ACAT 2000 October 18, 2000

1
Simultaneous Tracking and Vertexing with Elastic
Templates

• Andrew HaasUniversity of WashingtonACAT
  2000October 18, 2000

2
Particles, Clusters, and Ghosts
DØ Central Fiber Tracker Model
p
pbar
Stereo clusters
ghost
Radial clusters
ghost
3
Track Reconstruction

• Pattern RecognitionAssign each hit to a track
  or declare it to be detector noise
• Continuous OptimizationFit each track to the
  hits assigned to it

4
Reconstruction Flow
3D Hits
Raw Data
Clusters
Ghostbuster Histogramming
Primary Vertex Seeds
Elastic Fitting
Fit Tracks and Fit Primary Vertices
Track Seeds
Fit Tracks and Fit Primary and Secondary Vertices
Elastic Fitting
Secondary Vertex Seeds
5
Histogramming

• Split the detector into parameter-space slices
• Perform a semi-local Hough transform to map
  triplets of hits into a track parameter
  histogram
• For all combinations of 3 hits in a slice, place
  the cluster indices of the three hits in the
  corresponding track parameter bin

y
y
z
x
6
Ghostbusting Filtering

1. Loop through the bins, starting at the bin with
   the most entries, in order of their number of
   entries.
2. Remove all entries which contain a cluster
   already used by another bin.

Clusters
Track parameter bin index
7
Track Seeding Results
Z µµ, 0mb
8
Global Track Fitting

• The energy represents the quality of the global
  solution
• Minimize this energy by changing the assignments
  of hits to tracks, hits to ghosts or noise, and
  the parameters of tracks.

?2 of tracks to hits associated with each track
Penalty for hits not on any tracks
E

E
9
Mean-field Annealing

• Assign a probability for each hit to belong to
  each track, according to the mean-field
  equations.
• Move through this continuous space, rather than
  discrete combination space
• The probability depends not only on the distance,
  but also on the temperature.
• Successively lower the temperature while fitting
  the tracks.

P 0.01
P 0.5
10
Track Fitting Results
Z µµ, 0mb
10 sec/event 20 MB memory
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Simultaneous Primary Vertexing

• Fit tracks to hits and primary vertices, and,
  fit primary vertices to tracks, simultaneously

?2 of tracks to hits associated with each track
Penalty for hits not on any tracks
E

?2 of vertices to tracks associated with each
vertex
Penalty for tracks not on any vertex


?2 of vertices to beam-axis associated with each
primary vertex

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Track Fitting with Primary Vertexing Results
Z µµ, 0mb
13
Secondary Vertex Grid Search

• Measure the likelihood that some tracks came from
  a secondary vertex.
• Define a grid of points along the jet axis
• Put a secondary vertex candidate at each point
  and calculate the ?2 of the global fit for each
  location
• Keep the candidate with the lowest ?2

14
Simultaneous Tracking and Vertexing

• Place a secondary vertex candidate along the jet
  axis
• Do a global elastic fit
• Repeat for several initial candidate positions,
  and keep the lowest global energy solution
• Advantages
• Secondary vertices can move continuously, instead
  of being stuck at pre-defined grid point
  locations
• The primary vertices can move and be refit
  dynamically
• Tracks can change which hits are assigned to
  them, as they are fit to the vertices
• Better track assignments to the primary or
  secondary vertex

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Conclusions

• An alternative framework for track and vertex
  reconstruction has been developed, implemented,
  and tested, which consists of two parts
• An effective seeding algorithm based on the
  Hough-transform which is robust in a ghosty
  environment.
• An extended Elastic algorithm that performs a
  simultaneous fit of hits, tracks, and primary and
  secondary vertices.