Reconstruction Algorithms and Identification Techniques

ATLAS identifies electrons, photons, muons, jets and taus7 _{by converting raw detector data}

to fundamental physics objects using a dedicated set of algorithms, collectively referred to as event reconstruction. The basic building blocks for constructing these objects are the particle trajectories (tracks) reconstructed from hits in the inner detector and muon spectrometer (in the case of muons), providing an estimate of a particle’s momentum, and topological clusters constructed from energy deposits in the calorimeters. A second clustering algorithm for determining local energy deposits in the EM calorimeter, the sliding window algorithm, is used in the reconstruction of electrons and photons.

Track Reconstruction. Track reconstruction can be characterized in terms of three steps: a seeding step performed with hits in the silicon detectors, a pattern recognition step where the track seeds are extended to the rest of the ID, and a final track fitting step using the result of the pattern recognition. The tracking makes specific accommodations to increase the efficiency of finding tracks from electrons and converted photons.

The tracking steps are as follows:

• Segments of 3 silicon hits are found that meet basicpTand spatial requirements.

• The pattern recognition step is run with an algorithm based on the Kalman Filter [73]

with a pion track hypothesis (meaning that minimal energy loss is expected as the particle traverses the ID material).

• If the first pattern recognition fit fails, a second fit is attempted with a modified algo-

rithm that allows for energy loss at each hit surface. This procedure recovers electrons with significant energy loss due to bremsstrahlung.

3. Experimental Apparatus 29

• Successful tracks from the Kalman Filter are rerun using the ATLAS Globalχ2 _Track

Fitter [74]. A pion or an electron hypothesis is used, depending on which was used successfully in the previous step.

The track reconstruction process described above can be described as an “inside-out” algo- rithm, with tracking seeded by the silicon hits close to the interaction point and extrapolated outward toward the calorimeters. A complementary “outside-in” algorithm, in which tracks are seeded using segments in the TRT and extended inward, is run to aid in the reconstruction of converted photons.

Topological Energy Clusters. Energy clusters used for defining jets are reconstructed

using a topological clustering algorithm [75, 76]. Topological clusters are formed using the three-dimensional energy deposits in the EM and hadronic calorimeters. The process is it-

erative: beginning with a list of seed cells with a high signal-to-noise ratio _|Ecell|>4σnoise,

all cells touching the border of a seed cell (neighboring cells) are added to the cluster. If the

neighboring cell has a signal-to-noise ratio|Ecell|>2σnoisethen the border of the cell becomes

part of the seed border for the next iteration. The process repeats with the neighbors of the newly-defined border, until the border stops increasing. Jets are then formed using the

Anti-kt algorithm [77] with radius parameter R = 0.48 using the topological clusters as an

input.

The topological clustering algorithm is also used to construct lepton variables describing how isolated the lepton candidate is in the calorimeter (described later). For these applications the noise thresholds of the algorithm are slightly modified, but the basic principle is similar.

3. Experimental Apparatus 30

The Sliding Window Algorithm. Electromagnetic clusters for electron and photon re-

construction are formed using the sliding-widow algorithm [75]. Cells in the EM calorimeter

from all four layers are grouped into ∆η_×∆φtowers of 0.025_×0.025, and a window of 3_×5

towers is moved across the detector to identify local maxima above 2.5 GeV to form a collection

of seed clusters. A rectangular tower with its larger dimension inφis preferred over a square

template to accommodate electrons with bremsstrahlung energy loss. The electron bends in

the φ direction due to the axial magnetic field, but its collinear photon emissions are unaf-

fected by the field, thus smearing the energy disproportionately in theφdirection. The 5×7

window attempts to capture the full electron energy, including losses from bremsstrahlung.

Electrons. Electrons are formed by matching tracks reconstructed in the ID with electro- magnetic clusters found using the sliding window algorithm. Tracks and clusters are required

to be within a tolerance of _|∆η_| < 0.05, and ₋0.2 < ∆φ < 0.05, where positive values of

∆φ are associated with the case in which the fitted track is bending away from the cluster

barycenter.9 _{Failing these criteria, the track momentum is rescaled to match the measured}

cluster energy, and tested for the tolerances|∆η|<0.05 and−0.1<∆φ <0.05 [24].

Tracks are then refit using the Gaussian Sum Filter tracking algorithm, which further improves the track measurement in light of bremsstrahlung losses [78]. Information from the cluster and track are combined to measure the track momentum. Further corrections are applied to fully calibrate the electron energy [79].

Photons. Electromagnetic clusters formed using the sliding window algorithm and without

an associated track are automatically classified as photons. However, roughly 30-50% of all photons convert inside the detector material, occurring more often in the endcaps where the

9_{As with the choice of a 5×7 window for the sliding window algorithm, the greater tolerance on one side} of the ∆φdistribution is to accommodate electron energy loss due to bremsstrahlung.

3. Experimental Apparatus 31

photons traverse more material. Clusters with an associated track are initially classified as electrons, and a procedure is run to disambiguate converted photons and electrons by trying to find a two-track vertex inside the detector, or by checking whether the track leaves a hit in the innermost layer of the inner detector. Converted photons classified as electrons are a main electron background.

Muons. Muons can be reconstructed in one of several ways, depending on the instrumen-

tation of the detector in the region traversed by the muon:

• Combined muons: a MS track is matched to a reconstructed track in the ID, and the

measurements of the momenta are combined

• Segment-tagged muons: a partial MS track is matched to an ID track, and the muon

momentum is taken from the ID measurement

• Standalone muons: MS tracks found outside the ID acceptance (2.5 < _|η_| <2.7) and

momentum taken from the MS track

• Calorimeter-tagged muons: in the non-active “crack” of the MS at|η|<0.1 and ded-

icated to services, tracks in the ID with pT > 15 GeV and an associated calorimeter

deposit consistent with a minimum ionizing particle.

A number of quality requirements can be imposed on the reconstructed muons, including minimum requirements on the number of hits in each of the ID subdetectors and the MS, where applicable.

Prompt versus non-prompt leptons. Leptons (muons and electrons—excluding taus)

can be separated into two types. Prompt leptons are participants in the hard-scatter process,

3. Experimental Apparatus 32

leptons are the weak decay products of b-jets and c-jets, whose lifetimes are relatively long

(cτ ≈450 µm for b-jets, and as much as cτ ≈300 µm for c-jets). As a result, their decay

products can be traced back to a vertex that is displaced from the hard-scatter process. ATLAS lepton identification is designed to identify the prompt leptons involved in electroweak physics and to reject the non-prompt leptons from these heavy-flavor jets.

Lepton Impact Parameter Requirements. To reject non-prompt leptons, requirements

are placed on the distance of closest approach between the lepton’s track and the primary

collision vertex.10 _{Two variables from the track fit are used. The first is the transverse impact}

parameter,d0, defined as the track’s distance of closest approach to the collision vertex in the

transverse plane.11 _{This variable can also be formulated into an impact parameter significance:}

|d0/σd0|, whereσd0is the defined by the error matrix of the track fit. The second variable used

is _|z0sinθ|, wherez0 is the distance between the z-position of the vertex and thez-position

of the point on the track at whichd0is defined, and sinθis the polar angle of the track. The

d0 and|z0sinθ|of non-prompt leptons will have distributions with large tails, allowing many

of them to be rejected.

Lepton Isolation. Calorimeter and track isolation variables reflect the ambient energy in a cone surrounding a lepton candidate, and are used as a powerful discriminant for selecting prompt leptons against the non-isolated lepton decay products in heavy-flavor jets, or from

light-flavor jets (includingu,d, ands-quark-initiated jets or gluon-initiated jets). Figure 3.10

relates the cone sizes used to describe these isolation variables, and their relation to calorimeter cell sizes.

10_{The primary vertex is defined as the vertex with the highest}P p2

Tsummed over all tracks in the vertex. 11 _{In 2011 and 2012, the d}

0 is calculated with respect to the measured position of the primary vertex. Beginning in 2015, thed0 is calculated with respect to the beam line (labeleddBL0 ).

3. Experimental Apparatus 33

For both electrons and muons, track isolation is defined as the scalar sum of all track

momenta above a certainpTthreshold (typically around 0.4-1 GeV) in a cone ∆R= 0.2, 0.3

or 0.4 around the electron candidate, excluding the track matched to the lepton candidate.

Track isolation variables are typically formulated relative to the pT of the associated object,

e.g. piso

T /pTto improve the efficiency of isolation requirements for higher-pTobjects.

φ η

R=0.2 R=0.4

0.1

Size of a TileCal cell (0.1x0.1)

Size of LAr 2nd _{sampling (0.025x0.0245)}

Size of LAr 1st _{sampling (0.003x0.1)}

Antikt4 jet x

x

electron candidate

Figure 3.10: Depiction of isolation cones (∆R = 0.2, 0.3 and 0.4) in relation to detector

element sizes. The cone sizes are compared to LAr and Tile calorimeter cells, as

well as the 7×7 cell block used to construct electron calorimeter variables. An

artist’s rendition of energy deposits from an electron and a hadron is depicted, simulating energy deposits in the 2nd layer of the LAr calorimeter (green) and energy deposits in the hadronic calorimeter (red).

There are two types of calorimeter-based isolation: “cell-based” and “topological” isola- tion. Cell-based calorimeter isolation is computed using the energy in the electromagnetic and

hadronic calorimeters in a cone of ∆R = 0.2, 0.3 or 0.4, excluding energy in the calorimeter

associated with the lepton.12 _{This energy in the surrounding cone is referred to as the “iso-}

lation energy,” Eiso

T . The small amount of electron energy leaking out of its 5×7 window,

typically just a few percent, is subtracted fromEiso

T . Furthermore, a correction term repre-

senting the ambient energy density of the event due to underlying event and pileup events is

also subtracted fromEiso

T [81]. As in the case of track isolation, calorimeter isolation variables

12_{In the electron case, the energy in the 5×7 cell window surrounding the cluster in the EM calorimeter} is associated with the electron (corresponding to 0.125×0.172 inη−φspace). In the muon case, the energy associated to the muon object is optimized on a layer-by-layer basis in the EM and hadronic calorimeters [80].

3. Experimental Apparatus 34

are often formulated relative to theETof the associated object, e.g. ETiso/ETto improve the

efficiency of isolation requirements for high-ETobjects.

Topological isolation is an improvement over cell-based isolation, which has a dependence on out-of-time pile-up that changes the variable’s behavior as a function of the position of the collision in the bunch train. The topological isolation variable, which constructs topological

clusters in a cone ∆R= 0.4 around the electron candidate and computes the isolation using

these clusters, is much more stable as a function of bunch train position [82].