1. Faster tracking in hadron collider experiments  The problem  The solution  Conclusions Hans Drevermann (CERN) Nikos Konstantinidis ( Santa Cruz)

2. N. Konstantinidis Faster tracking in hadron collider experiments2 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 => longer processing time => 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 => LVL2 trigger algorithms should take not more than ~20ms

3. N. Konstantinidis Faster tracking in hadron collider experiments3 A typical event in ATLAS

4. N. Konstantinidis Faster tracking in hadron collider experiments4 A “traditional” approach (ATLAS)  To reduce combinatorics: work in a Region of Interest (RoI), defined from calorimeter info  RoI: a rectangular slice in ( ,  ), but extended in z

5. N. Konstantinidis Faster tracking in hadron collider experiments5 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:  z ~ 6 cm, i.e. pp interactions within ~ 30 cm)  the physics event has (on average) higher p T  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)

6. N. Konstantinidis Faster tracking in hadron collider experiments6 Physics event vs. pile-up

7. N. Konstantinidis Faster tracking in hadron collider experiments7 Quantitative Examples ATLAS at the LHC design luminosity Results demonstrated with RoIs from:  p T =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 (m H =100GeV/c 2 and H bb) Size of RoI:  =1.0  =1.0  z=15cm Average number of hits per RoI ~ 1250

8. N. Konstantinidis Faster tracking in hadron collider experiments8 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 p T tracks (i.e. physics event vs. pile-up)  they reduce combinatorics drastically, hence, reduce the quadratic time behaviour of the algorithm

9. N. Konstantinidis Faster tracking in hadron collider experiments9 Example of a z-histogram From a WH(100) jet RoI

10. N. Konstantinidis Faster tracking in hadron collider experiments10 Performance issues  Efficiency - Resolution - Timing ( Timing measurements with a Pentium- III 600MHz processor )  Flexibility - Robustness ( Very important for trigger algorithms )

11. N. Konstantinidis Faster tracking in hadron collider experiments11 Efficiency - Resolution - Timing Efficiency (p T =40GeV electrons): ( RoIs with |z reco -z true |<5mm ) Resolution (p T =40GeV electrons): Timing (in  s): p T =40GeV electrons: ~ 340  s QCD jets : ~ 370  s

12. N. Konstantinidis Faster tracking in hadron collider experiments12  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 340  sec => 230  sec  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-p T 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

13. N. Konstantinidis Faster tracking in hadron collider experiments13 The hit filter: a simple example (1) (2) (3)

14. N. Konstantinidis Faster tracking in hadron collider experiments14 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 p T ) 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!)

15. N. Konstantinidis Faster tracking in hadron collider experiments15 Example: electron RoI

16. N. Konstantinidis Faster tracking in hadron collider experiments16 Example: QCD jet RoI

17. N. Konstantinidis Faster tracking in hadron collider experiments17 Performance of the hit filter  The efficiency depends on the curvature of tracks (p T, magnetic field) and the size of  bins in the 2D-histogram  In ATLAS, for  bins of 2 o => eff~100% for p T >2GeV/c (modulo detector inefficiencies)  Timing: the algorithm is linear (for ATLAS: t(  s)=2.5xN hits )  pT=40GeV/c electron RoIs: ~ 600  s

18. N. Konstantinidis Faster tracking in hadron collider experiments18 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!