Faster tracking in hadron collider experiments

The problem The solution ConclusionsHans 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 layershigher combinatorics

=> longer processing time => increased hit misassociation (i.e. performance degradation of the tracking algorithms)

At the LHC (design L ) typically 20K-40K hits/eventbunch crossing every 25ns =>

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 infoRoI: a rectangular slice in (,), 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 differencespp interactions happen at different z positions

(at LHC: z ~ 6 cm, i.e. pp interactions within ~ 30 cm)

the physics event has (on average) higher pT

Use these two differences to reduce combinatoricsFirst, find the z position of the physics eventThen, 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 luminosityResults demonstrated with RoIs

from:pT=40GeV/c isolated electrons

• Size of RoI: =0.2 =0.2 z=11cm • Average number of hits per RoI ~ 230

Thin QCD jets (bkg to electron RoIs)• Size of RoI: =0.2 =0.2 z=11cm• Average number of hits per RoI ~ 250

Jets from WH (mH=100GeV/c2 and H bb)

• Size of RoI: =1.0 =1.0 z=15cm• Average number of hits per RoI ~ 1250

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The z - finder The principle:

Divide the RoI into many small bins

In each 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 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

2.5] 0, [for 96.5

Efficiency (pT=40GeV electrons):

( RoIs with |zreco-ztrue|<5mm )

Resolution (pT=40GeV electrons):

2.5] 0, [for 250 m

N104N1.2435s) (int 2h

4h

Timing (in s):

pT=40GeV electrons: <t> ~ 340s

QCD jets : <t> ~ 370s

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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% => 94.5%

Resolution 250mm => 400mm

Speed 340sec => 230sec

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 bin width

Example: electron RoIs: one high-pT track

giving the z-info, so very thin bins + use all layers ( benefit from combinatorics: 7 hits give 6x7/2=21 entries)

WH RoIs: several tracks, so no need to use more than 3 layers

Flexibility - Robustness

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The hit filter: a simple example

(1)

(2)

(3)

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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 ()

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 bins in the 2D-histogram In ATLAS, for bins of 2o => eff~100% for pT>2GeV/c

(modulo detector inefficiencies)

Timing: the algorithm is linear (for ATLAS:

t(s)=2.5xNhits) pT=40GeV/c electron RoIs: <t> ~ 600s

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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 => b-tagging at the LVL2 trigger

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

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