Systematic Studies

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Toys, SU3 var. corr. off /dof = 48.5/48 8x8 Tiles method: SM BG + SU3

Figure 11.16: Fitted number of SM t¯t events (left) and remaining SM events (right) for the 8×8 tile configuration in 5000 toy experiments, each corresponding to an integrated luminosity ofL= 1fb⁻¹. allows to improve the finesse of the background estimate, which reduces systematic errors.¹⁵ For Kindividual SM background contributions, the expected number of events for tileij is given by

N_ij = background components with sufficiently different shapes (and hence different fractionsf_ij,k^SM) can be constrained by the fit (cf. Fig.10.3in Section10.2). Shape similarity will lead to anticorrela-tions between the fittedN^SM_k .

As an example, we have decomposed the inclusive SM background contribution into t¯t (1532 events) and the remaining part (316W+jets,15Z+jets,5dibosons events) in the fit. Figure11.16 shows the two fitted SM yields obtained in5000toy experiments using 8×8 tiles. When signal correlations are absent, the true SM event yields are correctly reproduced by the fit. They exhibit a strong anticorrelation (on average we find a coefficient of−0.9), and the statistical error on the signal yield increases with respect to the nominal fit from45to53events. With signal correlations, the fit results are biased.

We point out that splitting the SM background into more than one components, with their yields determined by the fit, is equivalent to the treatment for “uncertainties in the tile fractions” dis-cussed in Section11.3.4when using Eq. (11.10) without adding the penalty (11.11). In most cases prior information on the expected yields from MC simulation is available and should be used via adding a penalty function to the fit.

11.3.8 Systematic Studies

The Tiles method depends on the SM MC fractions for each tile and we cannot expect the simu-lation to fully reproduce the data. We have thus studied the effects of systematic uncertainties in

15More precisely: parameters that suffer from systematic uncertainties are determined from data; hence systematic errors are transformed into statistical ones.

the SM fractions on the fitted signal event yield and tile fractions, to assess the sensitivity of the method to its inherent assumptions.

Where necessary, systematic variations have been propagated throughout the entire analysis chain to properly include all effects. This applies to the uncertainties in the JES andE_T^miss resolution.

Elsewhere, we simply rescale cross sections of certain processes. Examples here are uncertainties in the relative background composition and in the lepton ID and jet reconstruction efficiencies.

Common to all systematic effects is that they affect the distributions of the discriminating variables and thereby modify the SM tile fractions.

Various systematic effects are discussed in the following, the deviations in the SM tile fractions of which are explicitly given for the simplest 2×2 tiles configuration. Moreover, systematic effects on the signal yields are quantified for different tile configurations for the SUSY benchmark point SU3.

Note that the centralM_T tile boundary has been moved from100 GeVto110 GeVin this study, that is, away from the sharp edge in its distribution, which drastically reduces the sensitivity to systematic effects in that variable.

Jet Energy Scale (JES)

Assuming a 10% systematic uncertainty in the JES, the energies and momenta of all jets are correspondingly scaled up and down. The rescaling is subsequently propagated into the transverse components of theE_T^miss vector. All derived variables including E_T^miss, M_eff, andM_T and the corresponding tile fractions are then recomputed.

Figure11.17shows the SM MC distributions for the hardest jetp_T (top left),E_T^miss(top right),M_eff (bottom left), andM_T (bottom right), before and after applying a+10%JES shift. Table11.2gives the corresponding impact on the SM tile fractions for the 2×2 tiles configuration. The systematic effects on the fitted number of signal events (N^S) for SU3 versus the tile configuration are shown in Fig.11.18(left plot). A bias of order30(60) events is found for 2×2 (8×8) tiles, corresponding to a systematic error of4%(8%).

E^miss_T Resolution

The effect of a systematic uncertainty in theE_T^missresolution is studied by independently smearing the transverse components of theE_T^miss vector via addition of a Gaussian noise term of width in units of theE_T^miss resolution,0.64·P

E_T[ GeV], cf. top left of Fig.11.19. We have studied the impact of a degradation of the nominalE_T^missresolution by20%and100%.

Figure11.19shows the results of a 100% smearing onE_T^miss (top right),M_eff (bottom left), and M_T (bottom right). The independent smearing of the transverse components strongly affectsM_T. Table 11.2gives the corresponding systematic errors in the SM tile fractions for the 2×2 tiles configuration. The systematic errors inN^Sfor SU3 are given in the right plot of Fig.11.18versus the tiles setup. A bias of 10 (4) events for 2×2 (8×8) tiles is observed for a 100% smearing, corresponding to a systematic error of1%(<1%).

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Figure 11.17: SM background distributions before (open/blue squares) and after a JES rescaling by+10%

(filled/red circles) for the hardest jetpT (top left),E_T^miss(top right),Meff (bottom left), andMT (bottom right). All distributions are before applying the one-lepton selection requirements.

Tiles setup: NxN [N]

Tiles method on SM BG + SU3 toys, various NxN setups

Tiles setup: NxN [N] Tiles method on SM BG + SU3 toys, various NxN setups

Figure 11.18: Biases in the fitted signal yields introduced by the JES (left plot) and E_x,y^miss systematic effects (right plot) as a function of the tile configuration. All results are obtained with the Tiles method running on SU3 signal and SM background.

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Figure 11.19: Top left: MC resolution of the transverse components of theE_T^missvector. Other plots:

SM background before (open blue squares) and afterE^miss_x,y smearing (filled red circles) in the variables:

E_T^miss(top right),Meff (bottom left), andMT (bottom right). All plots are before the one-lepton SUSY event selection.

SM Cross Sections

The SM background comprises several processes whose cross sections have uncertainties. Since the tile fractions differ in general among these processes, the cross section uncertainties create systematic effects.¹⁶ Here only the dominantt¯t(92%) andW+jets (7%) contributions are consid-ered, to each of which is assigned a 50% cross section uncertainty, that are conservatively scaled in opposite directions. (The shapes of theMT andM_eff distributions fortt¯andW+jets are shown in Fig.11.21.)

The resulting systematic errors in the 2×2 tile fractions are given in Table11.2. The systematic errors onN^S for SU3 versus the tile configuration are shown in Fig.11.20(left plot). We find a bias of the order of90events (12%) for both 2×2 and 8×8 configurations.

Top Sample Composition

The composition of the t¯t background is affected by systematic uncertainties in the simulation of the lepton identification and jet reconstruction efficiencies. It is studied in an approximative

16Unless the SM background components are fitted separately, as described in Section11.3.7.

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Tiles method on SM BG + SU3 toys, various NxN setups

Tiles setup: NxN [N]

Tiles method on SM BG + SU3 toys, various NxN setups

Figure 11.20: Biases in the fitted signal yields introduced by the systematic uncertainties in thet¯t,W+jets cross sections (left) and the t¯t background composition (right). All results are obtained with the Tiles method running on SU3 signal and SM background.

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Figure 11.21: Distributions ofMeff (left) andMT (right) for SM background decomposed intoW+jets (open/black circles), tt → `ν`ν (filled/red squares), and tt → `ν`ν (filled/blue triangles) contributions.

Both plots are after the one-lepton event selection (theMT requirement has been dropped in theMT plot).

way, by varying the cross sections of the tt → `ν`ν and tt → `νqq processes in analogy to Section11.3.8, because these two processes exhibit different shapes – in particular forM_T (see Fig.11.21). We have applied relative cross section shifts of±10%to both processes in opposite directions.

Table11.2quotes the resulting systematic errors in the SM tile fractions for 2×2 tiles. The sys-tematic errors onN^Sfor SU3 versus the tile configuration is shown in the right plot of Fig.11.20.

A bias of48(33) events is observed for 2×2 (8×8) tiles, corresponding to a systematic error of 6%(4%).

Monte Carlo Generator

Uncertainties in the generation of the physics processes have been studied by replacing Alpgen t¯tsamples by MC@NLO ones. However, since the Alpgen sample is an efficiency corrected fast simulation of the ATLAS detector whereas the MC@NLO events passed through full GEANT