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ROBUSTIFICATION of the Belle Vertex Fitter

This presentation from the Belle Weekly Meeting on April 14th, 2003, introduces the robustification of the Belle Vertex Fitter through a new class called AdaptiveVtxFitter. The session covers the challenges in vertex finding and fitting, the types of outliers, and the proposed solutions using adaptive weighting to handle outliers effectively. The AdaptiveVtxFitter program is discussed along with its comparison to the kvertexfitter in a controlled test environment. The presentation concludes with future outlooks on deterministic annealing and physics analysis improvements for more accurate vertex positions.

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ROBUSTIFICATION of the Belle Vertex Fitter

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  1. April 14th 2003 Belle Weekly Meeting Johannes Rindhauser Hephy Vienna ROBUSTIFICATIONof theBelle Vertex Fitter (AdaptiveVtxFitter)

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

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

  4. ROBUSTIFICATION of the Belle Vertex Fitter Belle Weekly Meeting April 14th 2003 3 Vertex Finding • 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

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

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

  7. ROBUSTIFICATION of the Belle Vertex Fitter Belle Weekly Meeting April 14th 2003 6 Problem: Outlier • 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!

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

  9. ROBUSTIFICATION of the Belle Vertex Fitter Belle Weekly Meeting April 14th 2003 8 SOLUTION to handle OUTLIER • ROBUSTIFICATION: making fit (vertex estimate) less sensitive to outliers • One possible solution: adaptive fitter • Assigns weights to tracks according to its c2 • Result: • Outliers get larger c2 downweighted • Bias on vertex estimate reduced

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

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

  12. ROBUSTIFICATION of the Belle Vertex Fitter Belle Weekly Meeting April 14th 2003 11 AdaptiveVtxFitter • 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

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

  14. ROBUSTIFICATION of the Belle Vertex Fitter Belle Weekly Meeting April 14th 2003 13 AdaptiveVtxFitter vs. kvertexfitter 200 um shift 500 um shift No shift kvertexfitter AdaptiveVtxFitter AdaptiveVtxFitter reduces vertex bias and keeps RMS small AdaptiveVtxFitter reduces vertex bias No significant difference

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

  16. ROBUSTIFICATION of the Belle Vertex Fitter Belle Weekly Meeting April 14th 2003 15 AdaptiveVtxFitter vs. kvertexfitter Table (mm)

  17. ROBUSTIFICATION of the Belle Vertex Fitter Belle Weekly Meeting April 14th 2003 16 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

  18. ROBUSTIFICATION of the Belle Vertex Fitter Belle Weekly Meeting April 14th 2003 17 Outlook: Physics Analysis To be done: Tuning (T resp. annealing scheme, ) on specific event topologies: • Test on the B0_bar decay vertex of the “golden mode” B0 J/y Ks • Test on B0 D*+ D*- decay

  19. ROBUSTIFICATION of the Belle Vertex Fitter Belle Weekly Meeting April 14th 2003 18 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)

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

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