Search for excited leptons in proton-proton collisions at s=8\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \sqrt{s}=8 $$\end{document} TeV

A search for compositeness of electrons and muons is presented using a data sample of proton-proton collisions at a center-of-mass energy of s=8\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \sqrt{s} = 8 $$\end{document} TeV collected with the CMS detector at the LHC and corresponding to an integrated luminosity of 19.7 fb−1. Excited leptons (ℓ*) produced via contact interactions in conjunction with a standard model lepton are considered, and a search is made for their gauge decay modes. The decays considered are ℓ* → ℓγ and ℓ* → ℓZ, which give final states of two leptons and a photon or, depending on the Z-boson decay mode, four leptons or two leptons and two jets. The number of events observed in data is consistent with the standard model prediction. Exclusion limits are set on the excited lepton mass, and the compositeness scale Λ. For the case Mℓ* = Λ the existence of excited electrons (muons) is excluded up to masses of 2.45 (2.47) TeV at 95% confidence level. Neutral current decays of excited leptons are considered for the first time, and limits are extended to include the possibility that the weight factors f and f′, which determine the couplings between standard model leptons and excited leptons via gauge mediated interactions, have opposite sign.


Introduction
The standard model (SM) of particle physics describes the observed phenomena very successfully, however it provides no explanation for the three generations of the fermion families. Attempts to explain the observed hierarchy have led to a class of models postulating that quarks and leptons may be composite objects of fundamental constituents [1][2][3][4][5][6][7][8][9]. The fundamental constituents are bound by an asymptotically free gauge interaction that becomes strong at a characteristic scale Λ. Compositeness models predict the existence of excited states of quarks (q * ) and leptons ( * ) at the characteristic scale of the new binding interaction. Since these excited fermions couple to the ordinary SM fermions, they could be produced via contact interactions (CI) in collider experiments, with subsequent decay to ordinary fermions through the emission of a W/Z/γ boson, or via CI to other fermions.
In this paper, a search for excited leptons (e * and µ * ) is presented, using a data sample of pp collisions at a center-of-mass energy √ s = 8 TeV collected with the CMS detector at the LHC in 2012 and corresponding to an integrated luminosity of 19.7 ± 0.5 fb −1 [21]. We consider the production of an excited lepton in association with an oppositely charged lepton of the same flavor, with subsequent radiative decays ( * → γ) or neutral current decays ( Z).

Theory and model assumptions
The composite nature of quarks and leptons, if it exists, will manifest itself, above a characteristic energy scale Λ, as a spectrum of excited states. Such excited fermions, f * , may couple to SM leptons and quarks via a four-fermion CI that can be described by the effective Lagrangian where Λ is the energy scale of the substructure, assumed to be equal to or larger than the excited fermion mass. The quantities g 2 * = 4π, and j µ , defined in Ref. [7], involve only left-handed currents by convention. In addition to the coupling via CI, excited fermions can also interact with SM fermions via gauge interactions. For excited leptons, the corresponding Lagrangian for the gauge-mediated (GM) interaction is given by where W µν and B µν are the field-strength tensors of the SU(2) and U(1) gauge fields, and g = e/ sin θ W . The quantity, g = e/ cos θ W represents the electroweak gauge coupling with the Weinberg angle θ W , and Y and τ are the generators of the U(1) and SU(2) groups, respectively. The quantities f R and f L are the right and left-handed components of the lepton or excited lepton. The weight factors f and f define the couplings between SM leptons and excited leptons via gauge interactions [7]. The compositeness scales contained in L CI and L GM are assumed to be the same.
The excited lepton, * , can decay to a SM lepton via a CI * → ff, where f is a fermion, or through the mediation of a gauge boson via a gauge interaction. The following gaugeinteraction-mediated decays are possible: radiative decay * → γ, charged-current decay * → W, and neutral-current decay * → Z. All four transitions, the CI and the three gauge interactions, are possible if f = f , while f = − f forbids decays via photon emission. Since the exact relationship between the weight factors is unknown, the results are interpreted for two extreme values: f = f = 1 and f = − f = 1.  In the present analysis we search for the production of excited electrons and muons, e * and µ * , through a CI, which is dominant at the LHC for the model considered here. Excited leptons can also be produced via gauge interactions, but those processes involve electroweak couplings and contribute less than 1% to the cross section at the LHC; they have therefore been neglected here. For light * , the decay of excited leptons via gauge interactions is dominant, while the decay via a CI becomes dominant at high masses, as shown in Fig. 1. The decay via a CI is not considered in the simulated samples used here.
The search channels considered in this analysis are summarized in Table 1. The * → γ final state is represented by the Feynman diagram in Fig. 2 left. A second class of searches seeks decays via the emission of a Z boson (Fig. 2 right), with the Z boson decaying to either a pair of electrons, a pair of muons, or a pair of jets. This decay mode allows the phase space where f = − f , unexplored by previous LHC searches, to be investigated. The transverse momentum (p T ) of the Z boson coming from the decay of the excited lepton is larger for heavier excitedlepton masses, and at high p T the final-state particles are highly collimated. This characteristic is exploited in the * → Z → 2 2j decay mode, in which jet substructure techniques are used to reconstruct a "fat jet" corresponding to the Z boson, and in the leptonic channels where the lepton isolation is modified.
Signal samples for both e * and µ * are produced using PYTHIA8.153 [22,23], which uses the leading order (LO) compositeness model described in Ref. [7]. Thirteen * mass points from 200 to Table 1: Final states for excited lepton searches considered in this analysis, where = e, µ. The notation for a specific channel is provided in the right most column. For neutral currents, the last two characters in this notation refer to particles from the decay of the Z boson.

Decay mode
Search channel Notation Radiative decay * → γ ee * → eeγ eeγ 2600 GeV have been simulated for all channels except the jj channels, which starts at 600 GeV because of the analysis thresholds. Masses below 200 GeV are excluded by previous searches at 95% confidence level. All simulated events have been passed through the detailed simulation of the CMS detector based on GEANT4 [24] and have been re-weighted so that the distribution of pileup events (contributions from additional pp interactions in the same bunch crossing) matches that measured in data. The signal cross sections are calculated with PYTHIA8, and are corrected using the branching fraction to the 3-body decays via CI as predicted in Ref. [7], as this decay mode is not implemented in PYTHIA. The factorization and renormalization scales are set to the mass square of the excited lepton (M 2 * ), Λ is set to 10 TeV, and the CTEQ6L1 [25] parametrization for the parton distribution functions (PDF) is used. This particular choice of the value of Λ has no impact on the resulting kinematic distributions. Only the width of the * resonance and the * production cross section depend on Λ. As long as the width of the * is small compared to the mass resolution of the detector, the signal efficiency is independent of Λ. Mass-dependent next-to-leading order (NLO) k-factors ranging from 1.2 to 1.35 [26] are applied on the signal event yields. Production cross sections for the signals, as well as those of the different decay modes including the corresponding branching fractions are given in Table 2.   Table 2: Excited lepton production cross section, and product of cross section and branching fraction for each of the three processes investigated, as a function of the mass of the excited lepton. The values of the k-factors are taken from Ref. [26]. The case f = − f = 1 does not apply to the * → γ channel.   5.0 × 10 −6 1.9 × 10 −6 1.6 × 10 −7 1.7 × 10 −5 6.6 × 10 −6 5.7 × 10 −7

The CMS detector
The central feature of the CMS apparatus is a superconducting solenoid of 6 m internal diameter, providing a magnetic field of 3.8 T. Within the superconducting solenoid volume are a silicon pixel and strip tracker, a lead tungstate crystal electromagnetic calorimeter (ECAL), and a brass and scintillator hadron calorimeter (HCAL), each composed of a barrel and two endcap sections. Forward calorimeters extend the pseudorapidity (η) [27] coverage provided by the barrel and endcap detectors. Muons are measured in gas-ionization detectors embedded in the steel flux-return yoke outside the solenoid. In the barrel section of the ECAL, an energy resolution of about 1% is achieved for unconverted or late-converting photons in the tens of GeV energy range. The remaining barrel photons have a resolution of about 1.3% up to |η| = 1, rising to about 2.5% at |η| = 1.4. In the endcaps, the resolution of unconverted or late-converting photons is about 2.5%, while the remaining endcap photons have a resolution between 3 and 4% [28]. When combining information from the entire detector, the jet energy resolution amounts typically to 15% at 10 GeV, 8% at 100 GeV, and 4% at 1 TeV, to be compared to about 40%, 12%, and 5% obtained when the ECAL and HCAL calorimeters alone are used. The electron momentum is determined by combining the energy measurement in the ECAL with the momentum measurement in the tracker. The momentum resolution for electrons with p T ≈ 45 GeV from Z → ee decays ranges from 1.7% for non-showering electrons in the barrel region to 4.5% for showering electrons in the endcaps [29]. Muons are identified in the range |η| < 2.4, with detection planes made using three technologies: drift tubes, cathode strip chambers, and resistive plate chambers. Matching muons to tracks measured in the silicon tracker results in a relative p T resolution for muons with 20 < p T < 100 GeV of 1.3-2.0% in the barrel and better than 6% in the endcaps. The p T resolution in the barrel is better than 10% for muons with p T up to 1 TeV [30]. A more 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. [27].

Triggers
The selected trigger for each channel is summarized in Table 3. For all channels, except those with a 2e2µ final state, dilepton triggers are exploited: the double electron trigger is used for events with electrons in the final state, while muon events are selected by the dimuon trigger. Both triggers have identical p T thresholds, of 17 (8) GeV for the leading (subleading) lepton.
The two cross channels with 2e and 2µ in the final state exploit a muon-photon trigger with a p T threshold of 22 GeV for both objects, where the photon trigger selects either electrons (as needed for this analysis) or photons, since the tracking information is not used at trigger level. The muon-photon trigger is chosen because the isolation requirements of the muon-electron trigger lead to an inefficiency when the two electrons from the Z boson decay are close together. The trigger efficiencies are close to one in all cases because of the large number of possible trigger objects. The offline p T thresholds are set to 35 GeV for both electrons and muons, except for the 4-lepton channels, which require 25 GeV for each lepton. , based on the profile of the energy deposition in the ECAL and the matching between the track and the cluster, are imposed to remove jets misidentified as electrons. The p T sum of all other tracks (excluding the electron footprint) in a cone of ∆R = √ (∆η) 2 + (∆φ) 2 < 0.3 (where φ is the azimutal angle in radians) around the track of the electron candidate must be less than 5 GeV, a selection denoted as "tracker isolation". In computing the tracker isolation for electrons, tracks have to originate from within a distance |d z | < 0.2 cm from the primary vertex. This requirement reduces the impact of pileup interactions vetoing candidate events. The sum of the transverse energy (E T ) of calorimeter energy deposits in the same cone, referred to as "calorimeter isolation", must be less than 3% of the candidate's transverse energy. The calorimeter isolation energy is corrected for pileup by the subtraction of the average energy per unit area of (η, φ), computed for each event using the FASTJET package [32].
For the two electrons from the Z boson decay (in the ee * → eeZ → 4e and µµ * → µµZ → 2µ2e channels), the tracker isolation and calorimeter isolation for each electron are modified to remove the contribution of the other electron [33].

Muons
The muon candidates have to pass identification (ID) criteria that are optimized for the reconstruction of muons with high transverse momenta [30,31]. In the "global muon" reconstruction, muons are reconstructed within |η| < 2.4 by combining tracks from the inner tracker and the outer muon system. The following requirements are imposed: at least one hit in the pixel tracker; hits in more than five tracker layers; and the detection of the muon in at least two muon stations. Since the stations are separated by thick layers of iron, the latter requirement significantly reduces the probability of a hadron being misidentified as a muon. The relative uncertainty in the muon p T measurement must not exceed 30%. In order to reduce the cosmic ray muon background, the transverse impact parameter of the muon track with respect to the primary vertex of the event is required to be less than 0.2 cm. The primary vertex is chosen as the one with the highest Σp 2 T of all charged tracks associated with that vertex. Furthermore, the muon is required to be isolated by demanding that the scalar sum of the transverse momenta of all tracks, excluding the muon itself, within a cone of ∆R < 0.3 around its own track, be less than 5% of its p T .
In the ee * → eeZ → 2e2µ and µµ * → µµZ → 4µ channels, one oppositely charged muon pair comes from the decay of the boosted Z boson. The muons can be close enough that one muon is inside the isolation cone of the other. Therefore, for these muons, the isolation calculation is modified by removing the contribution of the other muon. Also, the identification requirements on one of these muons are loosened: the global muon requirement is removed; the muon candidate is only required to be reconstructed in the tracker. After these modifications, the reconstruction and identification efficiency of nearby muons are found to be comparable to those of separated muons [33]. These two variations are referred to as "modified identification" and "relaxed isolation".

Photons
For photons, identification criteria from Ref. [28] are applied to clusters in the ECAL that include requirements on the shower shapes, isolation variables, and H/E (ratio of deposits in the HCAL and ECAL in a cone around the photon direction). A photon candidate is required to have a cluster with E T > 35 GeV and to be in the barrel region of the ECAL, with |η| < 1.44.
Photons are required to be in the central region because the jet-to-photon fake rate becomes high in the forward region, while only 4% of a signal would lie in this region. The photon is also required to be isolated within a cone of radius ∆R < 0.3 both in the tracker and the calorimeter. The cone axis is taken to be the direction of the line joining the barycenter of the ECAL clusters to the primary vertex. The isolation criteria depend on the η of the photon, and distinguish between contributions from neutral and charged hadrons and electromagnetic particles. As with the electron isolation calculation, the sums do not include contributions from particles clearly associated with pileup vertices, and are adjusted for the estimated residual pileup.

Jets and Z → jj tagging
Hadronic jets are reconstructed from the list of particle flow (PF) candidates that are obtained with the PF algorithm [34], which reconstructs and identifies single particles by combining information from all sub-detectors. Charged PF constituents not associated to the primary vertex are not used in the jet clustering procedure. Good PF candidates are clustered into jets using the Cambridge-Aachen (CA) algorithm [35] with a distance parameter R = 0.8. An areabased correction is applied, to take into account the extra energy clustered in jets from neutral particles in pileup interactions, using the FASTJET software package [32]. Jet energy corrections are derived from the simulation, and are validated with in-situ measurements using the energy balance of dijet, photon+jet, and Z+jets events [36]. Additional quality criteria are applied to the jets in order to remove spurious jet-like features originating from isolated noise patterns from the calorimeters or the tracker. These jet quality requirements are found to be 99% efficient for signal events. The jets are required to have p T > 200 GeV and |η| < 2.4. Jets must also be separated from any well-identified lepton (passing selections of Sections 4.2.2 and 4.2.1) by a cone of radius ∆R > 0.8.
In the 2 2j channels, the search is optimized for high-mass excited leptons that produce a boosted, hadronically decaying Z boson. When such a highly boosted Z decays to two quarks, their separation is often so small that they are reconstructed as a single jet with a mass larger than that of a typical Quantum ChromoDynamics (QCD) jet. To achieve the best possible mass resolution for this single jet, a jet pruning algorithm [37,38] is applied, which is also used by the CMS collaboration for several other physics analyses with hadronic decays of boosted W and Z bosons [33,[39][40][41][42]. This pruning procedure involves reclustering the constituents of the original jet and applying additional requirements to eliminate soft QCD radiation and largeangle QCD radiation coming from sources other than the Z boson. The kinematic distributions of the resultant jet are a closer reflection of the hard process. In particular, the pruned jet mass is closer to the mass of the parent Z boson.
In addition, to further discriminate against jets from gluon and single-quark hadronization, a quantity called N-subjettiness is used [43][44][45]. Before the pruning procedure is applied, the jet constituents are re-clustered with the k T algorithm [46,47], until N joint objects, called "subjets", remain in the iterative combination procedure of the k T algorithm. The N-subjettiness, τ N , is then defined as: where the index k runs over the jet constituents and the distances ∆R n,k are calculated with respect to the axis of the n th subjet. The quantity R 0 is set equal to the jet radius of the original jet. The τ N variable measures the capability of clustering the reconstructed particles in the jet in exactly N-subjets: if it has a small value then it represents a configuration that is more compatible with the N-subjettiness hypothesis. In particular, the variable that is best able to discriminate between the jets from a boosted Z boson decay and standard QCD jets is the ratio of 2-to 1-subjettiness, τ 21 = τ 2 /τ 1 . If the jet has τ 21 < 0.5 and if its pruned mass falls in the range between 70-110 GeV, the jet is tagged as originating from a Z boson, and is referred to as a "fat jet" in this paper.
The mismodeling of the τ 21 variable can bias the signal efficiency estimated from the simulated samples. A discrepancy between data and simulation has been observed in the identification efficiency measured in events containing merged jets produced by boosted W-bosons from top decays that pass the same V-tag selections as the ones in this jj analysis [33]. Correction factors obtained from this sample are found to be 0.9 ± 0.1. These corrections are applied to the signal efficiencies obtained from simulation.

Signal selection
In addition to the trigger and object identification requirements, signal-candidate events are selected and SM backgrounds suppressed, sequentially as follows: 1. Selection of final state objects (see Section 4.3.1) and reconstruction of the boosted Z boson in those channels containing a Z boson.
2. Rejection of backgrounds with Z bosons (see Section 4.3.2) with an invariant mass requirement.
3. Rejection of other backgrounds using a dedicated search window (see Section 7.1) that uses two calculations of M * .

Preselection
As a first step, the final state objects are selected in the various search channels.
• * → γ: Selection of two same flavor isolated leptons and one isolated high E T photon within the acceptance and p T thresholds given in Table 3. In the case of µµγ, muon pairs that are back-to-back are rejected by removing those with an angle above π − 0.02 to avoid contributions from cosmic ray muons. Additionally, the muons are required to have opposite charges. Selected photons must be separated from the leptons by ∆R > 0.7 to reduce the contribution from final state radiation. • * → Z → 2 2j: Selection of two isolated same flavor leptons and one fat jet (as defined in Section 4.2.4) satisfying the acceptance and p T thresholds given in Table 3. If more than one fat jet is found, the one with the highest p T is used. In the channel with muons, the muons are required to have opposite charges. • * → Z → 4 : Selection of exactly four isolated leptons (four electrons, four muons or two electrons and two muons) within the acceptance and p T thresholds given in Table 3. First, the relaxed ID (for muons) and isolation are used for all leptons. Next, the boosted Z boson is reconstructed. In the 2µ2e (2e2µ) channel, the electron (muon) pair defines the reconstructed Z boson. In the 4e and 4µ channels, the lepton pair with invariant mass closest to the Z pole mass is chosen. As a final step, the requirements on the leptons are tightened. In channels with the boosted Z boson decaying to muons, an additional charge requirement is applied to both muons, and one of the muons originating from the Z boson decay is allowed to fulfill the relaxed ID only; all other leptons need to pass the full ID.
The invariant mass of the two leptons (in the 4 channels, of the two leptons that are not used to reconstruct the Z boson) is denoted as M in what follows. This di-lepton mass is used to reduce backgrounds that include Z bosons not associated with the decay of putative heavy leptons.

Invariant mass requirement
The invariant mass M is required to be above 106 GeV in the γ and 4 channels, and above 200 GeV for the 2 2j channels, to reduce backgrounds containing Z bosons. This cut efficiently removes contributions from Zγ (ZZ) to the γ and the 2 2j backgrounds. For the eeγ channel, there is an additional Z-veto on the two possible electron-photon invariant masses to remove electron pairs coming from a Z decay, where one electron is misidentified as a photon. Events are removed where any of the electron-photon invariant masses is within ±25 GeV of the nominal Z boson mass.

Sources of background
Several SM processes contribute to the expected background for the various channels. Those contributions are discussed in the following.
• * → γ channels: Drell-Yan (DY) production is the most important background for the * → γ channels, mostly originating from production of a photon in association with a Z, which has a very similar signature to the signal. It is simulated using SHERPA1.4 [48] and its production cross section is normalized using a NLO cross section calculated with the Monte Carlo (MC) program MCFM6.1&6.6 [49,50].
Subleading contributions to the background arise from diboson events with an additional high energy photon or events in which an electron is misidentified as a photon. Such events are simulated using PYTHIA6.4 [23]. Background contributions also arise from events in which an additional prompt photon is produced together with a top pair (tt+γ). These events are simulated with MADGRAPH5.1 [51] using a LO cross section. All these irreducible backgrounds arising from two prompt leptons and a prompt photon are estimated using MC simulation. Smaller contributions due to events with two genuine leptons and a jet which has been misidentified as a photon are estimated from data (see Section 5.2). For the eeγ channel, jets faking electrons may contribute, although at a negligible level (see Section 5.2.2 for details).
The contribution of muons faked by jets is negligible. • * → Z → 2 2j channels: The production of a Z boson (decaying to leptons) plus additional jets is the dominant background followed by the production of two top quarks and diboson events. These contributions have been estimated from data, using simulation to validate the data-driven method described in Section 5.2.3. All background contributions from simulation (tt, diboson and DY+jets) are simulated using MADGRAPH with NLO cross sections that were calculated using MCFM. • * → Z → 4 channels: The production of ZZ (including Zγ * ), with both bosons decaying leptonically, is the main background to the four-lepton channel and contributes about 90% of the total background expected. An additional smaller contribution arises from the production of three vector bosons where some of the leptons escape detection. The production of two top quarks, tt, with or without an additional vector boson, can contribute to each channel. The background due to Higgs boson production is negligible in the phase space considered here. In the four lepton channels, all the backgrounds have been estimated using predictions from simulations. The ZZ → 4 background is described with GG2ZZ [52] for production via gluon fusion and in the case of qq annihilation at NLO with POWHEG1.0 [53][54][55][56].
Processes involving tt+X (X = W, Z, γ) and triple boson samples are simulated with MADGRAPH. It has been checked that the simulation describes correctly a sample of 4-lepton events selected as in Section 4.3, but relaxing the Z-vetoes to increase the number of events. Table 4 summarizes the simulated background samples with the corresponding NLO cross sections, and the channels where these samples are used. PYTHIA has been used to perform the fragmentation and hadronization of samples generated with MADGRAPH. The pileup simulation has been re-weighted so that the distribution of pileup events matches that measured in data. All simulated events have been passed through the detailed simulation of the CMS detector based on GEANT4 [24]. Correction factors are also applied to allow for differences between the simulated and measured reconstruction efficiencies of the physics objects.

Misidentification of electrons
Backgrounds with zero or one real electron can contribute to the eeγ candidate sample. The largest contributions come from processes such as W(→ eν)+jet+γ where the jet in the event is misidentified as an electron. Misidentification can occur when photons coming from π 0 or η mesons inside a jet convert to an e + e − pair. Other possible sources include processes with a charged particle within a jet providing a track in the tracker and an electromagnetic cluster that together fake an electron signature, or a track from a charged particle that matches a nearby energy deposition in the calorimeter from another particle. The misidentification rate, f misid electron , is calculated as the ratio between the number of candidates passing the electron selection criteria with respect to those satisfying looser selection criteria. The looser criteria require only that the first tracker layer contributes a hit to the electron track and that loose identification requirements on the shower shape and the ratio H/E are satisfied. The misidentification rate is estimated as a function of E T in bins of η using a data sample selected with a trigger requiring at least one electromagnetic cluster.
In order to estimate the contribution of misidentified electrons to the selected events, the misidentification rate is applied to a subsample of data events containing one electron passing good electron criteria and a second one passing a loose set of criteria. This loose set of criteria includes cuts on shower shape and the ratio H/E, but allows one of the electron selection criteria to be missed. The events are required to satisfy all other selection criteria of the analysis.
The systematic uncertainty in f misid electron (E T , η) is determined using a sample of events containing two reconstructed electrons as in [31]. The contribution from jet events to the inclusive dielectron mass spectrum can be determined either by applying the misidentification rate twice on events with two loose electrons or by applying the misidentification rate once on events with one fully identified electron and one loose electron. The first estimate lacks contributions from W+jets and γ+jets events while the second estimate is contaminated with DY events. These effects are corrected for using simulated samples. The observed difference of 30% between the two estimates is taken as the systematic uncertainty in the jet-to-electron misidentification rate.

Misidentification of photons
Hadronic jets in which a π 0 or η meson carries a significant fraction of the energy may be misidentified as isolated photons. Thus Z+jet(s) events are a potential background for the γ search. The photon misidentification rate is measured directly from data using a data set collected using a single photon trigger. To avoid trigger biases, the events must contain at least one reconstructed super-cluster (energy deposit in the ECAL) besides the one that fired the trigger. In addition, the ratio of hadronic energy to the energy of that super-cluster is required to be less than 5%. The misidentification rate is defined as the ratio of the number of photon candidates that pass all the photon selection criteria (numerator) to the ones that pass a loose set of shower shape requirements but fail one of the photon isolation criteria (denominator). The numerator sample can have a contribution from isolated true photons. The contamination is estimated using the distribution of energy-weighted shower width computed in units of crystal lateral dimension. The shower shape for isolated true photons is obtained from a simulated sample. The shape of non-isolated photons is obtained from data by considering a background dominated region (side-band region) of the photon isolation variable. The true photon fraction in the numerator is estimated by fitting these two different shower shapes (signal and background templates) to the shower shape distribution of the numerator sample. The photon misidentification rate is calculated in photon E T bins. It decreases with increasing photon E T and is at most of the order of a few percent. As an example, for photons of E T = 100 GeV the jets-to-photon misidentification rate is about 1.5%.
In order to estimate the contribution of misidentified photons to the selected events, the misidentification rate is applied to a subsample of data events that satisfy all selection criteria listed in Section 4.3 except that the photon candidate must pass a looser set of shower shape requirements and fail one of the photon isolation criteria.
There are two main sources of uncertainties in the determination of jet to photon misidentification rate. First, the shower shape of non-isolated photons is obtained from data in the side band region: changing the side band region results in some change in the template for non-isolated photons. Second, the probability for a jet to fake a photon is different for quark and gluon jets and the fraction of jets due to quarks may not be the same in the sample used to obtain the fake rate and in the sample where this fake rate is applied. Considering these two sources of uncertainties, a conservative systematic uncertainty of 50% is assigned, independently of the photon E T .

Data-driven background in 2 2j
The backgrounds due to DY+jets, tt and di-boson production are estimated using the "ABCD" method, which relies on two variables to separate the signal from the background. The twodimensional plane of these two variables is divided in four disjoint rectangular regions A, B, C, and D, so that the region A is the signal region, while B, C, and D are the control regions, dominated by backgrounds. If the ratio of the backgrounds in regions A and B is the same as that for C and D (which holds if the two variables are independent), i.e.: N A /N B = N C /N D , then the background in the signal region A, N A can be estimated as: Several tests were performed using simulated samples to verify that the ABCD method using these variables reliably predicts the background yield. The relation given in Equation 4 is expected to be independent of the choice of boundaries for the control regions. This assumption has been tested by applying the ABCD method to simulated samples of DY+jets, tt+jets and diboson events. Moving the boundaries of regions B, C and D changed the calculated number of events in region A (whose definition is kept fixed) only slightly, as shown in Table 5.

Systematic uncertainties
Three types of systematic uncertainties are considered: • Overall uncertainties in the simulation: These include the uncertainty in the luminosity [21], the simulation of pileup and uncertainties in the cross sections used. These uncertainties affect the normalization and are treated similarly for all backgroundand signal simulations. • Object simulation uncertainties: These depend on the final state of the respective analysis and are applied to the simulation of signal and background events. They consist, for example, of uncertainties in the energy or momentum scale and resolution of the various particles, or in correction factors that were applied to account for differences between the simulated and the actual performance of the detector. • Uncertainties in background estimations from data: These uncertainties are applied to background components that were estimated from data and are only relevant to the * → γ and * → Z → 2 2j channels.
The sources of these systematic uncertainties are discussed in Section 6.1 and their implications for signal and background in Section 6.2.

Object-specific simulation uncertainties Electron uncertainties
For electrons, uncertainties exist for the electron energy scale and electron identification efficiency. In both the barrel and the endcap, the scale uncertainties are determined by shifting the transverse energy of the electrons by 0.3% [29]. Systematic uncertainties due to electron identification are 2% and 4% [31] for very high energy electrons in barrel and endcap, respectively.

Muon uncertainties
There are three sources of uncertainties for muons: uncertainties in the muon momentum scale; the muon momentum resolution; and the efficiency of the muon selection. As described in Ref.
[30] the uncertainty in the muon momentum scale is estimated to be 5% × p T / TeV and the effect of the scale uncertainty is estimated by changing the p T by this value. The uncertainty in the muon momentum resolution is 0.6% and the effect of this uncertainty is estimated by smearing the p T of the muons by an additional 0.6%. The uncertainty in the selection efficiency is 0.5% for the identification criteria, and 0.2% for the isolation criterion for each muon.

Photon uncertainties
The energy scale and resolution uncertainties for photons are very small compared to those of the other objects. The energy scale uncertainties are determined by shifting the transverse energies of the photons by 0.15% in the barrel section of the calorimeter [28].

Jet-energy scale
Jet-energy corrections are applied to account for the response function of the combined calorimeter system and other instrumental effects, based on in situ measurements using dijet, Z+jet, and photon+jet data samples [36]. Uncertainties due to these corrections are evaluated by shifting the jet energies by the calibration uncertainties (±1σ). The effect on signal yield was found to be less than 1%.

Implications of uncertainties on signal and background yield
The above sources of uncertainties are specifically associated with the simulation of the various objects. To quantify each uncertainty on the signal and background, the relevant quantity is varied by ±1σ, relative to the best estimate. Subsequently all kinematic selections are reapplied and the impact on the analysis is determined by calculating the difference of the result from that of the original parametrization.
For all channels, the impact of pileup uncertainties was estimated by shifting the mean number of additional interactions and the inelastic cross section by 5%. The uncertainty in the signal yield cross section is taken to be 10%, following Ref. [26].
In the case of the four lepton final states, the dominant uncertainty in the background is the uncertainty in the cross section of the ZZ background, which is conservatively assumed to be 15% ( [57]). Additional uncertainties with a large impact on the background yield are the electron energy scale (with impact on background yield of 12%), the electron selection efficiency (6%), and the uncertainty in the electron resolution (2.5%). The mixed channels suffer large effects from the electron energy scale (8%), electron efficiencies (5%), and muon efficiencies (3%).
In the four muon channel, the second largest uncertainty is associated with the muon selection efficiency (4%) followed by that on the muon momentum scale (1.6%). In this channel the uncertainties in the signal yield are completely dominated by the corresponding cross section uncertainty.
In the * → γ channel, the dominant systematic uncertainty in the background is the uncertainty in the production cross section arising from the parametrization of the parton distribution functions in the main background (Zγ), which was determined to be 10% by changing the choice of PDF set in the simulation according to Ref. [58,59]. Although the uncertainty in the data-derived background was determined to be 50%, its impact is rather small (4%), as the total contribution of this background is rather small. The impact of the photon energy scale and resolution are negligible. One of the dominant systematic uncertainties for the signal in the µµ * → µµγ channel is that in the muon momentum scale [30], which rises with increasing p T . As a result, the impact on the final event yield is rather small in case of the background, containing muons of moderate momenta, but reaches more than 5% in the high-mass signal samples.
In the * → Z → 2 2j channel, the dominant systematic uncertainty in the background is that associated with the background estimation method, mainly the signal contamination in control regions B, C and D of the ABCD matrix. This depends on the M * parameter; the lowest mass point represents the worst-case scenario where such contamination is maximal, and the highest mass point is the best-case scenario. The effect of the signal leakage in the control regions was estimated for various mass points between M * = 0.6 and 2.6 TeV, and found to be of the order of 30% in the worst cases. Another source of systematic uncertainties arises from the Z tagging, since there is a discrepancy between the Z tagging efficiency in data and simulation, as discussed in Section 4.2.4. Based on the correction factors measured, a 10% uncertainty is assigned the estimated signal efficiency. Table 6 summarizes the event yield for all channels after applying the selections for the leptons, photon or Z boson, and the invariant mass cuts given in Section 4.3. Data agree with the SM expectation and no evidence for new physics is seen.

Final selection and results
In the photon channels the main background (Zγ) contributes almost 90% of the total. The remaining contributions are ttγ ( 7%) and jet/ photon misidentification (estimated from data to be 3%), and are rather small in comparison. Similarly in the four lepton channels, about 90% of the backgound arises from ZZ. The jet channels have mixed composition. The main background (Z+Jets) contributes about 50%. The second largest contribution (tt) contributes 40% of the expected background. The description of the background is based on the data driven approach described above, but the composition is estimated using simulation, since this information cannot be obtained from the data.     considered, e * or µ * . Figures 4 and 5 show M X min for all excited electron and muon channels with the background and systematic uncertainties described previously.

L-shape search window
An illustrative plot of M X min versus M X max is given in Fig. 6. While the expected background tends to be at low invariant masses, a potential signal has the form of an inverted "L" around the excited lepton mass. Defining such a search window discriminates efficiently against background and is referred to in the following as the "final selection" or the "L-shape cut" when defining the final search regions.  Figure 6: Illustrative two dimensional minimal-versus-maximal invariant-mass distribution for the ee * → eeγ (left) and the 4µ channel (right). It can be seen that the resolution worsens with increasing signal mass and that the channels have different resolutions. The left plot clearly shows the effect of the additional Z-veto that is applied in this channel. Background contributions are normalized to the given integrated luminosity, while the normalization of the signal was chosen to enhance visibility.
The width of these L-shaped search regions depends on the channel and the * mass. Detailed values for all channels are given in the Appendix. In the muon channels, the mass resolution worsens with increasing energy and the widths of the search windows need to become broader. This can be achieved without affecting the sensitivity of the search, since the highmass regions are practically background-free. In the electron channels, the improving relative resolution of the electromagnetic calorimeter with increasing energy allows a more precise energy measurement at high masses. As a consequence, the width of the L-shaped windows is chosen individually for the different channels and mass points (by optimizing with respect to the best expected limit). Shown in Fig. 7 is a comparison of the width of search window with the intrinsic excited lepton width as a function of the excited lepton mass, for representative values of the compositeness scale Λ. This figure shows that the mass windows are in general much wider than the intrinsic width of the excited lepton, unless both its mass and Λ are small. The size of the mass window has a negligible effect on the final result, as will be discussed in Section 7.2.
The product of acceptance and efficiency as a function of * mass for all channels is shown in Fig. 8. The decreasing efficiency at high masses in the 2 2j channels results from the subjettiness algorithm, which loses ability to resolve the constituents of the fat jets, which overlap more and  Figure 7: Width of the widest search window (4µ channel) and of a narrow one (eeγ) compared with the intrinsic decay width of the excited lepton, as a function of the * mass and for different values of Λ. The latter shows the width of the excited leptons as defined in Ref. [7], including GM and CI decays, for the case f = − f = 1. more with increasing * mass.
The selected L-shaped search regions with positions given by the simulated signal masses do not cover the complete M min -M max plane in the low mass region, where the search windows are narrow. To avoid simulating more mass points, those regions are covered with additional L-shaped search regions based on a linear interpolation of the signal expectation between the two closest available simulated signal masses. The 4e channel is used to define the window positions that are adopted in all channels. There, the widths are estimated by linear interpolation between two consecutive masses such that the boundaries of all the search regions are connected. The central positions of these resulting interpolated search windows are then applied in all channels, while the corresponding widths are estimated for each channel individually.
The observed data, as well as the background expectation, in these newly defined L-shaped search regions are given by the M min -M max distributions. As there are no corresponding signal samples simulated for all these search regions (cf. simulated signal samples as explained in Section 2), this information is not available for the signal. The signal is therefore estimated by a fit to the signal expectation of the available simulated mass points including the systematic uncertainties.

Limits on cross section and compositeness scale Λ
The resulting limits of cross section times braching fraction are shown in Fig. 9. They range from 0.3 fb to 3 fb as a function of M * . The four lepton final states: 4e and 2e2µ, 4µ and 2µ2e, differing only in the decay of the SM Z boson, are combined. The other channels are shown individually. The black lines represent the theoretical cross sections including the NLO correction factors for different values of Λ. Solid lines are for the case f = f = 1 while the dashed lines are for f = − f = 1. The 95% confidence level (CL) upper limit on the excited lepton production cross section times branching fraction has been set using a single-bin counting method [61]. The computation has been performed using a Bayesian [62] approach.  Figure 8: The product of acceptance and efficiency after L-shape selection. In the left panel, the efficiencies for the * → γ and 2 2j channels are shown while the right panel gives the efficiencies of the four-lepton channels. For the 2 2j and 4 channels, the values do not include the branching fractions for the specific Z boson decay channel.
The uncertainty bands have interesting behavior in some regions. They become asymmetric and in some cases the 1σ band disappears. Both effects have their origin in the low background expectation in the corresponding search window. In such cases, fluctuations of the limit to lower values are not possible. Unstable behavior of both expected and observed limits is due to the limited number of (background) events in the search regions, with the consequence that the presence of a single event leads to a considerable upward fluctuation of the observed limit (see also tables in the appendix).
The corresponding observed limits on the compositeness scale Λ are displayed in Fig. 10(left) for the case of SM-like couplings ( f = f = 1) and in Fig. 10(right) for couplings of opposite sign ( f = − f = 1). In the latter case, * → γ cannot contribute. For low M * masses compositeness scales up to 16 TeV can be excluded. The sensitivity to Λ decreases with increasing M * . For the representative assumption of M * = Λ, the resulting limits are summarized in Table 7 and Fig. 11. Although, the assumption that the signal efficiency is independent of Λ is not valid for the phase space where Λ and M * are small (lower left corner of Figs. 10), the strong Λ dependence of the cross section, σ ∼ 1/Λ 4 , leads to a strong increase in sensitivity for low values of Λ and M * such that the complete region under the limit curves in Fig. 10 is nonetheless excluded.
Because of its considerably larger cross section times branching fraction, the * → γ final state provides the maximum sensitivity for excluding excited leptons with masses up to 2.45 TeV. This limit improves upon the existing ATLAS limit for single * production based on a partial 8 TeV data set [20] and exceeds significantly the limits of searches for single excited lepton production at previous colliders. The * → γ channel shows no sensitivity for the case f = − f = 1, which is therefore studied with Z boson radiation, with the * → Z → 2 2j channel being dominant. The excited muon channels are slightly more sensitive than those of the excited electron channels, even though the resolution and thus the signal separation ability of electron final states is higher than that of the muon channels. The higher exclusion power  Figure 9: Upper limits at 95% CL on the product of the production cross section and branching fraction for excited electrons (left) and excited muons (right). First row: * → γ, second row: * → Z → 2 2j, last row: combined four-lepton results. It is assumed that the signal efficiency is independent of Λ. Theory curves are shown as solid or dashed lines. is due to the better muon reconstruction efficiency, which leads to an overall higher signal selection efficiency. Table 7: Summary of the observed (expected) limits on * mass, assuming M * = Λ, for the cases f = f = 1 and f = − f = 1. The latter case is not applicable to * → γ.    Figure 11: Summary of all mass limits for the various channels and, including the combination of the four lepton channels, for M * = Λ.

Summary
A comprehensive search for excited leptons, e * and µ * , in various channels has been performed using 19.7 fb −1 of pp collision data at √ s = 8 TeV. The excited lepton is assumed to be produced via contact interactions in conjunction with the corresponding standard model lepton. Decaying to its ground state, the excited lepton may emit either a photon or a Z boson. No evidence of excited leptons is found and exclusion limits are set on the compositeness scale Λ as a function of the excited lepton mass M * .
The * → γ final state has the largest production cross section and has therefore previously been used for searches. Following convention, the limits for the assumption Λ = M * are included here. This final state yields the best limits, excluding excited electrons up to 2.45 TeV and excited muons up to 2.47 TeV, at 95% confidence level. These limits place the most stringent constraints to date on the existence of excited leptons.
The * → Z decay channel has been examined for the first time at hadron colliders, allowing the case where couplings between standard model leptons and excited leptons f = − f = 1 can be studied. The leptonic and hadronic (2-jet)

Appendix
Final numbers used to calculate the expected and observed cross section limits for the various excited lepton channels are shown in Tab. 8. 8-8.11. In all tables, "window" refers to the interval between the upper and lower invariant mass boundaries of the search windows for the given mass points. The interpolated search windows are not shown. The signal efficiency after all selection steps including the search window is signal . The expected number of events for the SM background and the number of observed data events are N bg and N data , respectively.