Search for baryon number violation in top-quark decays

Article history: Received 6 October 2013 Received in revised form 7 February 2014 Accepted 17 February 2014 Available online 20 February 2014 Editor: M. Doser


Introduction
In the standard model (SM) of particle physics [1][2][3], baryon number is a conserved quantity as a consequence of an accidental symmetry of the Lagrangian. In fact, it has been proven that extremely small violations can arise from non-perturbative effects [4]. Baryon number violation (BNV) is also predicted in several scenarios of physics beyond the SM such as supersymmetry [5,6], grand unification [7], and models with black holes [8]. Furthermore, BNV is a necessary condition for the observed asymmetry between baryons and antibaryons in the Universe, assuming an evolution from a symmetric initial state [9].
Despite these compelling reasons, no direct evidence of BNV processes has been found to date. Experiments have set stringent limits on BNV in nucleon [10], τ -lepton [11][12][13], c-and bhadrons [14][15][16], and Z-boson [17] decays. The possibility that BNV could occur in the decay of the top quark (t) was first considered in Ref. [18], in which a very stringent bound of about 10 −27 was derived on the branching fraction of the decay t → bc + , where is either an electron or a muon, using the experimental bound on the proton lifetime [10]. However, more recently it has been noted [19] that cancellations between different four-fermion interactions could allow much higher rates of occurrence for the BNV decays t → bcμ + (t → bcμ − ) and t → bue + (t → bue − ). Other BNV decays of the top quark, involving different flavors for the lep-E-mail address: cms-publication-committee-chair@cern.ch. ton and quarks, are also discussed in Ref. [19], where in all cases they are described as four-fermion effective interactions, in which both baryon number and lepton number are violated.
In this Letter we search for evidence of such BNV top-quark decays using 19.52 ± 0.49 fb −1 of pp collision data at √ s = 8 TeV, collected in 2012 with the Compact Muon Solenoid (CMS) detector [20] at the Large Hadron Collider (LHC). These decays are referred to as "BNV decays" in the following, as opposed to the SM decay of the top quark into a W boson and a down-type quark, the latter being a bottom quark in about 99.8% of the cases. Assuming that the BNV decay branching fraction (B) is 1, the most suitable process for its observation is expected to be pair production of top quarks (tt), where one top quark undergoes a SM decay into three jets and the other the BNV decay. This process would have the highest cross section among those involving at least one BNV decay and could be effectively separated from background. Two event selections, one for the muon and one for the electron channel, are defined and optimized for such a process. In both cases the final state consists of a lepton, five quarks, and no neutrino.
to the barrel and endcap detectors, CMS has extensive forward calorimetry. A two-stage trigger system selects pp collision events of interest for use in physics analyses. CMS uses a right-handed coordinate system, with the origin at the nominal interaction point, the x-axis pointing to the center of the LHC ring, the y-axis pointing up (perpendicular to the LHC plane), and the z-axis pointing along the counterclockwise-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. Muons (electrons) are reconstructed and identified in the pseudorapidity (η = − ln[tan(θ/2)]) range |η| < 2.4 (2.5). The pixel (strip) tracker consists of three (ten) co-axial detection layers in the central region and two (twelve) disk-shaped layers in the forward region. The inner tracker measures charged particle trajectories within the pseudorapidity range |η| < 2.5, and provides an impact parameter resolution of ∼15 μm.
A detailed description of the CMS detector can be found elsewhere [20].

Trigger and datasets
The data used for this analysis were collected using isolatedlepton (muon or electron) plus multijet triggers. In the muon (electron) trigger an isolated muon (electron) candidate is required to have a transverse momentum p T greater than 20 (25) GeV/c, |η| < 2.1 (2.5), and be accompanied by at least three jets in |η| < 2.4, with p T > 45,35,25 (50,40,30) GeV/c. The trigger efficiency for signal events passing the offline selection, described in Section 4, is 83 ± 2% (80 ± 2%) for the muon (electron) analysis.
A number of simulated event samples with the most important backgrounds are used to compare observations with SM expectations. The tt + jets, W + jets, and Z + jets events are generated with the MadGraph v5.1.3.30 event generator [21]. The top-quark mass is set to 172.5 GeV/c 2 and the branching fraction of top-quark decays to a W boson and a b quark is assumed to be one. MadGraph is interfaced with pythia v6.426 [22] to simulate parton fragmentation and hadronization. For each production process, data samples corresponding to 0, 1, 2, and 3 extra partons are merged using the "MLM" matching prescription [23] in order to yield a realistic spectrum of accompanying jets. Diboson and QCD multijet events are generated with pythia, whereas single-top-quark samples are generated with powheg [24,25]. Samples of ttW and ttZ events with up to one extra parton are generated with MadGraph.
A number of signal samples are generated with MadGraph v5.1.4.3 [26] interfaced with pythia v8.165 [27]. Two of these samples correspond to events with tt-pair production in which one or both top quarks have a BNV decay. Three other simulated signal samples correspond to the tW, t-channel, and s-channel processes giving rise to single top-quark production. In each of these cases the top quark has a BNV decay, and samples corresponding to zero and one extra parton are merged. All the fermion-flavor-dependent parameters, which appear in the effective BNV Lagrangian defined in [19], were set to unity. Different choices for these values can in principle lead to variations in the kinematical distributions of the top-quark decay products, but the resulting impact on the final results of the search is negligible.
For all simulated samples, the hard interaction collision is overlaid with a number of simulated minimum-bias collisions. The resulting events are weighted to reproduce the distribution of the number of inelastic collisions per bunch crossing (pileup) measured in data. A detailed simulation of particle propagation through the CMS apparatus and detector response is performed with the Geant4 v9.2 [28,29] toolkit.

Event reconstruction and selection
The signal search is performed by counting events passing a "tight" selection. As explained in Section 5, the sensitivity of the search is substantially improved by also using a "basic" selection that includes the tight one. These two event selections are described below.

Basic selection
Events are reconstructed using a particle-flow (PF) algorithm [30], which consists in reconstructing and identifying each particle with an optimized combination of all subdetector information. Reconstructed particles are categorized into muons, electrons, photons, charged hadrons and neutral hadrons. At least one primary vertex is required to be reconstructed in a cylindrical region defined by the longitudinal distance |z| < 24 cm and radial distance r < 2 cm relative to the center of the CMS detector. The average number of reconstructed primary vertices per event is approximately 15 for the 2012 data-taking period. The reconstructed primary vertex with the largest p 2 T of all associated tracks is assumed to be produced by the hard-scattering process. All reconstructed muons, electrons and charged hadrons used in this analysis are required to be associated with this primary vertex.
Muons are identified by performing a combined fit to position measurements from both the inner tracker and the muon detectors [31]. They are required to have p T > 25 GeV/c and |η| < 2.1.
Their associated tracks are required to have measurements in at least six of the inner tracker layers, including at least one pixel detector layer, a combined fit χ 2 per degree of freedom smaller than 10, and to be reconstructed using at least two muon detector layers. In addition, the transverse (longitudinal) impact parameter of the muon track relative to the reconstructed primary vertex is required to be smaller than 0.2 cm (0.5 cm).
Electrons are identified [32] as tracks reconstructed in the inner tracker with measured momenta compatible with their associated energy depositions in the ECAL. Electrons are required to have p T > 30 GeV/c and |η| < 2.5, with the exclusion of the transition region between barrel and endcaps defined by 1.444 < |η| < 1.566.
The transverse (longitudinal) impact parameter of the electron track relative to the reconstructed primary vertex is required to be smaller than 0.02 cm (0.1 cm). These requirements are tighter than in the case of muons in order to reject electrons originating from photon conversions, and misidentified hadrons coming from pileup collisions. Additional photon conversion rejection requirements [32] are also applied.
Muon and electron candidates are required to be isolated. Isolation is defined via the variable where p T is the lepton transverse momentum, E ch is the transverse energy deposited by charged hadrons in a cone with aperture Events with exactly one lepton candidate satisfying the above criteria are selected for further consideration. Events with one or more additional reconstructed muons (electrons) with p T > 10(15) GeV/c, |η| < 2.5, I rel < 0.2 are rejected.
All the particles identified by the PF algorithm that are associated with the primary vertex are clustered into jets using the anti-k T algorithm [33] with a distance parameter of 0.5. Corrections to the jet energy scale are applied to account for the dependence of the detector response to jets as a function of η and p T and the effects of pileup [34]. The energy of reconstructed jets in simulated events is also smeared to account for the 5-10% discrepancy in energy resolution that is observed between data and simulation [34]. At least five jets are required with p T > 70, 55,40,30,30 GeV/c and |η| < 2.4. The offline jet p T thresholds are chosen such that all selected jets are in the trigger efficiency plateau. In addition, at least one of these jets must be identified as originating from a b quark ("b tagging") by the "combined secondary-vertex" (CSV) algorithm tuned for high efficiency [35]. This algorithm combines information about the impact parameter of tracks and reconstructed secondary vertices within the jet. Its typical efficiency for tagging b-quark jets is about 80%, whereas the mistagging efficiency is about 10% for jets produced by the hadronization of light quarks (u, d, s) or gluons, and about 35% for jets from c quarks [35].

Tight selection
Two additional requirements define the tight event selection used for the signal search. The first is the presence of small missing transverse energy (E miss T ). In PF reconstruction, E miss T is defined as the modulus of the vector sum of the transverse momenta of all reconstructed particles (charged and neutral) in the event. The jet energy scale corrections are also used to correct the E miss T value [36]. In order to pass the tight selection, events are required to have E miss T < 20 GeV. The validity of the simulation for low-E miss T events is verified using a data sample enriched in Z + 4 jets → μ + μ − + 4 jets events. Events in this sample are required to have at least four jets with p T > 30 GeV/c and |η| < 2.4 in addition to two muons with p T > 20 GeV/c, |η| < 2.1, I rel < 0.10, and invariant mass in the range 76-104 GeV/c 2 . The E miss T distributions obtained in data and simulation for this event sample are shown in Fig. 1. The simulated distribution is normalized to that observed in data and the two agree within statistical uncertainties. The disagreement in overall yield before normalization is at the level of 7%, which is covered by statistical and theoretical [37] uncertainties. Very similar results are obtained with a di-electron data sample or by requiring five additional jets, instead of four, in either the muon or the electron data samples. With five additional jets, however, the statistical uncertainties are significantly larger.
The second requirement for an event to pass the tight selection is the compatibility of its kinematic properties with the final state produced by tt events where one top quark has a fully hadronic SM decay and the other the BNV decay. This compatibility is tested using the following variable: where the x i are the reconstructed invariant mass of the W boson from the hadronically decaying top quark, the reconstructed invariant mass of the hadronically decaying top quark, and the reconstructed invariant mass of the top quark with the BNV decay.
The values of x i and σ i are the expectation values and standard deviations of Gaussian fits to the x i distributions obtained from simulated tt events with the two top quarks undergoing the BNV and the fully hadronic SM decay, respectively. Simulation information is used to obtain the correct jet-to-parton association. The number of jet combinations is reduced by not associating jets tagged by the CSV algorithm with the W decay. All other combinations in the event are considered and the one with the smallest χ 2 is retained. For signal events, the correct jet combination is expected to be chosen in about 60% of the cases. In the tight selection, the smallest χ 2 is required to be less than 20.
The values of the thresholds on the lepton p T , E miss T , χ 2 , as well as the configuration of the b-tagging algorithm were chosen by minimizing the expected upper limit on B at 95% confidence level (CL). This procedure also retains high sensitivity for an observation of a BNV decay.

Signal search strategy
The search proceeds in the following way: for each assumed value of B, the expected contributions from tt (N B tt ) and tW (N B tW ) production to the yield in the basic selection are scaled such that the total expected yield is normalized to the observed number of events (N B obs ). The sum of the tt and tW yields in the tight selection (N T top ) is then extracted using the efficiencies, tW , to pass the tight selection for tt and tW events that satisfy the basic selection criteria. Finally, the comparison between the total expected and observed numbers of events in the tight selection, which is significantly more efficient for the signal than for the background, is used to infer the presence of a signal or set an upper limit on B. The impact of a number of systematic uncertainties is significantly reduced as a result of the normalization of simulation to data in the basic selection. Indeed, using this approach, the expected upper limit at 95% CL on B is found to improve by a factor of 2.5, while the expected significance of a signal-like deviation from SM expectations increases from about 1.2 standard deviations to 3.6 for a signal with B = 0.005. In this procedure we neglect the contributions to a possible BNV signal from events with single-top-quark production via s-and t-channels, ttW, and ttZ, which are treated as non-top background. These contributions are expected to be negligible, as can be inferred from the yields of these processes given in Tables 1 and 2, as estimated from simulation.
Following the approach outlined above, the expression for the expected total yield in the tight selection (N T exp ) is: where N B bck (N T bck ) is the yield of the non-top background (including s-and t-channel single-top-quark, ttW, and ttZ production events, as discussed above) in the basic (tight) selection.
All the quantities in the square brackets of Eq.
In Eq. (4), B tt ( T tt ) indicates the efficiency of the basic (tight) selection for tt events. Similarly, B tW ( T tW ) indicates the efficiency of the basic (tight) selection for tW events. Each of these four efficiency values is a function of B and of three (for tt events) or two (for tW events) efficiency values, which correspond to the different decay modes: where X = B, T with B and T denoting the basic and tight selection, respectively, and SM (BNV) indicating the SM (BNV) decay mode of the top quark. With the adopted approach, the search is mostly sensitive to uncertainties in the ratio of T SM,SM to B SM,SM , N B bck and N T bck .

Background evaluation
In order to evaluate the expected yield in the tight selection (Eq. (4)), a number of backgrounds need to be estimated.

Top-quark and electroweak backgrounds
The main background in this analysis is from tt events where one of the two top quarks decays to a lepton, a neutrino, and a b quark while the other one decays to three quarks. As described in Section 5, the estimates of the tt and tW yields require knowledge of the efficiencies for tt and tW events, which satisfy the basic selection criteria, to also pass the tight selection. These efficiencies are obtained from simulation. The required tt cross section is the prediction at next-to-next-to-leading order (NNLO) that includes soft-gluon resummation at next-to-next-to-leading log (NNLL) [38]. The tW cross section is the approximate NNLO prediction from soft-gluon resummation at NNLL [39].
The second-largest background is represented by W and Z production in association with jets. The theoretical predictions for the W + jets → ν + jets and Z/γ * + jets → + jets processes, where indicates a lepton, are computed by fewz [40,41] at nextto-next-to-leading order. The efficiencies for events produced by these processes to pass the basic and tight selections are evaluated from simulation and, using the measured value of the integrated luminosity [42], the yields in the basic and tight selections are obtained.
The contributions to the yield in the basic and tight selections from single-top-quark production via s-and t-channel processes, and from WW, WZ, ZZ, ttW, and ttZ production, are also evaluated from simulation. The cross section value for single-top-quark production via s-channel is computed using next-to-next-to-leadinglogarithm resummation of soft and collinear gluon corrections [43]. The cross section values for ttW and ttZ are computed at leadingorder (LO) as provided by MadGraph, including the contributions at LO from processes yielding one extra jet. In all other cases the next-to-leading order (NLO) theoretical predictions, as obtained from mcfm [44], are used. The sum of yields predicted by the simulation for all these processes is less than 1% of the total expected yield in both the basic and tight selections.
All cross section values used in the analysis are listed in the second column of Tables 1 and 2. The yields reported in these tables are discussed in Section 8.

QCD multijet background
The QCD multijet background yields are evaluated with two methods, depending on the event selection.
In the first method the isolation requirements for the leptons are inverted (becoming 0.12 < I rel < 0.2 for muons and 0.10 < I rel < 0.2 for electrons) in order to enhance the presence of QCD multijet events. These selections are denoted as anti-isolated basic and anti-isolated tight in the following, as opposed to the (isolated) basic and tight selections used in the analysis. The yield of the QCD multijet background in either the tight or basic selection (N QCD ) can thus be inferred using the following equation: where R is the ratio of the numbers of QCD multijet events in the isolated and anti-isolated selections, N antiiso data is the yield observed in data in the anti-isolated selection, and N antiiso nonQCD is the contribution in the anti-isolated selection from other SM processes. The value of N antiiso nonQCD is estimated from simulation using the cross section values discussed in Section 6.1. The value of R is estimated from data using the approximation is the so-called "misidentification rate". The misidentification rate is defined as the probability that a genuine jet that has passed all lepton-identification criteria and a looser isolation threshold (I rel < 0.2) also passes the final analysis isolation threshold. The value of f is obtained from data in five lepton p T bins using a sample of events enriched in Z + jets → μ + μ − + jets events, where a third, loosely isolated lepton, a muon or an electron, is also found. The estimate of the QCD multijet yield is then determined using Eq. (7) in each lepton p T bin. The misidentification rate is measured with events whose topology is different from that of events in the final selection. This difference gives rise to the dominant uncertainty in the estimation of the misidentification rate, which is assessed to be 20% from the difference observed in simulation between the true and predicted yields. The systematic uncertainty in N antiiso nonQCD is in the range 20-25% depending on the selection. After also taking into account the statistical uncertainties, this results in a 50. In the case of the muon basic selection the systematic uncertainty in N antiiso nonQCD is larger than the difference N antiiso data − N antiiso nonQCD and therefore prevents a sufficiently accurate estimate of the QCD multijet yield. For this reason, a second method, which is described Table 1 Muon channel: assumed cross section values, expected (as discussed in Section 6) and observed yields in the basic and tight selections for an assumed B value of zero. The "Basic" and "Corrected basic" columns report the yields in the basic selection before and after the normalization procedure described in Section 5. The uncertainties include both statistical and systematic contributions. Many of the reported uncertainties are either correlated or anticorrelated, which explains why the uncertainties in the total expected yields are smaller than those in some of their components. By construction the total expected yield after the normalization procedure is equal to the observed yield.  Table 2 Electron channel: assumed cross section values, expected (as discussed in Section 6) and observed yields in the basic and tight selections for an assumed B value of zero. The "Basic" and "Corrected basic" columns report the yields in the basic selection before and after the normalization procedure described in Section 5. The uncertainties include both statistical and systematic contributions. Many of the reported uncertainties are either correlated or anticorrelated, which explains why the uncertainties in the total expected yields are smaller than those in some of their components. By construction the total expected yield after the normalization procedure is equal to the observed yield.  Table 3 Muon and electron channels: numbers relevant for the estimate of the QCD multijet yield based on the misidentification rate measurement (Eq. (7)). Only the average value of f is reported, while values computed in bins of p T are used in the analysis. below, is used for this specific selection. In the electron analysis the uncertainties in the QCD multijet background estimates in the basic and tight selections are treated as fully correlated. The numbers relevant for the QCD multijet yield estimation with this first method are given in Table 3.
In the second method the assumption is made that E miss T and χ 2 are not correlated for QCD multijet events, and the estimated QCD multijet yield in the basic selection (N B QCD ) is obtained from the following equation: where N T QCD is the QCD multijet yield in the tight selection, as obtained with the first method, and E miss T ( χ 2 ) is the probability that a QCD multijet event that passes the basic selection has E miss T < 20 GeV (χ 2 < 20). The values of E miss T and χ 2 are taken from simulation. A total uncertainty of 50% in the product of E miss T and χ 2 is assumed, which yields, together with the 50% uncertainty in N T QCD , an overall 70% uncertainty in the estimate of the QCD multijet background in the muon basic selection. The partial correlation with the uncertainty in the QCD multijet background estimate in the muon tight selection is taken into account when determining the final results of the analysis. The numbers relevant for the QCD multijet yield estimation in the muon basic selection with this second method are given in Table 4.
In the electron analysis the contribution of γ + jets processes can potentially give rise to events that pass the basic and the tight selections. The isolated photon in the event can convert before reaching the calorimeters and be identified as a single isolated electron. From simulation studies it turns out that the central values of the QCD multijet yields estimated with the first method in both the basic and tight selections need to be increased by 2% to account for this contribution.

Systematic uncertainties
The observable of the likelihood function used in the analysis is the yield in data for the tight selection (N T obs ), while the parameter of interest is B. A number of other quantities appear in the likelihood function and affect the estimate of N T exp . They are N B bck , N T bck , the ratio σ tW /σ tt , and the ten efficiencies in Eqs. (4)- (6). They are estimated as described in Section 6. Many of these quantities are correlated because of common sources of systematic uncertainties. These correlations are handled using the method presented in Ref. [45], where the j-th source of systematic uncertainty is associated with a nuisance parameter of true value u j constrained by a normal probability density function (PDF) G(u j ). The method results in the parameterization, θ i (u j ), of the i-th likelihood quantity θ i in terms of all the u j nuisance parameters. Other quantities in the likelihood function are instead either assumed to be independent of any other (σ tW , σ tt , and N B obs ) or correlated with a single other quantity (the QCD multijet contributions to N B bck and N T bck ). In these cases the quantities are simply constrained in the likelihood function by a lognormal PDF ρ k (θ k | θ k ), which describes the probability of measuring a valueθ k for the k-th likelihood quantity should its true value be θ k , and which takes into account possible correlations. With this approach, the likelihood function L reads: (9) where P(N T obs | N T exp (B, θ i (u j ), θ k )) indicates the Poisson PDF evaluated at N T obs and with expectation value N T exp (B, θ i (u j ), θ k ) given by Eq. (4). The sources of systematic uncertainty are discussed below. Unless specified otherwise, each source of systematic uncertainty is varied by ±1 standard deviation to infer the relative variation in each of the quantities appearing in the likelihood function.
The uncertainty in the simulated jet energy scale depends on the jet p T and η, and is smaller than 3% [34]. This uncertainty is also propagated to the simulated E miss T calculation. It induces uncertainties of the order of 10% in the efficiency values and in the W/Z + jets contributions to N B bck and N T bck , but its impact on the final limits remains very limited because of the highly correlated effects on these quantities.
The jet energy resolution is varied in the simulation within its uncertainty, which is of the order of 10% [34]. This uncertainty is also propagated into the simulated E miss T calculation. Although it induces a relative change in the efficiency values and in the W/Z + jets yield of less than 5%, it is one of the sources of uncertainty with the largest impact on the final limits. In fact assuming no uncertainty in the jet energy resolution causes the expected upper limit at 95% CL on B to decrease by about 15%.
The uncertainty in the yield of the QCD multijet background is discussed in Section 6.2. This uncertainty has a significant impact only in the electron analysis, where its effect is comparable to that of the jet energy resolution uncertainty.
The uncertainties in the cross section values of the W + jets and Z + jets backgrounds largely dominate the uncertainty in the values of N B bck and N T bck for the muon analysis, whereas in the electron analysis they are comparable to the uncertainty in the QCD  [0.0016, 0.0046] multijet contribution. As described in Section 6, the W + jets and Z + jets cross section values used in this analysis are the theoretical inclusive predictions, which have an uncertainty of about 5% [46]. The CMS measurement [47] of the ratio of the W + 4 jets to the inclusive W cross section (the result for W + 5 jets is not available) is in agreement with the MadGraph predictions within the measurement uncertainty, which is at the level of 30%. In addition, the limited number of events in the simulated W + jets and Z + jets samples introduces a statistical uncertainty of about 10% in the yield of these processes in the tight selection. Taking these contributions into account, a conservative uncertainty of 50% in the W + jets and Z + jets cross sections is assumed. This uncertainty is found to have an impact comparable to that of the jet energy resolution on the final limits. The uncertainties in the final results, related to the factorization and renormalization scales and to the matching thresholds used for interfacing the matrix elements generated with MadGraph and the pythia parton showering, are evaluated with dedicated simulated data samples where the nominal values of the thresholds or scales are halved or doubled. The uncertainty in the scales is found to have an impact on the final limits comparable to that of the jet energy resolution uncertainty, while the impact of the uncertainty in the matching thresholds is almost a factor of two smaller than that of the jet energy resolution. The simulated samples are generated using the CTEQ 6.6 parton distribution functions [48]. The impact of the uncertainties in the parton distribution functions is studied following the PDF4LHC prescription [49][50][51][52][53] and is found to be very close to that of the matching thresholds.
A number of other sources of systematic uncertainties are found to have a negligible impact on the final results. They are summarized in the following. The uncertainty in the efficiency of the lepton trigger, identification, and isolation is assessed to be 5% [31,32] for both muons and electrons. Unclustered reconstructed particles are also used to compute E miss T [36], and thus an uncertainty in the model provided by simulation of these particles is reflected in an uncertainty in the final E miss T calculation. The associated systematic uncertainty is estimated by varying the contribution of unclustered particles to E miss T by ±10%. An uncertainty of 5% in the estimated mean number of pileup collisions is assumed. An uncertainty of 2.6% is assigned to the integrated luminosity [42]. This uncertainty affects only N B bck and N T bck , but is negligible compared with other sources of uncertainty. The uncertainty in the b-tagging efficiency results in an uncertainty in the event selection efficiency in the range 1% to 5% depending on the number, energy, η, and type of the jets in the event [35]. The consequent uncertainty induced in N T exp is about 3% for both the muon and electron channels. The uncertainties in the tt and tW production cross section values are about 5% [38] and 7% [39] arising from the uncertainties in the factorization and renormalization scales, the parton distribution functions and, in the case of the tt cross section, the top-quark mass. These two uncertainties affect the ratio σ tW /σ tt in Eq. (4) and are conservatively assumed to be uncorrelated. The uncertainties in the yields from the WW, WZ, and ZZ processes, as well as from s-and t-channel single-top-quark production are neglected since these processes make only small contributions to N B bck and N T bck . The central values and the overall uncertainties in the quantities used for the calculation of the likelihood function are reported in Table 5 for both the muon and electron analyses.

Results
Tables 1 and 2 report the yields expected from the different SM processes considered, and the yields observed in data for the muon and electron channels, respectively. In these tables B is assumed to be zero. The yields of the tt and tW processes in the basic selection before and after the normalization procedure described in Section 5 are both reported, the yields before normalization being simply calculated as the products of the theoretical cross sections, the measured values of the integrated luminosity, and the event selection efficiencies obtained from simulation. Because of the normalization procedure many of the uncertainties reported in Tables 1 and 2 are correlated or anticorrelated, which explains why the uncertainties in the total expected yields are smaller than those in some of their components. In both the muon and electron channels the observed total yield in the tight selection agrees with the SM expectations. Fig. 2 (Fig. 3) shows, for the muon (electron) channel, the observed and expected distributions of E miss T and χ 2 for the basic and tight selections assuming no BNV top-quark decays. The signal distribution expected for B = 0.005 is also shown. The methods adopted for the QCD multijet background estimates provide no detailed shape information for this contribution. Thus, for the sake of illustration in the plots, the shape of the QCD multijet background contribution in the E miss T distribution is obtained from simulation using events with at least three jets, instead of five, in order to reduce large statistical fluctuations. In the case of the χ 2 variable, whose calculation requires events with at least five jets, the shape of the QCD multijet background contribution is obtained from data in the anti-isolated regions defined in Section 6.2 after subtraction of the top-quark and electroweak components estimated from simulation. The discrepancy visible between the observed and expected E miss T distributions in the electron channel basic selection can be accommodated with the 50% uncertainty assumed in the total QCD multijet yield. These distributions are presented for purposes of illustration and are not used in the analysis.
The observed data samples are then used to calculate upper limits on the value of B. The upper limit on B at 95% CL is obtained with the Feldman-Cousins approach [54]. Pseudoexperiments are generated using the frequentist prescription described in Ref. [55]. The results are summarized in Table 6 for the muon and electron channels, and for their combination. The combined results are obtained by maximizing the product of the two likelihood functions, assuming a common value of B for the two channels.
Full correlation is assumed for each pair of corresponding nuisance parameters in the two analyses, except for those related to the lepton trigger, identification, and isolation, which are assumed to be independent. The combination of the muon and electron datasets does not significantly improve the upper limit because of the dominant systematic uncertainties related to the modeling of jets, E miss T , and event kinematic properties, which are fully correlated across the two channels.

Summary
Data recorded by the CMS detector have been used to search for baryon number violation in top-quark decays. The data correspond to an integrated luminosity of 19.52 ± 0.49 fb −1 at √ s = 8 TeV.
No significant excess is observed over the SM expectation for events with one isolated lepton (either a muon or an electron), at least five jets of which at least one is b tagged, and low missing transverse energy. These results are used to set an upper limit of 0.0016 (0.0017) at 95% confidence level on the branching fraction of a hypothetical baryon number violating top-quark decay into a muon (electron) and 2 jets. The combination of the two channels under the assumption of lepton universality yields an upper limit of 0.0015. These limits on baryon number violation are the first that have been obtained for a process involving the top quark.

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.