Pattern recognition in the Inner Detector

 Pattern recognition is a widely used term for all kind of processes where specific information is extracted from a large set of individual measurements. The part of the brain that analyses the information from the eye is probably one of the most advanced pattern recognition systems known. The eye has three different sensor types used during daytime which provides the brain with a highly segmented colour image. From this the eye can at the first level extract information like lines and coloured areas and at a deeper lying level recognising objects as faces or letters.

Pattern recognition systems developed for finding tracks in detectors are often evaluated by visual inspection making use of the eyes outstanding pattern recognition capabilities. A discussion of visualisation methods suited for the eye can be found in [58].

For the ATLAS Inner Detector it is a problem to find all the tracks. As an example of the task for the pattern recognition a Higgs particle decaying to two b-quarks is shown in fig. 6.1. The two jets from the b-quark fragmentation are clearly recognisable in the TRT as are many individual tracks. The tracks cannot be seen in the silicon detectors for two reasons: the number of hits on each track compared to the TRT is lower and the presentation is not optimal for the human eye.

  

Figure 6.1: An event display of the barrel part of the Inner Detector with the decay of a Higgs particle to b-quarks at high luminosity. The two jets from the b-quark fragmentation are clearly visible. The inner part of the figure shows the hits in the silicon detectors with the reconstructed tracks superimposed. The outer part of the figure shows the hits in the barrel TRT.

Some clear definitions are necessary for a discussion of pattern recognition:

Hit

A detection channel with an output signal above some threshold. In the silicon detectors the small cluster of channels with energy above threshold created by a charged particle or noise. In the TRT a straw with an energy deposition above the low threshold. With the drift-time included it is called a drift-time hit.

Occupancy

The fraction of detector channels with a hit in a local area.

Efficiency

The probability for a hit in a channel where the active detection area is crossed by a charged particle.

Noise level

The fraction of channels in a local area with hits caused by electronic noise.

Shared hits

Hits created by a combination of several charged particles or a combination of noise and a charged particle.

Space-point

The combination of two hits, in the two different projections of a silicon layer with a stereo-angle, to form a hit in three dimensions.

Raising the abstraction level and looking at the reconstruction of tracks the following definitions are used:

Track

The group of hits created by a single charged particle. Also used as a short form for the reconstructed parameters of a charged particle.

Pattern recognition

The process of finding the tracks.

Track fitting

After finding the track with the pattern recognition an optimal fit can be made with the positions of all hits on the track to extract the track parameters.

Wrong hit

An extra hit associated to a track which is not created by the charged particle giving rise to the other hits on the track.

Double counting

When one charged track is reconstructed as two tracks with almost identical parameters and sharing most of the hits. One or both tracks will have wrong and/or missing hits.

Track segment

A group of hits which contains only a small part of all the hits created by a given charged particle.

Fake tracks

A reconstructed track where the parameters do not match the parameters of any simulated charged track. In other places often defined as a track with above a certain fraction of wrong hits. Fake tracks mostly consist of several track segments randomly lining up.

Reconstructed tracks are in a solenoidal field described by the five parameters of a helix. The most commonly used parameterization is the Perigee representation where all five parameters and the corresponding 5 x 5 error matrix is given at the point where the track is closest to (x,y) = (0,0) in the transverse plane. The parameters are given as:

d

Transverse impact parameter. Its sign is defined as positive when the $\varphi$ angle of the point of closest approach is equal to $\varphi_{0}^{}$ + ${\frac{\pi}{2}}$ . See fig. 6.2.

z₀

z-coordinate of the track at the point of closest approach to origo in the transverse plane.

$\varphi_{0}^{}$

The $\varphi$ angle of the tangent to the track at the point of closest approach to origo in the transverse plane. See fig. 6.2.

T

The slope cot($\theta$) of the track.

1/p_T

The inverse p_T of the track (Negative for tracks with negative charge).

  

Figure: The definition of the impact parameter d and $\varphi_{0}^{}$ in the track parameterization. The illustrated track has positive impact parameter.

Each bunch crossing at the LHC will at high luminosity create many hundred charged particles within the pseudorapidity coverage of the tracker. To avoid high occupancy in the tracker the detecting elements must have a high granularity such as pixel detectors which have been chosen for the three innermost silicon layers of the ATLAS detector. The occupancy in the innermost pixel layer is estimated to reach 4.4 $\cdot$ 10^{- 4} at high luminosity while the occupancy for the innermost silicon strip layer will reach 6.1 $\cdot$ 10^{- 3}.

For the TRT the situation is quite different. Due to the larger area in ($\eta$,$\varphi$) covered by a single straw the occupancy is much higher but the number of hits on each track is also high which for the pattern recognition performance more than outweighs the high occupancy. In fig. 6.3 the occupancy in the TRT at high luminosity is shown. It is seen that the highest occupancies ( $\sim$ 40% ) are in the innermost layers of the barrel detector and the wheels at the highest rapidities in the end-cap detectors. In both cases it is caused by the layers reaching close to the beampipe where the track density is higher. The TRT has the lowest occupancy of around 13% in the outermost layers of the barrel TRT. The innermost layers in the barrel TRT do, as described in section 4.4.2, only have active wires for |z| > 40 cm which gives an acceptable occupancy for those layers.

  

Figure 6.3: The occupancy in the TRT at high luminosity. The x-axis denotes increasing radius in the barrel detector and increasing z in the end-cap wheels.

When the occupancy in a detector rises the most sensitive parameter is the rate of fake tracks since the probability of segments of different tracks lining up rises sharply with the occupancy. In section 6.2.2 details will be given on the rate of fake tracks in the TRT and the evolution with luminosity.