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B | Data-driven QCD multi-jet esti- esti-mate

B.1 Anti-electron selection

The most important ingredient for the anti-electron method is a modified electron object definition. We start by discussing the nominal definition: electron candidates are selected

1data11_7TeV.periodAllYear_DetStatus-v36-pro10_CoolRunQuery-00-04-08_Top_allchannels.xml

using recommendations from the ATLAS electron/photon performance group, which are regularly updated as the understanding of the detector improves. The following describes the situation in early 2012. Electron identification is made in several steps (see for ex-ample [84], section 10.2.5), starting with hit cluster identification in the silicon detectors, followed by track reconstruction (allowing for bremsstrahlung losses), and vertex finding.

Using information from the TRT, most importantly the number of high-threshold hits, it is possible to identify pions and photons that convert to electron-positron pairs. For each electron candidate, the most important features found by the identification algorithms are stored as a list of flags, which are then used to define several electron categories from loose++to tight++(table B.2). All of the input variables underlying the flag definitions are described in ref. [88]. The bits selected for the anti-electron method (as explained below) rely on the following variables, all of which use properties of the track associated to the electron candidate:

• TrackBlayer– the track has a hit in the innermost silicon layer (B-layer).

• TrackMatchEoverP – ratio of cluster energy and track momentum

• TrackTRThits – number of TRT hits

• TrackTRTratio– fraction of highly energetic TRT hits

The tighter selections have a lower selection efficiency but also a higher purity, i.e. a lower probability of incorrectly identifying objects as electrons. The nominal electron definition in the semi-leptonic t¯t analysis requires the tight++ bits to pass. There are further requirements on the electron transverse momentum and pseudo-rapidity (ET ą25 GeV,

|η| ă2.47, excluding the transition region1.37ă |η| ă1.52between the barrel and end-cap cryostats), and on the electron isolation (both track-based and calorimeter-based).

To obtain a data-driven QCD estimate, the electron definition is now replaced by an “anti-electron” definition, in which some of the tight bits are required to fail. The choice of suitable bits is an important part of this study. To make the modified selection orthogonal to the nominal one, events with a selected standard electron are rejected. The missing transverse energy ETmiss is adjusted such that the anti-electron contributes with the correct calibration (electromagnetic scale instead of jet energy scale). Lastly, the set of accepted triggers needs to be changed: the nominal selection uses a trigger optimised for medium electrons, but due to the bit-reversal the anti-electrons can fall outside the trigger acceptance. The choice of anti-electron triggers presented a challenge because the trigger menu changed several times over the course of 2011.

An earlier version of the anti-electron method relied solely on the reversal of the ClusterHadronicLeakage bit, which is not part of even the loosest available electron definition. The loose single electron triggers impose a requirement on the leakage variable, making the anti-electron definition sensitive to hardware features outside the control of

bit name loose++ medium++ tight++

0 ClusterEtaRange ˆ ˆ ˆ

1 ConversionMatch ˆ

2 ClusterHadronicLeakage ˆ ˆ ˆ

3 ClusterMiddleEnergy ˆ ˆ ˆ

4 ClusterMiddleEratio37 ˆ ˆ ˆ

5 ClusterMiddleEratio33

6 ClusterMiddleWidth ˆ ˆ ˆ

. . .

15 ClusterStripsDEmaxs1 ˆ ˆ ˆ

16 TrackBlayer ˆ ˆ

17 TrackPixel ˆ ˆ ˆ

18 TrackSi ˆ ˆ ˆ

19 TrackA0 ˆ ˆ

20 TrackMatchEta ˆ ˆ ˆ

21 TrackMatchPhi ˆ

22 TrackMatchEoverP ˆ

23

24 TrackTRThits ˆ

25 TrackTRTratio ˆ ˆ

. . .

Table B.2: Electron property bits and their use in different electron definitions. Not all bits are defined, and several bits are defined but not used. The table reflects the situation in early 2012 [88]. As detailed in the text, only the four bits in bold print are relevant for the anti-electron definition.

the analyser and without any physical meaning. A trigger match was not required in the earlier version, as this condition removed a significant fraction of the anti-electron candidates. This introduces a bias in the event selection, since events with an anti-electron candidate (with a failedClusterHadronicLeakagebit, not very likely to initiate a trigger) can be selected if another electron is present in the event. An important technical difficulty resulting from this earlier anti-electron definition is that none of the ETmiss terms in the available datasets account for electrons that do not fulfil the loose++

electron definition, making it impossible to correct the ETmiss in the manner described above.

To improve on this, only electron property bits that are required for tight++ but not for loose++ electrons have been considered for reversal. Within these require-ments, it is found that most of the ClusterStrips bits never fail, and only the fol-lowing bits remained to be studied: ConversionMatch, TrackBlayer, TrackA0, Track-MatchPhi,TrackMatchEoverP,TrackTRThitsandTrackTRTratio. TheTrackA0bit has been dropped because it fails very rarely, and the following bits were removed because of correlations: ConversionMatch (correlated with TrackBLayer), and TrackMatchPhi (correlated with TrackMatchEoverP). Four bits remain, each of them apriori suitable for building an anti-electron model: TrackBlayer, TrackMatchEoverP, TrackTRThits, TrackTRTratio.

Figure B.1: Distributions ofETmiss,mTand ∆φp`, ~ETmissq for anti-electron QCD multi-jet models based on the reversal of different electron property bits. Only one bit is reversed for each model.

To decide if the anti-electron definition based on a given bit, or set of bits, results in a reasonable QCD model, several kinematic distributions are built. As seen in figure B.1, most models behave similarly to each other, with the exception of the model obtained by reverting theTrackTRThits. For practical reasons, it was decided not to use this bit, and group the remaining bits. From here on, QCD models are only distinguished by the minimum number of failed bits used in the anti-electron definition2. While the QCD model built from events with one or more failed bits has the largest statistics, it also has the largest estimated contamination from real electrons. At least for the looser jet bins, it is preferable to require two or more failed bits.