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This paper discusses the components and algorithms used for track reconstruction in the MUCH and TRD detectors. It covers track propagation fundamentals, extrapolation of the covariant matrix, material effects, navigation, track finding, and track selection.

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## Track Reconstruction in MUCH and TRD

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**Track Reconstruction in MUCH and TRD**Andrey Lebedev 1,2 Gennady Ososkov 2 CBM Collaboration Meeting October 13-18, 2008 Dubna, Russia 1Gesellschaft für Schwerionenforschung, Darmstadt, Germany 2Laboratory of Information Technologies, Joint Institute for Nuclear Research, Dubna, Russia**Track propagation fundamentals**Track propagation algorithm transports the track in terms of its meanvalues and corresponding errors. The basic element of the extrapolation is the transport matrix: Track propagation algorithm transports the track in terms of its meanvalues and corresponding errors. 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: State vector Covariance matrix**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 4th 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**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.**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.**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**Test setups**MUCH Compact MUCH Standard MUCH Compact:5Fe absorbers (125 cm) 10 detector stations Standard:6 Feabsorbers (225 cm) 18 detector stations TRD Standard: 12 detector layers, grouped in 3 stations**Verification of the energy loss for muons in iron**total ionization pair production bremsstrahlung 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 table Energy loss for muons in iron Lit**Verification of the multiple scattering**Theta angle of the multiple scattering for muons passing 10 cm of iron**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. Pulls X Y Tx Ty Residuals Bold –sigma of the Gauss fit, (in brackets) – RMS value. F – first, M – middle, L – last station Pulls**Performance of the track finder in MUCH**Compact Standard 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)**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)**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

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