Measurement of the tt¯ production cross-section using e# events with b-tagged jets in pp collisions at √s=13TeV with the ATLAS detector

This paper describes a measurement of the inclusive top quark pair production cross-section ( σ t ¯ t ) with a data sample of 3.2 fb − 1 of proton–proton collisions at a centre-of-mass energy of √ s = 13 TeV, collected in 2015 by the ATLAS detector at the LHC. This measurement uses events with an opposite-charge electron–muon pair in the ﬁnal state. Jets containing b -quarks are tagged using an algorithm based on track impact parameters and reconstructed secondary vertices. The numbers of events with exactly one and exactly two b -tagged jets are counted and used to determine simultaneously σ t ¯ t and the e ﬃ ciency to reconstruct and b tag a jet from a top quark decay, thereby minimising the associated systematic uncertainties. The cross-section is measured to be: where the four uncertainties arise from data statistics, experimental and theoretical systematic e ﬀ ects, the integrated luminosity and the LHC beam energy, giving a total relative uncertainty of 4.4%. The result is consistent with theoretical QCD calculations at next-to-next-to-leading order. A ﬁducial measurement corresponding to the experimental acceptance of the leptons is also presented.


Introduction
The top quark is the heaviest known fundamental particle, with a mass m t which is much larger than any of the other quarks, and close to the scale of electroweak symmetry breaking. The study of its production and decay properties forms a core part of the LHC physics programme. At the LHC, top quarks are primarily produced in quark-antiquark pairs (tt), and the precise prediction of the corresponding inclusive crosssection is sensitive to the gluon parton distribution function (PDF) and the top quark mass, and presents a substantial challenge for QCD calculational techniques. Physics beyond the Standard Model may also lead to an enhancement of the tt production rate.
Calculations of the tt production cross-section at hadron colliders are available at full next-to-next-toleading-order (NNLO) accuracy in the strong coupling constant α S , including the resummation of nextto-next-to-leading logarithmic (NNLL) soft gluon terms [1][2][3][4][5]. In this paper a reference value of 832 +40 −46 pb at a centre-of-mass energy of √ s = 13 TeV assuming m t = 172.5 GeV is used, corresponding to a relative precision of +4.8 −5.5 %. This value was calculated using the top++ 2.0 program [6]. The combined PDF and α S uncertainties of ±35 pb were calculated using the PDF4LHC prescription [7] with the MSTW2008 68% CL NNLO [8,9], CT10 NNLO [10,11] and NNPDF2.3 5f FFN [12] PDF sets, and added in quadrature to the factorisation and renormalisation scale uncertainty of +20 −29 pb. The cross-section at √ s = 13 TeV is predicted to be 3.3 times larger than the cross-section at √ s = 8 TeV.
Measurements of σ tt have been made at √ s = 7 and 8 TeV by both ATLAS [13][14][15] and CMS [16][17][18]. The most precise ATLAS measurements of σ tt at these collision energies were made using events with an opposite-charge isolated electron and muon pair and additional b-tagged jets [13]. This paper documents a measurement of σ tt at √ s = 13 TeV using the same final state and analysis technique. Wherever possible, the analysis builds on the studies and procedures used in the earlier publication [13]. A fiducial measurement determining the cross-section in the region corresponding to the experimental lepton acceptance is also presented.
The data and Monte Carlo simulation samples are described in Section 2, followed by the object and event selection in Section 3 and the method for determining the tt cross-section in Section 4. The evaluation of backgrounds is discussed in Section 5 and the systematic uncertainties in Section 6. Finally, the results and conclusions are given in Section 7.

Data and simulation samples
The analysis is performed using the full 2015 proton-proton (pp) collision data sample at √ s = 13 TeV with 25 ns bunch spacing recorded by the ATLAS detector [19,20]. The data correspond to an integrated luminosity of 3.2 fb −1 after requiring stable LHC beams and that all detector subsystems were operational. Events are required to pass either a single-electron or single-muon trigger, with thresholds set to be almost fully efficient for leptons with transverse momentum p T > 25 GeV passing offline selections. Each event includes the signals from on average about 14 additional inelastic pp collisions in the same bunch crossing (known as pile-up).
Monte Carlo simulated event samples are used to optimise the analysis, to compare to the data, and to evaluate signal and background efficiencies and uncertainties. The samples used in the analysis are summarised in Table 1. The main tt signal and background samples were processed through the ATLAS detector simulation [21] based on GEANT4 [22]. Some of the systematic uncertainties were studied using alternative tt samples processed through a faster simulation making use of parameterised showers in the calorimeters [23]. Additional simulated pp collisions generated with Pythia8.186 [24] were overlaid to model the effects from additional collisions in the same and nearby bunch crossings. All simulated events were processed using the same reconstruction algorithms and analysis chain as the data, and small corrections were applied to lepton trigger and reconstruction efficiencies and resolutions to improve the agreement with the response observed in data.
The baseline tt simulation sample was produced at next-to-leading order (NLO) in QCD using the matrixelement generator Powheg-Box v2 [25][26][27] with CT10 PDFs [10], interfaced to Pythia6 [28] with the Perugia 2012 set of tuned parameters (tune) [29] for parton shower, fragmentation and underlying event modelling. The h damp parameter, which gives a cutoff scale for the first gluon emission, was set to m t , a value which was chosen to give good modelling of the tt system p T at √ s = 7 TeV [30]. The EvtGen [31] package was used to better simulate the decay of heavy-flavour hadrons.
Alternative tt simulation samples were generated using Powheg interfaced to Herwig++ [32], and Mad-graph5_aMC@NLO [33] interfaced to Herwig++. The effects of initial-and final-state radiation were explored using two alternative Powheg + Pythia6 samples: one with h damp set to 2m t , the factorisation and renormalisation scale varied by a factor of 0.5 and using the Perugia 2012 radHi tune, giving more parton shower radiation; and a second one with the Perugia 2012 radLo tune, h damp = m t and the factorisation and renormalisation scale varied by a factor of 2, giving less parton shower radiation. The samples were simulated following the recommendations documented in Ref. [34]. The top quark mass was set to 172.5 GeV in all these simulation samples and the t → Wb branching fraction to 100%.
Backgrounds in this measurement are classified into two types: those with two real prompt leptons from W or Z decays (including those produced via leptonic decays of τ-leptons), and those where at least one of the reconstructed lepton candidates is 'fake', i.e. a non-prompt lepton produced from the decay of a bottom or charm hadron, an electron arising from a photon conversion, a jet misidentified as an electron, or a muon produced from an in-flight decay of a pion or kaon. Backgrounds containing two real prompt leptons include single-top production in association with a W boson (Wt), Z+jets production with Z → ττ → eµ, and diboson production (WW, WZ and ZZ) where both bosons decay leptonically.
The dominant Wt single-top background was modelled using Powheg-Box v1 + Pythia6 with the CT10 PDFs and the Perugia 2012 tune, using the 'diagram removal' generation scheme [35]. The Z+jets background was modelled using Sherpa 2.1.1 [36]: matrix elements (ME) were calculated for up to two partons at NLO and four partons at leading order using the Comix [37] and OpenLoops [38] matrix-element generators and merged with the Sherpa parton shower (PS) using the ME + PS@NLO [39] prescription; the CT10 PDF set was used in conjunction with dedicated parton shower tuning in Sherpa. Diboson production with additional jets was also simulated using Sherpa 2.1.1 and CT10 PDFs as described above; the four-lepton final state, the three-lepton final state with two different-flavour leptons, and the two-lepton final state were simulated to cover ZZ, ZW and WW production, and include off-shell Z/γ * contributions. Same-charge WW production from QCD and electroweak processes was included. Alternative Wt and diboson simulation samples were generated using Powheg + Herwig++ and Powheg + Pythia8, respectively, to estimate the background modelling uncertainties.
The majority of the background with at least one fake lepton in the selected sample arises from tt production where only one of the W bosons from the top quarks decays leptonically, which was simulated as discussed earlier. Other processes with one real lepton which can contribute to this background include the t-channel single-top production, modelled using Powheg-Box v1 + Pythia6, and W+jets with the W efficiency of 95% for electrons from Z → ee decays with p T of 25 GeV which rises to 99% at 60 GeV. The efficiencies in tt events are smaller, due to the increased jet activity. To prevent double-counting of electron energy deposits as jets, the closest jet with ∆R < 0.2 of a reconstructed electron is removed. Finally, if the nearest jet surviving the above selection is within ∆R = 0.4 of the electron, the electron is discarded, to ensure it is sufficiently separated from nearby jet activity.
Muon candidates are reconstructed by combining matching tracks reconstructed in both the inner detector and muon spectrometer, and are required to satisfy p T > 25 GeV and |η| < 2.4 [43]. Muons are also required to be isolated, using requirements similar to those for electrons, with the selection criteria tuned to give similar efficiencies for Z → µµ events. The muon candidates must satisfy the requirements on the transverse impact parameter significance and on the longitudinal impact parameter of |d 0 |/σ d 0 < 3 and |∆z 0 sin θ| < 0.5 mm, respectively. To reduce the background from muons from heavy-flavour decays inside jets, muons are removed if they are separated from the nearest jet by ∆R < 0.4. However, if this jet has fewer than three associated tracks, the muon is kept and the jet is removed instead; this avoids an inefficiency for high-energy muons undergoing significant energy loss in the calorimeter. Events are rejected if the selected electron and muon are separated by ∆φ < 0.15 rad and ∆θ < 0.15 rad, where ∆φ and ∆θ are the differences in polar and azimuthal angles between the two leptons. This requirement rejects events where a muon undergoes significant energy loss in the electromagnetic calorimeter, thus leading to a reconstructed electron candidate. Events passing the above requirements, and having exactly one selected electron and one selected muon of opposite electric charge sign (OS), define the eµ preselected sample. The corresponding same-sign (SS) sample is used in the estimation of background from events with misidentified leptons. Events are then further classified into those with exactly one or exactly two b-tagged jets.

Extraction of the tt cross-section
The tt cross-section is measured in the dileptonic eµ channel, where one top quark decays as t → Wb → eνb and the other as t → Wb → µνb. 2 The final states from leptonic τ decays are also included. As in Ref.
[13], σ tt is determined by counting the numbers of opposite-sign eµ events with exactly one (N 1 ) and exactly two (N 2 ) b-tagged jets, ignoring any jets that are not b-tagged which may be present, due to e.g. light-quark or gluon jets from QCD radiation or b-jets from top quark decays which are not b-tagged.
The two event counts can be expressed as: where L is the integrated luminosity of the sample and ǫ eµ the efficiency for a tt event to pass the oppositesign eµ preselection. The combined probability for a jet from the quark q in the t → Wq decay to fall within the acceptance of the detector, be reconstructed as a jet with transverse momentum above the selection threshold, and be tagged as a b-jet, is denoted by ǫ b . If the decays of the two top quarks and the subsequent reconstruction of the two b-tagged jets are completely independent, the probability to tag both b-jets ǫ bb is given by ǫ bb = ǫ b 2 . In practice, small correlations are present for kinematic and instrumental reasons, and these are taken into account via the tagging correlation coefficient C b , defined as where N tt eµ is the number of preselected eµ tt events and N tt 1 and N tt 2 are the numbers of events with one and two b-tagged jets. Background from sources other than tt → eµννbb also contributes to the event counts N 1 and N 2 , and is given by the background terms N are estimated using a combination of simulation and data-based methods as described in Section 5, allowing the two equations (1) to be solved yielding σ tt and ǫ b by minimising a likelihood function.
In the method to measure the tt cross-section outlined above, some of the largest systematic uncertainties come from the use of simulation to estimate the preselection efficiency ǫ eµ . This efficiency can be factorised into the product of two terms: ǫ eµ = A eµ G eµ . The acceptance A eµ represents the fraction of tt events that have a true eµ pair within the detector acceptance (p T > 25 GeV and |η| < 2.5) and it is about 2.7% (2.3% excluding τ decays). The term G eµ represents the ratio of reconstructed tt events to tt events with a true eµ pair within the fiducial region, where the numerator includes the approximately 2% of reconstructed tt events where one or both leptons have true p T < 25 GeV. The fiducial cross-section σ fid tt is defined as σ fid tt = A eµ σ tt , avoiding the systematic uncertainties associated with the extrapolation from the measured lepton phase space to the full phase space, and measured following the same technique as in Ref.
[13]. The contribution of tt events produced in the fiducial region with at least one lepton originating via W → τ → l decay is estimated from simulation to be 12.2 ± 0.1%.
A total of 30879 data events passed the eµ opposite-sign preselection. Table 2 shows the number of events with one and two b-tagged jets, together with the estimates of non-tt background and their systematic uncertainties discussed below. The ratio of b-tagged events to preselected events (before b-tagging) is higher for 13 TeV than at 7 and 8 TeV due to the larger increase of the tt cross-section with √ s compared with the Z+jets and diboson background cross-sections. In simulation, the sample with one b-tagged jet is expected to be about 89% pure in tt events, with the dominant background originating from Wt single-top  Table 2: Observed numbers of opposite-sign eµ events with one and two b-tagged jets (N 1 and N 2 ), together with the estimates of non-tt backgrounds and associated systematic uncertainties. Uncertainties quoted as 0 are < 0.5.
production, and smaller contributions from events with misidentified leptons, Z+jets and dibosons. The sample with two b-tagged jets is expected to be about 96% pure in tt events, with Wt production again being the dominant background.
The distribution of the number of b-tagged jets in opposite-sign eµ events is shown in Figure 1, and compared to the baseline and alternative tt and background simulation samples. The tt contribution is normalised to the theoretical tt cross-section prediction at √ s = 13 TeV of 832 pb. The agreement between data and simulation in the one and two b-tagged bins used for the cross-section measurement is good. However, the data has about 40% more events with three or more b-tags than the baseline simulation, indicating a mismodelling of events with tt produced in association with additional heavyflavour jets, as discussed further in Section 6. There is also an approximately 11% excess of data over simulation for events with zero b-tagged jets which does not affect the measurement, and is compatible with the expected uncertainties in modelling WW [48] and Z+jets production. Distributions of the number of jets, the jet p T , and the electron and muon |η| and p T are shown for opposite-sign eµ events with at least one b-tagged jet in Figure 2, where the simulation is normalised to the same number of events as the data. In general, the data and simulation agree well.

Background estimation
Most background contributions are estimated from simulation. The Wt single-top background is normalised to the approximate NNLO cross-section of 71.7 ± 3.8 pb, determined as in Ref. [49]. The diboson background normalisation is estimated using Sherpa as discussed in Section 2. The normalisation of the Z+jets background, originating from events with a Z → ττ → eµ decay accompanied by one or two b-tagged jets, is determined by scaling the Sherpa simulation with scale factors obtained in Z → ee and Z → µµ events as described in Section 6.
The background from events with one real and one misidentified lepton is estimated from a combination of data and simulation, using the method employed in Ref. [13]. Simulation studies show that the samples with a same-sign eµ pair and one or two b-tagged jets are dominated by events with a misidentified lepton, with rates comparable to those in the opposite-sign sample. The contributions of events with misidentified leptons are therefore estimated using the same-sign event counts in data after subtraction of the estimated prompt same-sign contributions, multiplied by the opposite-to same-sign fake-lepton ratios R j for j = 1 and 2 b-tagged jets predicted from simulation. The results are shown in Table 2 and the procedure is illustrated in Table 3, which shows the expected breakdown of same-sign event counts in terms of prompt-lepton and misidentified-lepton events, and the corresponding predictions for misidentified  leptons in the opposite-sign sample with all contributions estimated from simulation. The misidentifiedlepton contributions are classified into those where the electron is from a photon conversion, from the decay of a heavy-flavour hadron or from other sources (e.g. a misidentified hadron within a jet), or the muon is from a heavy-flavour decay or other sources (e.g. a pion or kaon decay). The values of R j are taken to be R 1 = 1.55 ± 0.50 and R 2 = 1.99 ± 0.82, where the central values are taken from ratios of the total numbers of misidentified-lepton events in opposite-and same-sign samples. The uncertainties encompass the different values of R j predicted for the various sub-components of the misidentified-lepton background separately, allowing the background composition to be significantly different from that predicted by simulation, where it is dominated by electrons from photon conversions, followed by electrons and muons from the decays of heavy-flavour hadrons. A 50% uncertainty is assigned to the prompt samesign contribution, which includes events where the charge of the electron was misidentified (denoted by wrong-sign prompt in Table 3) or right-sign with two genuine same-sign leptons (e.g. from ttW/Z production). The largest uncertainties in the misidentified-lepton background come from the uncertainties in R j .
The modelling in simulation of the different components of the misidentified-lepton background is checked by studying kinematic distributions of same-sign events, as illustrated for the p T and |η| distributions of the leptons in events with at least one b-tagged jet in Figure 3. The simulation models the shapes of the distributions well, but underestimates the number of data events with two b-tagged jets by about 40%, as shown in Table 3. This deficit in simulation is attributed to a larger rate of misidentified-lepton events in data, which increases the estimate of misidentified leptons in the opposite-sign two-b-tag sample accordingly. The modelling is also checked in same-sign control samples with relaxed isolation cuts, enhancing the contributions of heavy-flavour decays, and similar levels of agreement were found, giving confid-     Table 3: The expected numbers of events with at least one misidentified lepton in the one-and two-b-tag oppositeand same-sign eµ samples, broken down into different categories as described in the text. For the same-sign samples, the contributions from wrong-sign (where the electron charge sign is misreconstructed) and right-sign prompt lepton events are also shown, and the total expected numbers of events are compared to the data. The uncertainties are due to simulation statistics, and numbers quoted as '0.0' are smaller than 0.05.
ence that the simulation adequately models the different sources of misidentified leptons in the selected sample.

Systematic uncertainties
The systematic uncertainties in the extracted cross-sections, σ tt and σ fid tt , are shown in Table 4, together with their effects (where relevant) on the tt preselection efficiency ǫ eµ , tagging correlation C b and reconstruction efficiency G eµ . Each source of uncertainty is evaluated by repeating the cross-section extraction with all relevant input parameters simultaneously changed by ±1 standard deviation. Correlations between input parameters (in particular significant anti-correlations between ǫ eµ and C b which contribute with opposite signs to σ tt ) are thus taken into account. The total uncertainties are calculated by adding the effects of all the individual systematic components in quadrature, assuming them to be independent. The sources of systematic uncertainty are discussed in detail below. tt modelling: The modelling uncertainties in ǫ eµ and C b due to the choice of tt generator are assessed by comparing the predictions of the baseline Powheg + Pythia6 sample with the various alternative samples discussed in Section 2. Three separate uncertainties are considered: the NLO generator uncertainty (evaluated by considering the relative difference between MadGraph5_aMC@NLO + Herwig++ and Powheg + Herwig++), the parton shower and hadronisation uncertainty (evaluated by considering the relative difference between Powheg + Pythia6 and Powheg + Herwig++), and the radiation uncertainty (evaluated by considering half the relative difference between the Powheg + Pythia6 samples with more or less radiation). The prediction for ǫ eµ is found to be particularly sensitive to the amount of hadronic activity near the leptons, which strongly affects the efficiency of the lepton isolation requirements described in Section 3. These isolation efficiencies are therefore measured directly from data, as discussed below, and thus no modelling uncertainty is considered for the lepton isolation. Motivated by the level of agreement for events with at least three b-tags seen in Figure 1, an additional uncertainty in C b is determined by calculating in data and simulation the   Table 4: Summary of the systematic uncertainties in ǫ eµ , G eµ and C b (with their relative signs where relevant), and the statistical, systematic, luminosity and beam energy uncertainties in the measured tt cross-section σ tt at √ s = 13 TeV. All uncertainties from the inclusive cross-section measurement apply to the fiducial measurement; in the lower part of the table only the systematic uncertainties that are different for the measurement of the fiducial cross-section σ fid tt are given, together with the total analysis systematic uncertainties and total uncertainties in σ fid tt . Uncertainties quoted as '0.0' are smaller than 0.05%, whilst '-' indicates that the corresponding uncertainty is not applicable.
ratio R 32 of the number of events with at least three b-tagged jets to the number with at least two. The baseline simulation sample is reweighted to change the fraction of events with at least three b-jets at generator level, which effectively changes the tt plus heavy-flavour fraction and the values of both C b and R 32 . A linear relation between changes in C b and R 32 is found, and used to translate the difference between the R 32 values found in data (3.1 ± 0.2%) and simulation (2.21 ± 0.05%) to a shift in C b of 0.39%. This shift is treated as an additional uncertainty in C b due to the modelling of heavy-flavour production in tt events, uncorrelated to the NLO, hadronisation and radiation uncertainties discussed above.

Parton distribution functions:
The uncertainties in ǫ eµ and C b due to limited knowledge of the proton PDFs are evaluated by reweighting simulated events produced with MadGraph5_aMC@NLO using the error sets of the NNPDF 3.0 PDF sets [50]. The eigenvectors consist of a central PDF and 100 Monte Carlo replicas, for which the root mean square was taken to calculate the uncertainty. The MadGraph5_aMC@NLO sample was produced with CT10; therefore the cross-section was corrected for the relative difference between the central prediction of CT10 and NNPDF 3.0, which is about 1%. The uncertainty using the PDF4LHC Run-2 recommendations with 100 eigenvectors [51] is very similar to that obtained with NNPDF 3.0.

Single-top modelling:
The uncertainties related to Wt single-top modelling are assessed by comparing the predictions of Powheg + Pythia6 and Powheg + Herwig++ and considering the relative difference, comparing the diagram removal and diagram subtraction schemes for dealing with the interference between the tt and Wt final states, and also considering half the relative difference between the Powheg + Pythia6 samples with more or less radiation. Production of single top quarks via the t-and s-channels gives rise to final states with only one prompt lepton, and is accounted for as part of the misidentified-lepton background. Z+jets extrapolation: The cross-sections for Z+jets and especially Z+heavy-flavour jets are subject to large theoretical uncertainties, making purely simulation-based estimates unreliable. This background was therefore determined by measuring the rates of Z → ee and Z → µµ events with one and two b-tagged jets in both data and simulation, and using the resulting ratio to scale the simulation estimate of background from Z → ττ+jets. The Z+jets background prediction from simulation was scaled by 1.1 for the background with one b-tagged jet and by 1.2 for the background with two b-tagged jets. A 50% uncertainty was applied to the Z+jets contributions which cover the differences observed on the event yields comparing Z+jets Sherpa vs Powheg+Pythia8.

Lepton-related uncertainties:
The modelling of the electron and muon trigger efficiencies, identification efficiencies, energy scales and resolutions are studied using Z → ee and Z → µµ decays in data and simulation. Small corrections are applied to the simulation to improve the agreement with the response observed in data. These corrections have associated uncertainties that are propagated to the cross-section measurement. The uncertainty in the trigger efficiency is small compared to those for electron or muon identification since most events are triggered redundantly by both leptons. The efficiency of the lepton isolation requirements was measured directly in data tt events, thus including the effects of pile-up, by relaxing the cuts alternately on electrons and muons as in Ref.
[13]. The results, after the correction for the contamination from misidentified leptons estimated using the same-sign eµ samples as described in Section 5, showed that the baseline Powheg+Pythia6 simulation overestimates the efficiencies of the isolation requirements by about 0.2% for both the electrons and muons. These corrections were applied to ǫ eµ and the corresponding uncertainties are dominated by the subtraction of misidentified leptons.

Jet-related uncertainties:
Although the efficiency to reconstruct and b-tag jets from tt events is extracted from the data, uncertainties in the jet energy scale, energy resolution and reconstruction efficiency affect the backgrounds estimated from simulation and the estimate of the tagging correlation C b . They also have a small effect on ǫ eµ via the lepton-jet ∆R separation cuts. The jet energy scale is varied in simulation according to the uncertainties derived from the √ s = 8 TeV simulation and data calibration, extrapolated to √ s = 13 TeV [53]. The uncertainties are evaluated using a model with 19 separate orthogonal components and the resulting variations were added in quadrature. The jet energy resolution uncertainty is also assessed using √ s = 8 TeV data, and extrapolated to √ s = 13 TeV.

b-tagging uncertainties:
The correlation factor C b depends weakly on the b-tagging and mistagging efficiencies predicted by the simulation, as it is evaluated from the numbers of events with one and two b-tagged jets. The uncertainties are determined from √ s = 8 TeV data, with additional uncertainties to account for the presence of the newly-installed insertable B-layer detector (IBL) [20] and the extrapolation to √ s = 13 TeV. Since the definition of ǫ eµ does not involve b-tagged jets, it has no b-tagging or mistagging-related uncertainties.

Misidentified leptons:
The uncertainties in the number of events with misidentified leptons in the one and two b-tagged samples are derived from the statistical uncertainties in the numbers of samesign lepton events, the systematic uncertainties in the opposite-to same-sign ratios R j , and the uncertainties in the numbers of prompt same-sign events, as discussed in detail in Section 5.

Integrated luminosity:
The uncertainty in the integrated luminosity is 2.1%. It is derived, following a methodology similar to that detailed in Ref.
[54], from a calibration of the luminosity scale using xy beam-separation scans performed in August 2015. The effect on the cross-section measurement is slightly larger than 2.1% because the Wt single-top and diboson backgrounds are evaluated from simulation, so they are also sensitive to the assumed integrated luminosity.

LHC beam energy:
The LHC beam energy during the 2012 pp run was calibrated to be 0.30 ± 0.66% smaller than the nominal value of 4 TeV per beam, using the revolution frequency difference of protons and lead ions during p+Pb runs in early 2013 [55]. This relative uncertainty is also applicable to the 2015 pp run. Since this calibration is compatible with the nominal centre-of-mass energy of 13 TeV, no correction is applied to the measured σ tt value. However, an uncertainty of 1.5%, corresponding to the expected change in σ tt for a 0.66% change in centre-of-mass energy, is quoted separately for the final result.
Top quark mass: Alternative tt samples generated with different m t from 170 to 177.5 GeV are used to quantify the dependence of the acceptance for tt events on the assumed m t value. The level of Wt single-top background based on the change of the Wt cross-section for the same mass range is also considered. The tt acceptance and background effects partially cancel, and the final dependence of the result on the assumed m t value is determined to be dσ tt /dm t = −0.3%/GeV. The result of the analysis is reported for a top quark mass of 172.5 GeV, and the small dependence of the cross-section on the assumed mass is not included in the total systematic uncertainty.
The total systematic uncertainties in ǫ eµ , C b , G eµ and the fitted values of σ tt and σ fid tt are shown in Table 4, and the total systematic uncertainties in the individual background components are shown in Table 2. The dominant uncertainties in the cross-section result come from the luminosity determination and tt modelling, in particular from the tt shower and hadronisation uncertainty.

Results and conclusions
The inclusive tt production cross-section is measured in the dilepton tt → eµννbb decay channel using 3.2 fb −1 of √ s = 13 TeV pp collisions recorded by the ATLAS detector at the LHC. The numbers of opposite-sign eµ events with one and two b-tagged jets are counted, allowing a simultaneous determination of the tt cross-section σ tt and the probability to reconstruct and b-tag a jet from a tt decay. Assuming a top quark mass of m t = 172.5 GeV, the result is: where the four uncertainties are due to data statistics, experimental and theoretical systematic effects, the integrated luminosity and the LHC beam energy, giving a total relative uncertainty of 4.4%. The combined probability for a jet from a top quark decay to be within the detector acceptance and tagged as a b-jet is measured to be ǫ b = 0.559 ± 0.004 ± 0.003, where the first error is statistical and the second systematic, in fair agreement with the nominal prediction from simulation of 0.549. This cross-section measurement is consistent with the theoretical prediction based on NNLO+NNLL calculations of 832 +40 −46 pb at m t = 172.5 GeV. Figure 4 shows the result of this σ tt measurement together with the most precise ATLAS results at √ s = 7 and 8 TeV [13]. The data are compared to the NNLO+NNLL predictions as a function of the centre-of-mass energy. The result is also consistent with a recent measurement by CMS at √ s = 13 TeV using a smaller data sample [56].
The measured fiducial cross-section σ fid tt for a tt event producing an eµ pair, each lepton originating directly from t → W → ℓ or via a leptonic τ decay t → W → τ → ℓ and satisfying p T > 25 GeV and |η| < 2.5 is: σ fid tt = 11.32 ± 0.10 (stat) ± 0.29 (syst) ± 0.26 (lumi) ± 0.17 (beam) pb, with uncertainties due to data statistics, systematic effects, the knowledge of the integrated luminosity and the LHC beam energy, corresponding to a total relative uncertainty of 3.9% and an internal systematic uncertainty excluding the luminosity and the LHC beam energy of 2.5%. The breakdown of the systematic uncertainties is presented in Table 4. Overall, the analysis systematic uncertainties in the fiducial crosssection are smaller than those in the inclusive cross-section, due to the substantial reductions in the PDF and hadronisation uncertainties that contribute significantly to both the acceptance A eµ and reconstruction efficiency G eµ .