The calibration analysis is based on data recorded by ATLAS in 2015
and 2016, for an integrated luminosity of 3.2 fb−1 and 32.9 fb−1 re-
spectively, after requiring that all sub-detectors were functioning as ex- pected and the LHC has declared that the conditions for stable beams were fulfilled.
All simulated events are processed through a software based on the
GEANT4 toolkit [77] to simulate the response of the ATLAS detec-
tor and they are subsequently reconstructed using the same software as used for data. Samples generated with a fast simulation software, for which the calorimeter response is replaced by a parametrization of the shower shapes, are used to estimate modelling systematic uncer- tainties. In all the simulations, the top quark mass is fixed to the value
of mt =172.5 GeV. The EvtGen (v1.2.0) program [132] is used to
model the properties of bottom and charm hadron decays for all the
non-SHERPA samples. Finally, to simulate the effects of pileup, addi-
tional interactions were generated using PYTHIA8 and overlaid on the
simulated hard-scatter event. Each event is then reweighted to match the pileup profile seen in data.
Nominal t¯t + jets sample
The nominal t¯t + jets sample is produced using the POWHEG next-
to-leading order (NLO) matrix element generator interfaced with the PYTHIA8 parton shower and hadronization processes (PS). It is normal-
ized to the predicted theoretical cross section of σt¯t=832+46−51 pb, cal-
culated with the Top++2.0 program [133] at the next-to-next-to-leading order (NNLO) in perturbative QCD, including resummation of next-to- next-to-leading logarithm (NNLL) soft gluon terms [134–138].
An important tune parameter of the POWHEG generator is hdamp,
which controls the pT of the first additional emission beyond the Born
configuration. It is set to 1.5 · mt, as it was found to provide the best
Alternative t¯t + jets samples
Alternative t¯t Monte Carlo samples are generated for checking the mod- elling of the t¯t system, as well as studying systematic uncertainties due to the matrix element generator, parton shower and hadronization model, or the initial and final state radiation.
The MC generator uncertainty for the hard process is evaluated by
comparing the default POWHEG+PYTHIA8 sample to one generated by
MADGRAPH5_aMC@NLO and interfaced to PYTHIA8. The parton
shower and hadronization uncertainties are estimated by comparing the
nominal POWHEG+PYTHIA8 sample to one where POWHEG is inter-
faced to Herwig7. Radiation systematics are evaluated by comparing
the default POWHEG+PYTHIA8 sample with samples generated with
“up” and “down” parameter variations.
The up variation has renormalization and factorization scales divided
by two, the hdampparameter up by a factor of two and shower radiation
parameters up; on the contrary, the down variation has renormalization and factorization scales multiplied by two and the shower radiation pa- rameters down. All variations are relative with respect to the nominal t¯t sample. Additional details can be found in Ref. [140].
Single top
The production of Wt, s-channel and the electroweak t-channel single
top quark final states is modelled via the POWHEG generator. All the
single top quark samples are generated at NLO accuracy and later nor- malized to the approximate NNLO theoretical cross sections [141–143]. The parton shower and hadronization process is modelled with the us-
age of PYTHIA6 [144].
Overlap between the t¯t and Wt final states is removed using the “dia- gram removal” procedure [145].
W /Z+jets and diboson
The W /Z+jets samples are generated using SHERPA. Matrix elements
are calculated up to two partons at NLO and four partons at leading
ement generators and merged with the SHERPA parton shower [148]. These samples are later normalized to the NNLO cross-sections [149].
Samples of diboson events produced in association with jets are gen-
erated using SHERPAfollowing the description presented in Ref. [150]
and are normalized to their respective NLO cross-sections calculated by the generator.
Fake leptons
The only background not estimated using Monte Carlo simulation is the one composed of non-prompt and misidentified muons and electrons, collectively referred to as “fake” leptons. This background arises mostly from in-jet (semi-)leptonic decays of b- and c-hadrons and from photon conversions. The majority of this background is composed of multi-jet production with one fake lepton and non genuine missing energy. These processes are not well understood and therefore are difficult to model accurately, hence the estimation is done with a data-driven technique, the Matrix Method [151].
The calculations are based on the measurement of the number of events satisfying the nominal (“tight”) lepton identification and isola- tion criteria as well as that satisfying more relaxed (“loose”) criteria, together with measurements of the efficiencies for loose prompt and fake leptons to satisfy the tight criteria. In this analysis, the estima- tion is carried out separately for the 2015 and 2016 datasets; the loose criteria are defined by removing the isolation criteria and relaxing the identification criteria.
The efficiencies for loose leptons to pass the tight selection are mea- sured in data for both real prompt and fake leptons. In this way it is possible to estimate the number of fake leptons passing the tight selec- tion criteria by solving the system of equation:
Nl =Nrl+Nlf
Nt = εrNrl+ εfNlf (4.3)
where Nl (Nt) is the number of events observed in data passing the
loose (tight) lepton selection, Nrl (Ntf) is the number of events with a
of real (fake) leptons in the loose selection that also pass the tight one. For real prompt leptons the efficiency is measured in Z boson events, while for fakes it is estimated from events with low missing transverse momentum and low values of the reconstructed leptonic W boson trans- verse mass.
From a generalization of the formula to extract the number of fake
leptons passing the tight selection, Nt
f = εfNlf, a weight is assigned to
each of the selected events in the loose lepton data sample. The method thus provides a straightforward way to predict both the normalization and the kinematic distributions of this background.