1. ROBUSTIFICATION of the Belle Vertex Fitter April 14 th 2003Johannes Rindhauser Hephy Vienna Belle Weekly Meeting (AdaptiveVtxFitter)

2. 1 Overview Vertex Fitting Robustification New class made: AdaptiveVtxFitter Results (comparison of kvertexfitter and AdaptiveVtxFitter) ROBUSTIFICATION of the Belle Vertex Fitter Belle Weekly Meeting April 14th 2003 1

3. Vertex Finding: find decay vertices Vertex Fitting: determine their position with high accuracy Introduction: Vertex Reconstruction ROBUSTIFICATION of the Belle Vertex Fitter Belle Weekly Meeting April 14th 2003 2

4. Identification of vertices Assignment of tracks to vertices Possible estimation of vertex position Eg. Finding through fitting: fit all tracks to common vertex discard incompatible tracks discarded tracks: secondary vertex search Vertex Finding ROBUSTIFICATION of the Belle Vertex Fitter Belle Weekly Meeting April 14th 2003 3

5. Estimation of Vertex position and track parameters Result: tracks are more precise due to vertex constraint Vertex Fitting ROBUSTIFICATION of the Belle Vertex Fitter Belle Weekly Meeting April 14th 2003 4

6. Ingredients Trackmodel: parameters at vertex  measurement space Minimization Ansatz Normal Least Squares Method (global) Kalman Filter (local) Belle: Constraint Ansatz (global) ROBUSTIFICATION of the Belle Vertex Fitter Belle Weekly Meeting April 14th 2003 5

7. Error of tracks greater than expected (  covariance matrix) Problems using LSM or Constraint Ansatz  Outliers are not recognized and used as normal (good) tracks  Outliers bias the vertex position! Problem: Outlier ROBUSTIFICATION of the Belle Vertex Fitter Belle Weekly Meeting April 14th 2003 6

8. Genuine Outlier: track is from particle, but with larger error than expected (eg.  - electrons, multiple scattering) Corrupted track: partially wrong associated hits (other track, detector noise) Outlier: background track or track from secondary vertex Outlier Types ROBUSTIFICATION of the Belle Vertex Fitter Belle Weekly Meeting April 14th 2003 7

9. ROBUSTIFICATION: making fit (vertex estimate) less sensitive to outliers One possible solution: adaptive fitter –Assigns weights to tracks according to its   Result: –Outliers get larger    downweighted –Bias on vertex estimate reduced SOLUTION to handle OUTLIER ROBUSTIFICATION of the Belle Vertex Fitter Belle Weekly Meeting April 14th 2003 8

10. Weighting Weight calculation for track k: Where is calculated for every track and is a cut value. T is the temperature. ROBUSTIFICATION of the Belle Vertex Fitter Belle Weekly Meeting April 14th 2003 9

11. Weighting: Plot =4 ROBUSTIFICATION of the Belle Vertex Fitter Belle Weekly Meeting April 14th 2003 10

12. Fully programmed: Extension of the kvertexfitter Comparison between AdaptiveVtxFitter and kvertexfitter in special testenvironment: –Controlled Gaussian smearing of the tracks –Detailed study of fitter possible AdaptiveVtxFitter ROBUSTIFICATION of the Belle Vertex Fitter Belle Weekly Meeting April 14th 2003 11

13. z-Shift: Use all tracks of ‘Mdst_charged’ (6prong) Shift 1 track (eg. B decay vertex) Outlier Production ROBUSTIFICATION of the Belle Vertex Fitter Belle Weekly Meeting April 14th 2003 12 z

14. AdaptiveVtxFitter vs. kvertexfitter ROBUSTIFICATION of the Belle Vertex Fitter Belle Weekly Meeting April 14th 2003 13 No shift200 um shift No significant difference AdaptiveVtxFitter reduces vertex bias kvertexfitter 500 um shift AdaptiveVtxFitter AdaptiveVtxFitter reduces vertex bias and keeps RMS small

15. AdaptiveVtxFitter vs. kvertexfitter T=1 ROBUSTIFICATION of the Belle Vertex Fitter Belle Weekly Meeting April 14th 2003 14 Plot of vertex z-deviation with respect to z-shift

16. AdaptiveVtxFitter vs. kvertexfitter ROBUSTIFICATION of the Belle Vertex Fitter Belle Weekly Meeting April 14th 2003 15 Table (  m) z-shift normalFit chiSqCut=5.99 (5% cut) chiSqCut=9.21 (1% cut) chiSqCut=13.8 (0.1% cut) 10,001,501,51,41,5 20,003,103,1 50,008,307,67,87,9 100,0016,501112,314,3 200,0032,706,8812,2 500,0081,903,432,4

17. Outlook: Deterministic Annealing Starting with high temperature Cooling down (T1, T2, …. ) Tuned for specific event topology Result: Avoiding suboptimal solutions (local minima)  more accurate vertex position ROBUSTIFICATION of the Belle Vertex Fitter Belle Weekly Meeting April 14th 2003 16

18. Outlook: Physics Analysis To be done: Tuning (T resp. annealing scheme, ) on specific event topologies: Test on the B 0 _bar decay vertex of the “golden mode” B 0  J/  s Test on B 0  D* + D* - decay ROBUSTIFICATION of the Belle Vertex Fitter Belle Weekly Meeting April 14th 2003 17

19. Work on Robust Fitter Literature: –Comp.Phys.Comm. 120, 197 (1999) –J.Phys.G: Nucl. Part. Phys. 29 (2003) 561- 574 Mathematical Support: –R. Frühwirth (Hephy Vienna) ROBUSTIFICATION of the Belle Vertex Fitter Belle Weekly Meeting April 14th 2003 18

20. THE END April 14 th 2003Johannes Rindhauser Hephy Vienna Belle Weekly Meeting