Search for new physics in final states with a lepton and missing transverse energy in pp collisions at the LHC

This Letter describes the search for an enhanced production rate of events with a charged lepton and a neutrino in high-energy pp collisions at the LHC. The analysis uses data collected with the CMS detector, with an integrated luminosity of 5.0 inverse femtobarns at sqrt(s) = 7 TeV, and a further 3.7 inverse femtobarns at sqrt(s) = 8 TeV. No evidence is found for an excess. The results are interpreted in terms of limits on a heavy charged gauge boson (W') in the sequential standard model, a split universal extra dimension model, and contact interactions in the helicity-nonconserving model. For the last, values of the binding energy below 10.5 (8.8) TeV in the electron (muon) channel are excluded at a 95% confidence level. Interpreting the ell nu final state in terms of a heavy W' with standard model couplings, masses below 2.90 TeV are excluded.


Introduction
New heavy gauge bosons are predicted by various extensions of the standard model (SM). The sequential standard model (SSM) [1] postulates the existence of a W boson, a heavy analogue of the W. In such a theory, the W is expected to appear as a narrow resonance with decay modes and branching fractions similar to those of the W. For W masses above 180 GeV, where the tb decay channel opens up, the predicted branching fraction is about 8.5% for each of the leptonic final states. Previous searches [2,3] with pp collision data at √ s = 7 TeV by the Compact Muon Solenoid (CMS) and ATLAS experiments at the Large Hadron Collider (LHC), based on an integrated luminosity of up to 5 fb −1 , have excluded SSM W bosons with masses up to 2.6 TeV.
Other models for new physics predict the same final state, such as those with universal extra dimensions (UED) and bulk fermions, or split UED [4,5]. Such models of extended spacetime assume one additional compact dimension of radius R. The split-UED parameter space is defined by 1/R and µ, with µ being the bulk mass parameter of the fermion field in five dimensions. For suitable non-zero values of µ, as assumed by split-UED models, the cross sections are sufficiently large to allow observation by LHC experiments. All SM particles have corresponding Kaluza-Klein (KK) partners, for instance W n KK , where n denotes the n-th KK excitation mode. Only KK-even modes of W n KK couple to SM fermions, owing to KK-parity conservation [6]. Modes with n ≥ 4 have a smaller cross section and are not expected to be accessible at √ s = 8 TeV, hence the only mode considered is n = 2.
Motivated by the observation of mass hierarchies in the fermion sector, theories have been developed where leptons and quarks are composite objects [7]. At energies much lower than the binding energy of these fundamental constituents, typically called Λ, quark and lepton compositeness would manifest itself as a four-fermion contact interaction (CI). One of the possible contact interactions between two quarks, a neutrino and a charged lepton is described by the helicity-non-conserving (HNC) model [8]. The corresponding cross section is proportional to the square of the partonic centre-of-mass energy and to Λ −4 . While CDF has set a limit on Λ > 2.81 TeV [9] based on a final state with an electron and a neutrino, no limit in the HNC model has yet been set in the muon channel.
In this letter, a search is presented for an excess of events with an isolated charged lepton (an electron or muon) and a neutrino in the final state, using the CMS detector. The data sample corresponds to an integrated luminosity of 5.0 fb −1 at √ s = 7 TeV collected in 2011, and 3.7 fb −1 at √ s = 8 TeV collected in 2012. The CMS 2011 result has been published in ref. [2].

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/scintillator hadron calorimeter (HCAL). Muons are measured in gas-ionization detectors embedded in the steel return yoke. Extensive forward calorimetry complements the coverage provided by the barrel and endcap detectors. A more detailed description of the CMS detector can be found in Ref. [10]. CMS uses a right-handed coordinate system, with the origin at the nominal interaction point, the x axis pointing to the centre of the LHC, the y axis pointing up (perpendicular to the LHC plane), and the z axis along the anticlockwise-beam direction. The polar angle θ is measured from the positive z axis and the azimuthal angle φ is measured in the x-y plane.

Signal and backgrounds 3 The search strategy
Candidate events with at least one high transverse momentum (p T ) electron or muon are selected using single-lepton triggers. Isolated high-p T leptons are reconstructed using very stringent quality criteria while the neutrino gives rise to experimentally observed missing transverse energy (E miss T ). The details on lepton identification and E miss T reconstruction, as optimized for the 2011 analysis, can be found in Ref. [2]. The discriminating variable of this analysis is the transverse mass M T of the lepton-E miss T system, calculated as where ∆φ ,ν is the azimuthal angle between the charged lepton's transverse momentum p T and the E miss T direction.
In W decays, as well as for the other models considered, the lepton and E miss T are expected to be almost back-to-back in the transverse plane, and balanced in transverse energy. Additional kinematic criteria therefore select events with a ratio of the lepton p T and the E miss T , 0.4 < p T /E miss T < 1.5, along with the requirement of the angular difference, |∆φ ,ν − π| < 0.2π. For simulated SSM W events with masses between 0.5 and 2.5 TeV passing these selection criteria, the signal efficiency (including 90% geometrical acceptance) is found to be 70-75% with 2% uncertainty in the electron channel and 67-72% with 1% uncertainty in the muon channel. For the HNC contact-interaction model the signal efficiency is independent of the interaction scale Λ and has been determined from simulation to be 80% with 1% uncertainty for the electron channel and 77% with 4% uncertainty for the muon channel. The transverse mass distributions for accepted SM events in the electron and muon channels are shown in Fig. 1, along with two example W signals. The observed event with the highest transverse mass in the electron channel has M T = 2.38 ± 0.05 TeV based on E T = 1.2 TeV with 1% uncertainty. In the muon channel the maximum transverse mass is M T = 1.33 ± 0.03 TeV with a measured p T of 690 ± 22 GeV. The two types of processes, W production and compositeness, can be distinguished by examining the shape of the lepton-E miss T transverse-mass spectrum. Both processes manifest themselves through an excess of events at the high end of the spectrum. The W signal events are expected to concentrate in a Jacobian peak around the W mass, as shown in        Figure 3: Limits on the cross section times the single channel branching fraction (σ × B) for heavy W bosons based on the 2012 data for the electron and the muon channels. For the individual channels, only the observed limits are shown. For the combination, the observed limit, the expected limit, the 1σ, and the 2σ bands are displayed. The model assumes equal branching fractions for the electron and the muon channel, hence the combination corresponds to doubling the number of events. All limits are displayed for the single channel branching fraction. The W mass limits are derived with a Bayesian method for the models of a SSM W and W n=2 KK in split UED. The W n=2 KK is the lowest mass state that can couple to SM fermions and has the same final state as the SM-like W . Since it has even KK parity it can be produced singly. Plotted is the signal strength modifier σ excl. /σ SSM W as a function of the W mass, where σ excl. is the cross section excluded at a 95% confidence level and σ SSM W is the cross section predicted by the SSM. All W mass points below the ratio σ excl. /σ SSM W = 1, shown as a red dashed line, are excluded in the sequential standard model.  lution make comparable contributions to the overall uncertainty in the electron channel: the energy scale has an uncertainty of 1(3)% in the barrel(endcaps) and the resolution has an uncertainty of 1.4(3)% for the barrel (endcaps) [16]. For muons, the dominant uncertainty stems from the momentum scale, which is taken to be 5% × p T / TeV [17] and results in larger errors on the background and signal event yields in the muon channel, as can be seen in Table 1. The muon p T resolution has been determined with cosmic ray muons to be 10% at high p T with an uncertainty of 0.6% [17].
Similarly, the impact of the E miss T energy scale is modelled by shifting the hadronic component event-by-event by 10%, while the resolution is taken into account by a 10% smearing. In all cases, the impact on the expected number of signal events is around 1% for each source of uncertainty. The background parametrization procedure is repeated using the distorted distributions. Additionally, an uncertainty is derived by fitting the undistorted background with two different functions. The estimates shown in Table 1 include a systematic uncertainty that covers the range of results from these fits, with the statistical uncertainty coming from the fit to the original distribution. Additionally, an uncertainty of 4.4% is considered on the integrated luminosity [18].
The number of data events above a transverse mass threshold M min T is compared to the expected number of signal and background events, with the M min T threshold being optimized for the best expected exclusion limit, using steps of 50 GeV. Very similar results are achieved when optimizing for discovery. The same optimization procedure is applied for the W and CI searches but the optimized M T thresholds are specific to each analysis. For a W mass of up to 2.5 TeV the optimization tends to select a value for M min T a little below the peak of the Jacobian, retaining most of the events in the peak. To keep a significant signal contribution for higher masses, the M min T threshold is shifted to lower values owing to the increasing off-shell fraction. For CI no such effect exists and the optimized M min T threshold is roughly constant around 1 TeV.
No significant excess has been observed in the data, and upper limits are set on the production cross section times the branching fraction σ × B(W → ν), with = e or µ, using a Bayesian method with the assumption of a flat prior for the parameter of interest. The expected and observed upper cross section limits on a SSM W , at 95% confidence level (CL), for √ s = 8 TeV data, are shown in Fig. 3 for both channels and their combination. Using the central value of the theoretical NNLO SSM W cross section times branching fraction, which is assumed to be identical in the two channels, we exclude masses less than 2.60 TeV in the electron and 2.75 TeV in the muon channel. The expected limits are 2.70 TeV and 2.65 TeV, respectively. The observed limit for W → eν is slightly lower than the expectation because of one event with a transverse mass of 2.3 TeV (Fig. 1). Combining both channels, the limit increases to 2.85 TeV ( Table 2). To further enhance the sensitivity the new results can be combined with the published [2] √ s = 7 TeV results, based on an integrated luminosity of 5 fb −1 , thus extending the limit to 2.90 TeV as shown in Fig. 4 and Table 2.
The limit can be reinterpreted in terms of W n=2 KK mass, as shown in Fig. 3, for values of the Dirac mass term µ = 0.05 TeV and µ = 10 TeV and directly translated to bounds on the split-UED parameter space, (1/R, µ) (Fig. 5). The four-fermion contact interaction of the HNC model is excluded for values of Λ < 10.5 TeV in the electron channel and Λ < 8.8 TeV in the muon channel (Fig. 6). While the expected sensitivity is comparable in both search channels, the exclusion limit in the electron channel is higher because of a downward fluctuation of data (see Table 1) in the search region of M T > 1 TeV. These limits are summarized in Table 3.

Summary
A search for new physics has been carried out using pp collisions recorded with the CMS detector at centre-of-mass energies of √ s = 7 TeV and 8 TeV. The transverse mass spectrum of either electrons or muons and missing transverse energy has been measured. The observed spectra are consistent with the standard model expectation, and mass limits on sequential standard model W and W n=2 KK have been set at the 95% CL. These are the most stringent limits to date. For the first time, a limit on the compositeness scale Λ has been set for contact interactions in the HNC model based on the final state with a muon and E miss T . The corresponding exclusion limit in the electron channel significantly improves the existing one.

Acknowledgements
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 centres 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: BMWF and FWF (Austria); FNRS and