Measurement of $t$-channel single-top-quark production in $pp$ collisions at $\sqrt{s} = 5.02$ TeV with the ATLAS detector

The observation of the electroweak production of single-top-quarks is made using 255 $\text{pb}^{-1}$ of proton-proton collision data recorded at $\sqrt{s} = 5.02$ TeV with the ATLAS detector at the Large Hadron Collider. An event selection is used to identify single-top-quark candidates arising from $t$-channel production with the top quark decaying semi-leptonically. Events passing the selection are then used to measure the inclusive cross-section for the combined production of single-top-quarks and antiquarks, $\sigma({tq + \bar{t}q})$, and the ratio $R_t$ between these two. They are measured to be $\sigma({tq + \bar{t}q}) = 27.1^{+4.4}_{-4.1} (\text{stat.}) ^{+4.4}_{-3.7} (\text{syst.})$ pb and $R_t = 2.73^{+1.43}_{-0.82} (\text{stat.}) ^{+1.01}_{-0.29} (\text{syst.})$. The individual single-top-quark ($t q$) and single-top-antiquark ($\bar{t} q$) production cross-sections are measured to be $\sigma(t q) = 19.8^{+3.9}_{-3.1} (\text{stat.}) ^{+2.9}_{-2.2} (\text{syst.})$ pb and $\sigma(\bar{t}q) = 7.3^{+3.2}_{-2.1} (\text{stat.}) ^{+2.8}_{-1.5} (\text{syst.})$ pb. All measurements are in good agreement with the Standard Model predictions.


Introduction
Top quarks can be produced in pairs via the strong interaction or singly via the electroweak interaction at hadron colliders [1].Single-top-quark production was first observed in anti-proton-proton collisions at the Tevatron [2][3][4] and since then it has been extensively studied as a window into the properties of the top quark itself [5].These include studies of the unitarity of the Cabibbo-Kobayashi-Maskawa matrix [4,[6][7][8], tests of higher-order corrections from quantum chromodynamics (QCD) [9], and constraints on the parton distribution functions (PDF) of the proton [10].
Electroweak theory predicts three primary mechanisms for single-top-quark production in proton-proton (pp) collisions at the Large Hadron Collider (LHC): -channel, -channel, and  (or -associated) production.The -channel mechanism for single-top-quark production, shown in Figure 1, has the largest cross-section of the three mechanisms and also the final-state topology with the highest signal-to-background ratio, due to the presence of a light-quark jet recoiling against the top quark that assists in identifying this topology.The -channel production cross-section, ( + t), was measured by both the ATLAS and CMS collaborations at centre-of-mass energies of √  = 7 TeV [11][12][13][14], √  = 8 TeV [15,16] and ).The diagrams include the leptonic decay of the top quark and top antiquark.
The observation of -channel single-top-quark production and a measurement of its cross-section at √  = 5.02 TeV is reported using 255 pb −1 of pp collision data collected with the ATLAS detector.The analysis includes selection criteria to isolate the -channel topology from the Standard Model (SM) backgrounds in the leptonic-decay channels of the W boson ( → ,  → , and  →  with leptonic -lepton decays).Separate measurements of the single-top-quark final states with a top quark and a top-antiquark are used to measure the CKM matrix element    .This measurement at a lower centre-of-mass energy than other proton-proton results provides an independent test of the SM, with different levels of backgrounds and instrumental uncertainties.
The backgrounds arise from the production of  bosons in association with jets (W+ jets), top-quark pair (tt) production, and either misidentified or non-prompt leptons, wherein a jet is mis-reconstructed as an electron, or a heavy-flavour quark that decays into a muon which satisfies the selection criteria.The two subleading single-top-quark production mechanisms, the production of  bosons in association with jets correction is used to account for the modified calorimeter response in the low-pile-up data sample [20].Jet candidates are required to have  T > 23 GeV and || < 4.0.Jets with  T < 60 GeV and || < 2.4 are subject to additional pile-up rejection criteria using a multivariate jet-vertex tagger [35].
Jets originating from long-lived -hadrons are identified using the DL1r algorithm [36], a multivariate discriminant based on deep-learning techniques using information from track impact parameters and reconstructed secondary vertices.A working point with 60% efficiency for tagging -quark jets from top-quark decays in simulated tt events is used.At this working point, the tagger has rejection factors of 30 against charm jets and 1200 against light-quark jets.Jets passing this requirement are denoted as -tagged jets.
The missing transverse momentum, whose magnitude is denoted by  miss T , is reconstructed as the negative vector sum of the transverse momenta of all identified physics objects (electrons, muons, and jets), together with a 'soft term' built from all tracks matched with the reconstructed primary vertex but not with any of the identified physics objects [37].
Selected events are required to have exactly one electron or muon candidate, and exactly two jets.Exactly one of the jets must be -tagged and be in the central region || < 2.5.Since the spectator-quark jet tends to be produced in the forward direction in the -channel process, the pseudorapidity of the untagged jet must satisfy 1.5 < || < 4.0.To reduce contributions from the tt process, the pseudorapidity separation between the untagged jet and the -tagged jet is required to be >1.5.A W boson candidate is identified by the electron or muon candidate and the missing transverse momentum.To suppress contributions from misidentified leptons, the following cuts on  miss T and the transverse mass of the W boson 2  ( W T ) are applied:  W T > 35 GeV,  miss T > 15 GeV, and  miss T +  W T > 70 GeV.To increase the purity of the signal events, the  T is required to be greater than 185 GeV, where  T is defined as the scalar sum of the  T of the jets, the  T of the lepton, and  miss T .
A top-quark candidate is reconstructed in each event by combining the -tagged jet with a  boson candidate.The latter is kinematically reconstructed by imposing the  boson mass as a kinematic constraint on the sum of the electron or muon candidate and the missing transverse momentum, leading to a quadratic equation in the longitudinal neutrino momentum,  , .When two solutions are found, the one that gives a reconstructed top-quark mass closest to the on-shell mass (172.5 GeV) is chosen.For complex solutions only the real component is considered, which results in a reconstructed mass greater than the  boson mass.This phenomena is observed in approximately 30% of the events.To further suppress contributions from processes not involving top quarks, the invariant mass of the lepton and the -tagged jet must be <165 GeV, the invariant mass of the reconstructed  boson must be <102 GeV, and the invariant mass of the reconstructed top quark must be between 140 GeV and 225 GeV.

Modelling and theoretical predictions
The MCFM program [38][39][40] employing the NNPDF3.0nloPDFs [41] was used to calculate predictions for the single-top-quark () and single-top-antiquark (t) production cross-sections in the -channel at next-to-next-to-leading-order (NNLO) in QCD for pp collisions at where  ℓ T is the transverse momentum of the charged lepton and  is the opening azimuthal angle between the charged lepton and the missing transverse momentum.is predicted to be   = 2.03 +0.06 −0.07 .All predictions are assuming a top-quark mass of 172.5 GeV.The quoted uncertainties include contributions from the choice of renormalisation scale  r and the factorisation scale  f , the uncertainty in the PDFs, and uncertainty in the value of  s .
Monte Carlo (MC) simulated samples are used to model the single-top-quark -channel signal process and contributions from other physics processes with prompt leptons.The signal was simulated using the next-to-leading-order (NLO) in QCD MC event generator Powheg Box v2 [42] with the four-flavour scheme.The parton showering, hadronisation, and the underlying event was modelled using the Pythia 8.2 [43] program with the A14 tune [44].The Powheg Box v2 program also was used to simulate tt, single-top-quark -and -channel backgrounds.All these samples use Pythia 8.2 with the NNPDF3.0nloPDFs and the A14 tune as the parton-shower and hadronisation models.The tt background is normalised using an NNLO cross-section, while the  background is normalised using an approximate NNLO cross-section including the resummation of next-to-next-to-leading logarithmic soft-gluon terms [45,46].The -channel sample is normalised to the generator-level NLO cross-section prediction.
The Z + jets and W+ jets events were simulated with the Sherpa 2.2 generator [47] using NLO matrix elements with up to two partons, and leading-order (LO) matrix elements for up to four partons, and normalised using an NNLO cross-section prediction [48].The NNPDF3.0nnloPDF sets [49] were used for all Z + jets and W+ jets simulated samples.The smaller backgrounds from diboson production with additional jets were simulated using the Sherpa 2.1 generator with the CT10 PDF set [50].
All generated events underwent a full simulation of the ATLAS detector response based on the Geant4 [51] framework.The effects of pile-up are included in the simulation.To improve the agreement with the response observed in data, small corrections derived from comparisons of data and simulation at both √  = 5.02 TeV and √  = 13 TeV were applied as scale factors to the simulated lepton-trigger and lepton-reconstruction efficiencies.
The backgrounds arising from the non-prompt and misidentified leptons were determined using the 'matrix method' technique [52].Events were selected using looser isolation or identification requirements for the lepton and were then weighted according to the efficiencies for both the prompt and background (misidentified and non-prompt) leptons to pass the tighter baseline selection.The method was validated by comparing predictions with data in dedicated validation regions with a larger fraction of misidentified-lepton candidates than expected in the analysis regions.Good agreement between data and the prediction in these validation regions was found.

Signal and cross-section extraction
Boosted decision trees (BDT) are used to enhance the separation between signal and background.A single BDT is trained using nine input variables that include information about object kinematics, variables based on combinations of four-vectors, and the global event topology.The BDT is trained with the XGBoost [53] package using MC signal, MC background, and the data-driven misidentified-lepton background events.The variables with the highest discriminating power between signal and background are the total scalar sum of the transverse momentum from all objects in an event ( T ), and the magnitude of the  T difference between the reconstructed W boson and the four-vector sum of the untagged and -tagged jet (|Δ  (, )|).
A three-fold cross-validation procedure is used to produce the final discriminant that is calculated for the observed data and the predictions.The sample is divided into three subsamples while the training is performed on a pair of the subsamples and tested against the third.The procedure is iterated with three different pairings to produce a combined BDT discriminant, which is applied to the data events.A binned profile-likelihood fit of the sum of the BDT response distribution for signal and background MC samples to the observed BDT response distribution is performed.
The () and (t) cross-sections are determined by dividing the event sample into a top-quark and top-antiquark subsample defined by the charge of the reconstructed lepton, ℓ + +jets and ℓ − +jets, respectively.These cross-sections are parameterised as functions of ( + t) and   , and are determined by the fit to the observed BDT distributions in these two subsamples.The  T and |Δ  (, )| distributions for the inclusive ℓ+jets sample (the sum of the ℓ + +jets and ℓ − +jets regions) are shown in Figure 2, along with the predictions from the signal and background model.The predicted distributions show the signal assuming the SM single-top-quark -channel production cross-section and the estimated backgrounds for the two subsamples before the fit is performed (pre-fit).The predicted shapes of the distributions for this variable and the others used in the analysis are found to be in good agreement with the observed distributions.

Systematic uncertainties
Systematic uncertainties are included in the likelihood fit as nuisance parameters constrained by Gaussian probability density functions.Correlations between systematic uncertainties arising from common sources are maintained across processes and bins in the two regions.
Uncertainties arising from the modelling of signal-and background-related processes are evaluated using alternative MC samples.The  + t signal has uncertainties arising from the matrix-element matching, the parton-shower and hadronisation model, initial and final-state radiation (ISR and FSR), the  r and  f scales in the matrix element, and the proton PDFs [44,54].Two alternative -channel samples were used to evaluate the matching uncertainty and uncertainties in the parton-shower model: one was generated using the nominal matrix-element model and the pTHard parameter in Pythia 8 changed from zero to one, and the second generated using the Powheg+Herwig 7.1.6generator.
The W+ jets modelling uncertainties are evaluated by first splitting the MC generated W+ jets background into three categories  + ≥1,  + ≥1, and  + ≥1 (light quarks or gluons) based on the flavour of additional jets in the event, with fractions in each category of 57%, 39%, and 4%, respectively.The uncertainty in each fraction is calculated by adding in quadrature a 24% uncertainty for each successive jet in the event using Berends scaling [55].Thus, a conservative W+ jets normalisation uncertainty of 34% is used for all categories of W+ jets background in lieu of generator comparisons since alternate MC event samples were not available at √  = 5.02 TeV.The  r and  f scales are varied by factors of 1/2 and 2 and an envelope built from six possible variations is used to estimate additional shape uncertainties for the three categories of W+ jets background.
The uncertainty in the cross-section of the tt background is taken to be +7.5 −7.7 % [45,46], while modelling uncertainties are estimated by using the techniques in Ref. [20].Uncertainties in the cross-sections for the  and -channel single-top-quark background processes are taken to be +5.6 −5.9 % and 9.5%, respectively [56,57].Uncertainties related to parton-shower, modelling of ISR and FSR, and the  r and  f scales for these three background processes are included in the fit.The PDF uncertainties are also included for the tt background.A conservative 50% uncertainty in the cross-section, acceptance, and modelling of the Z + jets and diboson backgrounds is applied [38].The fit also includes a 50% uncertainty in the normalisation of the misidentified-lepton background estimate that is determined by comparing different parameterisations and selections for extracting the lepton efficiencies used in the matrix method.The uncertainty is separated according to the flavour of the misidentified lepton.
Instrumental systematic uncertainties related to the lepton trigger efficiency [58,59], reconstruction, isolation and identification [28,29,60], lepton energy scale and resolution [61], and jet-energy scale and resolution [34] are measured in the √  = 5.02 TeV data sample or taken from high-pile-up √  = 13 TeV data with additional uncertainties to account for the extrapolation to the low-pile-up √  = 5.02 TeV data.Due to the additional correction to the jet-energy scale specific to this low-pile-up data sample, statistical and modelling uncertainties of 1%-2% on the jet-energy scale arising from the correction are incorporated into the systematic uncertainties in the fit.The uncertainty on the -tagging efficiency is measured to be ∼ 1% [36].Additional uncertainties arise from jet-vertex tagging [35] and modelling of  miss T [37].The uncertainty in the integrated luminosity is 1.0% and the uncertainty in the beam energy is negligible.+jets and ℓ − +jets regions.The 'Other single top' category contains the  associated production and -channel contributions.The uncertainties in the signal and background yields include the statistical uncertainties, all systematic uncertainties, and the correlations between them.The uncertainty in the total prediction includes correlations between all systematic uncertainties and thus does not equal the sum in quadrature from the individual components.In this table, the uncertainties have been symmetrised, but full asymmetric uncertainties are used to obtain the final results.

Source
Number

Results
The results of the profile likelihood fit are ( + t) = 27.1 +4.4 −4.1 (stat.)+4.4 −3.7 (syst.)pb and   = 2.73 +1. 43 −0.82 (stat.)+1.01 −0.29 (syst.).The Pearson correlation coefficient between ( + t) and   is measured to be −30% and all other correlations are found to be small.Table 1 shows the fitted signal-and background-event yields (post-fit) and the observed yield in the ℓ + +jets and ℓ − +jets regions.The fit to the BDT response distributions is shown in Figure 3.The pulls of all nuisance parameters in the fit are found to be within 0.2 standard deviations of their input values.
Using the asymptotic approximation [62], the background-only hypothesis is rejected with an observed (expected) significance of 6.1 (6.4) standard deviations.
The statistical uncertainty from the sample size is the largest contribution to the total uncertainty in the single-top-quark -channel production cross-section, followed by a 8.5% uncertainty contribution from signal-modelling and a 6.3% contribution from modelling uncertainties in the misidentified-lepton background.The signal-modelling uncertainty is dominated by the uncertainty in the choice of partonshower and hadronisation models.Table 2 shows the breakdown of the sources of uncertainty in the cross-section and cross-section ratio measurements.The squared uncertainties are calculated by fixing the set of nuisance parameters corresponding to a category, repeating the fit, and taking a difference between the squares of the resulting uncertainty and the total uncertainty of the nominal fit.The total uncertainty is the sum in quadrature of the total systematic uncertainty and the data's statistical uncertainty.From the fitted ratio and the total cross-section, the individual single-top-quark and single-top-antiquark cross-sections are () = 19.8+3.9 −3.1 (stat.)+2.9 −2.2 (syst.)pb and (t) = 7.3 +3.2 −2.1 (stat.)+2.8 −1.5 (syst.)pb.
The -channel single-top-quark production cross-section depends on , where  LV is a left-handed form factor that is unity in the SM and    is a component of the CKM matrix [8].By assuming that the CKM matrix elements |   | and |   | are much smaller than |   | and that the  vertex is left-handed, the measured cross-section gives  LV • |   | = 0.94 +0.11  −0.10 .The experimental uncertainties in the measured ( + t) and the uncertainties in the predicted ( + t) arising from scale variations, choice of PDF,  s , and   dependence are all summed in quadrature.In (a), the measurements are compared with theoretical calculations at NLO in QCD [56,57].In (b), the dashed line and the dot show the measured value, the yellow band displays the statistical uncertainty, and the green band displays the total uncertainty on the measurement.For comparison, the predictions of MCFM based on different PDFs are included.The gray (orange) band represents the uncertainty on the predictions arising from the scale variations (scale, PDF and  s variations added in quadrature).

Conclusions
The single-top-quark -channel production cross-section is measured at √  = 5.02 TeV using pp data collected with the ATLAS detector corresponding to an integrated luminosity of 255 pb −1  .The analysis is performed by selecting semileptonic decays of the top quark with exactly two jets in the final state, one of which is required to be -tagged.After performing a profile maximum-likelihood fit to the BDT discriminant distributions in the ℓ + +jets and ℓ − +jets channels, the combined single-top-quark and single-top-antiquark production cross-section in the -channel is 27.1 +4.4 −4.1 (stat.)+4.4 −3.7 (syst.)pb.
This measurement of single-top-quark production at √  = 5.02 TeV is in good agreement with the SM prediction.Although its uncertainty is four times larger than measurements at higher centre-of-mass energies, it provides another independent test of the SM predictions.

Figure 1 :
Figure 1: Feynman diagrams at leading-order in QCD for (a) single-top-quark production and (b) single-top-antiquark production via the -channel exchange of a virtual  boson ( *).The diagrams include the leptonic decay of the top quark and top antiquark.

Figure 2 :
Figure 2: The pre-fit (a)  T and (b) |Δ  (, )| distributions for data (dots) in the inclusive ℓ+jets channel.The MC simulation of the signal (red histograms) and various backgrounds (represented by histograms of different colours) are also included.The error bars on the dots represent the statistical uncertainty on the data while the blue cross-hatched lines correspond to the total uncertainties on the prediction.The lower panels show the ratio of the data and the prediction, along with the uncertainty in the ratio.The last bin includes any event overflows.The  2/degrees of freedom are evaluated to be 2.5/6 for (a) and 5.9/5 for (b).

Figure 4
Figure 4 presents a summary of -channel single-top-quark cross-section measurements by the ATLAS Collaboration as a function of the centre-of-mass energy and the measurement at √  = 5.02 TeV.The NLO prediction from the MCFM MC generator is compared with the measured cross-sections and describes well the evolution of the single-top-quark production cross-section in the -channel as a function of √ .

Figure 3 :
Figure 3: The post-fit BDT response distribution for data (dots) in the (a) ℓ + +jets and (b) ℓ − +jets channels.The MC simulation of the signal (red histograms) and various backgrounds (represented by histograms of different colours) are also included.The error bars on the dots represent the statistical uncertainty on the data while the blue cross-hatched lines correspond to the total uncertainties on the prediction.The lower panels show the ratio of the data and the prediction, along with the uncertainty in the ratio.Bins with BDT response values outside of the bins shown are empty.

Figure 4 :
Figure 4: Summary of (a) ATLAS measurements of the -channel single-top-quark production cross-sections as a function of the centre-of mass energy and (b) the measured ( + t) at √  = 5.02 TeV.In (a), the measurements are compared with theoretical calculations at NLO in QCD[56,57].In (b), the dashed line and the dot show the measured value, the yellow band displays the statistical uncertainty, and the green band displays the total uncertainty on the measurement.For comparison, the predictions of MCFM based on different PDFs are included.The gray (orange) band represents the uncertainty on the predictions arising from the scale variations (scale, PDF and  s variations added in quadrature).

Table 1 :
Number of post-fit signal, background and observed data events in the ℓ +

Table 2 :
Sources of uncertainty for measurements of ( + t) and   at √  = 5.02 TeV.The systematic uncertainties for both the values do not add up in quadrature to the total systematic uncertainty because of correlations in the fit parameters.In this table, the uncertainties have been symmetrised, but full asymmetric uncertainties are used to obtain the final results.Category ( + t)/( + t) [%]   /  [%] Measurement of the inclusive cross-sections of single top-quark and top-antiquark -channel production in   collisions at √  = 13 TeV with the ATLAS detector, JHEP 04 (2017) 086, arXiv: 1609.03920[hep-ex].