Systematic Uncertainties

The MC modelling relies on certain choices and implementations of the generator, as discussed in Section 4.2, which leads tomodellinguncertainties. In addition, reconstruc-tion and identificareconstruc-tion of each object defined in Secreconstruc-tion 4 is based on measurements with dedicated uncertainties of the corresponding sub-detector. In this section, the systematic uncertainties in the 1L+OS channel are summarised.

5.5.1. Signal Uncertainties

The uncertainty of the t¯tt¯t ME generator is estimated by varying the renormalisation and factorisations scale simultaneously by a factor of 2 (0.5) to obtain an up (down) variation of the scale applied in the MadGraph5 aMC@NLO prediction. The parton-shower uncertainty is estimated by comparing the nominal MadGraph5 aMC@NLO +Pythia 8 prediction withMadGraph5 aMC@NLO +Herwig 7.

5.5. Systematic Uncertainties

5.5.2. tt¯Modelling Uncertainties

The uncertainties of thett¯modelling are expected to have the largest impact on the final result as t¯t+jets itself is the dominating background. For t¯t+jets, the uncertainties are split by the effect of the different jet-flavours on the b-tagging algorithm leading to a total of 23 parameters. In addition, there are 102 nuisance parameters (NPs) representing the uncertainties of the reweighting (RW) in the fit as discussed in Section 5.6.

Matrix-element The uncertainty on the choice of the ME generator is evaluated by comparing the nominal prediction of Powheg with MadGraph5 aMC@NLO where both generators are interfaced with Pythia. In addition, the factorisation and renor-malisation scale inPowhegare varied by 2 (0.5) leading to a total of three parameters for each t¯t+jets flavour.

Parton-shower The uncertainty on the choice of the parton-shower generator is evalu-ated by comparing the nominal prediction of Powheg+Pythia8 withPowheg +Her-wig 7 leading to one parameter for each tt+jets flavour. In addition, the parton-shower¯ uncertainty for b-jets is split intot¯t+b,t¯t+≥2band t¯t+B.

Additional Radiation The uncertainty on the additional jets is split in uncertainties for the initial state (ISR), the final state (FSR) and the choice ofhdamp. For ISR,αs is varied at the Z-boson mass scale around the tuned values in Pythia 8. For FSR, the NPs are obtained by varying the factorisation scale by 2 (0.5) in Pythia8. Forh_damp, the nominal prediction of hdamp = 1.5×mtop is compared with 3.0×mtop. In total, there are three parameters for each t¯t+jets flavour.

Flavour Composition The MC-method does not predict the normalisation oftt¯+≥1b andtt¯+≥1c jets. Therefore, a conservatively flat uncertainty, based on recent measure-ments [139], of±50% was chosen for these two flavours essentially making the normali-sations a free parameter in the fit. In addition, the parton-shower uncertainty for c- and b-jets is split intot¯t+b/c,tt+¯ ≥2b/c and tt¯+B/C.

Reweighting Factors For each scale factor derived by the MC-method, the statistical uncertainty is propagated as NP. In addition, for the parametrisation of H_T^all,red, the three fit parameters are decorrelated. In total, there are 102 parameters for the 1L- and 68 parameters for the OS-channel. Most of the statistical uncertainties are relatively small and are not expected to significantly impact the fit.

5.5.3. Smaller Background Uncertainties

Based on the treatment of the modelling uncertainties, all other backgrounds are grouped int¯t+W/Z/H, single-top, and diboson + minor backgrounds (triboson,V H,t¯t+W W, tritop).

t¯t+W/Z/H The choice of the simulation is evaluated by comparing the nominal Sherpaprediction withMadGraph5 aMC@NLO fort¯t+W, the nominalMadGraph5 aMC@NLO prediction with Sherpa for tt¯+Z and the nominal Powheg prediction with MadGraph5 aMC@NLO for t¯t+H. For all three samples, the renormalisation and factorisation scales are varied by a factor 2 (0.5). A cross-section uncertainty of 15%

is applied on t¯t+W/Z and of 20% on t¯t+H. Further normalisation uncertainties for the production with additional jets are derived based on the mismodelling in 2b regions before reweighting. They correspond to 10%, 20% and 30% in the 9 (7), 10 (8) and≥11 (≥9) for the 1L (OS) channel.

Single top The t-, s- andW-associated channel are treated similarly by comparing the nominal production of PowhegwithMadGraph5 aMC@NLO to obtain a ME uncer-tainty. For parton-shower, Pythia 8 is compared to Herwig 7. For the W-associated channel, the interference schemes of diagram removal and subtraction are compared.

Similar to other processes, the renormalisation and factorisation scales are varied by a factor of 2 (0.5). A 30% cross-section uncertainty is applied as well [140, 141].

Minor Processes No dedicated generator comparison is done for the V+jets and Di-boson backgrounds. Instead, the cross-section uncertainty is conservatively chosen to be 50%.

5.5.4. Reconstruction Uncertainties

Reconstruction uncertainties are based on the uncertainties of the calibration of each object. Typically, dedicated measurements are performed to extract the calibration and to determine the uncertainties.

Data Taking Conditions As discussed in Section 3.2, the luminosity in Atlasis mea-sured by LUCID-2. Since all MC samples are scaled by the meamea-sured luminosity, the uncertainty of 1.7% for the full Run II dataset propagates to all MC samples. Differ-ences coming from pile-up are taken into account by reweighting MC events to data. The weights are derived from a dedicated simulation during which events are overlayed to match the expected luminosity profile in data (minimum-bias) [142]. The uncertainties for each weight is propagated to all MC samples.

Electrons and Muons The tag-and-probe method is used to derive scale factors in the calibration of the reconstruction, identification, isolation and trigger performance. They cover the differences between data and MC for a variety of object dependent effects such as energy and momentum scales and charge dependencies in the reconstruction for muons. For each of the 7 (13) scale factors for electrons (muons), the uncertainties are propagated to MC simulated events.

5.6. Statistical Analysis