for prompt muons with p T > 20 GeV. Muons are also subject to a loose isolation requirement that uses ID tracks [59] and is 99% efficient for prompt muons at any relevant p T and η. Muons are further required to originate from the primary vertex by imposing the same criteria as for electrons on the ID track's longitudinal impact parameter and transverse impact parameter significance less then 3.
Hadronic jets are reconstructed from clustered energy deposits in the calorimeters using the anti-k t algorithm [60] with radius parameters R = 0.4 and R = 1.0. The reconstructed jets with R = 1.0 are trimmed [61] to reduce contributions from pile-up interactions and underlying event by reclustering the jet constituents into subjets using a k t algorithm with R = 0.2 and removing subjets carrying less than 5% of the boosted jet's p T . Jet calibrations are applied as described in Refs. [62,63].
An event is removed if it contains a jet reconstructed with R = 0.4 and originating from non-collision backgrounds, which is identified either by a substantial fraction of the jet energy being deposited in known noisy calorimeter cells or by a low fraction of the jet energy being carried by charged particles originating from the primary vertex and lying within a ∆R = 0.4 cone around the jet axis [64]. Rejection of pile-up jets with |η| < 2.4 and p T < 60 GeV is achieved using a jet-vertex-tagger (JVT) discriminant [65] quantifying the relative probability for a jet to originate from the primary vertex. To discriminate boosted jets originating from W boson decays from those produced through strong interactions, the jet mass obtained by combining measurements from the calorimeter and tracking systems and the substructure variable D variable is specifically sensitive to a two-prong substructure within a jet and tends to zero in a two-body decay limit. A boosted jet is tagged as a W candidate if its mass falls within a certain mass window around m W and its D The missing transverse momentum, with magnitude E miss T , is calculated as the negative vector sum of all reconstructed objects associated with the primary vertex. This includes calibrated electrons, muons, and R = 0.4 jets, and a track-based soft term (TST) using ID tracks not associated with the preselected hard objects [73]. The TST is built from tracks with p T > 400 MeV and |η| < 2.5 which have a sufficient number of hits in the ID, a good fit quality, and an origin consistent with the primary vertex.
Double counting of electrons, muons, and jets reconstructed by more than one lepton and/or jet algorithm as well as misreconstruction of distinct physics objects produced in close proximity are resolved by the overlap removal procedure. The procedure is applied to the baseline objects in the following order: • electron-electron: if two electrons share an ID track then the lower quality electron is removed; if both electrons are of the same quality then the lower-p T electron is removed; • electron-muon: remove the electron which shares an ID track with the muon; • electron-jet with R = 0.4: remove the jet if ∆R(e, jet) < 0.2 and, in the eνJ channel only, the jet is not b-tagged; after repeating this step for all pairs of electrons and surviving jets, electrons within ∆R = 0.4 of a jet are removed; • muon-jet with R = 0.4: if ∆R(µ, jet) < 0.2 and the jet has less than three ID tracks originating from the muon production vertex and, in the eνJ channel only, the jet is not b-tagged, then the jet is removed; after repeating this step for all pairs of muons and surviving jets, muons within ∆R = 0.4 of a jet are removed.
The second overlap removal procedure applied only in the eνJ channel involves baseline electrons and final boosted jets. The boosted jet is removed if a baseline electron is present within ∆R = 1.0 of the boosted jet direction. Table 1: Object definitions in the ee j j and eνJ channels. Muon selections are given in parentheses.
Selection type Objects ee j j eνJ

Baseline
Electrons One of the background sources common to both channels is a misidentification of hadronic jets, photon conversions in the material or electrons from hadron decays as prompt electrons, referred to as the fake-electron background (Section 5). As this background is estimated in a data-driven way, to avoid double counting, the selected electrons in simulated background events are required to coincide with electrons from the event generators (referred to as 'truth matching' in Table 2).
To correct for differences in various object reconstruction and identification efficiencies between the data and simulated event samples, the simulated events are weighted to correct for differences in the trigger, object reconstruction and identification efficiencies between the data and simulation [57,59,68]. The correction weights are estimated using measurements in control data samples and are typically consistent with unity to within 5%.
The dominant backgrounds in the eνJ channel are due to the production of a W boson in association with jets W(→ eν) + jets and tt → bW(eν)bW(J) followed by single-top, Z/γ * (→ ee/ττ) + jets, W(→ τν) + jets, diboson, and multi-jet background production. The only sizeable source of events with a misidentified electron is the multi-jet production.
The overall background composition in the ee j j and eνJ preselected event samples is shown in Table 3. Table 3: Relative contributions of background processes to the total number of preselected background events. The event yields are normalized to the theoretical cross sections. Contributions included into the fake-electron background are denoted by "-". The 'fake electron' row includes all sources of events with misidentified electrons. These events are vetoed in the simulated event samples to prevent double counting.
Background processes with real electrons are predicted using the simulated event samples. Backgrounds with misidentified electrons are evaluated with a data-driven matrix method as in Ref. [74].

Analysis strategy
The analysis is based on measurements of event yields in a number of phase-space regions defined by the discriminating variables described below. Signal regions (SRs) are constructed to maximize sensitivity to the signal process as predicted by the benchmark model for given values of m e * , in the presence of the SM background. The signal selection efficiency is nearly independent of Λ, and therefore the SRs are optimized for the different values of m e * instead of using a two-dimensional Λ-m e * signal optimization. Simulated dominant background processes are constrained in dedicated control regions (CRs). The analysis is blind, and to verify the background predictions after they are constrained by the CRs and before the SRs are unblinded, validation regions (VRs) serve as transitions between CRs and SRs. Signal contamination of all CRs and VRs is negligible. The following section discusses the selection criteria used in the various SRs, CRs, and VRs, which do not overlap.

Signal regions
The SRs for the ee j j channel are constructed using the m , S T , m j j discriminating variables, where • m is the invariant mass of the electron pair, • S T is the scalar sum of the transverse momenta of the two electrons and the two jets with the highest p T , and • m j j is the invariant mass of the two electrons and the two jets with the highest p T .
The definition of the SRs is identical to the one used in the search for a singly produced excited muon decaying into a muon and two jets at √ s = 8 TeV with the ATLAS detector [22]. Further optimization of the ee j j channel SRs does not result in a conclusive improvement of sensitivity to the signal process compared to the initial SR definition given in Ref. [22]. The distributions of the discriminating variables for the ee j j channel are shown in Figure 3 after applying the preselection requirements (Table 2) and performing a background-only fit in the corresponding CRs.
The selection criteria for the SRs as well as the selection efficiencies for the ee j j channel are shown in Table 4.
The SRs in the eνJ channel are optimized with discriminating variables at each value of m e * by maximization of the modified significance defined in Ref.
[75] as where S is the signal yield and B is the background yield in the defined region. This method is checked with minimization of expected upper limit for cross section of the signal, which gives a similar result. The maximization is performed by varying the criteria on the set of variables found to provide a maximum discrimination between the signal and the background, m νW T and ∆φ(e, ì E miss T ) , simultaneously, where:   Table 2). Signal efficiencies are presented as the number of signal events in each SR relative to that after the preselection and relative to that before any selection. Each signal region is valid for one or more mass hypotheses, as shown in the second column. • m νW T coincides with the transverse mass of the system of the missing transverse momentum and the W boson in signal events and is given by is the x(y)-component of the momentum of the W boson candidate reconstructed as the R = 1.0 jet. The m νW T is required to exceed a threshold that grows with m e * .
• ∆φ(e, ì E miss T ) coincides with the absolute value of the azimuthal angle between the neutrino and the electron in signal events. This quantity provides discrimination between signal events and SM processes involving the leptonic decay of a W boson.
Different sets of selection criteria are examined for each m e * by applying a maximum or minimum requirement on each of the two variables, i.e., min m νW T , max m νW T , min ∆φ(e, ì E miss T ) , and the most effective one is used for the corresponding SR. The distributions of the m νW T and ∆φ(e, ì E miss T ) , as well as in m J variables are shown in Figure 4 for the eνJ channel after applying the preselection requirements and the background-only fit in the CRs as discussed in Section 6.2 and Section 8. In the eνJ channel, the observables m νW T and ∆φ(e, ì E miss T ) are used to create the nine optimized SRs.
Each SR targets a model with a given mass of the excited electron. The SR is defined by applying the preselection introduced in Section 4 and additionally requiring the criteria defined in Table 5, which include a b-jet veto and selection on m νW T and ∆φ(e, ì E miss T ) . The large-R jet also passes the 50% signal efficiency requirement on m J from the W-tagger.  9  1500  43  10  1750  44  10  2000  45  10  2250  45  10  2500  43  10  2750  44  10  3000  44  10  3250  42  10  3500  43  10  3750  42  10  4000 42 9

Control regions
The control regions are used to derive normalization factors and to constrain systematic uncertainties in the respective background yields (Section 8). The CRs are defined so as to ensure a high purity in the corresponding background processes and a sufficient number of events, while having no overlap with events in the respective SRs. To ensure that extrapolation uncertainties are small, the selection criteria for the CRs closely follow those used in the corresponding SRs. An individual selection criterion is changed to enrich the background of interest while ensuring no overlap with the signal region. Hence, separate control regions are defined for each signal region. The other selection criteria are the same as for the signal regions.
The CRs of the ee j j channel (Table 6) are introduced for the two largest sources of background, Z/γ * + jets and tt. The Z/γ * CRs are defined by requiring m − m Z < 20 GeV and the same S T and m j j selections as in the corresponding SRs. The tt CRs are defined by the full SR selections but at the preselection require a single-muon trigger and exactly one electron and exactly one muon in the event, leading to an eµ j j signature. The kinematic criteria used for the eµ j j signature (apart from the lepton preselection) are identical to those in the nominal ee j j SR selection.
The CRs for the eνJ channel (Table 7) are defined for the W + jets and tt background processes. The W CR is defined by applying the same selection requirements as in the SRs (Table 5), including the b-jet veto, but requiring the jets to fail the boosted jet mass W-tagger with the 80% signal efficiency (W-tag80). Also, the ∆φ(e, ì E miss T ) selection is removed for all W CRs in order to reduce the statistical uncertainties. There is no W CR corresponding to SR1 since the W + jets background process is subdominant in such a CR. The tt CR events are required to have at least two b-jets, fulfil the respective SR selections from Table 5, and have a leading large-R jet satisfying the m J W-tag50 criterion. No additional requirements on the kinematic properties of the b-jets are applied in the tt CR. The tt background prediction is corrected for the difference in b-jet identification efficiencies between data and simulated events, and the corresponding systematic uncertainties are accounted for. Theoretical uncertainties in the tt kinematic distributions are accounted for as described in Section 7.

Validation regions
The background estimation in the CRs is validated in additional phase space regions, the VRs. The VRs are not included in any fits aimed at a signal search.
In the ee j j channel, a m VR is defined as the intermediate range between SR and Z/γ * CR. A further requirement on the E miss T is introduced to split the m VR into regions dominated by Z/γ * and tt processes. A same-sign (SS) VR is defined in order to validate the fake-electron background estimate by selecting events with m > 160 GeV in which both electrons are required to have the same electric charge Q e ( Table 6).
The m J and b-jet VRs are introduced for the eνJ channel. The m J VRs are defined by applying the preselection requirements while inverting the requirement on the boosted jet mass W-tagger interval relative to the W CRs and SRs (Table 7). The b-jet VRs require the number of b-jets to be equal to one to validate the application of tt normalization derived in tt CR with the two b-jets requirement to the SR with zero b-jets. The requirements on m νW T and ∆φ(e, ì E miss T ) in the VRs are the same as in the corresponding SRs.

Systematic uncertainties
The systematic uncertainties of the search are divided into two categories: the experimental uncertatinties and theoretical uncertainties in signal and background prediction. Details of the evaluation of experimental uncertainties are provided in the references in Section 4.
The uncertainty in the combined 2015+2016 integrated luminosity is 2.1%. It is derived from the calibration of the luminosity scale using x-y beam-separation scans, following a methodology similar to that detailed in Ref. [76], and using the LUCID-2 detector for the baseline luminosity measurements [77].
The uncertainties in the electron energy scale and resolution result in less than a 1% effect for simulated background or signal event yields in the SRs. In addition, uncertainties are taken into account for the electron trigger (< 2%), identification (< 3%), and reconstruction (< 1%) efficiencies, and for the isolation requirements (< 6%).
The effect of the uncertainty in the muon momentum on tt background event yields in the tt CRs of the ee j j channel does not exceed 1%. Differences between data and simulated event samples in the muon identification and trigger efficiencies are also taken into account and are less than 1%.
The impact of the R = 0.4 jet energy scale (JES) and resolution (JER) uncertainties on the background event yields is 1-5% (JES) and 1-6% (JER) in the SRs of the ee j j channel. The signal selection efficiency change in the SRs of the ee j j channel due to the JES uncertainties never exceeds 2%, while the effect of the JER uncertainty is negligible. Uncertainties associated with R = 1.0 jets in the eνJ channel arise from uncertainties in the calibration of the JES and the jet mass scale. The impact on the background event yields in the SRs ranges between 20% and 40%, and the effect on signal yields is below 10%. Uncertainties related to the b-tagging efficiency corrections are also taken into account in the eνJ channel, and the effect on tt yields is always below 5%.
The procedure to estimate fake-electron background includes a systematic uncertainty, which is 10-40% of the fake-electron background estimate in the SRs, depending on the p T of the electron candidates.
Theoretical uncertainties affect the simulated event samples of backgrounds and signal. For the background samples, they lie in the PDF set, the value of α S , and missing higher order corrections in perturbative calculations. The latter effect is estimated by varying the renormalization and factorization scales by factors of one-half and two, excluding those variations where both differ by factor of four. The PDF uncertainty is estimated using the envelope of the NNPDF3.0 PDF set [78] and the two alternative PDF sets, the MMHT2014 [79] and CT14nnlo [80]. The uncertainty due to α S is estimated by varying its nominal value of 0.118 by ±0.001. For the tt background, the theoretical uncertainty also includes effects of the matching between ME and PS via the variation of the P -B h damp parameter. The effects of the ME and hadronization model choice are assessed for tt and single-top MC samples by replacing the P -B ME by aMC@NLO [81] and the P 8 hadronization model by the one implemented in H 7 [82]. The theoretical uncertainties in the signal prediction are estimated using the PDF set variations only. The theoretical uncertainties for background yields range from 7% to 22% in the SRs of the ee j j channel and from 3% to 10% in the SRs of the eνJ channel.

Statistical analysis and results
The statistical analysis of the search is based on a maximum-likelihood fit. The signal hypothesis test is performed using a likelihood-ratio test statistic in the asymptotic approach [75].
The likelihood function is constructed as the product of Poisson probabilities of the SR and the CRs as in Ref. [83]. The normalizations of the backgrounds which have CRs, i.e., Z/γ * + jets and tt for the ee j j channel and W + jets and tt for the eνJ channel, are free parameters, denoted by β, in the fit. These corrections are used to scale the background predictions in the SRs. Their values and uncertainties after the background-only fit in the CRs are summarized in Table 8. The deviation of the β values from unity reflects the fact that at high S T the simulated events do not accurately describe the data. This is also observed, for example, in the leptoquark search by ATLAS [84]. After the fit in the corresponding CR, the background yields agree with the data in all VRs within the uncertainties. The final fit combining CRs and SRs results in negligible shifts of the background normalization factors with respect to the CR-only fits. Systematic uncertainties are incorporated into the likelihood function with a set of nuisance parameters with Gaussian constraint terms. Statistical uncertainties from the simulated event samples are included as nuisance parameters with Poisson constraint terms. Correlations of the systematic uncertainty effects across regions are taken into account. The signal normalization (strength) is obtained by maximizing the likelihood function for each signal hypothesis. The statistical analysis is performed using the RooStats [85] and HistFitter [86] software.

N/A N/A
The observed and expected yields in the SRs for the ee j j and eνJ channels after the combined maximumlikelihood fits to only background processes in the CRs and SRs are shown in Tables 9 and 10, respectively. When calculating the uncertainties on the expected yields in the SRs, all correlations between the nuisance parameters estimates are taken into account. No significant excess above the expected SM background is observed, and limits on the excited lepton model parameters are set at 95% confidence level (CL), using the CL s method [87]. The upper limits on the signal production cross section times branching ratio σ × B as a function of m e * are presented in Figures 5(a) and 5(b) for the ee j j and eνJ channels, respectively. The fluctuations observed in the limit for the eνJ channel for m e * points below 1 TeV are caused by the selection criteria optimized separately at each mass points.  Table 4. A unified likelihood function is constructed for the ee j j and eνJ channels at each m e * value considered in order to extract a combined limit on Λ as a function of m e * . The correlations of systematic uncertainty effects between the two search channels are included. The combined limit is presented in Figure 6(c) along with the individual limits from the ee j j and eνJ channels as well as the limit set by ATLAS in the eeγ search channel at Observed and expected model-independent upper limits on the number of signal events in the signal regions of the ee j j and eνJ channels are shown in Table 11 along with the upper limits on the visible signal cross section, which is defined as the production cross-section times the overall signal efficiency.   11.2 11.3 +4.6(10.5)

Conclusion
A search for a singly produced excited electron in association with a SM electron is performed using ee j j and eνJ final states with the ATLAS detector at the LHC. The search utilizes data from pp collisions at √ s = 13 TeV with an integrated luminosity of 36.1 fb −1 . No significant deviation from the SM background expectation is observed in either channel. Upper limits are calculated for the pp → ee * → eeqq and pp → ee * → eνW production cross sections as a function of the excited electron mass m e * at 95% confidence level. Lower limits on the compositeness scale parameter Λ are set at 95% confidence level as a function of m e * . For excited electrons with m e * < 1.5 TeV, the lower limit on Λ is 11 TeV, and it decreases to 7 TeV at m e * = 4 TeV. In the special case of the excited lepton model where m e * = Λ, the values of m e * < 4.8 TeV are excluded. The sensitivity of the search is significantly better than the previous results obtained by ATLAS and CMS from LHC Run 1. Model-independent upper limits on the number of signal events and on the visible signal cross section in the signal regions are presented. The latter vary between 0.20 (0.26) fb and 3.34 (0.88) fb for the ee j j (eνJ) channel.