The data-to-prediction comparisons as well as the modelling of signal efficiency in data are both impacted by a number of systematic uncertainties. These include uncertainties due to theoretical assumptions made within the MC predictions as well as uncertainties on the reconstruction, calibration and detector response of the physics objects employed in this measurement. For each systematic uncertainty, a systematically-shifted prediction of the distribution is obtained, for both up and down variation of the uncertainty. One-sided systematic uncertainties are symmetrised by mirroring the shift in up and down direction. In the data-to-prediction comparisons in Sec.6.3, the two-sided variation are also symmetrised, taking the maximum of the up/down shifts. The individual uncertainties are summed in quadrature.
In the signal efficiency fit, systematic uncertainties are propagated by repeating the fit with a systematically-shifted set of templates. The systematic uncertainty on the signal efficiency is estimated as the difference between the fit result obtained from the systematically-shifted templates and the nominal set of templates. The uncertainties considered are described in the following paragraphs.
6.4.1 Experimental uncertainties
In this section, the uncertainties related to object reconstruction, identification, pile-up modelling and the luminosity measurement are outlined.
Lepton-related uncertainties
The lepton efficiencies of trigger, reconstruction, identification and isolation differ between data and the MC predictions. These differences are corrected using scale factors applied to MC simulations, which are obtained in dedicated tag-and-probe measurements inZ →`+`−andJ/ψ→`+`−events,
6.4. Systematic uncertainties
as described in Sec.4.2and4.3. The uncertainties on these scale-factor measurements [113,116]
are propagated in the analysis by varying the nominal scale factors by the systematically-shifted ones.
Similarly, the aforementioned event topologies are used to calibrate the lepton momentum scale and resolution in MC simulation to data, where the uncertainties on these measurements [114,116] are propagated by shifting the scale and smearing the resolution in MC simulations by the systematic variations.
Small-Rcalorimeter jet uncertainties
The calibration of jet energy described in Sec.4.4.3contains many sources of uncertainties, which are constructed as an uncorrelated set of almost hundred eigenvectors. The signal efficiency measurement was found to be insensitive to the JES of small-Rjets, and therefore a strongly-reduced set of four NPs is used [124]. The jet energy resolution (JER) in MC simulation is compared to data in a dedicated in-situ measurement [181] in dijet events. The uncertainty on the JER calibration, when averaged over the central calorimeterη, ranges approximately from 20 % for jets withpT∼30 GeV down to 10 % for jets withpT ∼500 GeV [181]. A single nuisance parameter is used to parametrise the JER uncertainty.
Finally, the JVT algorithm is used to suppress contribution of small-Rjets originating from pile-up.
The efficiency of the JVT is calibrated inZ →µ+µ−events with additional production of jets [182].
Per-jet SFs are used to correct the JVT efficiency in MC simulations to match that in data. The SFs are varied in the analysis within the uncertainties of the JVT efficiency measurement in data.
Large-Rjet uncertainties
In contrast to the small-Rjets, for the large-Rjets uncertainties are derived for JES as well as jet mass scale (JMS) and the scale for relevant substructure observables. In this analysis, the in-situ calibration of large-Rjets described in Sec.4.4.4was not yet available, only the MC-based calibration of energy scale and mass scale is performed. A simplified in-situ method to estimate the uncertainty on this calibration was used, based on comparing calorimeter response to ID response [126]. In this method a double ratio ofD
Xjet/XrefE
data/D
Xjet/XrefE
MCfor a quantityX is measured, where the reference value Xrefis calculated using ID tracks associated to the calorimeter jet. Using this method, the uncertainties on JES, JMS and the scale of the substructure observables are estimated.
The JER and jet mass resolution (JMR) uncertainties are based on previous studies. The JER uncertainty is estimated using the same techniques as those for small-R jets, and is found to be approximately 10 % for the jet pT > 200 GeV [126]. The JMR uncertainty is estimated from the data/MC variations in the width of the mass peak of large-R jets identified as W bosons in t¯t events [126,127], thus the JMR is propagated by an additional 20 % smearing of the nominal JMR.
Missing transverse energy uncertainties
TheETmissquantity is computed from several sources of objects described in Sec.4.5. The uncertainties on these objects, described in this sub-section, are propagated into theETmisscalculation. Additionally, ETmissincludes the soft term, which has an uncertainty estimated in-situ usingZ → µ+µ−events [183].
This event topology is suitable due to the high signal-to-noise ratio, the precise muon kinematics
6. Measurement of signal efficiency of boosted top-quark andW-boson taggers
reconstruction and the expected trueETmissvalue being zero. It is therefore primarily sensitive to the ETmisssoft-term effects.
Flavour tagging uncertainties
The modelling of the MV2c10b-tagging algorithm is judged based on the level of agreement of the efficiency to tagb, cand light jets between MC prediction and data. The differences between the efficiencies in data and MC simulations are corrected using scale-factors determined in dedicated measurements [130,131,184], as a function of the jetpT. Theb-tagging efficiency is calibrated using di-leptontt¯events. Thec-tagging efficiency is calibrated using single-leptontt¯events, exploiting the fact that theW-boson decay branching fraction of final states including a charm hadron is approximately 33 % [33]. Finally, the light-jet efficiency is calibrated in multijet events, and is parametrised as a function of both jet pT andη. The uncertainties on the scale factors are constructed as a set of uncorrelated nuisance parameters.
Luminosity uncertainty
The estimates of processes modelled using MC simulations are normalised to the product of corre-sponding cross-section and integrated luminosity. The luminosity is measured experimentally using the LUCID-2 detector [185]. The uncertainty on the integrated luminosity of the 2015-16 dataset is 2.1 % [186].
Pile-up modelling uncertainty
The modelling of the additionalpp collisions per bunch crossing multiplicity µvia the overlay of minimum-bias events onto the hard-scattering simulation is not sufficiently accurate to describe the data. Therefore, the MC simulations are reweighted event-by-event to match the pile-up profile in data based onµ. The per-event weights are varied within their uncertainties, which are derived from the luminosity measurements ofµprofile in data [186] .
6.4.2 Signal and background modelling uncertainties
A number of assumptions enter the MC-simulated predictions, which have associated theoretical uncertainties, discussed in this section.
Normalisation uncertainties of MC-predicted processes
In addition to the luminosity uncertainty, the inclusive yield of the MC-simulated signal and background estimates is impacted by the uncertainty on the respective theoretical cross-section predictions. The theoretical uncertainties on normalisation oftt¯as well as single-top andW+jets backgrounds are listed in Table6.5. In the signal efficiency fit, thett¯normalisation has no impact, since the normalisation of tt¯is determined in the fit. The normalisation uncertainty of the diboson production is neglected due to the very small contribution of this background.
6.4. Systematic uncertainties
Table 6.5: The uncertainties on the normalisation of the individual MC-simulated processes considered in the boosted tagging efficiency measurement. The uncertainty values quoted here are based on the theory predictions cited in Sec.6.1. The uncertainties on the cross-section typically include variation of theµRandµF scales as well uncertainties related to the PDF set.
Process Normalisation uncertainty (%)
tt¯ 5.5
Single-top 5.3
W+jets 5.0
Modelling uncertainties of theW+jets background
TheW+jets is the dominant MC-simulated background in the signal efficiency fit and as such, additional modelling uncertainties impact the acceptance and the shape of distributions. Firstly, the CKKW scale, controlling the matching of the ME and PS, is varied by a factor×0.75 and×1.5 with respect to the nominal value of 30 GeV, and the soft-gluon resummation scale QSF is varied by a factor×0.5 and ×2.0 [187,188]. Finally, factor×0.5 and×2.0 variations of µR and µF scales in the ME are considered, both in an uncorrelated and correlated and anti-correlated way. The maximum of the various correlation scenarios ofµR andµF scale variations is considered as the final uncertainty.
Uncertainties on the fake and non-prompt leptons estimate
The fake and non-prompt leptons background is estimated using data-driven matrix method. To account for limitations of this estimate, two sources of uncertainties are considered. Firstly, a conservative normalisation uncertainty of 50 % is propagated in the analysis, based on previous studies of non-prompt and fake lepton estimates [189]. Secondly, the real and fake efficiencies are varied within their statistical uncertainties in a manner that maximises the impact on the matrix-method weight in Eq.6.4.
This is done by simultaneously varying therealefficiency up andfakeefficiency down within their statistical uncertainties obtaining an “up” variation, and vice-versa for a “down” variation. This uncertainty induces a variation in shape as well as normalisation.
Signal modelling uncertainties
A number of systematic uncertainties on the signal modelling are considered, all of which are based on comparing various generator setups described in Sec.6.1.1. Firstly, the uncertainty on the modelling of the PS and hadronisation is estimated as the difference between predictions from the nominal Powheg+Pythia sample and the sample generated using Powheg+Herwig. The uncertainty on the matching of the ME and PS is estimated by taking the difference between the nominal sample and the sample generated using MadGraph5_aMC@NLO+Pythia8. An uncertainty on the modelling of additional QCD radiation is estimated by comparing the nominal sample with a sample with simultaneously varied µRandµF scales and variation ofhdampparameter, as previously described in Sec.6.1.1.
Finally, an uncertainty on the choice of PDF set in the signal sample is assessed using the PDF4LHC15 prescription [190] which combines several PDF sets with their uncertainties into a set of
6. Measurement of signal efficiency of boosted top-quark andW-boson taggers
30 one-sided uncorrelated variations, which are symmetrised into two-sided variations.