Search for excited leptons in $\ell\ell\gamma$ final states in proton-proton collisions at $\sqrt{s} =$ 13 TeV

A search is presented for excited electrons and muons in $\ell\ell\gamma$ final states at the LHC. The search is based on a data sample corresponding to an integrated luminosity of 35.9 fb$^{-1}$ of proton-proton collisions at a center-of-mass energy of 13 TeV, collected with the CMS detector in 2016. This is the first search for excited leptons at $\sqrt{s} =$ 13 TeV. The observation is consistent with the standard model background prediction, and the most stringent exclusion limits to date are set on the excited lepton mass and the compositeness scale, at 95% confidence level. Excited electrons and muons are excluded for masses below 3.9 and 3.8 TeV, respectively, under the assumption that the excited lepton mass equals the compositeness scale. The best observed limit on the compositeness scale is obtained with an excited lepton mass of around 1.0 TeV, excluding values below 25 TeV for both excited electrons and muons.


Introduction
The standard model (SM) provides a very precise description of various phenomena in particle physics observed over the last half century. Notwithstanding its huge success, it does not explain the origin of the mass hierarchy and the number of generations of quarks and leptons. As an attempt to answer such fundamental questions, compositeness of quarks and leptons is introduced in many models [1][2][3][4][5][6][7][8][9][10]. These compositeness models suggest that quarks and leptons are themselves made of fundamental constituents that are bound by a new strong interaction with a characteristic energy scale Λ (called the compositeness scale).
An important prediction of compositeness models is the existence of excited states of quarks and leptons. In proton-proton (pp) collisions, excited fermions could be produced via contact interactions (CI) and decay either through SM gauge interactions or via CI to SM fermions. This paper presents a search for excited leptons ( * = e * , µ * ) in γ ( = e, µ) final states where the excited lepton decays to a SM lepton and a photon ( * → γ) as illustrated in Fig. 1. A clear signature of a same-flavor (SF) lepton pair and a photon allows highly efficient signal selection. However, there is an ambiguity in reconstructing the excited lepton mass because of the two possible pairings of a lepton and the photon. For this search, information of both invariant masses is used to discriminate the excited lepton signal from SM background processes. We consider a benchmark model based on the formalism described in Ref. [8]. The effective Lagrangian of four-fermion CI, the main production mechanisms of excited leptons at the LHC, is given by where g * is the coupling constant, which is set to be equal to √ 4π in the model, and j µ represents the fermion currents for SM fermions and their excited states, neglecting right-handed currents. In addition, excited lepton decays via SM gauge interactions are described by the corresponding Lagrangian where and * denote the lepton and excited lepton fields, and W µν and B µν are the SU(2) and U(1) gauge fields. The quantities g = e/ sin θ W and g = e/ cos θ W represent the corresponding electroweak gauge couplings with the Weinberg mixing angle θ W , and τ and Y are the generators of the SU(2) and U(1) groups. The symbols f and f describe the couplings between SM leptons and excited leptons via gauge interactions and are chosen to be equal to 1 in the model.
Searches for excited leptons have been previously performed by the CMS Collaboration [11,12], but no evidence for their existence was found, excluding m * < 2.5 TeV for the case Λ = The generated events are processed through the full GEANT4 [34] simulation of the CMS detector. The effect of multiple pp interactions within the same bunch crossing or adjacent bunch crossings (pileup) is emulated by superimposing minimum bias events on the simulated events. The simulated events are weighted to match the pileup distribution observed in the data.

Event reconstruction and selection
The event selection uses a particle-flow algorithm [35] for optimal efficiency, kinematic resolution and purity in physics object reconstruction and identification. The particle-flow algorithm aims to reconstruct and identify individual particles in an event using an optimized combination of information from the various elements of the CMS detector. The energy of photons is directly obtained from the ECAL measurement. The energy of electrons is determined from a combination of the electron momentum at the primary interaction vertex as determined by the tracker, the energy of the corresponding ECAL cluster, and the energy sum of all bremsstrahlung photons spatially compatible with originating from the electron track. The momentum of muons is obtained from the curvature of the corresponding track. The energy of charged hadrons is determined from a combination of their momentum measured in the tracker and the matching ECAL and HCAL energy deposits, corrected for zero-suppression effects and for the response function of the calorimeters to hadronic showers. Finally, the energy of neutral hadrons is obtained from the corresponding corrected ECAL and HCAL energies.
Events must have at least one primary vertex with at least four associated tracks, with the transverse (longitudinal) position within 2 (24) cm from the nominal collision point. The reconstructed vertex with the largest value of summed physics-object p 2 T is taken to be the primary pp interaction vertex. Here the physics objects are the jets, clustered using a jet finding algorithm [36,37] with the tracks assigned to the vertex as inputs, and the associated missing transverse momentum (p miss T ), taken as the negative vector sum of the p T of those jets. Electron candidates are reconstructed by matching clusters of ECAL energy deposits with tracks in the inner tracker. The momentum resolution ranges from 1.7 to 4.5% for electrons from Z boson decays, depending on the electron η and the bremsstrahlung energy emitted [38]. The electron candidates are required to have p T > 35 GeV and to be within the region |η| < 2.5. The barrel-endcap transition region 1.44 < |η| < 1.56 is excluded. The electron candidates have to pass a set of identification requirements on the spatial distribution of energy deposits in the ECAL, on the ratio of the associated HCAL and ECAL energy deposits, on the isolation in the calorimeters, on the quality of the matching between the ECAL clusters and the associated track in the inner tracker, and on the agreement between the energy reconstructed in the ECAL and the momentum of the associated track.
Muon candidates are reconstructed as tracks in the muon detector that are matched to the tracks found in the inner tracker. The momentum resolution for muons with p T up to 100 GeV is 1% in the barrel and 3% in the endcaps. The resolution in the barrel is better than 10% for muons with p T up to 1 TeV [39]. The muon candidates must have p T > 35 GeV and be within |η| < 2.4. The muon candidates are required to pass identification criteria optimized for muons having large p T [39] and to be isolated in the tracking systems.
Photon reconstruction starts from energy deposits in the ECAL, and photon candidates that have associated tracks are rejected. The photon energy resolution ranges from 1 to 5%, depending on photon η and showers in the ECAL [40]. The photon candidates are required to have p T > 35 GeV and |η| < 2.5, with those in the transition region 1.44 < |η| < 1.56 being excluded from the analysis. A multivariate analysis (MVA) technique is used for photon iden-tification, with shower shape variables and photon isolation sums in the ECAL and HCAL as inputs [40,41].
Events are required to have two SF leptons and a photon. The two SF leptons are not required to be of opposite-sign charge because this would result in a signal efficiency loss of a few % at high lepton p T , especially for the eeγ channel [42], whereas the background arising from events with same-sign dileptons is minimal. The selected leptons must be separated from the photon by ∆R = √ (∆η) 2 + (∆φ) 2 > 0.7, where φ is the azimuthal angle measured in radians. In addition, the invariant mass of the two SF leptons m is required to be larger than 116 GeV in order to suppress the dominant background contribution from Z boson production (Z boson veto criteria).

Background modeling
The major backgrounds in this search originate from SM processes with final states consisting of two prompt SF leptons and a prompt photon or a jet misidentified as a photon. The expected fraction of background events that have a jet misidentified as a lepton is less than 1% for both channels [43], therefore this background source is not considered in the analysis. Backgrounds associated with a prompt photon are estimated using simulation, while the yield of those associated with a jet is derived from the data.
The dominant background arises from Drell-Yan process accompanied by a prompt photon (DY+γ), which has a signature similar to the signal. Within the detector acceptance, Z boson production dominates the process, and its contribution is efficiently suppressed by applying the Z boson veto criteria described in Section 4. The fraction of DY+γ events after the event selection is approximately 70% of the background. Another prompt photon background comes from top quark pair production in association with a photon (tt+γ). These events form approximately 10% of the background. In addition, triboson processes such as WWγ, WZγ, and ZZγ (VVγ) also give rise to 5% of the background.
The other major background contribution consists of events with two prompt leptons and a photon that originates from a jet, hereafter referred to as the jet background. The estimation of this background is derived from data in a control region composed of events with two leptons and a photon passing all the kinematic requirements and lepton identification criteria defined in the event selection but failing the photon identification. The events in the control region, scaled by a weight factor derived from the misidentification rate of photon candidates from jets, provide the jet background prediction in the signal region.
The misidentification rate is measured using data in a sideband (50 < m < 116 GeV) of the dilepton mass distribution in the signal region (m > 116 GeV). The photon identification is not required for events in the sideband, thereby the data in the sideband are enriched with Z boson events associated with a photon originating from a jet. To remove prompt photon contamination in the data, the distribution of the MVA variable used for the photon identification is employed, fitting the MVA variable distribution of the data events with template distributions for prompt photons and photons originating from jets. The MVA distribution of simulated prompt photon background events in the sideband is used as the template distribution for prompt photons. The template for photons originating from jets is obtained from a data sample enriched with W+jets events, where the W boson decays leptonically and a jet supplies a photon candidate. Events in the sample are required to have a muon of p T > 35 GeV, ] between 50 and 110 GeV, and a photon candidate. The misidentification rate is evaluated in several photon p T bins separately for the barrel and endcaps of ECAL. The measured misidentification rate ranges from 2 (3)% at p T = 35 GeV to 0.2 (0.4)% at p T = 1 TeV in the barrel (endcaps). In the signal region, the estimated fraction of events arising from background with a jet misidentified as a photon is in the range 5-15%, depending on the photon p T .
The kinematic distributions of the parent jets of the misidentified photons in the control region and those of the signal region are not identical in the same photon p T range, owing to isolation requirements in the MVA identification. Consequently, the p T distributions of leptons, which are correlated with the recoil of the jet in the same event, are different in the signal region and the control region. Therefore, an appropriate correction must be applied to the estimate of the lepton p T distribution obtained by scaling the control region by a weight factor based on the misidentification rate. Using the p T of the dilepton pair as a proxy of the jet recoil, the dilepton p T distribution of the jet background estimate is reweighted to match the correct shape of the dilepton p T distribution of the jet background events in the signal region. The shape is directly taken from data in the signal region, removing prompt photon contamination using simulated events. The reweighting is done for separate photon p T bins used for the misidentification rate measurement, in order to retain the yield and the photon p T spectrum obtained from the previous step. To validate the estimation procedures, closure tests are performed by applying the same method to derive background on simulated events, and the observed discrepancies are taken as estimates of the associated systematic uncertainties. After the correction, the lepton kinematic distributions from the total background prediction including the corrected jet background obtained from control samples in data are in good agreement with the distributions in data.

Signal modeling
The production of an excited lepton involves two SM leptons in the final state, one from the excited lepton decay and another from CI, and therefore there are two possible pairings of a lepton with the photon. The corresponding two invariant masses are referred to as m min γ and m max γ . The m min γ and m max γ distributions of observed events along with the background prediction in the signal region are shown in Fig. 2.
A search window is set in the two-dimensional distribution of m max γ versus m min γ . For * events, either m min γ or m max γ corresponds to the reconstructed invariant mass of * . Therefore, the mass resonance of the signal is concentrated in the shape of a reflected "L" as shown in Fig. 3. On the other hand, background events have no such correlation in m min γ and m max γ in the low mass region below 1 TeV. The distribution of the dominant DY+γ background is shown in Fig. 4. This clear distinction between signal and background events in the distribution of m max γ versus m min γ is used to define L-shaped search windows enhancing the discrimination between signal and background.
For low signal masses, m * ≤ 1 TeV, setting an L-shaped search window significantly improves a discrimination against the background with only a small loss in the signal acceptance. Therefore, the search window for m * ≤ 1 TeV is set to be a narrow L-shape centered at m * , consisting of lower and upper thresholds of m min γ and m max γ as shown in Fig. 3. The thresholds are optimized for the best expected exclusion limit, which also provides the optimal discovery potential. The impact of the energy scale and resolution uncertainties on the signal acceptance is taken into account for the optimization. The optimized thresholds have values that are within ±8% of the simulated mass for e * , and within ranges that vary from ±4.5% to ±8% of the simulated mass for µ * . The search windows defined for m * > 1 TeV, where the background contribution is expected to be negligible, only impose the lower m max γ threshold of 1 TeV, thereby maximizing the signal acceptance.
The product of signal acceptance and efficiency (A sig ) has been measured from the simulated signal samples, and ranges from 30 to 49% and from 33 to 59% for excited electrons and muons, respectively. The relatively low values of A sig at low masses mainly result from lepton and photon p T thresholds. To determine A sig for mass points other than those of the simulated samples, a polynomial fit to the dependence on m * is used for interpolation, as shown in Fig. 5.

Systematic uncertainties
The systematic uncertainties in the signal and the background yields are summarized in Table 1. The statistical uncertainties in the data and the simulated samples used for the back-  The integrated luminosity has been measured with a precision of 2.5% [44]. The effect of pileup modeling on the selection efficiency is measured to be less than a percent over all mass points, and a 1% uncertainty is assigned for it. Systematic uncertainties in the signal selection efficiency include uncertainties arising from the trigger selection, lepton identification [39] and photon identification [40,41]. Various sources of potential biases in the selection efficiency measurements are considered to determine such uncertainties. Uncertainties in the e/γ energy scale and resolution, and muon momentum scale and resolution translate into uncertainties in the signal acceptance. The effect on the signal acceptance is evaluated by shifting and smear-ing the p T of each object by ±1 standard deviation. Although the fraction of energy affected by the e/γ energy scale and resolution uncertainties is larger for eeγ events than for µµγ events, because the mass window is narrower and the mass resolution is worse, the impact on the acceptance is measured to be stronger in the latter case.
Systematic uncertainties in the signal acceptance and background cross sections due to the PDF choice have been estimated by following the PDF4LHC prescription [45]. Renormalization and factorization scale uncertainties are evaluated by varying the scales up and down by a factor of 2, both simultaneously and independently. The maximum change observed among the corresponding variations in the signal and the background yields is taken as an estimate of the associated systematic uncertainty. Uncertainties of 2 and 10% are assigned for the PDF and scale uncertainties in the signal acceptance and the background yields, respectively.
For the jet background estimate, the following uncertainties are taken into account: statistical uncertainties in the jet-to-photon misidentification rate measurement (8-72%), systematic uncertainties in the template distributions used for the misidentification rate measurement (20%), and systematic uncertainties based on the discrepancies observed in the closure tests for the jet background determination procedure performed on simulated samples (50%). The total systematic uncertainty in the jet background prediction is evaluated by summing these uncertainties in quadrature and amounts to 54%, increasing to 90% for masses above 1 TeV.

Results
Within the uncertainties, the data are found to be consistent with the background prediction as summarized in Tables 2 and 3 Table 4.  Table 3: The observed yield and the SM prediction in the search window of the given m * in the µµγ channel. The symbols N data , N prompt , and N jet represent the number of events in data, the prompt photon background prediction, and the jet background estimate, respectively, together with statistical and systematical uncertainties.   Figure 6: Observed (solid) and expected (dashed) 95% CL upper limits on the product of the production cross section and branching fraction (left column) and lower limits on the compositeness scale (right column) as a function of signal mass m * , together with the 68% (green, inner) and 95% (yellow, outer) quantiles of the expected limit, for e * (upper row) and µ * (lower row).

Acknowledgments
We congratulate our colleagues in the CERN accelerator departments for the excellent performance of the LHC and thank the technical and administrative staffs at CERN and at other CMS institutes for their contributions to the success of the CMS effort. In addition, we gratefully acknowledge the computing centers and personnel of the Worldwide LHC Computing Grid for delivering so effectively the computing infrastructure essential to our analyses. Finally, we acknowledge the enduring support for the construction and operation of the LHC and the CMS detector provided by the following funding agencies: