Faster tracking in hadron collider experiments

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Faster tracking in hadron collider experiments

• The problem
• The solution
• Conclusions

Hans Drevermann (CERN) Nikos Konstantinidis
( Santa Cruz)
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The problem

• General problem with tracking is combinatorics
• Soon, at hadron colliders many pp interactions in
  one the physics event plus several pile-up
  events (20 at LHC design L )
• increased hit occupancy, especially in inner
  layers
• higher combinatorics
  
  gt longer processing time gt increased hit
  misassociation
  (i.e. performance
  degradation of the tracking algorithms)
• At the LHC (design L )
• typically 20K-40K hits/event
• bunch crossing every 25ns
  gt LVL2
  trigger algorithms should take not more than 20ms

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A typical event in ATLAS
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A traditional approach (ATLAS)

• To reduce combinatorics work in a Region of
  Interest (RoI), defined from calorimeter info
• RoI a rectangular slice in (h,f), but extended
  in z

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The new idea

• Use differences between physics event and pile-up
  to clean up the event first!
• Physics event vs. pile-up two main differences
• pp interactions happen at different z positions
• (at LHC sz 6 cm, i.e. pp interactions within
  30 cm)
• the physics event has (on average) higher pT
• Use these two differences to reduce combinatorics
• First, find the z position of the physics event
• Then, select groups of hits which could be due to
  a track coming from the above z position, reject
  all other hits (pile-up, noise, ghost)

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Physics event vs. pile-up
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Quantitative Examples

• ATLAS at the LHC design luminosity
• Results demonstrated with RoIs from
• pT40GeV/c isolated electrons
• Size of RoI Dh0.2 Df0.2 Dz11cm
• Average number of hits per RoI 230
• Thin QCD jets (bkg to electron RoIs)
• Size of RoI Dh0.2 Df0.2 Dz11cm
• Average number of hits per RoI 250
• Jets from WH (mH100GeV/c2 and H bb)
• Size of RoI Dh1.0 Df1.0 Dz15cm
• Average number of hits per RoI 1250

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The z - finder

• The principle
• Divide the RoI into many small f bins
• In each f bin, make all pairs of hits from
  different layers
• For each pair, find the z by linear extrapolation
  and fill a 1D-histogram
• z is the bin of the 1D-histogram with the max.
  of entries
• No need to reconstruct tracks
• Key are the small f bins
• they naturally give more weight to high pT tracks
  (i.e. physics event vs. pile-up)
• they reduce combinatorics drastically, hence,
  reduce the quadratic time behaviour of the
  algorithm

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Example of a z-histogram
From a WH(100) jet RoI
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Performance issues

• Efficiency - Resolution - Timing
• ( Timing measurements with a Pentium- III 600MHz
  processor )
• Flexibility - Robustness
• ( Very important for trigger algorithms )

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Efficiency - Resolution - Timing
Efficiency (pT40GeV electrons)
( RoIs with zreco-ztruelt5mm )
Resolution (pT40GeV electrons)
Timing (in ms)
pT40GeV electrons lttgt 340ms
QCD jets lttgt 370ms
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Flexibility - Robustness

• Robustness is very important for trigger
  algorithms and is closely linked to flexibility
• Example what if the first pixel layer of ATLAS
  dies (due to radiation)? (studied with electron
  RoIs)
• Efficiency 96.5 gt 94.5
• Resolution 250mm gt 400mm
• Speed 340msec gt 230msec

• Same algorithm can be used in widely different
  physics cases (e.g. electrons/jets), by simple
  change of parameters
• first / last Si layer to be used
• f bin width
• Example
• electron RoIs one high-pT track giving the
  z-info, so very thin f bins use all layers (
  benefit from combinatorics 7 hits give 6x7/221
  entries)
• WH RoIs several tracks, so no need to use more
  than 3 layers

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The hit filter a simple example
(3)
(1)
(2)
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The hit filter in words

• The principle
• After finding the z position of the physics
  event, make a 2D-histogram in
  (h,f)
• Each bin in that histo corresponds to a small
  solid angle
• A track (above certain pT) from the physics event
  will be fully contained in one such bin, while a
  pile-up track from a different z will cross many
  bins
• Therefore, in each bin, count how many DIFFERENT
  LAYERS have been hit. If more than N, accept all
  hits in this bin, else reject all hits in this
  bin
• Cluster hits from neighboring bins into groups
  (very often a group contains the hits of just one
  track, i.e. this is a 1st order pattern
  recognition!)

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Example electron RoI
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Example QCD jet RoI
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Performance of the hit filter

• The efficiency depends on the curvature of tracks
  (pT, magnetic field) and the size of f bins in
  the 2D-histogram
• In ATLAS, for f bins of 2o gt eff100 for
  pTgt2GeV/c (modulo detector inefficiencies)
• Timing the algorithm is linear (for ATLAS
  t(ms)2.5xNhits)
• pT40GeV/c electron RoIs lttgt 600ms

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Summary

• Two general algorithms to clean up the
  spacepoints of the tracking detectors at hadron
  collider experiments
• z-finder it determines the z-position of the
  physics event
• hit-filter once z is known, it rejects
  pile-up/noise/ghost hits
• Both algorithms are fast / efficient / robust /
  flexible
• Can help to prepare data for further processing,
  leading to significant reduction of
  combinatorics.
• General enough to be usable in many physics cases
  
• single isolated electron/muon track
  reconstruction
• tracking inside hadronic jets gt b-tagging at the
  LVL2 trigger

Focusing on just the physics event at the trigger
level should give great benefits in performance!