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Introduction
Many theories beyond the standard model (BSM) predict enhanced production of events with large missing energy in association with a single reconstructed object. Such events have been searched for at the large hadron collider (LHC), when the single object is either a photon [1,2], a jet [3,4], or a W or Z boson [5,6]. This paper presents a search for singly produced top quarks in association with significant missing energy, corresponding to the associated production of one or several undetected neutral particles, and without any other reconstructed object. These neutral particles can be either stable and/or weakly interacting with ordinary matter -providing an interesting interpretation in terms of dark-matter candie-mail: atlas.publications@cern.ch dates -or long-lived and decaying outside of the detector. The observation of such final states, commonly referred to as monotop events, would be evidence for new phenomena. Moreover, processes involving top quarks are sensitive to BSM physics, due to the large mass of this standard model (SM) particle which is close to the electroweak symmetrybreaking scale.
No such process is possible in the SM at tree level: the direct production of a top quark and a Z boson decaying into a pair of neutrinos, without any additional quark, is suppressed by the Glashow-Iliopoulos-Maiani mechanism [7].
This search is performed with the ATLAS detector [8] in pp collisions at √ s = 8 TeV with the data collected in 2012 at the LHC and corresponding to an integrated luminosity of 20.3 fb −1 . The ATLAS detector covers the pseudorapidity range |η| < 4.9 and the full azimuthal angle φ. 1 It consists of an inner tracking detector covering the pseudorapidity range |η| < 2.5 surrounded by a superconducting solenoid, electromagnetic and hadronic calorimeters, and an external muon spectrometer with large superconducting toroidal magnets.
The search is based on the analysis of top-quark events where the W boson from the top quark decays into a lepton and a neutrino. Previous results of a search for monotop production, exploiting the case of fully hadronic topquark decays, have been published by the CDF Collaboration using p p collision data at √ s = 1.96 TeV, corresponding to an integrated luminosity of 7.7 fb −1 [9], and more recently by the CMS Collaboration using pp collision data at √ s = 8 TeV, corresponding to an integrated luminosity of 19.7 fb −1 [10]. 1 The ATLAS experiment uses a right-handed coordinate system with its origin at the nominal interaction point (IP) in the centre of the detector and the z-axis along the beam pipe. The x-axis points from the IP to the centre of the LHC ring, and the y-axis points upwards. Cylindrical coordinates (r, φ) are used in the transverse plane, φ being the azimuthal angle around the beam pipe. The pseudorapidity is defined in terms of the polar angle θ as η = − ln tan(θ/2).

Signal models
Many theoretical models predicting the production of monotop events in hadron colliders have been proposed. In a first class of theories, a charged resonance is produced by down-type antiquark fusion and decays into a top quark and a neutral particle, as in SU (5) models [11], in R-parityviolating SUSY [12] or in hylogenesis models [13,14]. In a second class of theories, the monotop final state is produced through a non-resonant process, as in R-parity-conserving SUSY [15], or in models where an interaction of a gluon with an up-type quark allows production of a set of invisible particles via a u-t or c-t coupling [16][17][18][19].
Because of the variety of these theories, effective models [20,21] are used for the search reported in this paper. Furthermore, as minimal extensions of the SM, the effective models tested in this search are required to respect the electroweak gauge structure [22]. The possibilities for monotop production in pp collisions considered are thus: • Resonant production of a +2/3 charged spin-0 boson, S, decaying into a right-handed top quark and a neutral, colour singlet, spin-1/2 fermion, f met ; • Non-resonant production of a neutral, colour singlet, spin-1 boson, v met , in association with a right-handed top quark.
The Feynman diagrams for monotop production in the resonant and non-resonant models are shown in Fig. 1. Each of these effective models corresponds to one of the two classes of BSM theories detailed above. A detailed study of the phenomenology of the resonant model is available in Ref. [23]. The interaction Lagrangians of the resonant and non-resonants models are given in Eqs. (1) and (2), respectively.
The fields ϕ, χ , and V μ correspond to the S, f met , and v met exotic particles, respectively, the field u (d) represents an uptype (down-type) quark, (a q res ) i j , (a 1/2 res ) k , and (a non-res ) i j are the coupling matrices in the quark-flavour space, the indices i, j, k, represent the quark-generation number, and αβγ is the fully antisymmetric tensor, the indices α, β, and γ being the colour indices. The superscript c denotes the charge conjugation. The number of free parameters is reduced by assuming (a q res ) 12 = (a q res ) 21 = (a 1/2 res ) 3 ≡ a res for the resonant model and (a non-res ) 13 = (a non-res ) 31 ≡ a non-res for the nonresonant model, all other elements of these coupling matrices being equal to 0. For each model, the coupling parameter a res or a non-res and the masses of the exotic particles are independent.
The choice of model parameters -the effective couplings and the masses of the particles -is driven by phenomenological considerations: the particles f met and v met in the resonant and non-resonant models, respectively, are required to have missing transverse momentum as an experimental signature. For the resonant model, in which the f met fermion can decay into a five-body final state, Ref. [23] suggests that for m(S) = 500 GeV and an effective coupling of a res = 0.2, the decay length of f met is large enough to be considered as invisible for the detector, as long as m( f met ) is below 100 GeV. For the non-resonant model, in which the v met boson can decay into a two-body final state either through a tree-level or a loop-induced interaction, Ref. [22] assumes that the v met boson decays into a set of invisible particles which can be dark-matter candidates. This assumption follows the spirit of several BSM models [16][17][18]. Hence, the v met particle in the non-resonant model can be considered to be an invisible spin-1 state with mass m(v met ). Studies of possible direct and indirect constraints on monotop model parameters using experimental signatures other than monotop processes are discussed in Refs. [22,23]. The data used for this analysis are selected from the recorded data streams using single-electron and single-muon triggers [24]. Stringent detector and data quality criteria are applied offline, resulting in a data sample corresponding to an integrated luminosity of 20.3 ± 0.6 fb −1 [25].
The signal samples are generated at leading order (LO) in QCD with the matrix-element generator MadGraph5 v1. 5.11 [26] using FeynRules [27][28][29] and interfaced with Pythia v8.175 [30,31] for parton showering and hadronisation. The parton distribution function (PDF) set MSTW2008LO [32,33] is used. Resonant signal samples are generated with the mass of the invisible state f met varying from 0 to 100 GeV, the mass of the S resonance being fixed at 500 GeV -following the suggestion in Ref. [23] -and non-resonant signal samples are generated with the mass of the invisible state v met varying from 0 to 1,000 GeV. The couplings a res and a non-res are set at a fixed value of 0.2. In addition, two samples are produced for the resonant model for m( f met ) = 100 GeV, with coupling strengths fixed at a res = 0.5 and a res = 1.0, in order to check the effect of the resonance width on the signal event kinematics. The total width of the resonance varies quadratically with the coupling strength, corresponding to a width of 3.5, 21.6, and 86.5 GeV at a res = 0.2, a res = 0.5, and a res = 1.0, respectively.
The tt cross-section for pp collisions at a centre-of-mass energy of √ s = 8 TeV is σ tt = 253 +13 −15 pb for a topquark mass of 172.5 GeV. It has been calculated at nextto-next-to-leading order (NNLO) in QCD including resummation of next-to-next-to-leading logarithmic ( The Alpgen LO generator v2.14 [53] is used with Pythia v6.426 to generate events with a W boson produced in association with light or heavy quarks (W +light-quarks, W +bb, W +cc, W +c) and Z +jets events. The Alpgen matrix elements include diagrams with up to five additional partons.
To remove overlaps between the n and n + 1 parton samples the MLM matching scheme [54] is used. Double counting between the W +n parton samples and samples with associated heavy-quark pair production is removed utilising an overlap removal based on a R = ( η) 2 + ( φ) 2 matching criterion. Diboson samples (W W , Z Z, and W Z) where at least one of the bosons decays leptonically are modelled by Herwig v6.52 [55]. The single-boson and diboson simulation samples are normalised to the production cross-sections calculated at NNLO [56,57] and NLO [58], respectively.
After event generation, all signal and background samples are passed through the full simulation of the ATLAS detector [59] based on GEANT4 [60] and reconstructed using the same procedure as for collision data. All Monte Carlo (MC) samples are simulated with pile-up 2 and re-weighted to have the same distribution of the mean number of interactions per bunch-crossing as in the data sample (20.7 on average).

Selection and background estimation
The experimental signature of the monotop events is one isolated charged lepton (electron or muon) from the W decay, large missing transverse momentum, and one jet identified as likely to have originated from a b-quark (b-tagged).
Electrons are identified as energy clusters in the electromagnetic calorimeter matched to reconstructed tracks in the inner detector [61-63]. Electron candidates are required to be isolated from other objects in the event and from hadronic activity to reduce the contamination by mis-reconstructed hadrons, electrons from heavy-flavour decays, and photon conversions. Muons are reconstructed using information from the muon spectrometer and the inner detector [64]. An isolation criterion [65] is applied to reduce the contribution of muons from heavy-flavour decays. The reconstructed charged lepton is required to have a transverse momentum p T > 30 GeV to ensure a constant trigger efficiency and to have |η| < 2.5 for muons and |η| < 2.47 for electrons (for the latter, the electromagnetic calorimeter barrel-endcap transition region 1.37 < |η| < 1.52 is excluded).
Jets are reconstructed using the anti-k t algorithm [66] with a radius parameter R = 0.4 and calibrated to the hadronic energy scale [67]. Jets are required to have p T > 25 GeV and |η| < 2.5. To suppress jets from in-time pileup, at least 50 % of the scalar p T sum of the tracks associated with a jet is required to be from tracks associated with the primary vertex. This jet vertex fraction requirement is applied only for jets with p T < 50 GeV and |η| < 2.4.
Exactly one jet is selected, and is required to be b-tagged. The main background to this final-state selection are tt pairs where both top quarks decay semi-leptonically, t → νb, with large E miss T due to one lepton and one jet not being reconstructed, and W +jets production, particularly with jets from heavy-flavour quarks. The background from multijet production due to misidentification as leptons is reduced by imposing a requirement on the sum of the E miss and t Z processes [72] in the Z → νν decay mode are found to be negligible.
A counting experiment approach is followed. The monotop signal is prominent in regions of the phase space characterised by high m T ( , E miss T ) values, as suggested by Refs. [18,21]. Hence, in addition to the pre-selection described previously, a criterion requiring m T ( , E miss T ) > 150 GeV is used to define the signal region. In order to improve the sensitivity of the search, an optimisation of the event selection is performed with simulated data, using wellmodelled variables. The lepton and the b-tagged jet are closer to each other when originating from the decay of a top quark than in the case of W +jets and multijet background events. Hence, a criterion imposing the rejection of events with large values of the difference in azimuth between the lepton and the b-tagged jet | φ( , b)| is tested, together with increased m T ( , E miss T ) threshold values. Figure 2 shows the distributions of these two variables for the expected background contribution, and for two mass hypotheses considered for each signal model. For each set of cuts on m T ( , E miss T ) and | φ( , b)|, the sensitivity is estimated by calculating the expected limit on the production cross-section with the procedure described in Sect. 6 including the systematic uncertainties detailed in Sect. 5. The optimisation was performed using one mass hypothesis m( f met ) = 100 GeV for the resonant model, for which the kinematic distributions have only small variations in the studied mass range. For the non-resonant model, characterised by larger variations of the kinematic distributions with v met , four signal mass hypotheses were studied: m(v met ) = 0, 100, 300, and 600 GeV. The resulting bestperforming selections, for the tested mass hypotheses, are: In order to validate the background model, three control regions orthogonal to the signal region are defined. Figure 3 is a sketch describing the signal and control regions in the (m T ( , The first control region (CR1) is enriched in W +jets and multijet background events by requiring events to satisfy 60 GeV < m T ( , E miss T ) < 120 GeV in addition to the pre-selection criteria. In the second control region (CR2) with a kinematic regime closer to the one of the signal region, the pre-selected events are required to satisfy 120 GeV < m T ( , E miss T ) < 150 GeV and the azimuthal separation φ( , b) between the lepton and the b-tagged jet must be less than 1.8. Finally, the third control region (CR3) is defined in order to validate the modelling of the background arising from tt events. An event sample dominated by tt events is obtained by selecting events with a second b-tagged jet; both b-tagged jets are identified with a b-tagging criterion with an efficiency of 80 %, the sub-leading jet satisfies p T < 50 GeV, and the events must satisfy m T ( , E miss T ) > 150 GeV and | φ( , b)| < 1.8 in addition to the pre-selection criteria. The distributions of m T ( , E miss T ) and of φ( , b) in the three control regions are depicted in Fig. 4. Reasonable agreement between the data and the predicted background estimate is found.

Systematic uncertainties
The impact of systematic uncertainties is considered on the yields of individual background and signal processes. The main systematic uncertainties are those related to the jet energy scale, the b-tagging efficiency, the effect of the choice of PDF on signal and background acceptance, the effect of the choice of MC generator and of additional radiation on tt modelling, and the effect of the limited size of the samples.

Sample size
Due to the stringent kinematic cuts in the signal regions, the impact of the limited size of the data and simulated samples on the signal and background estimates is a significant source of systematic uncertainty. For the Z +jets, multijet, and single-top-quark s-and t-channel processes, the expected event yield is zero in both channels, for the SRI and SRII selections, respectively. In such cases, a 68 % confidence level (CL) upper limit on the yields is calculated, assuming a Poisson distribution, and is taken into account in the limit-setting procedure. This upper limit represents at most 10 % of the background contribution.
For the other processes, which have non-negligible contributions, the effect of the limited sample size on expected signal (background) yields varies between 2 and 5 % (2 and 9 %).

Object modelling
The effect of the uncertainty on the jet energy scale [67] is a change in the signal (background) event yields of 1-5 % (9-10 %), depending on the channel and on the signal region. The impact of the jet energy resolution uncertainty, evaluated by smearing the jet energy in the simulation [73], is a 2-3 % (1-2 %) effect on the signal (background) rates. The systematic uncertainty associated with the efficiency of the cut on the jet vertex fraction results in yield variations of 2-3 % (2-6 %) in the signal (background). Uncertainties on b-tagging efficiency and mistagging rates are estimated from data [68]; the effect on signal and background yields is 3-5 %. The jet reconstruction efficiency uncertainty has an effect below 1 %, except for the background in the SRII region (up to 3 %).
Smaller uncertainties arise from the lepton trigger, reconstruction, and identification efficiencies (up to 1 %) and from lepton energy scale and resolution (up to 1 % for signal and between 1 and 3 % for background). The systematic uncertainties related to leptons and jets are propagated to the E miss T . In addition, uncertainties on the estimation of the contributions of calorimeter energy deposits not associated with any reconstructed objects have an effect below 1 % (up to 4 %) on expected signal (background) contribution.

Signal and background acceptance modelling
The uncertainties on the signal and background acceptance due to the choice of PDF are estimated using the The dependence of the tt process on the generator and parton showering simulation is evaluated by comparing the nominal sample produced with Powheg+Pythia with three samples generated using the CT10 PDF, one sample produced with Powheg-Box v1_r2129, one sample using the Alpgen LO multileg generator v2. 14  for the underlying event. The largest variation, representing 5-11 % of the total background yield, arises from the comparison with the Alpgen+Herwig sample. For W t production, the nominal Powheg+Pythia sample is compared with a sample produced with MC@NLO v4.06, leading to a variation of 4-6 % on the total background yield. Furthermore, the uncertainty associated with the NLO calculation schemes for the W t process is evaluated by comparing the nominal sample generated with the diagram removal scheme to a sample using the diagram subtraction (DS) scheme [78]; this uncertainty is 3-5 % on the total background yield.
The dependence of the tt event rate on additional radiation is evaluated using a tt sample generated with the AcerMC LO generator v3.8 [38,39], with the CTEQ6L1 PDF set [40], and coupled with Pythia v6.426. The Pythia parameters are varied in a manner consistent with a measurement of tt production with additional jet activity [79]. The related variation in the total background is around 5 % (9 %) in the SRI (SRII) region.

Background normalisation
Theoretical uncertainties are −5.9/+5.1 % for the inclusive tt cross-section [41-47], and 6.8 % for the W t-channel cross-section [51]. An uncertainty of 24.5 % on diboson and W +light-quarks rates is also assigned. These estimates come from the uncertainty on the inclusive diboson and W -boson production cross-sections [57] (5 and 4 %, respectively) and from a conservative assessment based on a prediction for the ratio of the event rate with n + 1 jets to the event rate with n jets [80,81], resulting in 24 % per additional jet, added in quadrature. A 50 % uncertainty, as evaluated in Ref. [82], is assigned to the W +bb, W +cc, and W +c rates.

Luminosity
The uncertainty on the integrated luminosity is 2.8 % [25], affecting the signal estimates as well as the simulated backgrounds. ical cross-sections, and the expected resonant (non-resonant) signal is normalised to the theoretical cross-section corresponding to a res = 0.2 (a non-res = 0.2). The error bands on the expected backgrounds correspond to the uncertainties due to all systematic sources added in quadrature. The first (last) bin includes underflows (overflows). The ratios of the observed distributions to the predicted background distributions are shown in the lower frame Table 1 Expected and observed event yields in the SRI (SRII) signal region, combining the electron and muon channels. The expected contribution of resonant (non-resonant) signal corresponding to the lowest and highest mass hypotheses considered in this analysis and of SM backgrounds are given. The first quoted uncertainty gives the uncertainty due to statistics. The second one gives the uncertainties due to all other systematic effects, symmetrised, regrouped, and summed quadratically, without taking into account possible anticorrelations between systematic uncertainties and between processes, for the purpose of this W +light-quarks 2 ± 2 ± 4 3 ± 3 ± 4 W +bb 10 ± 3 ± 5 9 ± 3 ± 7

Results and interpretation
Total background 240 ± 10 ±50 124 ± 11 ±27   respectively. The predicted signal cross-sections for different coupling strengths are also shown resonant) signal contribution for the m( f met ) = 100 GeV (m(v met ) = 700 GeV) hypothesis, normalised to the theoretical cross-section corresponding to a res = 0.2 (a non-res = 0.2), is also shown. Table 1 reports the expected event yields for the background and signal processes and the observed event yields in the SRI and SRII signal regions. As no excess is observed in data, 95 % CL upper limits on the signal production crosssections are set with the CL s procedure [83,84]. A loglikelihood ratio (LLR) is used as the test statistic, defined as the ratio of the signal-plus-background hypothesis to the background-only hypothesis. For a given hypothesis, the combined likelihood is the product of the likelihoods for the two channels considered (electron and muon), each resulting from the product of a Poisson distribution representing the statistical fluctuations of the expected total event yield, and of Gaussian distributions representing the effect of the systematic uncertainties. Pseudo-experiments are generated for both hypotheses, taking into account correlations across channels and processes. The fraction of pseudo-experiments for the signal-plus-background (background-only) hypothesis with LLR larger than a threshold defines CL s+b (CL b ). This threshold is set to the observed (background median) LLR for the observed (expected) limit. Signal cross-sections for which CL s = CL s+b /CL b < 0.05 are considered excluded at the 95 % CL. Figure 6 shows the expected and observed 95 % CL excluded cross-section times branching ratio as a function The cross-sections are proportional to the square of the effective coupling. Thus, a 95 % CL upper limit on a res and a non-res as a function of the mass of the invisible states is extracted. The results are shown in Fig. 7. This upper limit is set assuming that the coupling has no effect on the signal acceptance modelling. In the case of the resonant model, in which the increase of the resonance width with increasing coupling strength changes the signal kinematics, this assumption is validated by using two dedicated simulated samples produced with a res = 0.5 and a res = 1.0 instead of a res = 0.2. These two hypotheses are excluded at 95 % CL with the same limit-setting procedure. Since the kinematic distributions are similar in the whole m( f met ) range, this assumption is valid for all values of the f met mass. Tables 2  and 3 give the expected and observed 95 % CL upper lim- its on the effective coupling as a function of the mass of the invisible state, for the resonant and non-resonant model, respectively.

Summary and conclusion
Monotop events are searched for in the √ s = 8 TeV pp collision data collected in 2012 by the ATLAS experiment at the LHC corresponding to an integrated luminosity of 20.3 fb −1 . Two classes of signal models are studied, producing right-handed top quarks together with exotic neutral particles giving rise to missing energy. The semi-leptonic decay mode of the top quark is exploited: events with one isolated electron or muon and one b-tagged jet are selected. No significant deviation from the standard model predictions is observed. Upper limits on the signal cross-sections and on the corresponding effective couplings are set at 95 % CL using the CL s method. In the case of the production of a 500 GeV spin-0 resonance, effective coupling strengths above a res = 0.15 are excluded for a mass of the invisible spin-1/2 state between 0 and 100 GeV. In the case of non-resonant production, effective coupling strengths above a non-res = 0.1, 0.2, and 0.3 are excluded for a mass of the invisible spin-1 state up to 432, 657, and 796 GeV, respectively. The observed 95 % CL limits are compatible with the expectations.