FTPC Conformal Mapping Tracker

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FTPC Conformal Mapping Tracker

• Markus D. Oldenburg
• Max-Planck-Institut für Physik, München
• 24.02.2000

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Overview

• Introduction
• Algorithm
• Conformal Mapping
• Data organization
• Track finding
• Performance
• First Results
• Outlook

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Introduction

• Global tracking algorithms
• treat all clusters equally
• Local tracking algorithms
• try to extend given track by adding a new cluster
• look for the next point in the expected direction

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Conformal Mapping I

• Assumption Particles follow helical
  trajectories.
• ? circular path in the bending plane
• ? straight line in (s, z) space, with
• s length of track in 3-dimensional space
• z coordinate along magnetic field

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Conformal Mapping II

• Fitting of straight lines is easier and faster
  than fitting cirlces.
• ? transform x, y coordinates of a cluster to x,
  y with
• x (x - xt) / r2
• y (yt - y) / r2
• r2 (x - xt)2 (y - yt)2

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Data organization I

• Clusters are organized in sub-volumes.
• Sub-volumes are obtained by segmenting the
  tracking volume into cubes in (r, ?? ?) with
• r row,
• ? azimuthal angle, and
• ? pseudorapidity.
• The origin of this coordinate system is the main
  vertex.

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Data organization II

• Each volume is identified by three indexes (ir,
  i?, i?).
• Each cluster is uniquely associated with one
  sub-volume.

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Track finding

• Program starts with
• outermost padrows and proceeds towards inner most
  ones
• clusters with smaller ?
• ? uncrowded regions are searched first

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Where to look for the next cluster?

• If cluster k is located in sub-volume (kr,
  k?, k?) only look for the next cluster on this
  track in sub-volume (jr, j?, j?) with
• kr - Nr ? jr ? kr - 1
• k? - N? ? j? ? k? N?
• k? - N? ? j? ? k? N?
• parameters Nr, N?, N?

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Tracklet search build track segments

• link a cluster k to its closest unused cluster j
• distance d ? kr - jr (?k - ?j ?k - ?j)
• iterate until tracklet consists of a certain
  number of clusters N

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Tracklet extension to tracks

• if clusters on track is ? N
• fit clusters to straight lines in
• conformal space for bending plane
• tracklength s vs. z s(z)
• iterate until
• no additional cluster found ? track ends here
• all found clusters exceeds cut(s)
  ? track ended before
• maximal amount of clusters attained

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Vertex constraint on/off

• tracking is done twice
• with (main) vertex constraint
  (conformal mapping transformation includes main
  vertex xt, yt 0)
• without vertex constraint
  (first cluster on track gives xt, yt)

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Parameters

• General of segments in (r, ?? ?)
• Different settings for main vertex tracks and
  tracks without vertex constraint
• of clusters to perform tracklet search N
• minimal of clusters on a track
• of row segm. to look into for clusters Nr
• for tracklet extension
• for track extension
• of segm. to look into for clusters N?, N?

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Cuts to reject new clusters

• Different cuts for main vertex tracks and tracks
  without vertex constraint
• maximal angle for tracklets
• maximal angle for tracks
• maximal distance from circle fit
• maximal distance from length fit

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Outlook

• Track Evaluator has to be completed
• to be able to understand current problems
• to be able to compare different track algorithms
• Cuts have to be refined by looking into simulated
  data