1. Global Tracking for CBM Andrey Lebedev 1,2 Ivan Kisel 1 Gennady Ososkov 2 1 GSI Helmholtzzentrum für Schwerionenforschung GmbH, Darmstadt, Germany 2 Laboratory of Information Technologies, Joint Institute for Nuclear Research, Dubna, Russia 1 st CBM Russia Meeting May 18-22, 2009 JINR, Dubna, Russia

2. 2 A.Lebedev, I.Kisel, G.Ososkov, Global Tracking for CBM Outline Global tracking – Geometries – Requirements – Tracking – Results Speed up of the tracking software

3. 3 A.Lebedev, I.Kisel, G.Ososkov, Global Tracking for CBM CBM setups “Muon” setup – STS+MUCH+(TRD)+(TOF) “Electron” setup – STS+(RICH)+(TRD)+(TOF)+(ECAL)

4. 4 A.Lebedev, I.Kisel, G.Ososkov, Global Tracking for CBM Segmented MUCH 6 absorbers – 225 cm of iron 2 stations in first 5 gaps 3 stations in the last gap for trigger 2 sides in each station Back sideFront side Optionally: STRAW TUBES in the last stations (V.Peshehonov et al) V.Nikulin E.Kryshen M.Ryzhinskiy Front sideBack sideFront sideBack sideFront side

5. 5 A.Lebedev, I.Kisel, G.Ososkov, Global Tracking for CBM Segmented TRD – Segmented geometry – 2 cm thick support frames – More dead zones Leads to detector inefficiency

6. 6 A.Lebedev, I.Kisel, G.Ososkov, Global Tracking for CBM Global tracking procedure CbmLitFindGlobalTracks – Tracking + Merging – Automatic configuration, depending on the setup STS+(TRD)+(TOF) STS+MUCH+(TRD)+(TOF) STS MUCH TRD TOF L1 STS tracking LIT tracking Hit-to-track merging

7. 7 A.Lebedev, I.Kisel, G.Ososkov, Global Tracking for CBM Tracking Initial seeds are tracks reconstructed in STS (L1 tracking) Tracking is based on – Track following – Kalman Filter – Validation gate – Different hit-to-track association techniques

8. 8 A.Lebedev, I.Kisel, G.Ososkov, Global Tracking for CBM Tracking methods Branching – Branch is created for each hit in the validation gate. Nearest Neighbor – The closest by a Euclidean statistical distance hit from a validation gate is assigned to track. Weighting – Doesn’t allow track splitting, it collects all the hits in the validation gate.

9. 9 A.Lebedev, I.Kisel, G.Ososkov, Global Tracking for CBM Simulation parameters Events – Muons: 1000 UrQMD at 25 AGeV + 10 mu in each event – Electrons: 500 UrQMD at 25 AGeV + 10 electrons in each event Efficiency ( CbmLitReconstructionQa ) – Global tracking: STS – 4 MC STS points STS+TRD(MUCH) – 4 MC STS and 8(12) MC TRD(MUCH) points STS+TRD(MUCH)+TOF - 4 MC STS and 8(12) MC TRD(MUCH) points + TOF point – Local tracking and merging: TRD(MUCH) – STS as 100% + 8(12) MC points in TRD(MUCH) TOF merging – STS+TRD(MUCH) as 100% + TOF point

10. 10 A.Lebedev, I.Kisel, G.Ososkov, Global Tracking for CBM Muons muonsall STSSTS+MUCH STS+MUCH+TOF MUCHTOF all74.990.090.792.198.7 reference94.890.991.092.798.7 muons98.091.491.093.198.7 Efficiency in %

11. 11 A.Lebedev, I.Kisel, G.Ososkov, Global Tracking for CBM Electrons electronsall STSSTS+TRD STS+TRD+TOF TRDTOF all81.785.077.692.991.1 reference95.591.383.194.991.1 electrons96.687.974.589.384.6 Efficiency in %

12. 12 A.Lebedev, I.Kisel, G.Ososkov, Global Tracking for CBM Speed up [1]: number of branches Motivation: The main problem with branching algorithm is that its computational and memory requirements can grow with time and saturate computing system. Solution: Only a limited number of the nearest hits in the validation gate can start a new branch. Maximum number of hits in the validation gate 30201510754321 Tracking efficiency,% 93.1 92.9 91.8 Time, s/event 1.911.631.371.050.80.620.520.440.340.20 MUCH tracking, UrQMD 25 AGeV Au-Au + 10 muons 4 times faster! CPU: Intel C2D P8400

13. 13 A.Lebedev, I.Kisel, G.Ososkov, Global Tracking for CBM Speed up [2]: fast search of hits Motivation -Hits are sorted by x position -Binary search is used to find Min and Max index Maximum measurement error on the station Fast search of hits Loop over MIN and MAX indices Loop over MIN and MAX indices 2 times increase in speed! 1.05 s/event -> 0.52 s/event (MUCH tracking, UrQMD+10mu) CPU: Intel C2D P8400

14. 14 A.Lebedev, I.Kisel, G.Ososkov, Global Tracking for CBM Speed up [3]: simplification of the geometry Simplified geometry – TGeoManager: storage + navigation – Stations are approximated as planes Reduction of number of nodes from 800k to 100 0.52 s/event  0.3 s/event Future plans – Custom navigation (assuming detector planes are perpendicular to z) – Optimization of the step size in the track propagation CPU: Intel C2D P8400

15. 15 A.Lebedev, I.Kisel, G.Ososkov, Global Tracking for CBM Speed up: plans of further developments Magnetic field access (same as for L1) – approximation of the magnetic field Parallelism – SIMDization 46% of total track propagation costs is due to access to the magnetic field Reachable gain of speed: 100? 1000?...

16. 16 A.Lebedev, I.Kisel, G.Ososkov, Global Tracking for CBM Summary and outlook Summary: – The Lit track reconstruction package has been significantly improved global tracking procedure implemented algorithm speed up results in 0.3 s/event for MUCH tracking Outlook – Continue speed up studies – MUCH trigger

17. 17 A.Lebedev, I.Kisel, G.Ososkov, Global Tracking for CBM Back up

18. 18 A.Lebedev, I.Kisel, G.Ososkov, Global Tracking for CBM Track propagation Extrapolation. Two models: – Straight line in case of absence of magnetic field. – Solution of the equation of motion in a magnetic field with the 4 th order Runge-Kutta method. Material Effects. – Energy loss (ionization: Bethe-Bloch, bremsstrahlung: Bethe-Heitler, pair production) – Multiple scattering (Gaussian approximation) Navigation. – Based on the ROOT TGeoManager. The Algorithm: Trajectory is divided into steps. For each step: Straight line approximation for finding intersections with different materials (geometry navigator) Geometrical extrapolation of the trajectory Material effects are added at each intersection point Track propagation components

19. 19 A.Lebedev, I.Kisel, G.Ososkov, Global Tracking for CBM Weighted track fit Weight is assigned to each hit Weight is proportional to the multivariate Gaussian distribution and includes temperature parameter T Weighted hit is calculated as a weighted mean of the hits from the same station Weighted track is fitted with standard KF Temperature is gradually decreasing. Simulated annealing is applied to track fit 1) The process starts at a high temperature, all hits have the same weights. 2) Weights are updated at a lower temperature. 3) Weights are frozen.