Reconstruction algorithms

There are two main electron-finding algorithms in the ATLAS reconstruction software.

The standard “egamma” electron reconstruction, which is used in this analysis, ranges over the full acceptance of the Inner Detector system (|η| < 2.5) [83, 84]. This algorithm is more widely used throughout the physics analyses due to its wide range in η and ET in comparison with the second track-seeded reconstruction algorithm (“softe”), which is more suitable for lower energy electrons.

The reconstruction of an egamma electron begins with the creation of a prelimi-nary set of seed clusters in the EM calorimeter with an energy threshold of 2.5 GeV.

The clusters are formed with a sliding window algorithm, where the seed clusters are of the size 3×5 in middle layer cell units of the calorimeter (0.025 × 0.025 in η/φ).

After an energy comparison has been carried out, duplicate clusters are removed from nearby seed clusters.

The middle layer of the cluster is then matched to a track in the Inner Detector within a window of ∆η×∆φ= 0.05×0.1. The track is required to have a transverse momentum of at least 0.5 GeV. The extrapolation uses the η and φ coordinates from the last measurement on the track. If there are multiple tracks matched to the cluster, the closest match is kept as the electron track, with priority given to tracks with at least 4 silicon hits over TRT-only tracks. For the latter case, only track-cluster matching within ∆φ= 0.1 is applied since the TRT lacks resolution in η.

The final electron cluster has a size of ∆η×∆φ = 0.075×0.175 in the calorimeter barrel and 0.125×0.125 in the end-caps. The energy measured from the cells belonging to the electron cluster defines the electron energy in this analysis. The transition

(“crack”) regions between the barrel and end-caps of the EM calorimeter, 1.37<|η|<

1.52, are expected to have poorer performance due to the large amounts of material in front of the first active calorimeter layer.

5.1.2 Electron identification

The electron reconstruction provides a very loose definition of an electron in order to keep the reconstruction efficiency as high as possible. This indicates that further iden-tification cuts are necessary to remove the majority of the large hadronic background.

A sequence of calorimeter and track variable cuts have been optimized in order to provide efficient electron identification together with sufficient background rejection.

The selection cuts depend on the kinematics of the electron and are therefore binned in |η^e| and E_T^e. The optimization has been performed in 10 bins in cluster η within

|η|<2.47 (computed from the middle layer of the calorimeter), which have been de-fined by detector properties, and 11 bins in clusterET, starting from 5 GeV. There also exists pre-defined sets of identification cuts for the forward region (2.5<|η|< 4.9), optimized purely on calorimeter variables such as topocluster moments (described in section 4.4.5).

Three sets of requirements have been defined for central electrons (|η|<2.47) with increasing background rejection capacity: “loose”, “medium” and “tight”¹. Each selection set includes the requirements of the previous selection. The loose, medium and tight identification cuts are briefly described below and are outlined in more detail in Table 5.1. For more explicit details on electron identification, consult [83].

• Loose ID - This selection uses shower variables from the second layer in the EM calorimeter such as lateral shower containment and shower width. It also includes energy leakage in the hadronic calorimeter. The jet rejection obtained from the loose requirements for electron candidates withET >17 GeV has been estimated on Monte Carlo to be of the order of 6·10² [23].

• Medium ID - The medium identification cuts include the loose electron re-quirements with the addition of applying rere-quirements on the energy deposit variables in the first layer of the EM calorimeter cluster (the shower width and the ratio of the energy difference between the most energetic and second most energetic cell and the total sum of these energies). Furthermore, the set includes requirements on track quality variables, such as number of hits in the Pixel and the SCT as well as on the transverse impact parameter. Finally a cut is applied on the ∆η between the track and the first layer of the cluster. The jet rejection obtained by applying medium requirements is of the order of 2·10³ [23].

1Medium WithTrackMatch and Tight WithTrackMatch are applied as the standard medium and tight identification in release 16.

• Tight ID - This set of requirements provides additional hadronic background rejection using cuts on the ratio of the energy from the cluster and the momen-tum from the track, number of TRT hits and the ratio of high threshold TRT hits (as discussed in section 4.4.4). Secondary electrons from conversions are rejected by requiring at least one hit in the innermost layer of the Pixel detector (the b-layer) as well as removing electrons matching reconstructed conversion photons. The impact parameter cut from the medium level is further tightened as well as the track cluster matching through adding a cut on ∆φ. Jet rejection at tight level has been estimated to be of the order of 9·10⁴ [23].

5.1.3 Reconstruction and identification efficiency

The efficiency of the electron reconstruction and identification algorithms and se-lections must be accurately estimated from the data to correctly measure the cross section times branching ratio of for instanceW →eν and Z →ee decays. Two data-driven methods have been used for this purpose; Z and W tag-and-probe [57, 81].

Since the electron efficiency is intrinsically slightly different if it originates from a W or a Z (largely due to the differences of the η and ET distributions of the electrons), it is important to compare the data/MC efficiency ratio (scale factor) for the two methods. In addition, the scale factors have the advantage of being easily incorpo-rated in any physics analysis to correct the simulated data. The scale factors from W andZ tag-and-probe are thus combined to obtain smaller statistical uncertainties and hence more robust results.

While the methodology of Z tag-and-probe is discussed in great detail in the following sections, the W tag-and-probe is only briefly summarized here (for further details consult [57, 81]). The W tag-and-probe method consists of selecting events with a large value of E_T^miss and probing for an electron to perform the efficiency calculation on. To keep the electron from the W unbiased an E_T^miss trigger is used, instead of an electron trigger, for the event selection. To perform the necessary background subtraction at each level of the efficiency calculation, distributions from different calorimeter isolation variables are fitted.

5.2 Z → ee tag-and-probe methodology

One of the principal methods of assessing the electron efficiency with a data-driven technique is by applying “tag-and-probe” on Z → ee events. The Z tag-and-probe method consists of tagging a relatively clean sample of Z →ee events in data by applying strict electron requirements to one of the electrons, leaving the second electron unbiased to be used for the efficiency calculation.

Type Description Symbol Loose cuts

Hadronic leakage • ET ratio between the first layer of the Rhad1

hadronic calorimeter and the EM cluster (used over the range |η|<0.8 and|η|>1.37)

• ET ratio of the hadronic calorimeter and the EM Rhad

cluster (used over the range|η|>0.8 and|η|<1.37)

Second layer of • Energy ratio inη of 3 ×7 versus 7×7 cells. Rη

the EM calorimeter • Lateral width of the shower wη2

Medium cuts(including Loose)

First layer of • Total shower width wstot

the EM calorimeter. • Ratio between the energy difference associated with Eratio

the largest and second largest energy deposit and their total energy

Track quality • Number of hits in the pixel detector (≥1). nPix

• Number of hits in the pixels and SCT (≥7). nSi

• Transverse impact parameter (<5 mm). d0

Track matching • ∆η between the cluster and the track (<0.01). ∆η1

Tight cuts(including Medium)

b-layer • Number of hits in the b-layer (≥1) b-layer Track matching • ∆φbetween the cluster and the track (<0.02) ∆φ2

• Ratio of the cluster energy and the track momentum E/p

• Tight ∆η cut (<0.005) ∆η1

Track quality • Tight transverse impact parameter cut (<1 mm) d0

TRT • Total number of hits in the TRT nTRT

• Ratio of the number of high-threshold TRratio hits and the total number of hits in the TRT

Conversions • Electron candidates matching to reconstructed conversion photon conversions are rejected

Table 5.1: Definition of variables used for loose, medium and tight electron identifi-cation requirements for the central region of the detector (|η|<2.47)

Figure 5.1 shows an Atlantis event display of the firstZ →eecandidate observed in ATLAS, in May 2010. The two electrons originating from theZ boson can clearly be distinguished in the event. The tag-and-probe method implies first tagging one of the electrons (tag electron) through applying tight identification. The tag is also matched to the equivalent trigger that the event is required to pass by searching within a cone of ∆R < 0.15 between the trigger object and the offline electron reconstruction.

Cluster variables are used for the L1 trigger matching, while track variables are used for the EF. In this manner, the probe is left unbiased from the trigger selection of the event. The probe electron is then asked to pass different sets of identification criteria and the efficiencies can be estimated. The event can be used more than once if both electrons pass the requirement of the tag, which thus increases the statistics of the probe sample. The method hence selects one of the electrons passing the tag requirements and probes for the other electron in the event. Subsequently the method investigates if there is another electron passing the tag requirements and then again probes for a different electron than the current tag and now finds the initial tag as the probe.

Figure 5.1: Atlantis event display of the first Z → ee event seen in ATLAS in May 2010. All ATLAS public event displays are available in [85].

Since there is a non-negligible amount of background present, which decreases when applying the different sets of identification requirements to the probe, it needs to be properly subtracted at each level in order to obtain the signal efficiencies. The background subtraction can be performed with several methods, which are discussed in section 5.2.3 below. Due to the small combinatorial background present in the sig-nal Monte Carlo, the data-driven efficiencies are compared to identification efficiencies for truth-matched electrons in MC (see section 5.2.4).

After the efficiencies have been obtained in both the data and MC, data/MC scale

factors can be calculated. The scale factors are used by physics groups to correct the simulated data for the data-MC discrepancies. This is done for theW/Z cross section measurements outlined in the following chapters of this thesis.

The relatively low statistics of Z events available in the 2010 data does not allow for an efficiency measurement to be carried out in two-dimensional (η,ET) space in sufficiently fine binning. The efficiencies are therefore estimated separately as a function ofη and ET using different background subtraction methods. The following one-dimensional binning has been chosen:

(E_T, η) binning

η^probe = -2.47, -2.01, -1.52, -1.37, -0.80, 0.0, 0.80, 1.37, 1.52, 2.01, 2.47 E_T^probe (GeV) = 20, 25, 30, 35, 40, 45, 50, 80

Table 5.2: Definition of binning in ET, η space for electron efficiency measurements with 2010 data, chosen due to the limited statistics.