1. Track Reconstruction in MUCH and TRD Andrey Lebedev 1,2 Gennady Ososkov 2 1 Gesellschaft für Schwerionenforschung, Darmstadt, Germany 2 Laboratory of Information Technologies, Joint Institute for Nuclear Research, Dubna, Russia CBM Collaboration Meeting October 13-18, 2008 Dubna, Russia

2. 2/14 A.Lebedev and G.Ososkov, Track Reconstruction in MUCH and TRD Track reconstruction components

3. 3/14 A.Lebedev and G.Ososkov, Track Reconstruction in MUCH and TRD Track propagation fundamentals Track propagation algorithm transports the track in terms of its mean values and corresponding errors. The basic element of the extrapolation is the transport matrix: Extrapolation of the covariant matrix: Dividing extrapolation into n steps, the transport matrix is calculated as a consecutive multiplications of transport matrices for each step: Track propagation algorithm transports the track in terms of its mean values and corresponding errors. State vector Covariance matrix

4. 4/14 A.Lebedev and G.Ososkov, Track Reconstruction in MUCH and TRD Track propagation algorithm Extrapolation. Two models: – Straight line in case of the absence of the magnetic field. – Solution of the equation of motion in the magnetic field with the 4 th order Runge-Kutta method, with a parallel integration of the derivatives. 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

5. 5/14 A.Lebedev and G.Ososkov, Track Reconstruction in MUCH and TRD Track fitter Forward Kalman filter – Sequence of prediction and update operations Backward Kalman Smoother – Estimations based on all the hits in the track, using Kalman smoother equations Iterative KF fit with outlier removal – Consecutive applications of the forward and backward track fitters – After the backward fitter the chi-square of the hit is used to identify the outliers.

6. 6/14 A.Lebedev and G.Ososkov, Track Reconstruction in MUCH and TRD Track finding Based on the track following and the Kalman filter methods. Uses branching. Branch is created for each hit, passed the test to be assigned to the track segment and for the missing hit. Initial seeds: - MUCH: tracks reconstructed in STS. - TRD: track reconstructed in STS or standalone. The main components of the track finding algorithm are track following and track selection.

7. 7/14 A.Lebedev and G.Ososkov, Track Reconstruction in MUCH and TRD Track finding Track selection – Tracks are sorted by their quality, obtained by chi- square and track length – Check of the shared hits procedure is executed Check of the shared hits - Remove clone tracks, i.e. track that -have similar set of hits

8. 8/14 A.Lebedev and G.Ososkov, Track Reconstruction in MUCH and TRD Test setups Compact: 5 Fe absorbers (125 cm) 10 detector stations Standard: 6 Fe absorbers (225 cm) 18 detector stations Compact MUCH Standard MUCH TRD MUCH Standard: 12 detector layers, grouped in 3 stations

9. 9/14 A.Lebedev and G.Ososkov, Track Reconstruction in MUCH and TRD Verification of the energy loss for muons in iron D.E.Groom, N.V.Mokhov and S.I.Striganov, Muon stopping power and range tables 10 MeV-100 TeV, Atomic Data and Nuclear Tables, 78, 2001 Energy loss for muons in iron total ionization bremsstrahlung pair production table Lit

10. 10/14 A.Lebedev and G.Ososkov, Track Reconstruction in MUCH and TRD Verification of the multiple scattering Theta angle of the multiple scattering for muons passing 10 cm of iron

11. 11/14 A.Lebedev and G.Ososkov, Track Reconstruction in MUCH and TRD Performance of the track propagation Simulated data: 100k mu+ and mu- with momentum range 1-10 GeV/c. Track parameters are updated with the Kalman filter on each station. xytx * 10 -2 ty * 10 -2 q/p * 10 -2 res. p, % F0.17 1.06 1.07 0.27( 0.66 )0.28( 0.67 )1.51( 2.43 )1.60( 2.44 ) M 0.36 0.640.621.411.401.621.610.53( 1.46 )0.59( 1.63 )2.78( 4.11 )3.19( 4.23 ) L 0.20 0.530.521.17 1.641.631.06 (2.39 )1.23( 2.48 )5.17 (6.93 )6.12( 7.73 ) GEANELit xytxtyq/p F1.320.981.330.981.041.061.041.070.82(1.14)0.78(1.00) M 1.001.051.091.071.011.091.041.100.77(1.19)1.02(1.27) L 0.981.011.021.010.951.110.991.080.74(1.04)1.49(1.88) Pulls Residuals Bold – sigma of the Gauss fit, (in brackets) – RMS value. F – first, M – middle, L – last station XYTxTy Pulls

12. 12/14 A.Lebedev and G.Ososkov, Track Reconstruction in MUCH and TRD Performance of the track finder in MUCH CompactStandard all96.2%97.5% ref97.1%97.6% prim96.4%97.5% sec89.2%89.0% muons96.8%97.5% ghost1.5%0.21% clone0.0% Events: URQMD central Au+Au at 25 AGeV + 5 mu+ and 5 mu- in each event (p=1.5..10 GeV/c for compact p=2.5..25 GeV/c for standard) CompactStandard

13. 13/14 A.Lebedev and G.Ososkov, Track Reconstruction in MUCH and TRD Performance of the track finder in TRD Events: URQMD central Au+Au at 25 AGeV + 25 e+ and 25 e- in each event (p=1..10 GeV/c) all94.6% ref95.2% prim94.7% sec93.4% electrons90.7% ghost3.4% clone0.0%

14. 14/14 A.Lebedev and G.Ososkov, Track Reconstruction in MUCH and TRD Summary The design of the Lit track reconstruction package has been improved which lead to easier support and better flexibility Track selection algorithms has been considerably improved The track propagation algorithm has been improved: – More accurate calculation of the material effects – Usage of TGeoManager for navigation – Stepping – Compare to GEANE