Search for top squarks in R-parity-violating supersymmetry using three or more leptons and b-tagged jets.

A search for anomalous production of events with three or more isolated leptons and bottom-quark jets produced in pp collisions at √s=8 TeV is presented. The analysis is based on a data sample corresponding to an integrated luminosity of 19.5 fb(-1) collected by the CMS experiment at the LHC in 2012. No excess above the standard model expectations is observed. The results are interpreted in the context of supersymmetric models with signatures that have low missing transverse energy arising from light top-squark pair production with R-parity-violating decays of the lightest supersymmetric particle. In two models with different R-parity-violating couplings, top squarks are excluded below masses of 1020 GeV and 820 GeV when the lightest supersymmetric particle has a mass of 200 GeV.

1 Supersymmetric (SUSY) extensions of the standard model (SM) offer a solution to the hierarchy problem and provide a mechanism for unifying particle interactions [1,2]. Assigning R-parity [3] to fields as R = (−1) 3B+L+2s , where B and L are baryon and lepton numbers, and s is the particle spin, all SM particle fields have R = +1 while all superpartner fields have R = −1. In models where R-parity is conserved, superpartners can only be produced in pairs, and the lightest superpartner (LSP) is stable and could serve as a dark-matter candidate. Rparity conservation also ensures proton stability.
Supersymmetric models with R-parity violating (RPV) interactions necessarily violate either B or L but can avoid proton decay limits [4,5]. The superpotential W RPV includes three trilinear terms parametrized by the Yukawa couplings λ ijk , λ ijk , and λ ijk : where i, j, and k are generation indices; L and Q are the SU(2) L doublet superfields of the lepton and quark; and the E, D, and U are the SU(2) L singlet superfields of the charged lepton, downlike quark, and up-like quark. The third term violates baryon number conservation, while the first and second terms violate lepton number conservation.
The RPV interactions allow for single production of SUSY particles (sparticles) and for sparticle decay into SM particles only. The latter is explored in this Letter. Prior searches for RPV interactions in multilepton final states include those by the ALEPH [6], DELPHI [7], and L3 [8]  Among modern SUSY models, those characterized as "natural" play a prominent role. Natural supersymmetry is characterized by a relatively small fine tuning to describe particle spectra. In particular, it requires top squarks (stops), the top-quark superpartners, to be lighter than about 1 TeV. The introduction of RPV couplings does not preclude a natural hierarchy and can allow the constraints on the stop mass to be relaxed [16].
In RPV models, the LSP is unstable, and a common experimental strategy of SUSY searchesselecting events with large missing transverse energy (E miss T )-is not optimal [4]. Instead, we use S T , which is the scalar sum of E miss T and the transverse energy of jets and charged leptons, to provide separation between signal and standard model backgrounds.
In this Letter we present the result of a search for pair production of top squarks with RPV decays of the lightest sparticle, using multilepton events with one or more bottom-tagged (btagged) jets. The data set used in this analysis corresponds to an integrated luminosity of 19.5 fb −1 , recorded in 2012 with the CMS detector at the LHC in proton-proton collisions at a center-of-mass energy of 8 TeV.
The coordinate system in CMS is right-handed, with the origin at the nominal interaction point. The x axis points towards the center of the LHC ring, the y axis points up, and the z axis points along the counterclockwise-beam direction. The polar angle θ is measured with respect to the positive z axis and the azimuthal angle φ is measured in the x-y plane. Pseudorapidity is given by η ≡ − ln[tan(θ/2)].
The CMS detector [17] has cylindrical symmetry around the pp beam axis with tracking and muon detectors covering the pseudorapidity range |η| < 2.4. The tracking system, used to measure the trajectory and momentum of charged particles, consists of multilayered silicon pixel and strip detectors in a 3.8 T solenoidal magnetic field. Particle energies are measured with concentric electromagnetic and hadron calorimeters, which cover |η| < 3.0 and |η| < 5.0, respectively. Muon detectors consisting of wire chambers are embedded in the steel return yoke outside the solenoid. The trigger thresholds in a two-level trigger system are tuned to accept a few hundred data events per second from the pp interactions.
We select events with three or more leptons (including tau leptons) that are accepted by a trigger requiring two light leptons, which may be electrons or muons. Any opposite-sign, same-flavor (OSSF) pair of electrons or muons has to have an invariant mass m > 12 GeV. This requirement removes low-mass bound states and γ * → + − production.
Electrons and muons are reconstructed using quantities from the tracker, calorimeter, and muon systems. Details of reconstruction and identification can be found in Ref.
[18] for electrons and in Ref.
[19] for muons. We require that at least one electron or muon in each event has transverse momentum of p T > 20 GeV. Additional electrons and muons must have p T > 10 GeV and all of them must be within |η| < 2.4.
The majority of hadronic decays of tau leptons (τ h ) yield either a single charged track (oneprong) or three charged tracks (three-prong), occasionally with additional electromagnetic energy from neutral pion decays. Both one-and three-prong τ h candidates are used in this analysis if they have p T > 20 GeV, reconstructed with the "hadron plus strips" method [20]. Leptonically decaying taus are included with other electrons and muons.
To ensure that electrons, muons, and τ h candidates are isolated, we use a particle-flow (PF) algorithm [21,22] to identify the source of transverse energy deposits in the trackers and calorimeters. We then sum the contribution in a cone of radius 0.3 in ∆R = (∆η) 2 + (∆φ) 2 around the candidate and subtract the lepton p T to calculate E cone . The energy from additional proton-proton collisions that occur simultaneously is subtracted [18,23]. For electrons and muons, we divide the summed energy by the lepton p T to find the relative isolation I rel = E cone /p T , which has to be less than 0.15. We require E cone < 2 GeV for τ h candidates.
We use jets reconstructed from all of the PF candidates [23] using the anti-k T algorithm [24] with a distance parameter of 0.5, that have |η| < 2.5 and p T > 30 GeV. Jets are required to be a distance ∆R > 0.3 away from any isolated electron, muon, or τ h candidate. To determine if the jet originated from a bottom quark, we use the combined secondary-vertex algorithm, which calculates a likelihood discriminant using the track impact parameter and secondaryvertex information. This discrimination selects heavy-flavor jets with an efficiency of 70% and suppresses light-flavor jets with a misidentification probability of 1.5% [25].
Monte Carlo (MC) simulations are used to estimate some of the SM backgrounds and to understand the efficiency and acceptance of the signal models we are investigating. The SM background samples are generated using MADGRAPH [26] with parton showering and fragmentation modeled using PYTHIA (version 6.420) [27] and passed through a GEANT4-based [28] representation of the CMS detector. Signal samples [16] are generated with MADGRAPH and PYTHIA and passed through the CMS fast-simulation package [29]. Next-to-leading-and nextto-leading-log-order cross sections and their uncertainties for the SUSY signal processes are from the LHC SUSY cross sections working group [30][31][32][33][34].
Multilepton signals have two main sources of backgrounds, the first arising from processes that produce genuine multilepton events. The most significant examples are WZ and ZZ production, but rare processes such as tt W ± and tt Z can also contribute. We assess the contribution from these processes using samples simulated by MADGRAPH. For WZ and ZZ production, these simulated samples have been validated in control regions in data. For the rarer background processes, we rely solely on simulation.
The second source originates from objects that are misclassified as prompt, isolated leptons, but are actually hadrons, leptons from a hadron decay (heavy-or light-flavored), etc. Misidentified leptons are classified in three categories in our analysis: misidentified light leptons (electrons and muons), misidentified τ h leptons, and light leptons originating from asymmetric internal conversions.
We estimate the contribution of misidentified light leptons by measuring the number of isolated tracks and applying a scale factor between isolated leptons and isolated tracks. These scale factors are measured in control regions that contain leptonically decaying Z-bosons and a third, isolated track. The scale factor is then the probability for the third track to pass the lepton identification criteria. We find the scale factors to be (0.9 ± 0.2)% for electrons and (0.7 ± 0.2)% for muons. The scale factors are applied to the sideband region with two light leptons and an isolated track. The scale factors depend on the heavy-flavor content in the different signal regions changes. We parametrize this dependance as a function of the impact parameter distribution of non-isolated tracks. The tt contribution here is taken from simulation.
The τ h misidentification rate is measured in jet-dominated data by comparing the number of τ h candidates in the signal region defined by E cone < 2 GeV to the number of non-isolated τ h candidates, which have 6 < E cone < 30 GeV. We measure this misidentification rate to have an average value of 15% and assign a systematic uncertainty of 30% based on the variation in different control samples. We apply this rate to the sideband region with two light leptons and one non-isolated τ h candidate.
Another source of background leptons are internal conversions, where a virtual photon decays promptly to a dilepton pair. These conversions produce muons almost as often as electrons. In the case of asymmetric conversions, where one lepton has very low p T and/or does not pass the selection criteria, Drell-Yan type processes can lead to a significant background for three lepton signatures. We measure the conversion factors of photons to light leptons in a control region where no new physics is expected (low E miss T and low hadronic activity). The ratio of the number of + − ± candidates to the number of + − γ candidates in the Z boson decays defines the conversion factor, which is 2.1% ± 0.3% (0.5% ± 0.1%) for electrons (muons) [14]. These uncertainties are statistical only. We assign systematic uncertainties of 100% to these conversion factors from our underlying assumption of proportionality between virtual and onshell photons, as well as our inability to remove misidentified photons from sideband regions.
A systematic uncertainty of 4.4% in the normalization of the simulated samples accounts for imperfect knowledge of the integrated luminosity of the data sample [35]. Signal cross sections have varying uncertainties from 15% to 51% in the range of stop masses between 250 GeV and 1.5 TeV, which come from the parton distribution function uncertainties and the renormalization and factorization scale uncertainties [36]. We scale the WZ and ZZ simulation samples to match data in control regions. The overall systematic uncertainty on WZ and ZZ contributions to the signal regions varies between 15% and 30% depending on the kinematics, and is the combination of the normalization uncertainties with efficiency and resolution uncertainties. Muon identification efficiency uncertainty is 11% at muon p T of 10 GeV and 0.2% at 100 GeV. For electrons the uncertainties are 14% at 10 GeV and 0.6% at 100 GeV. The uncertainty on the efficiency of the bottom-quark tagger is 6%. The uncertainty on the E miss T resolution contributes a 4% uncertainty and the jet energy scale uncertainty contributes 0.5% in our background estimates [37]. An uncertainty of 50% for the tt background contribution is due to the low event counts in the isolation distributions in high-S T bins, which are used to validate the misidentification rate in the tt simulation sample. We apply a 50% uncertainty to the normalization of all rare processes. Table 1: Observed yields for three-and four-lepton events from 19.5 fb −1 recorded in 2012. The channels are broken down by the total number of leptons (N L ), the number of τ h candidates (N τ ), and the S T . Expected yields are the sum of simulation and estimates of backgrounds from data in each channel. SR1-SR4 require a b-tagged jet and veto events containing Z bosons. SR5-SR8 contain events that either contain a Z boson or have no b-tagged jet. The channels are mutually exclusive. The uncertainties include both statistical and systematic uncertainties. The S T values are given in GeV. GeV. We gain additional sensitivity in regions with S T > 600 GeV by removing the b-tag and Z-veto requirements for events, so the SR5-SR8 contain the events that fail one or both of these requirements.
The observed and expected yields for SR1-SR8 are shown in Table 1. We also show the S T distribution for SR1 in Fig. 1 with the background expectations from different sources shown separately. Data are in good agreement with the SM predictions in all signal regions. To demonstrate how natural SUSY might manifest itself with RPV couplings, we examine a stop RPV model where the light stop decays to a top quark and intermediate on-or off-shell bino, t 1 → χ 0 * 1 + t. The bino then decays to two leptons and a neutrino through the leptonic Rparity violating interactions, χ 0 * 1 → i + ν j + k and ν i + j + k , or through the semileptonic R-parity violating interactions, χ 0 * 1 → i + q j + q k and ν i + q j + q k , where the indices i, j, k refer to those appearing in Eq. 1. The stop is assumed to be right-handed and RPV couplings are large enough that all decays are prompt.
We generate simulated samples to evaluate models with simplified mass spectra and the only non-zero leptonic RPV couplings λ 122 or λ 233 . The stop masses in these samples range from 700-1250 GeV in 50 GeV steps, and bino masses range from 100-1300 GeV in 100 GeV steps. In a model with only the semi-leptonic RPV coupling λ 233 non-zero, we use stop masses 300- 1000 GeV in 50 GeV steps and bino masses 200-850 GeV in 50 GeV steps. In both cases, slepton and sneutrino masses are 200 GeV above the bino mass. Other particles are irrelevant to the interpretation of our results in these models.
To calculate our limits, we divide the channels shown in Table 1 by lepton flavor and perform a counting experiment using the observed event yields, the background expectations, and the signal expectations as inputs. We combine the limits from the channels with the highest individual sensitivities, which we require in aggregate to contain at least 90% of the signal acceptance at the relevant model grid point [14]. We use the LHC-type CL s method in the limit calculation, which uses the ratio of profiled likelihoods as the test statistic [38,39]. We introduce log-normal nuisance parameters to account for uncertainties on the signal and background estimates.
For all of the couplings, we expect two bottom-quark jets and up to two leptons from the two top quarks. For the leptonic RPV coupling λ 122 , we also expect four electrons or muons. For leptonic coupling λ 233 , we expect four leptons with up to two muons and the rest tau leptons. We use all tau lepton decay channels. For the semileptonic coupling λ 233 , we expect up to two muons, as well as two top quarks and two bottom quarks.
In the models with leptonic couplings, we find that the limits are approximately independent of the bino mass, and, using the conservative minus-one-standard-deviation result where the bino mass is 200 GeV, we are able to exclude models with the stop mass below 1020 GeV when λ 122 is non-zero, and below 820 GeV when λ 233 is non-zero. These limits are shown in Fig. 2.
There is a change in kinematics at the line m χ 0 1 = m t 1 − m t , below which the stop decay is twobody, while above it is a four-body decay. Near this line, the χ 0 1 and top are produced almost at rest, which results in soft leptons, reducing our acceptance. This loss of acceptance is more pronounced in the λ 233 = 0 case and causes the loss of observed sensitivity near the line at m χ 0 1 = 800 GeV. This feature is enhanced in the observed limit because the data has a lower number of events in the relevant signal regions than the simulated signal samples.
In the semileptonic RPV model, which has non-zero λ 233 , the kinematics of the decay are more complicated. These different kinematic regions are described in Table 2. The most significant effect is when the decay χ 0 1 → µ + t + b is kinematically disfavored, which reduces the number of available leptons. The different regions where this effect is pronounced drive the shape of the exclusion for λ 233 . The area inside the curve is excluded. The observed limit is stronger than the expected one, which allows the observed exclusion region to reach into the regime where the bino decouples.
We have performed a search for RPV supersymmetry in models with top-squark pair production using a variety of multilepton final states. We see good agreement between observations and SM expectations. We set stringent limits on the top-squark mass in models with leptonic   Table 2.
RPV couplings λ 122 and λ 233 . For a bino mass of 200 GeV, these limits are 1020 GeV and 820 GeV, respectively. We also set limits in a model with the semi-leptonic RPV coupling λ 233 .
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 [9] D0 Collaboration, "Search for R-parity violating supersymmetry via the LLE couplings λ 121 , λ 122 or λ 133 in pp collisions at   [17] CMS Collaboration, "The CMS experiment at the CERN LHC", JINST 03 (2008) S08004, doi:10.1088/1748-0221/3/08/S08004.