1. Tracking at LHCb Introduction: Tracking Performance at LHCb Kalman Filter Technique Speed Optimization Status & Plans

2. Jeroen van Hunen June 4, 2004NIKHEF B-physics meeting 2 Detector response: test-beam data (resolution, efficiency, noise, cross- talk) Spill-over effects included (25 ns bunch spacing) PYTHIA and GEANT simulation Trigger simulation: thresholds tuned to get maximal signal efficiencies at limited output rates of 1 MHz (L0) and 40 kHz (L1) Offline reconstruction: Full pattern recognition (track finding, RICH reco.)

3. Jeroen van Hunen June 4, 2004NIKHEF B-physics meeting 3 Track finding strategy VELO seeds Long track (forward) Long track (matched) T seeds Upstream track Downstream track T track VELO track T tracks  useful for RICH2 pattern recognition Long tracks  highest quality for physics (good IP & p resolution) Downstream tracks  needed for efficient K S finding (good p resolution) Upstream tracks  lower p, worse p resolution, but useful for RICH1 pattern recognition VELO tracks  useful for primary vertex reconstruction (good IP resolution)

4. Jeroen van Hunen June 4, 2004NIKHEF B-physics meeting 4 Tracking performance Red: Geant hits Blue: reconstructed tracks - 20  50 hits assigned to a long track - 98.7% correctly assigned - Efficiency: 94% On average: 26 long tracks 11 upstream tracks 4 downstream tracks 5 T tracks 26 VELO tracks

5. Jeroen van Hunen June 4, 2004NIKHEF B-physics meeting 5 Tracking performance Eff = 94% (p > 10 GeV) Ghost rate = 3% (for p T > 0.5 GeV)

6. Jeroen van Hunen June 4, 2004NIKHEF B-physics meeting 6 Tracking performance IP resolution  p/p Typical:

7. Jeroen van Hunen June 4, 2004NIKHEF B-physics meeting 7 Kalman Filter Technique

8. Jeroen van Hunen June 4, 2004NIKHEF B-physics meeting 8 Prediction and filter step Kalman technique : Efficient iterative solution for a least-squares fit Detector planes Measurement and error State vector (x,y,t x,t y,q/p) is updated at each measurement by performing a prediction and filter step. prediction  Estimate of state at a given z-position based on previous planes filter (update)  Weighted mean of the prediction and measurement at given z-pos. Direction of Kalman filter

9. Jeroen van Hunen June 4, 2004NIKHEF B-physics meeting 9 Detector Material Detector material is taken into account by adjusting the state vector and it’s covariance matrix: Multiple scattering  For small deflection angles  Gaussian, increases the covariance matrix elements of t x, t y. Additional factor tuned to give track parameters with  pull =1. Energy loss:  Charged hadrons + muons ( )  Affects the momentum, but not the covariance matrix. The factor c ion is tuned to give a momentum pull that is centered around zero.  Electrons (bremsstrahlung)  Affects the momentum and the covariance matrix. (Increase of covariance allows to correct a sudden momentum change  LHCb classic only) Note : Covariance matrix V:

10. Jeroen van Hunen June 4, 2004NIKHEF B-physics meeting 10 Magnetic field Prediction and with F k = Propagation matrix. F k : determined using Runge-Kutta (The LHCb B-field is not homogeneous and has B x,B y and B z components). A 5 th order adaptive Runge-Kutta is used (the step size is automatically adjusted to obtain a given precision, by comparing with a fourth order Runge-Kutta). Filter (update)  Weighted mean of the prediction and measurement. Smoother  Information of last state is propagated backwards to earlier states.

11. Jeroen van Hunen June 4, 2004NIKHEF B-physics meeting 11 Kalman Filter needs a state to start with ( )  taken from pattern recognition Seeding (example): Seed for Kalman filter magnet Covariance matrix should be ‘infinite’ in order to use the measurements only one time and create artificially small errors

12. Jeroen van Hunen June 4, 2004NIKHEF B-physics meeting 12 Speed Issues

13. Jeroen van Hunen June 4, 2004NIKHEF B-physics meeting 13 Long Tracks  Filter and Smooth : 17ms per track on (1GHz Pentium III) Filtering (prediction and update) Smoothing Outlier removal Reference : HLT processing time  60 ms (1GHz Pentium III). HLT should do pattern recognition, track fitting and a selection for specific final states. States  Including the determination of the states at 5 specified z-positions (beam line, RICH1, RICH2 ) it is 24ms. From this 24 ms, 21ms is used for the Transport Service (88%). How long takes the Kalman filtering ( FilterandSmooth = 240s, for 14000 tracks from which 13000 have 3 hits in the Velo and 3 hits in the OT ) Tool to obtain the radiation length of detector material that is encountered by the particle VELO (50%), OT/IT (19%), RICH2 (13%), TT (9%), RICH1 (4%)

14. Jeroen van Hunen June 4, 2004NIKHEF B-physics meeting 14 Gaining time Look for possible improvements in: -TransportSvc / XML -Extrapolation (Runge-Kutta)  TransportSvc / XML TransportSvc implementation ( C ++ and Gaudi) XML Check if we can simplify Volume distribution Used logical volumes with solid Use assemblies (but reimplemented)

15. Jeroen van Hunen June 4, 2004NIKHEF B-physics meeting 15 Gaining time Use Transport service differently: Request the transport service less often, but for longer distances, thus: Call transportSvc for long distance Store information from transportSvc Take small steps in extrapolation using stored information until the deviation of the track with respect to the original estimate is too large.  Needs testing Extrapolation (Runge-Kutta) C++ and Gaudi (only use msgSvc in case of error, etc.) Runge-kutta (4 th, 5 th, other ?) Use of extrapolator : Runge-kutta  parabolic extrapolator (small steps) In Velo region: It is 3.8 times faster to call the TransportSvc one time for 80 cm than 10 times for 8 cm

16. Jeroen van Hunen June 4, 2004NIKHEF B-physics meeting 16 Other applications of Kalman Technique Kalman technique is generally implemented because it is fast  Higher level trigger applications At LHCb: - HLT processing time  60 ms -Current track fit  17 ms/track, thus about 0.5 sec/event.  Would like to do the track fit in a few ms/event, thus need to speed up by a factor 100 Seems possible : - Ignore detector material (gives factor  10) - Replace/Improve Runge-Kutta (G. Raven : P t -kick to get through magnet) - Only prediction and update (no smoother step)

17. Jeroen van Hunen June 4, 2004NIKHEF B-physics meeting 17 Status & Plans Implement fast Kalman Fit (for HLT, etc.) without material, Runge-kutta, smoother, etc. (a first version exist, but still has some strange features) Try improve use of transport svc, by calling it less often (at the moment 700.000 times for 500 events) and store information.